Note: Descriptions are shown in the official language in which they were submitted.
~S5~
OPTICAL TRANSMI SION FILTER
Background of the Invention
1. Field of Invention
This invention relates to optical
transmission filters for systems employing polarized
coherent beams, and more pa.rticularly to
filters exhibiting a dierential phase delay to the
components of a polarized beam element as a
function of element position within the filter
aperture. The invention further relates to
adjustable optical transmission filters.
2. Description of the Prior Art
The invention is applicable to
optical systems, such as lasers employing polarized
coherent radiation. In lasers, the optical
SS9'~
resonator acting to provide optical feedback for the
gain medium aids in esta~lishing an internal
beam and the two influence the characteristics
of the beam produced. Since t~ae external beam
derived from the laser s derivea from the
internal beam, the resonator and the gain
medium also affect the nature of the external
beam.
An ideal characteristic of a laser
apparatus is that it have a large natural
aperture and produce a large, high energy
high quality beam. ~he "larger" ~he beam,
the-higher the energy, and the smaller the
far field beam divergence (ideally a minimum),
! 15 the aperture being the critical parameter in
defining this beam property. seam quality is
a relative term used to characterize a beam
in reference to a standard beam. Beams resulting from
__ _
~25S~f~7
- 3 - - ~ ~
operation of an optical resonator in a pure TEMoo mode
for instance, may be represented as providing a standard
beam referred to as "Gaussian". In a "Gaussian" beam,
the intensity peaks in the center of the beam and grad~
ually decreases to the margin of the beam. Meanwhile,
the phase of the ~Gaussian" beam remains relatively
constant at the center of the beam and then changes
rapidly at the perimeter of the beam to a large value
leading to a phase reversal. Conversely, in an intensity
profile of the beam, the phase is changing most rapidly
where the beam intensity is approaching a minimum. In a
beam showing evidence of multi-moding, the intensity then
may reappear as a second fringe whose phase may be dis-
placed lBOD from the phase of the central fringe.
In practical apparatus, the beams are often of
substantially poorer quality than standard "Gaussian"
beams, unless correction is provided. Typical issues
in the design of an optical resonator, which influence
beam quality, are whether the optical resonator is stable,
unstable, or a combination of the two termed "stable/un-
stable". ~ypical issues in the design of the gain medium
are whether the medium is circular or square or rectangular
~IL2SS~'7
in cross-section, whether it has slanted end faces~
(cut at the Brewster angle),-~nd the presence of thermal
focusing effects as the medium is operated. In all such
designs, the quality of the beam is likely to suffer as
the aperture of the system is increased or as the power
is increased. In laser systems, polarized operation is
frequently desirable in that it permits electro-optically
"Q-switched" operation and aids in achieving improved
laser operation, the improvement being in improved b~am
quality and increased power.
Accordingly, within the optical resonator where the
beam is formed, in the near field where a beam is coupled
from an optical resonator to a utilization device and in
; the far field, means for adjusting the phase of a waveIront
1, may be of advantage in improving operation of a laser or
a laser system.
A further problem posed in practical laser systems,
is the requirement of fractional wave accuracy in the phase
correction means itself, making it desirable that the
correction filter be adjustable to simplify its own fabri-
cation. Adjustability has the additional advantage, in
the event that the system parameters are not accurately
known, of making the filter more adaptable to the actual
system requirements.
~L255~'7
- 5 -
Summar of The Invention
y
Accordingly, it is a-n object of the i~vention to
provide a novel optical transmission filter applicable
to polarized coherent radiation having a phase response
which is a function of the position of a radiation element
relative to the filter axis.
; A further object of the invention is to provide
a novel optical transmission filter applicable to polar-
ized coherent radiation, in which a differential phase
delay is provided, which is a continuous function of ~he
radial distance of each radiation element from the filter
axis.
It is still another object of the invention to
provide a novel optical transmission filter applicable
to polarized coherent radiation in which differential
phase delay is provided which is a contin~ous function of
; a coordinate in a plane orthogonal to the filter axis.
It is an additional object of the present in-
vention to provide a novel optical transmission filter
applicable to polarized coherent radiation having
adjustable phase response.
These and other objects of the invention are
achieved in a nov~l optical ~ransmission filter for
~Z5~ 7
- 6 -
effecting continuous phase compensation Qf a beam of
light, polarized in a P dime~sion, the filter having
an optical axis which is concentric with the beam axis.
The filter comprises a first lens of birefringent
material of a first center thickness having a surface,
which has a predetermined radius of curvature, and a
second lens of birefringent material of a second center
thickness, having a surface, which has a radius of
curvature equal to the radius of curvature of the first
lens but of opposi~e sign. The lenses are oriented
orthogonal to and concentric with the axis of the beam
with the curved surfaces adjacent.
In addition, the crystal optical axes of the
materials of the lenses are oriented in mutually orthog-
15 onal positions along the axis and at an angle of 45D toa P dimension. The surfaces of the filter lenses, de-
pending upon the filter characteristic sought, may ~e
spherical or cylindrical.
The phase response of the filter, will have a
zero differential phase delay at a zero coordinate value
(or zero radius with reference to the filter axis) when
the center thicknesses of the lenses are equal. The phase
~2~5~'17
- 7 ~
response may have a non-zero differential phase delay on
the axis (and a zero differe-ntial phase delay at some
other coordinate value), when the center thicknesses
of the lenses are unequal. Accordi~gly, if one desires
to translate the differential phase delay characteristic
by adding or subtracting a fixed reference delay, the
transmission filter may be made to have one lens of
adjustable center thickness. This may be accomplished
by the compound design of one lens in which the lens
consists of a wedged shaped (plane faced) member taper-
ing at an angle equal to the tapering angle of the other
lens me~ber which provides the curvature. Tile joint
tapering restores the filter surfaces to orthogonality
to the fil,er axis. ~hen the tapering angle is made
sufficiently small, a very fine adjustment of the
spacial reference of the filter characteristic, may be
~btained.
,
47
- 8 -
Brief Desc iption o~ the Drawin~s
The novel and distinctive featur.es of the invent-
ion are set forth in the appended claims. ~he invention
itself, however, together with further objects and ad
5 vantages thereof may best be understood by reference ~o
~he following description and accompanying drawings, i~
which:
Figures lA, lB, lC and lD are optical ~ransmission
filters for application to laser systems producing
10 pola~i~ed coherent light
Pigure lA i9 a two lens optical transmis~ion
ilter using orthogonally arranged birefringent materials,
the lenses having mating spherical surfaces with fixed,
on-axis thicknesses;
lS Figure lB is a three element variation of the
optical transmission filter illustrated in F.igure lA,
wherein a slideable wedge cooperating with a wedge shaped
lens provides a compound lens, whose on~axi~ thickness iB
adjustable in relation to the other lens;
Figure lC is a two lens optical transmisslon filter
similar to that illustrated in Figure lA but having
mating cylindrical surfaces, the lenses having fixed on-
aXiB thicknesses; and
~;~55~47
Figure lD is a three element variation of the
optical transmission filter illustrated in Eigure lC,
wherein a slideable wedge, cooperating with a wedge shaped
lens provides a compound lens, whose on-axis thickness is
adjustable in relation to the other lens;
Figure 2A is a perspective view o~ a portion of
a coherent optical system comhining an optical transmission
filter, which is spherical, and a polarizer, the combina-
tion producing a positionally dependent attenuation function
in reference to the system axis;
Figures 2B through 2E are auxiliary illustratlons
of the na-ture o the bcam as it pxoceeds through the op-tical
components illustrated in ~igure 2A, the filter hav:Lnc~
spherical surfaces. The illustrations show .respectively
the polarization rotation and the intensity of individual
rays forming the beam as a function of their position,
Figure 2A after a first polarizer, 2C after the Eilter,
2D after passage through the second polarizer, and 2E
upon reflection at the second polarizer;
2~ Figures 3A and 3B are respectively side elevation
and perspective Views of a stable, Q-switched laser
resonator utilizing polarized light and incorporating a
spherical optical transmission filter-polarizer combination
for supporting resonator operation in a TEMoo mode
1255~
-- 10 --
and for suppression of other modes, and Figure 3C is
a graph illustrating the operation of the optical
resonator components in mode suppression;
Figures 4A through 4F illustrate the
Q-switching sequence of the Figure 3A-3s embodiment,
Figure 4A showing the pump light output, 4A the optical
gain, 4C the trigger pulse, 4D the Pockel's cell voltag~,
4E the loss and 4F the laser output pulse;
Figure S is a schematic diagram illustrating a
control circuit or the Pockel's cell of the Figures 3A-3B
embodimen-t designed to favour TEMoo mode operation;
Fi~u.re 6 is a graphical illustration oE the
transmission profil~s or the laser cavity of the
Figures 3A-3B embodiment as a function of the voltage applied
to the Pockel's cell during the Q-switchin~ sequence, the
process "seeding" the optical resonator Eor TEMoo mode
operation;
Figures 7A and 7B are respectively side
elevation and perspeckive views of a stable/unstable
resonator incorporating a face pumped laser and
incorporating a cylindrical optical trans~ission filter-
polarizer combination for improved resonator performance;
Figure 8A illustrates a laser system incorporating
a spherical optical transmission filter-polarizer combi-
nation, in which the lenses of the optical transmission
; filter have an adjustable on-axis thickness. The filter-
.~
~L25;5i'~
polari~er co~bination is used to ancrease the extraction
efficiency of the ampllfier by~~increasing the "fill
factor~ of the ac~ive material of the amplifier.
Figure 8B illu~trat~ the variation of the tran~-
miRsion profile of the filter-pola~izer co~bi~tion of
Figure 8A as a function of cha~ge in the center thickness
difference between the two lenses of the optical filter;
and
Figure 8C illustrates the intensity of the input
beam, the filter transmissiQn ~nd the intensity of the
transmitted beam in the laser system of Figure BA at a
preferred adjustment of the filter; and
Fi~ure 9A illustrates a laser sy6tem in which a
spheric31 optical transmis6io~ filter i~ employed to
: 15 enhance the quality of a beam produced by a pol~rized
coherent source;
Figure 9B illustrates the correction of far field
~ivergence of a beam produced by an unstable laser
resonator having a Fresnel number of 7.5 (magnification
1.5) by a spherical optical transmission filter;
~ igure 9C illustrates the correction of far field
divergence of a beam produced by a ~table laser resonator
having a Fresnel number of 8.5 by a spherical optical
:
. "
~S59~7
transmission filter; and
Figure 9D i}lustrates ~he e~fect of phase devi-
ation across the beam or far field beam divergence.
Description of the Preferred Embodiment
The optical transmission filters disclosed in
Figures lA, 13, lC and lD are two or three piece optical
components designed for use with beams of polarized
coherent llght centered on the axis of the filters. The
filterq each i,nclude a pair of mating len~es of dou~ly
refracti~g material whos~ cxystal optic axes are mutua~ly
orthogonal and whose mating surfaces are e~ther spherical
~convex - concave respectively) or cylindrical (convex -
concave respectively).
The optical transmission filter 10 of Figure lA,
using two spherically surfaced lenses, has a differential
phase response to light of a preferred polarization which
is a function of the radial coordinate ~f a ray within
the filter field. The function i9 symmetrical about t},e
axis of the filter. In particular, when the rays are
located o~ the filter ~xis, a near zero change in differ-
ential phase delay is exhibited between the two selected
- orthogonal compQnents of the preferred polarization. As
~ will be seen, the selected components are oriented 45
~LZ5S~'7
- 13 ~
angle to the preferred (P) polarization and ~re in
alignment with the crystal optlc axes of the doubly
refracting materials. In one exa~ple, the differential
phaqe delay between these selected components, in-
crehses as the radial coordinate of the ray measuredfr~m the filter axis increases, the differential delays
~eing e~ual at the same radial c~ordinate irrespective
of the angular position about the filter axis. The wave
transmission filter may be employed to bring about a
rotation o~ th~ polariz~tion vector by 90 in one
passage throu~h the filter of a ray at the perimeter of
the filter field (analogo~s to a "half wave plate") or
to bring about a comparable differential delay upon two
passages through the filter of a ray at the perimeter of
the filter field ~analogous t~ a "quarter w~e plate").
The wave transmission filter 30, using cylindri-
cally surfaced lenses (e.g. Figure lC), has a phase
respanqe to light of a preferred polaxi2ation which i5
a function of a transverse coordinate (the S coordinate)
of a ray within the filter field. The function is
symmetrical about the filter axis. In one example, a
near zero di~ferential phase occurs between two selected
~SS~7
- 14 - ~ ~
orthogonal components of the preferred polarization when
~he rays are located on the filter axis, d~fferential
phase delay increasing as the S coordinate of thP ray
measured from the filter axi~ increases.
sDth the spherical ~10) and cylindrical ~30~
filters are available in an adjustable configuration.
In the adjustable configurations ~20, 40), one lens has
an adjustable thickness permitting one to adjust the on-
axis differential delay to a value in which the differ-
ential phaqe shift between the desired orthogonal
components is zero, positive, or negative.
The filters 10, 20, 30 and 40, may he used in
combination with suitable polarizers to con~ert the phase
response to an amplitude response having the same co-
ordinate dependance. The filtera her~in de~cribed may
be applied as an optical component within an optical
resonator of a laser, in the path between an optical
resonator and an optical amplifier, or for far field
correction.
The optical transmission filter 10, illustrated
in Figure lA, is a two piece spherical unit in which the
le~ses 12, 14 are of equal thickness at their centers.
1;Z5S9'~7
-- 15 --
The centers are aligned upon the axi~ Z of the as~ciatedoptical system. The lens 12 placed to the }eft in the
filter 10 ha~ a first surface 11 to the left (and hidden
in the Figure), which i~ flat and a second surface 16
to the right which is spherically concave with a pre-
determined radius of curvature (R). The surfaces of
the lens 12 are oriented orthogonal to the optical
axis (Z).
The lens 1~ has its crystal optic axis oriented
at a 45 ~ngle to the P and S axes. The P and S axes
are established in the associated optical system by the
orientation of the laser medium, which in the case of a
face pumped square slab laser, with ends cut at the
Brewster angle, lie in planes parallel to the lateral
surfaces of the slab. The P coordinate is oriented in
a vertical plane, using the orientation~ of Figures lA
and 3A, between the upper and lower (lateral) surfaces
of the laser slab and the S coordinate i~ oriented in
a horizontal plane between the front and bac~ ~lateral)
surfaces of the laser slab. These coordinates define the
P and S polariza~ion vectors which are of interes~ in
the following description. The crystal optic axis of
~2~4~7
- 16 - ~
the doubly refracting material of the lens 12 is illus-
trated by the arrows 13. Thi~ axi~ 19 oriented at 45
to the P-S coordinate~.
The second lens 14, placed to the right in the
filter 10, has a first surface 15 to the left (and
hidden in the Figure), which is spherically conYe~..
with a radius of curvature R equal to the first lens
but of oppo~ite sign. When the two lenses 12 And 14
are assembled togethe~, the surfaces 15, 16 are designed
to fit closely together. The second surface 17 of the
second ler)s lq to the right, i5 flat. The surfaces (lS,
17) of the lens 14 are oriented orthogonal to the
Z axis.
The lens 14 has its crystal optic axis oriented
at a 45 angle to the P and S axes. This axis, as
indicated by the arrows 18, is oriented orthogonal t
the crystal optic axis of the lens 12.
The optical transmission filter 10, which is
constructed of the two lenses 12 and 14, exhibits a
positionally dependent differential phase shift to the
selected components of rays of polarized light passing
through the system. The differential phase shift prod~ced
~5~4~7
- 17 - ~ :
is a function of the distance of a ray .from the filter
axis. Assuming in a first example, equal radii of
curvature for the concave and convex spherical surfaces
of the lenses 12 and 14, and an exact match between the
thickness of the two lenses at their centers, then the
differential phase shift provided to the selected
orthogona} components will ~e zero at the filter center,
coincident with the z axis. H~wever, if a ray iB
located at the periph~ral portion of the filter fi~ld
the ray will pass through a greater thic~ness in the
first lens than in the second lens and experience the
greatest differential phase ~hift contemplated by the
design. When a ray of P polarization is resolved into
two selected orthogonal components parallel to the
crystal optic axes of the two doubly refr~cting materials
and then recombined, the resultant will produce a polari-
zation rotation of 90. This will occur when one of the
selected orthogonal components experiences a dif ferential
phase shift of 180 in relation to the other, which
produces a polarization rotation of 90 upon recombin-
ation, resulting in an S polarization.
A phase rotation of 30 may occur either upon a
~2555~
~ 18 - ~
sinqle paQsage of a ray at the perimet:er of the filter
as de~cribed ln the above example, or upon a second
pas~age (also at the perimeter) through a filter of
modlfied design. In the Qecond ex~mple, a mirror may
be provided to effect a second passage of the ray through
the filter, and the filter may have a shallower design
in which the differential phase shift at the limits of
the field i5 only 90 upon a single passaye of the beam.
After a single passage, the polarization of a ray
emerging at the perimeter of the field will be circular.
Upon re~lection from the mirror~ reentry into the filter
and a second passage through the filter at the perimeter
of the field, the circular polarl2ation of the beam is
converted to a linear polarization, rotated 90~ from
the original P polarization, to an S polarization.
The spherical optical transmission filter ~ay ta~e
either the form illustrated in ~igure lA using two
lenses of fixed and equal center thicknesses, or it may
take the form illustrated at 20 in Figure lB in which a
three element construction is used to provide adjustment
of the center thickness of one lens in relation to the
other~ The adjustment may be used to bring the center
~5~
-- 1 9 -- ~ ~
thic~nesses of the two len~es into exact equality or into
a desired inequality. ~he e~-fect of an unequal adjust-
me~t is to produce a net differential phaqe ~hift on the
filter axiR and to displace the locus o~ minimum differ-
S ential phase shift to a ring around ~he filter axis.
C~nsistently, when the center thic~nesses become unequal,
the differential phase shift may become slightly smaller
at the peripheral portion of the filter field.
The adjustable spherical optical transmission
filter 20, a~ illustrated in Figure 1~, consist~ of A
compound left l~ns 21, 22 and a single element rig~t
lens 24. The compound lens is formed of a slideable
wedge 21 having flat front and back surfaces and a
wedge shaped lens 22 having its flat surface set at an
angle orthogonal to the filter axis. When the two
elements 21 and 22 are assem~led in correctly aligned
slidea~le engagement, with their upper and lower lateral
surfaces coplanar, the crystal optic axis of the wedge 21,
as illustrated by the arrows 23, has the same rotational
orientation as the crystal optic axis of the ler,s eleme~t,
as illustrated by the arrows 2S. In acldition, the angle
of tapering of the wedge 21 and the angle of tapering of
the lens 22 are made equal so that when assembled and
~z~s~
- 20 -
correctly aligned in slideable engagement, the external
surfaces of the compound lQn~ 20 ars oriented orthogonal
to the Z axis. Thus, the positionally dependent di~fer-
ential phase response of the compound three element lans
(21, 22, Z4) at specific p~sitions of the wedge will be
ub~tantially the same as tha of a comparable two
el~m~nt lens of that specific thickness.
In order to permit a fine adjustment of the
diferential phase shift so that one may adjust the
differential phase shift to a small part o ~ wave length,
the angle of tapering of the two lens components (21, 22)
is made small enough to effect this precisi~n in ad~ust-
ment with a conventional micrometer screw. In a
particular case, the angle of the wedge is 21 minutes
of arc.
The ~ptical transmi~sion filter 30, illustrated in
Figure lC is a two piece unit in which two cylindrical
lenses are employed and in which the indi~idual lense~
(32, 34) are of equal thickness at their centers. ~s in
the Figure lA embodiment, the centers of the lens elements
- ~3Z, 34) are aligned upon the Z axis. The lens 32 placed
to the left in the filter 30 has a first surface 31 to
r ~
- 21 -
the left wh~ch is flat and a second surface 36 to the
right wh?ch is cylindrically concave with a predetermined
radius of curvature (R). The curvature is maxi~um in the
S-Z plane and is negligible in the P-Z plane. The
surfaces of the lens are oriented orthogonal to the
Z axis~
The second lens 34 is placed ~o the right in the
filter. It has a surface 35 to the left (and hidden)
which is cylindrically con~ex. with a radius of curvature
~R) equal to the first lens but of Dppoqite sign. As
with the lens 32, the curvature is maximum in the S-Z
plane and negligible in the P-Z plane. When the two
lenses 32 and 3~ are assembled together, the surfaces
are designed to fit closely together. The second
surface 37 to the right of the jecDnd lens is flat.
The surfaces of the lens 32, 34 are oriented orthogonal
to the Z axis. ~he individual lenses 32 and 34 of the
- filter 30 have their crystal optical axes oriented at a
45~ angle to the P an~ S axes. As before, the crystal
optic axis of the lens 32, as illustrated by the arrows
33, is ~rthugonal to the crystal optic axis of the lens
34, as illustrated by the arrows 38.
~S~ '7
-- 2 2 --
The optical tra~smission filter 30 which ie con-
structed of the two lenses 32 and 34, exhibits a
positi~nally dependent di~ferenti~l ph~e shift to
the polarized rays of light. The differential phase
S shift varies as a function of the distance of a ~ay
from the center of the filter measured along the S
axis. The amount of differential phase shift will be
equal for rays at S coordinates of equal magnitude.
Assuming equal curvatures for the concave and convex
surfaces of the lenses 32 and 34 and an exact m~tch o
the thic~nesses o~ the two lenses at their centers,
then the differential phase shift provided to selected
components of a polarized ray sn the axis of the system
will be zero. However, if a polarized ray is located
at the outer limits of the filter field, at the near
and far edges of the cylindrical lenses, light will
pass through a greater thickness in the first lens (32)
than in the second lens ~34) and experience the greatest
differential phase shift.
The cylindrical optical transmission filter may
also take the adjustable form illustrated in Figure lD
i~ which a three element (41, 42, 44) construction is
~2SS5~ 7
.
- 23 -
: used to provide adjustment of the center thickness of
one compound (41, 42) lens in~-relation to the other lens
(4~).
The adjustable cylindrical optical transmission
~ilter 40 a~ illustrated ln Figure lD consist3 of ~
compound left lens (41, 42) cooperating with a right,
single element lens 44. The compound lens is formed of
a slideable wedqe (41) and a wedge shaped lens 42, the
two beinq assen~lable to maintain orthogonal external
~urfaces ~nd pa~allel crystal optic axe~.
As in the prior adjustable configuration, the
adjustment may be used to bring the center thic~ness of
the two lenses (41, 42 and 44) into exact equality or
into a desired inequality. In the example of an equal
center thickness, the differential pha3e for the
selected components of the polarized ray i8 zero on-
axis, and varies equally at equal plus or minus S
coordinates.
The effect of an unequal adjustment of the center
thic~nesses of the lenses 41, 42 and 44 is to produce a
net differential phase shift on the Z axis and to dis-
place the locus of minimum differential phase shift to
1~5S~'1'7
- 24 - ~ ~-
two stra~ght lines parallel to the P cDordinate axi5
spaced at equal S coordinate distance6 from the ~ axis.
With the une~ual adjustment, the differential phase
shift will ~e smaller at the outer margins of the filter
S than when the center thicknesses are equal.
In Figures 2A through 2E, an optical transmission
filter 10 ~i~h spherical surfaces, as illustrated in
Figure lA, is shown in combination with polarizers (51-
52), the combination producing a radial attenuation
~unctlon for P polarized light.
As illustrated in ~igure 2A, the combination i~
adjusted to provide a minimu~ attenuation of P polarized
light near the Z axis in the filter field and a maximum
attenuation near the perimeter of the filter field.
Assuming an applied beam, whose cross-section is analo-
gized to a "doughnut" filling the filter field, the
filter selects the "hole" of the 'Idoughnut" and rejects
the "doughnut". Alternatively the combination may be
adjusted to provide maximum attenuation at the central
portion of the filter field and minimum attenuation at
the peripheral portion of the filter field. Finally,
one may make transitional selections intermediate to
~1 2~S~3~7
- 25 -
the fir~t and second adj~stment~ as by using the adjust-
able filter 20, in ~hich the c~nter of the field is
attenuated to a desired degree ~nd the margin of the
beam is less deeply attenuated, the efEect of which i3
to increase the spot size of real beam~ between desired
attenuation limits.
In Figure 2A, it is assumed that unpolarized
light at the left margin illustrated by the intersecting
vertical (53) and horizontal ~54) lines proyresses to
the right and impinges on ~he left ~ace o~ the polarizer
51. Only liqht which is of P polarization i9 trans-
mitted through the polarizer 51 while light of an S
polarization is ejected off axis and discarded. The
nature of the polarization of the light after passage
throuqh the polariæer is illustrated in Figure 2B,
which shows a magnified cross-section of the field. In
particular, the center of the field, as represented by
a single full length vertical line, is vertically polar-
ized. Also the successive zones surrounding the center,
23 and completing the field, are represented by four rows of
four radially positioned, full length vertical lines,
are vertically polarized. A plot of the light intensity
- 2 6 ~
as a f unction o f the ~adial position of a ray in the
filter field i~ illustrated i~-the lower,portion of
~igure 2s. The field may be regarded as uniformly
filled with rays of unit intensity.
The P polarized rays 53 then continue until they
impinge on the optical transmission filter 10, which,
as indicated ~y the arrows (13, 18) has its mutually
orthogonal crystal optic axes oriented at 45D to the
P polarization. The selected orthogonal components of
the ~ays of P polarization, a~ a functlon of increasing
radial di~tances from the Z aXi5, receive greatex differ-
ential phase ~hi~ts upon passage thro~gh the fllter, and
produce correspondingly different polarization rotations.
The rays exiting the filter 10, are symbolized in
~igure 2A by the dots 57, ~paced at wave length intervals,
which continue until impingement at the polarizer 52.
The effect of the filter 10 over the different
zones of the filter field are best illustrated in
; Figure 2C, which is a magnified cross-section of the
field. The upper portion of Figure 2C represents the
polarization rotation a~ a function of ray position in
successively larger diameter zones lying within the
~ L~t7
- 27 - ~ ~
filter field. The lower portion of the figure illus-
trates the S~tensity aa a functton of the radial
position of a ray within the field.
The upper portion of ~ig~re 2C i~lustrates the
progressi~n of the polarization of the output rays from
the filter 10, as the input ray position progresses
from the center to the perimeter of the filter field.
The full length vertical lines repre~ent P polarization;
the full length horizontal lines represent S polarization;
10 and the circles indicate circular polarlzation. Ray~ at
the center o the filter represented by single ~ull
length vertical lines have emerged from the filter 10
without a change in polari~ation and remain of P
polarization. Emerging rays at the next zone repre~ented
15 by four circles have been ~ubjected to a 45 polarization
rotatlon and are now circul~rly pol~ri~ed. ~ay~ emerging
from the next outer zone represented by four full length
horizontal lines have been ~ubjected t~ a 9~ polariza~ion
rotation and are now horizontally polarized. At the next
20 outer zone, the emerging rays are circularly polarized as
represented by four circles. At the final zone pictured,
3L~Z55~7
- 28 -
emerging rays are again of P polarization as represented
by four full length vertical l*nes.
The plot of the intensity of the filtered beam as
a function of the radial position of a ray is illustrated
1n the lower portion of Figuxe 2C. The Figure 2C plot
resembles the plot provided in Figure 2s, indicating
that the filter 10 has provided no significant attenu-
ation.
The rays havi~g di~fering polarizations a~ a
function o~ po3ition within the fllter field a~ ~
result of passage thrcugh the filter 10, next impin~e
on the left face of the polarizer 52.
Ray components of vertical polarization are trans-
mitted through the polarizer 52 and continue to the right
along the Z axis as indicated by the vertical lines sa.
Ray components of horizontal polarization are reflected
by the polarizer 52, and are ejected from the axiR a
indicated by the horizontal lines 59.
The effect of the polarizer 52 upon transmitted
and reflected rays at different portions of the filter
field are illustrated in Figures 2D and 2E, which are
magnified views of the field.
~53~L7
-- 2 9 --
The effect of the polarizer 52 upon trsn~mitted
rays at successive zones of the filter field are illus-
trated in Fiqure 2D. The upper portion of Figure 2D
represents the intensity of the transmitted vertically
polarized output rays 58 as a function of ray position
in successively larger diameter zones lying within the
field. The lower portion of Figure 2D illustrates the
intensity as a function of the radial position of a ray
within the field.
The upper portion of Figure 2D illu~trate.q the
progre~sion of inten~iey of the output xays ~s the ray
position progresses from the center to the perimeter
of the filter field. The int~i~es are represented
by "full" length lines repre~enting full intensity,
shortened lines representing less than normal intensity,
and dots representing zero intensity. Rays at the
center of the field represented by a single full length
~ertical line have emerged from the polarizer without a
change in inte~si~ indicating that the filter-polarizer
20 combination has transmitted that ray without phase shift
or attenuation. Emerging rays at the next ZGne repre-
6ented by four shortened lines represent the vertical
~,~55~ '7
- 30 - - ~
component of rays, which had been circularly polarized,
and are now transmitted to the~output at less than normal
inte~sity, Rays at the next outer zone, represented by
four d~ts had been subjected to 90 of polariza~ion
rotati~n, and are now rejected by the polarizer, pro-
ducing a zero o~tput, At the next outer zone, the
emerging r~ys from the polarizer are of reduced length,
indicating that they had been derived from previously
circularly polarized rays. At the fi~al zone pictured,
emerging rays are represented by four full length
vertical lines indicating that the rays have been trans-
mitted through the filter-polarizer combination without
attenuation.
The lower po~tion of Figure 2D illustrates the
selection of rays at a broad central zone of the fiel~,
the rejection of rays in a narrower second zone s~rround-
ing the central zone, the selection of rays in a still
narrower third zone, surrounding the second zone by
passaqe of rays of initially P polarization through
the filter-polarizer combination.
The effect of the polarizer 52 upon reflected
ray~ is illustrated in Figure 2E. The upper portion of
l~S~ 7
- 31 ~
~igure 2E represents ~ntenaity of the reflected horLzon-
tally p~larized output rays as_a function of ray po~ition
in successively larger dlameter zones lying within the
field. The lower portion of Figure 2E represent~ the
inte~sity ~s a ~unction of the radial poqition of a ray
within the field.
The upper portion of Figure 2E illustrates the
progression of ~he intensity of the rays 59 reflected
cff axi~ as the ray po~ition progresses from the center
to ~he perimete~ of the ilt~r ~ield. ~he intensltie~
are represented as in Figure 2D. Ray at the center
of the filter field represented by a ~ingle dot have
been subjected to no polarization rotation and
are not reflected off axis. Reflected rays at the next
zone, represented by four reduced lines represent the
vertical component of rays, which had been circularly
polarized and are reflected off-axis at less tha~ normal
i~ten~ity. Reflected rays at the next outer zone repre-
~ented by ~our full length h~rizontal line~, have been
subjected to 9D~ of polarization rotation, and now appear
unattenuated, in the off-axis output. At the next outer
zone the reflected rays 59 are of reduced length indicat-
ing that they have been derived from previously circularly
;
- 32 ~
pol~rized rays. At the final zone pic~ured, reflected
r~ys are represented by dots indicating th~t the rays
had been transmitted through the filte:r but not
reflected off-axis.,
S ~he lower portion of Figure 2E illustratefi the
rejection of rays at a broad central zone of the field.
The selection of rays of a narrower second zone surround-
ing the central zone, the rejection of rays in a still
narrower third zone surroundinq the second zone by
pa~sage o~ rays of initiall~ P polarizatlon thrDugh the
filter-polarizer co~ination.
For purpo~es of introduction to the embo~iment
illustrated in Figures 3A and 3B in which the aperture
67 is a critical element, the cross-section of the
aperture 67 has been imposed in the Figure 2D embodi-
ment illustrating that the aperture 67, lf placed
in the transmitted output of the polari2er, should be
6et to allow passage of the broad central zone of the
field and be aligned approximately at the lowest point
of the second zone surrounding the second zone (a zone
of rejection) ~hus, the filtex, the polarizer and the
aperture combine to permit unat~enuated passage of a
. .
Ll î~
-- 33 -- :
single band of rayB ~lowly yoing from a minimum t~ a
maximum and returning to a mi~imum acrosfi the physical
aperture 67.
The ~pherical optical transmission filter-polar-
izer combination may be employed in the cavity of astable Q-switched laser oscillator for improved operation.
The laser oscillator and its operation are explained with
reference to Figure 3A-3C; with Figures 4A-4F, 5 and ~
dealing primarily with the Q-switching operaticn. The
fllter-polari~er comblnatlon ls designed to ~acilitate
laser operation in a single TE~oo mode ;and to suppress
operation in the TE~ol and TEMlo modes. The consequence
of single mode operation is an improvement in the uni-
formity of the output beam and in divergence in the far
lS field region.
The combination offsets the tendency of the laser
to produce multiple modes as a result of a thermo optical
distortion of the laser gain medium or from an increase
in the aperture of the resonator. The optical distortion
will tend to cause break up of a single mode beam and to
cause the development of higher order modes. Decreasing
the intracavity bea~ aperture can be used to control the
- 3~ - `
laser beam mode, but results in a l~w lntensity output
and inefficient use of energy stored in a gain medium,
since the energy not passed by the aperture i~ 108t~
A typical beam aperture for a single mode rod
S laser is designed to maintain the Fresnel number N~ at
less than 1 i~ order to obtain the desired mode selec-
tivity; where Nf = a2/~L, in which a s the laser ~eam
radius, ~ is the laser beam wavelength, and L is the
optical resonator length. The small beam aperture requir-
ed for TEMoo mode operation i5 ~olely dependent on de-
fraction loss. The Fresnel numbered mode amplitude and
phase relationships in a face pumped laser are described
in an article entitled "Resonant Mode Analysis of Single
Mode Face Pumped Lasers" in Applied Optics, Vol. 16, page
; 15 1067 and following, on April 1~77, authored by ~.K. Chun
et al. The be~m intensity distribution of the TEMoo
mode is concentrated at the beam center ~aussian
intensity profile~, while in the higher order modes
the majsr port.ion of intensity di~tribution is away
from the beam center. For a number of la~er appli-
cations, operating in the TEMDo mode with the laser
energy concentrated at the beam center i8 e~sential to
- 35 -
efficient la~er operation, bu~ limiting the beam aperture
to control mode also Ii~its beam ~nergy.o~tput. ~he
present embodiment e~fect3 increa~e~ in energy and in
~uality of the output beam.
~he laser appa~atus designed f~r ~ingle mode
operation comprises a slab 60 of the gain medium of a
square cross-section, optical pumping means 61 arranged
adjacent to the upper and lower lateral surfaces of the
slab, an optical.cavity which includes a first flat
partially tranqparent mlrror 62, deini~g o~e end of the
optical cavity and a second concave spherical mirror 63
defin1ng the other end of the optical cavity, and the
wave transmission filter 10, a Pockel's cell 64, a
polarizer 52, and an aperture 67 all installed within
the cavity. Light rays generated within the slab and
passing through the slab, pass through the two end
surfaces of the slab, and are coupled to the optical
resonator caYity 62, 63. The slab may be either of a
Nd:YAG, or Nd:glass or any suitable laser material
designed for laser operation. The Pockells cell 64 and
the polarizer 52 cooperate, in operating the optical
resonator in a ~-switched mode, the polarizer S2 being
'7
- 36 - ~
the means by which energy is diverted f:rom the cavity to
prevent oscillation. The partially transmittinq mirror
62 is the point from which the optical output is taken
from the cavity.
The optical elements of the l~ser app~ratus of
Figures 3A and 3B are arranged alony the ~ axis in pre-
scribed orientations in relation to the P and S axes.
As earlier noted, the P and S axes in Figure~ 3A and
3B are e~t~blish~d by the rotational orientation of the
slab 6~ about the Z axl~. In particular, the end face~
65 and 66 oE the slabs are cut ~t the Brewster angle ln
relation to the upper and lower surfaces. The Brewster
angle defines an anglç at which a ray polarized perpen-
dicular to the upper and lower surfaces of the slab (P
polarizatio,n) will enter the slab with zero reflection.
At the same time, the srewster cut has the effect of
gradually dispersing horizontal polarization, since a
horizontally (5) polari7ed component of a ray will l~se
a ~ubstantial percentage (typically 20%) in reflection
upon each passaqe through the slab.
The laser apparatus illustrated in Figures 3A,
3B and 3C produce~ a short duration high intensity
~ Z~ L?~ 7
- 37 ~
polarized beam o~ coherent electro-maqnetic radiation.
The energy for the output be~m~is ~upE~lied to the gain
medium 60 by the flash lamps 61 acting as pumps to pro-
duce a population increase (or inversion) of high
energy electronic ~tates in the gain medium. The energy
stored in the gain medium, which accompanies each flash
of the flash lamp, is extracted by the optical resonator
under the control of the Pockel's cell 64, to effect
"Q-switched" short pulse high intensity operation.
In ~-~witched operation, the Pockel ~Y cell which
is installed within the laser cavity, forms an electri-
cally controlled optical shutter, operating the resonator
cavity between a gain prohibiting (low Q) and a gain
permitting (high Q) state. The Pockel's cell effects
thi~ change by producing a phase rotation to incident
light of suitable polarizati~n, when a control voltage
is applied to its crystal constituent. The slab 60,
as a result of the use of end faces cut at the Brewster
angle, tends to form a beam of P polarization. The
ene~gized Pockel's cell, which produces a net 90 polar-
ization rotation in the apparatus, combined with the
polarizer 52, combines to eject the originally P
1~35'~'7
- 38
polarized radiation from the res~nating cavity. ~hiC
reduces the feedback of the c~vity re~onator below that
re~uired for lasing. When the control. voltage applied
to the Pockel's cell, is removed, the phase rotation
disappears, and the feedback of the resonator cavity
for rays of P polarization is restored allowing las.ing
to occur.
Energized operation of the Pockel' 8 cell pre-
cludes resonance within the cavity in the following
manner, When the Pockel'g cell i3 in an energi2ed state,
it produces a ne~ 90 rotation o the polarization to
the components of polarized rays experiencing a double
passage through the Pockel's cell. The double passage
occurs in the leftward path from the sla~ 60 ~ia the
lS polarizer 52 to the end mirror 63 and in the return
path to the riyht from the mirror 63 via the polarizer
52 to the slab 60. Essentially all of the light imping-
ing on the polarizer 52 from the slab 60 is of a P
polarization, and is transmitted to the Pockel's cell.
When the Pockel's cell is in an energized state, the
double passage which' produces a 90 polarization rotation,
convertQ the light from a P polarization to S polarizat~,
i
~ ~S~7
; - 39 -
in which state it i8 rejected fr~m the res~nator by the
polarizer 52 as shown at 68.~-The ejection of this light
reduce~ the optical "Q~ of the reso~ator ca~ity below
the level required to sustain resonance.
Q-switched short pul~e oper~tion occurs in the
following sequence. Before a pumping n flash" ha~ oc-
curred a control voltage is applied to the Po~el'~
cell to preclude resonance and allow the population
inversion operation. When the peaX ~i.e. a maximum
population inversion) has been attained, the voltage
applied to the Pockel's cell is removed to allow the
rapid depletion of stored energy necessary to produce
the desired short duration high intensity output pulse.
Shortly after the output pul6e has occurred, the voltage
is reapplied to the Pockel' 8 cell to preven~ resonance
~ntil adequate energy ha~ been stored to generate A
second pulse.
The above sequence of events for Q-switched oper-
ation is illustrated in Figures 4A through 4F and utilizes
20 the control circuit of Figure 5. The gain medium is re-
currently pumped by flashlamps which has a time dependent
optical gain in a laser medium as shown in Figure 4B,
s~
- 40 - ~ ~
the period of each se~uence starting at t . The voltage
necessary to effecting a 90~ polarizat:ion rotation iB
-
applied to the Q-switch prior to to and sustained into
the flashlamp pumping period as will be described bPlow,
As a result of a pumping flash, optical gain in the lase~
gain medium is created, having a time dependent charac-
teristic as shown in Figure 4B. As a next step in Q-
switched operation, ~rigger pulses are applied to the
control circuit for the Pockel's cell at predetermined
time~ ~tl, t2) to cause the Poc~el's cell voltage to
decay at prescribed rates from the initial value to
zero. This induces a controlled depletlon of the
electronic inversion in the gain medium, allowing
resonance in the optical resonator with the controlled
lS onset of amplification in the gai~ medium. The effect
; is the production of an output laser pulse of improved
beam quality.
The control circuit shown in Figure 5, is used
to operate the PocXel'a cell, in the Flgures 4A through
4F sequence. In the control network of Figure S, the
electronically controlled switches Sl and S2 are
connected via two switching networks to the Pockel's
,.
.
1~5~
- 41 -
cell (64). The~e switching networks each entail a
capacitor and two resistors. Each capacitor (.003 micro-
farad~ is connected in series with a ~0 megohm resi~tor,
the combination connected in shunt with each switch. The
inter-connection ~f a first cap~citor-resi~tor pair is
connected to the high voltage terminal of the Poc~el's
cell via the moderately sized reqistor 78 ~56K). The
inter-connection of the second capacitor-resistor pair
is connected to the high voltage terminal of the Pockel's
cell Via a small slzed re~istor 80 (5~ ohms). One
terminal o~ each switch Sl, S2 and the Pockel's cell is
returned to ground. A voltage source (not shown) having
a value adjusted to produce a 90 polarization rotation
for a double beam passage (i.e., a quarter wave differ-
ential phase shift) is connected to the control networkto operate the Pockel's cell. In the exemplary circuit
the control terminal of the source is connected via three
(unnumbered) isolating resistors respectively to the
ungrounded terminal of switch Sl, of switch S2, and of
the Pockel's cell 64. In the example, ~he voltage re-
quired for a KD~P Pockel's cell is 3.2 kilovolts. The
negative terminal of the source is connected to ground
~s~
- 42 -
to complete the energization circuit.
In the operational eequence, ~he high voltage ie
applied to the control network just prior to the time to
(at which time the flashlamp is turnecl on) with the
electronically controlled switche~ Sl, S2 open. ~hus,
from just prior to the time to and from the ti~e to to
tl, the Pockel's cell has a constant quarter wave voltaqe
applied, which blocks resonant operation of the optical
cavity. This blockage i5 a function of radial distance
from the axis of the optical system, a~ illustrated by
the trans~ission profile 82 of Figure 6 and specifically
prevents resonance at the fundamental TEMoo mode and --
re.4onance in general. In Figure 6, the radial distance
is normalized to the size of the laser beam. At time tl,
lS a voltage qpike occurs as shown in Figure lC, closing the
electronically controlled switch Sl, and initiatiny a
discharye of the Pockel's cell at a first alow decay
rate. Since the Pockel 1 5 cell may be represented as a
fully charged capacitor of ab~ut 30 picofarads, the
voltage on the Pockel's cell will decay with a time
constant established by the 56 kilo-ohm resistor 78,
and the capacity of the Pockel' 6 cell. The R-C time
- 43 -
constant of this discharge path is on the order of ~
few (e.g. 1-3) micro-seconds ~nd produce~ the rate of
decay shown in ~igure 4D during the perio~ between tl
a~d t2. ~uring the tl-t2 period, the voltage applied to
the Pockel 1 5 cell will drop gradually to a voltage
~lightly above the threshold required for single mode
Dperation within the cavity, corresponding to the seoond
transmission profile illustrated at 86 in Figure 6. The
new profile ~86) represents a change from the previous
prof~le (82) c~nd permits generation of a slowly growing
single mode seed beam. At the time t2, a~s shown in
Figure 4C, the electronically controlled s~itch S2 is
closed in response to a further control pulse. This
closes a second discharge path for the voltage on the
Pockel's cell 64 through 50 ohm resistor 80. The R-C
time constant of this discharge path is on the order of
a few (e.g. 2.0 - 4.0) nanoseconds, or about one thDu-
sandth the time constant for the discharqe path through
resistor 78. After time t2, a rapid decay of the Pockel's
cell voltage occurs, as shown in Figure 4D. The drop in
Pockel's cell voltage allows growth of internal feedback
within the resonator cavity, passing through three
s~
- 44 -
illustrated intermediate stages until the "final" ~rans-
mission profile shown at 84 in Figure 6 i~ reached.
Maximum ~timulation of emis~ion occurs in this tate
and the laser output pulse illu~trated at 4F i~ pr~d~ed
5 as the popul ation inYersiOn ln the gain med~um 1R
rapldly dissipated.
The natural decay indicated as a dotted line in
Figure 4B as a result of the stimulation is hastened by
four orders of magnitud~, producing an actual decay more
accurately represented by a vertical ~olid lino. While
slopes have been indicated after t2, in the 4B, 4F illus-
trations, the microsecond and nanosecond period~ require
mixed time scales for'exact illustration. One may
explain that approximately 30 nanoseconds after t2, the
short duration output pulse of 10 to 30 nanoseconds
(represented in Figure 4F) takes place simultaneously
with the actual population depletion ~represented in
~igure 4B).
The final transmission proPile 84 of Figure 6 for
the Figures 3A-3s embodiment corresponds to the trans-
mission profile produced by the filter-polarizer combin-
ation which was illustrated in Figure 2D. When these two
.
,
~5~ '7
- 45 ~
elements axe present in the resonator cavity, they impose
a transmission profile upon t~e total la~er apparatus
favoring operation in a TEMoo mode and favoring pro-
duction of an output beam 69 of high purity.
S A simple expl~nation for selectlon of the TEMo~
mode in the ~igures 3A, 3~ embodiment is that the trans-
mission profile approximates the Gaussin intensity profile
of the TEMoo mode. Thus operation in the TEMoo mode is
facilitated and operation on the higher order modes, which
require facilitation by a spacially inconsistent inte~sity
profile, are suppressed. In particular, the be~m
intensity of the TEMoo mode is concentrated near the beam
center, while the beam intensity for the higher order
modes is distributed over distances remote from the beam
center. The filter-polarizer combination of the present
invention, provides a nearly lossless optical transmission
characteristic is pro~ided to the two next higher order
modes. This results in conditioning the optical cavity
to maximize operation on the TEMoo mode.
The operation of the laser apparatus in effecting
selection of the TEMoo mode may be further explained by
; reference to Figure 3C, which illustrates the radial
transmiSsion profile of the filter-polarizer combination
'7
- 46 -
in the context of the normal distribution of energy in
the three releve~t modes. The drawing further illus- '
trates the effect of the aperture 67, which may be
regarded as a spaclal filter, and tha intensity profile
of the laser beam. The laser b~am profile wi~hin the
resonator cavity, ~ut after spacial filtering by aperture
67, approximates the profile of the output beam after
passage via the mirror 62 and thus the two may be regarded
as quite similar.
The upper graph in Figure 3C illustrates the
differential phase shift o the filter 10 as a function
of the,radial position of an impinging ray. The phase
shift is a second power of the coordinate of the ray.
The transmission profile of the filter-polarizer combin-
lS ation is the second graph of Figure 3C. The profile
includes a broad central area of high transmission, a
narrower ~surrounding~ second zone of low transmission
and a third still narrower, surrounding zone of high
transmisSion~ The Gaussian TEMo~ mode has a somewhat
narrower intensity profile than the transmission profile
and is passed substantially unattenuated to the outputO
This is shown at the lowest graph of Figure 3C which is
- 47 - ~ -
the intensity profile of the output beam of the laser.
Rejection of the two higher order m~des may also
be explained using Figure 3C, which shows these intensity
profiles. The next higher order mode, the T~Mol mode,
has an intensity profile which is low at the beam center
and whic~ has two maxima, which occur near the minima
of the transmis&iDn profile of the filter-polarizer
combination. These zones are usually o~ unlike breadth,
and so rejection may not be complete. When, how~ver,
an aperture acting a~ a spacial filter is imposed at
approximately the point of minimum transmission in the
secon~ zone of the filter-polarizer combination, add-
itional suppression of the TEMol mode will usually
occur. The potential contribution of the TEMol mode
1~ is thus usually quite small, and in a suitable design,
the actual contribution may be negligable.
The second higher order mode, the TEMlo mode, is
also potentially present but suppressed in the design.
This mode has an intensity profile in which the energy
is distributed into three peaks of comparable intensity~
The central intensity peak of the TEMlo mode is at the
center of the filter-polarizer transmission profile,
~S~'~'7
- g8
which is also a transmission peak, In addition, the two
outer peak~ of the TEMlo mode ~pacially overlap the two
outer transmis~ion peaks of the filter-polarizer combln-
ation. Thus the TEMlo mode mignt be expected to be
present. The spacial f~lter 67 re~ects the two outer
peaks, and thus removes a co~siderable portio~ of the
TEMlo energy, normally enough to suppress that mode.
In practice, the mechanism for mode selection in the
resonator cavity i9 interactive, and the rejection of
unwanted modes need not be complete to achieve nearly
pure TEMoo mode operation.
The filter-polarizer combination in the Figure
3A-3C embodiment produces several major advantages in
laser operation. These advantages flow primarily from
th~ suppression of the undesired higher modes and
selection of the desired TEMoo mode. One conse~uence
of single mode operation is that a higher quality beam
both within and without the cavity is produced. In
particular, the phase and the amplitude (intensity)
across the beam is more accurate and the far field
divergence is reduced. A second effect, an indirect
consequence of single mode operation, is that when an
-- D~9 _ ,
aperture is employed, of which the edge is
placed at the minimum point of the TEMoo mode, the
aperture ~ecomes a "soft aperture". This implies,
that the beam intensity is small at the margin
of the aperture and that Yreanel fringes, which
would otherwise worsen the quality of the beam
at its boundaries are not present.
In the actual design, the cavity
is operated in a stable mode in both dimensions,
using a filter of spherical design with Fresnel
numbers of about four. The beam diame-ter is
approximately ~ millimeters in a slab oE 8 by
16 m:illimet~rs cross-s~c~ion. q'h~ energy per pul~3e :is
approximately 150 millijoules.
The cylindrical optical transmission
filter-polarizer combination may be employed in a
cavity of a stable/unstable Q-switched laser
oscillator for improved operation. The laser
oscillator and its operation are explained with
refere ce to ~igures 7~-7b.
~ .
,55~ 7
The laser Psc~ ~lator of Figures 7~, 7~ comprl~es
a ~la~ 81 of the gain mediu~ of rect:angular croq~-6ec~on,
optical pumping means 82 arranged adjacent to the larger
lateral ~urfaces of the ~lab, an optic~l cavity which
includes a first convex cylindrical mirror 83 defining
one end of the optical cavity, and a second concave
spherical mirror 84 defining the other end of the
optical cavity; and a Pockel's cell 85, a polarizer 86,
a rectangular aperture 87, a polarizer 89, and an adjust-
able cylindrical filter 90 installed within the cavity.
~ he optical elemen~s o~ the laser oscillator arearranged along the optical axis (Z axis) of the apparatus
as illustrated in both Figures 7A and 7s. In a left to
right sequence, the concave spherical mirror 84 is first,
the Pockel's cell 85 is second, and the polarizer 86, the
slab 81, the aperture 87, the polarizer 89, the adjust-
able cylindrical optical transmission filter 90, and
the convex cyli~drical mirror a3 follow in succession.
The optical output of the laser oscillator is
derived as a reflection from the le~t face of the polar-
izer ~6 as shown at 98. An unused outpu~ 97 also appears
as a reflection fro~n the right face of the polarizer 89.
1~5~
The unused output 97 acts as a discard of unwanted energy
from the main path of the optical resonator as a result
of operation o~ the polarizer filter combination (89, 90),
which provides a "soft aperture" active along the
S unstable axis of the re~onator. The polari2er-filter
combination facilitates operation of the laser-oscillator
at high power using a rectangular glab laser at l~rge
apertures (e.g. P~nel n~xrs of 40, measured along the
unstable axis) while still providing an output ~eam o~
9 ood qua 1 i ty .
The length (L) of the cavity, the radius (Rl) of
the convex cylindrical mirror 83 and the radius (R2) of
the concave cylindrical mirror 84 define an optical
resonator in which stable operation is achieved in a
vertical dimension of the beam, the beam being prevented
from expanding in the vertical of P dimension beyond the
aperture of the oscillator. ~nstable operation is
achieved in a horizontal dimension, the beam being per-
mitted to expand in the S dimension beyond the apertures
~0 o f th e appara~us.
As noted in the above cited patent application,
the slab 81 whose end faces are cut at the Brew~ter
.~L;ZS5~9L~L7
- 52 ~
angle has a polarization selective act:ion by which the
8lab i8 optically coupled to rays ~95) of P polarization
transversing the optical resonator defined by the end
mirrors 83, 84. In the cited arranqement the Pockel 1 8
cell 85 acts as a variable opt~cal power divider within
the cavity, capable ~f facilitating or precludil~g lasing
by adjustment of the light diverted to the output. The
Pockel's cell is ordinarily operated at an intermediate
setting by which the amounts of light retained within the
cavity and the amounts diverted from the cavity to th~
outpu~ are adjusted to optimize the ou~put. At
the right of the slab, in the Figures 7A, 7B embodiment,
the polarizer-filter combi~ation 89, 90 ~not present
in the cited arrangement), cooperate to provide the soft
lS filtering action noted earlier.
The laser oscillator o~ Figure~ 7A, 7B osclllates
with light pursuing the following path through the
resonator rays 95 of P polarization, which have exited
t~e right face of the rectangular laser slab 81, proceed
to the risht along the Z axis via the polarizer 89 to the
filter 90. The vertical lines ~95) which continue from
the slab 81 via the polarizer 89 to the filter 90 i~dicate
.
4~
- 53 ~
the p~ssage of P polarized light to the filter 90.
Upon passage through the filter 90, the polari7ation
components of individual ray~ of the beam, dependiny
upon thB S coordinates of each ray, experience differe~t
individual phase 6hifts which pr~duce differi~g polar-
ization rotations. The polarization characteristic of
the cylindrical filter is comparable to that illustrated
in the upper portion of Figure 2C, which illustrates the
polarization rotation over the beam cross-section pro-
duced by a spherical filter. The polarization charact-
eri.~tic Por the cylindric~l unit 90 may be described
as lackinq the vertical and retaining the horizontal
development of the Figure 2C illustration. More
particularly, it may be descrihed as a horizontal section
of the Figure 2C illus~ration taken through the center
of the beam. The rays modified by the filter 90 are
thus approximately represented at 96 in Figure 7A by
alter~atinq circles and vertical lines and in Figure 7
by circles implying some degree of mixed polarization.
20 The filtered rays continue rightward until they impinge
upon the convex cylindrical mirror 83. The mirror 83
has a l~o~ reflective coating, which causes the rays to
S~
- 54 ~
be reflected leftwards. The cylindrical mirror 83 is
oriented in relation to the ~xes of the apparatus such
that a trace of the mirror in the P-Z plane will be a
traight :line while a trace of the mirror in the S-Z
plane will be a circle having a radiu~ Rl.
The rays re~lected leftward from tAe mirror 83
retain the mixed polarization 96 already noted and re-
enter the filter 90 at its left face. The rays exit
the left face of the filter and proceed leftward until
they impinqe on the right face of the polarizer 89.
Any ray components (95) of a P polarization proceed
via the polarizer 89 substantially without reflection
to the right end of the slab 81. Any ray components (97)
of an S polarization exiting the left face of the filter
90, as shown at 97, pIoceed to the right face of the
polarizer 89 and are reflected off-axis and discarded
as shown.
Continuing now to the left of the slab Bl, ray
components 9S of P polarization exiting the left face
of the slab 81 continue via the polarizer 86 to the
Poc~el's cell 85, passing throu~h the polarizer sub-
stantially without reflection. Assuming that the
. ,~
:~2~ '7
- 55 - ~
Pockel 1 8 cell i~ in a ~uitably energized condition to
effect a 45 polarization, rays components entering the
Pockel' 5 cell 85 from the right of a P polarization are
subjected to a polarization rotation of 4S producing
circular polarization ~g ~hown at 99 in Figure~ 7A and
7B. Upon reflection from the concave spherical mirror
84, and a second pass~ge through the Pockel's cell as,
the ray components 95 previously of circular P polar-
ization, are rotated an additional 45 converting them
to S polari~ation ~98). Vpon impinging upon the left
face of the polarizer 86, the components 98 of S polar-
ization are directed off-axis forming in the main output
path of the laser oscillator.
The ill~strative Pockel' 8 cell setting is one
which reduces the feedback within the optical re~onator
to zero, and is used to extinguish oscillation. }n
practice, the voltage on the Pockel's cell is an
intermediate selection in which a division occurs
between light derived from the cavity, and that
allowed to remain in the cavity.
~ ~5~ 7
- 56 - ~ ~
In ~peration of the ~tablefuns~able resonator~ the
be~m which ha~ pursued the pa~h~ described, i9 periodi-
cally re~ocused in the P dimen ion by the c~rvatur~ of
-the spherical mirror 84 ~nd the mirror 83, effectively
flat in the P dimension. The optical design of the
resonator is thus chosen to provide a reasonable beam
sizé within the laser material. The vertical dimension
of the beam is typically approximately half the cross-
section of the laser slab, e.g. ~ millimeters, with
Fresnel ~umbers of ~bout 4. The other deslgn d~men~io~s
are as follow~: slab 139.37 mm long, l5 mm wide, 8 mm
thick, Rl is 6 meters, L (cavity length) is 1 meter~
Along the unstable axis, i.e. the S dimension
modes are not formally defined, and individual rays,
lS when traced through the cavity, "walk off" the lateral
apertures of the apparatus. In a practical embodiment,
the radius of curvature of the cylindrical mirror ~R2)
is 4 meters, producing a "G" stability factor o 1.25.
While higher Fresnel numbers are permitted (e.g. 4D),
the quality of the beam is disturbed by Fresnel defraction
effects at the lateral edges of the aperture if the
filter-polarizer combination i~ not present~ A tapering
.
- 57 - -:~
of the intensity profile of the beam in the S dimension
provides a s gnificant improvement in beam quality, or
conversely, permits higher power operat.ion or larger
apertures at the same beam qu~lity.
The filter-pola,rizer combination 90, 89 illu9-
trated at the right of the Figure 7A, 7B embodiment
produces a "soft" lateral aperture reducing the edge
diffraction effects. Typically the design of the
filter 90 is adjusted in relation to the lateral edges
o~ the apert~re so as to produce a null at the aperture
edges to waves transmitted through the polarizer B9
corresponding to the intensity plot illustrated at
the lower portion of Figure 2D, The reflected waves
are ejected from the cavity as illustrated at the lower
plot of ~igure 2E.
The benefit of the filter-polari~er com~ination
in the Pigure 7A, 7~ configuration, is primarily the
consequence of a "soft" lateral aperture in which a
graduated attenuati~n generally following the curves
in the Figure 2B-2E series is produced along the S
- 58 - ~-
coordinate of the aperture. The primary effect is the
avoidance of Fresnel edge defraction effects by reducing
the beam amplitude at the lateral margins of the aperture.
~he intensity at these margins would remain unacceptably
; 5 high without such a reductlon. ~he :L~teral amplitude
adjustment, recognizing that the modes are undefined
- along the unstable axis, permits a somewhat m~re efficient
extraction of stored energy from the slab by using more
of the width dimension of the slab.
In a practical application, the filter 90 may
take either the nonadjustable form illustrated in Figure
lC or the adjustable form in Figure lD. In principle,
the central thicknesses of the two components of the
filter should be equal, and achievement of equality is
most easily achieved by the adjustable arrangement.
The filter-polarizer combination may also be used
to advantage in more fully utilizing the interaction
volume of a laser amplifier used to amplify the output
of a laser oscillator as shown in Figure 8A.
~2~
-- 59 --
A Gaussian inten~ity proflle 114 from a la~r o~c~ tor
101 operating in a eingle tran0ver~e mode (TEMoo~ may
be converted to a more nearly U~lat top" beam inten~ity
proflle 115 by operation of the filter-polarizer ~o~bin-
ation 103, 104, 105, before application to the inputaperture 107 of a laser ampli~ier 1~8. The ~flat top"
beam intensity profile 115 is preferrable i~ order to
obtain a more efficient extraction of stored energy
from an amplifier.
The apparatus illu~t~ated in Figure 8A functions
in the foregoing manner. The outpu~ o~ the la~er
oscillator 101 aq indicated by thë vertical and
horizontal marks 109 and 110, may be assumed to contain
some components of both P and S polarization, but P
polarization is the primary polarization. The output
of the oscillator may otherwise be a~sumed to exhibit
an ideal Gaussian amplitude profile as more accurately
illustrated at 114 in Figure ~C. The la~er oscillator
output proceeds to the right impinging next on the
S~'7
- 60 ~
polarizer 103 which transmita light of P polarization
to the filter 104 and ejects l-i-ght of S polarization
from the transmission path. The polarizer 103 is not
essential to the operation of the 6ystem to the degree
that the output of the l~Ber o~cillator i8 reBtriCted
to P polarization. The filter 104 is preferably an
adjustable ~pherical two lens filter as illustrated
in Figure lB. The first lens of the filter is a
compound lens which includes a slideable wedge for
adjusting the center thickne~s of the first lens in
relation to the center thickness of the second lens.
The cry~tal optical axes of the two lenRes of the
filter 104 are mutually perpendicular and are oriented
at a 45 angle to the P coordinate. The curvatures
of the lenses are selected to provide the desired polar-
ization rotation in a single passage of the beam through
the filter. The radius of the lens curvature is in turn
determined by the design cross-section of the beam. In
particular, for the single passage design, a spot
~0 diameter o~ .90 centimeters requires a radius of curv-
ature of approximately 33 centimeters. (For double
... . .. .
pa6sage the radius of curvature i3 approximately double.)
The filter~d light nex~ impinges on the polarizer
105 which is oriented parallel to the polarizer 103, for
transmi6sion of ray component~ of P polarization and
S reflection of componen~s of S polarization. Due to the
polariz~tion rotation produced by the filter 104,
components of S polarization appear ~nd are ejected
by reflection from the transmission path by the polar-
izer lOS. The tr~n~smltted remainder i~ ~upplied to
the aperture 104 o~ the laser amplifier 108. ~he
justif.ication of a spherical design for the filter
lenses haQ been on the assumption that the interaction
cross-section of the laser material is sguare, and that
the entrance aperture 114 is circular. The spherical
design will produce an improvement in the fill factor
along both the P and S coordinates of the beam.
The transmission profile of the filter polarizer
combination is illustrated in Figure 8s for five differ-
ent adjustments of the center thickness of the first
lens. The independent variable in Figure 8B is the beam
~2S~
- 62 -
r~dius and dependent variable is the re:~ative optical
transmission. The entrance ~pe~-ture 107 o~ the laser
amplifier should be adju~ted to lie ju~t: within the
desired i~teraction 2ro6s-section of the active laser
material of the a~plifier. The entrance aperture 107
is set at the minimu~ of the transmission characteristic
to minimize Fresnel fringing. When the lenses have
equal center thicknesses, the transmission profile 111
i9 followed. ~his profile remains near unity until
nearly .2 of the beam radi~3; fall~ to approximately
85~ at .4 o~ the be~m radlus and then falls to ~ero ~t
approximately .8 of the beam radius, where the aperture
should be set.
As the center thickness difference increases,
however, the transmission at the center of the profile
falls, and the beam width increases. In the right most
member (112) of the family of curves, the beam width
provides .85 transm.ission at the center of the beam.
The width of the beam at the .85 transmission point i8
~0 increased from approximately 0.4 to 0.55 of the beam
~2~
- 63 -
radius. ~he width of the beam measured at the low point
shifts from approximately 0. a to .Q9, and defines a new
position for setting the entrance aperture of the laser
amplifier.
S ~he beam "fill factor" may be increased in typicAl
case~ from a ~alue of 40~ to 70~ using suitable design
par&meters. The "fill factor" is defined as the fraction
of the volume of the lasing material occupied by the beam
in relation to an idealized case in which the volume of
the l~sing material is completely filled with full
intensity illumin~tion. At constant ~nplitude, the
sharp edge of the aperture acting upon the idealized
beam would cause severe Fresnel diffraction effects.
Accordingly, a "fill factor" substantially less than
lS 100% is a practical and desirable compromise.
An illustration of a more nearly optimum trans-
mitted beam profile achieved by application of the present
inYention is shown in ~i~ure 8C. In ~igure 8C, the in-
tensity of a Gaussian input beam i~ qhown at 114, the
transmission of the filter-polarizer oombination is
~ss~
- 64 -
shown at 113, ~nd the intensity of the transmitted beam
with an improved profile is ~hown at 115. In the cal-
culated graph of Figure 8C, The intensity of the trans-
; mitted beam remains substa~tially constant to approxi-
mately .35 of the beam radius and falls to zero at
slightly under .90 of the beam radius. The entrance
aperture 107 should be set to this value. The trans-
mission curve 113 employed in Figure 8C is an inter-
mediate one, second from the right of those illustrated
in Pigure 8B. The filter-polarizer combination can
provide widely varying transmission characteristics.
The radial position dependent phase shift can be con-
trolled with a birefringent lens having one flat face
and a positive or negative curvature on its opposite
face, defined by
~r) = (2~n~1) It + r2/2R~
in which t = the center thickness of the lens
R = the radius of curvature of the lens
r = the radius of the lens
~n = the birefringence
~ = the wave length of the light beam.
- 65 -
The ideal homogenous linear phase retardation matrix i~
A iB- _
~r
~s A~
where A - ~CQ~ (~/2) ] +j ~s~n (~/2) co~ 2a~ ~ A* equal~ the
complex conjugate of A, B eguals sin (~/2) sin 2~, C
equals the phase retardation angle (i.e. the differential
phaYe delay) and B equals the azimuth angle of the
crystal op'tic axes in relation to reference ~P) polar-
0 ization. ~he transmitted intensity when ~ is 45P iQT(r) _ co~2 [ ~r)/2].
Th2 matching set of egual but opposite curvature phase
retardation plates can avoid a lensing effect avoiding
an`unwanted beam expansion. ~y choosing a proper co~bin-
5 ation o~ a radius of curvature R, thicknesq t, and azimuth
- angle ~, a wide varie~y of tran6mission characteristics
for a particular wavelength for a particular gain medium
with a filter unit combined with a polarizer ca~ be
selected.
2~ The m~trix relation in the case of two lenses
placed between two parallel polarizer9 as shown in
Figure 2 can be written as
-- 66 --
[1 ~l rA1 jB~ rA2 j~21 1~l 1
J L 11 ~ ljB2 A2 l ~
~AlA2-BlB
1 0 J
where
1 C g (~i/23 + i ~in (~i/2)(cos 2 ~
Bi = ~sin (~i/2) (sin 2 ~
and i = the phase retardation angle in A~Bi.
Th~refore, the transmitted inten6ity T where T MxM
T = (AlA2 BlB2) ~AlA2 al~2)~
and T - cos (nl/2 - ~2/2~,
for 41 = 45~ and ~2 - 45 (the orthogonal arrange-
ment of the crystal axes)
for the matching concave and convex phaQe-plates,
T(r) ~ c08 [--~~ (tl t2 ( )]
where r ~ the rad~ U8,
- the radius of curvature,
~n = the ~ixefringence,
20 tl-t2 = the center thickness difference,
~ ~ the wavelength.
As n~ted earlier, with unequal center thicknesses, the
- maximum transmission is displaced from the center. When
the center thickness of both lense~ i8 equal, khe maximu~
'7
- 67 - -~
transmission 1~ displaced from the centeI. When the
center thlckness of both lenses i9 e~ual, the maximum
transmission i8 obtained at the center, i.e. r = 0.
For the case of equal lens thicknesses, tl-t2 = 0,
and the two-pass transmission ran be expressed as
T(r) = cos2 [2~ ~nr2/R~]
The radius of the curvature of the phase plates, R~ is
selected upon the basis of ~he desired beam spot size.
The equation indicates that the transmission of light at
the center of the phase plate~ will be nearly 100 per-
cent by selectiny the design parameters for the plates
of the zero order spherical retardation unit, the inter-
cavity beam radius may be expanded to maximize utiliz-
ation of the laser gain medium and simultaneously
maintain the beam transmission characteristics at their
opti~um Yalues over the radius of the beam.
Fiqures 9A, 9B and 9C deal with usage of the
filter of ~igure lB in particular, for phase correction
o~ the output beam of a laser source. When the filter i5
properly desiqned and adjusted, a simple, efficient and
practical means is provided to improve beam quality in
larqe spertDre face pumped la6er resonatorr ~.d ~,plifiers.
.. . . .
~2~
- 68 - ~ -
The correction der~es from ~ m~themati.cal analysts of
resonator mode formation ~nd ~he fAr field diffraction
of beams formed under these circ~anc:es. The radial
pha e deviation of the be~m within the re~onator in-
creases as the Fre~nel number of the resonator increasesand the far field beam, which i~ formed in such a
resonator, has a divergence which increases as the radial
phase deviation of the beam within the resonator in-
creases. When a properly deaigned and adju6ted phase
correction filter i8 applicd to the output o~ ~uch a
reson~tor, or ampli~ier, op~imized to p~oduce a reduction
in far field beam divergence, then the output beam
quallty is impxoved without deleteriou~ side effects.
The improvement has application to resonators where large
Fresnel numbers are involved, involYing both stable or
un~table re~o~at~rs.
While the correction haa application to the radial
phase deviation of a re~onator, it ahould be noted that
. the correction may be applied with good effect to the
output of an optical ~mp1ifier. The phase correction
scheme may be applied to certain optical amplifiers which
- :j f .': ~
-- 69 --
h~ve an internal radial pha~e d~viat-on or to those
who~e input has been supplied from a resonator having
the indicated radial phase deviation.
With a face p~mped laser (FPL) having a rec-
tangular-slab ~eometry, such as is illustrated n
Figure3 7~, ~B, it has been possible to generate a
large Gau3sian intensity pro~ile of the beam. Despite
the fact that beam intensity profile is similar to that
of a Gaussian inte~sity beam in the TEMoo mode, the
measured far field be~m divergence of this large
Gaussian be~m has been several times larger than the
diffraction limited case. .Thus the presence of an
apparent Gaussian intensity profile will be a necessary
but not a sufficient condition for diffraction limited
beam divergence~
Analysis, indicates that with such a beam, that
the radial phase de~iation between the beam center and
edge will increase as the ~re~nel number of the res~nator
increases ~his is also true ~or both the stable and the
unstable case. Yurthermore, the radial phase deviation
will increase f or a fixe~ resonator-cavity length 3S tha
beam aperture size increases.
~;ii5~7
- 73 - ~ ~
Applying the Hugen~-~re~nel principle, each point
in a resonator mode i~ b~sed on the contri~utions from
all the point~ on an OppOQite resonator reflector. Thus,
aa the Fre~nel number of the re~ona~or increase~, the
radial pha~e ~ariation of the mode increases due to the
increased path lenqth differences from all the points
of an opposite resonator reflector.
~he resonator modes may be analyzed based on the
Kirchhoff-Fresnel diffraction theory. In the one-
dimensional case
~'~1 ' ' .,
YU(X2) = 'J K~X1~ X2~U~Xl)dXl
where u(x21 : the resonator mode (eigenvect~r) at
the reflector 2
y : the mode reduction factor (eigenvalue)
Klxl,x23 : the geometry of resonator (kernel)
Xl'X2 : the coordinate at reflector 1, and 2
al : the half dimension of aperture at
reflector 1.
~rom the abD~e, one can define the resultant mode u(x)
as
u~x) = A(x)exp~ (x)~
where A(x) : the mode amplitude
~ (x) : the coordinate dependent ph~se of mode.
i50~ '7
- 71 - : ~ ~
The far field beam divergence can be estimated
by the far field integration of the reson~tor mode,
which can be performe~ based on the Fraunhofer dif-
fraction theory, which provide~ the b~iq of diffraction-
angle-dependent far field beam (V(p)):
~a
V~p) = J u(x)exp[-ikpx~dx
-a
where ~=2~/ ~ : the wavevector
10 ~ : the wavelength
u~x) : the resona~o~ rnode
p : the diffractlon angle coordinate
x : the phyqical coordinate
a : the half dimension of ~perture.
Thus, the diffraction angle dependent far field beam
intensity will be
l~p) = V~p) 2exp[-if(p)3
where f(p) : the angle dependent phase of far
field intensity
P : the diffraction angle.
The diffraction-angle-dependent far field intensity
patterns of resonator modes are of the general form shown
in Figures gB and 9C becoming successively more di~ergent
5~947
- 72 -
as the e~ui~alent Fresne! numbers increase. In the
range of 2.5 to 7.5, the beam width changes fr~m 5 mm
to 8.75 mm, and the maximum phase deviation of the mode
increa~es from about 1.2 to 5.1 times the diffraction
limited beam divergence.
The effect o~ phase deviati~n in the far field is
illustrated in Figure 9D. The horizontal coordinate is
the relative far field beam divergence and the vertical
coordinate is the normalized far field intensity. The
individual curves are plotted for differing pha~e devi- -
ations, the "phase deviation" being the observed phase
difference between the center and the beam edge for a
constant amplitude beam (far field). The individual
curves are plotted at 0.2~ intervals from zero to 2~.
The maximum phase deviation plotted (2~) exhibits the
greatest far field beam divergence and the lowest phase
deviation (uniphase) produces the diffraction li~i~ed
far field beam diverge~ce.
Pigure 9D illustrates that the greater the max-
imum phase deviation of the mode, the greater the farfield beam divergence. When the phase deviation
increases, the peak intensity moves out from the center
~25~47
- 73 -
of the beam and the b~am divergence increa~es. In
short, the beam width, phAse devi~tion of the modes,
affec~ the f~r field divergence of the output beam.
Analysis indicates that in unstable resonators
the phase deviation acr~ss the beam increases rath~r
~mo~thly as the beam aperture size increa~e~. Analysis
a3so indicates that the same rate applies in stable
resonators with large Gaussian modes. Therefore, it i8
posqible to model thi~ phase deviation as being created
by a simple quar~z radial phase plate, and to us~ the
model to make a correqponding correction.
0(r) = (2~n/~)[~ + (r /2R)~
where ~n : the birefringence
A : the wavelength
r : the radial dis~ance
: the center thickness
R : the rad!us of curvature
A computed equivalent radius of a quart~ lens may
be obtained from the above radi~l phase relation ~vr
different ~mpling points of beam aperture ~iqureR 9B
and 9C demonstrate, for the unstable resonator and ~table
resonator, respectively, th~ far field intensity improve-
ment that is obtained through this phase correction scheme
~.ZS,S,9'~7
- 74 ~
The phase correction provided i.n the Figure 9B ~nd
9C examplea may be seen tD produce a far field diver~enoe
o~ le~ than twice that of a ~diffract.ion iimitëd
be~D.
The Figure 9A emb~diment, which m~y be adjusted
to proYide the correctton of either the F~gure 9B or
9C examp~e, consi~ts of ~ la~er source 110, the adjust-
able spherical filter 111, simil~r to that provided in
Figure lB, ~nd for con~enience,the focu~ing len~ 112
of coherent accuracy or focu~ing the ~eam upon the
~creen 113. An lnten~ity plot of the beam croQ~-~ection
1~ provided at 114 as it impinges on the screen 113.
The lens element 112 1~ provided to permit the repro-
duction of far field conditions within the confines of
a room. For purposes of accuracy, the focal length of
the lens should be a~ large as possible consistent with
available space and i~ surfaces must be of fractional
wave ~ccuracy so as~not t~ lntroduce error. In the
absence of the lens 112, the far ~ield pattern may be
examined at the neare~t measurement di~tance ~ppropriate
for far field conditions.
I -
s,,r3~7
:
-- 7 5 -- ~
'
The Figure 9B filter utllizeg quart~ in an ad-
~u~table design ~8~ ng cyllndrlcal_lens surfacei. The
componen~ lenses have a center thic~ness clifference of
~,0716 c~nt~meter~, and a radlu~ of curvat~lre of 7.11 cmO
5 Using ~S" coordinate measurements, the beam width is
8.75 mm, the "equivalent~' Fresnel num~er is 7.5 and
the magnification of the resonator optics is l.5.
The Figure 9C filter is also of quartz in an
adjustable design using spherical surfaces. The radii
lO of curvature of the lenses are 29.56 cm and the center .
thickness difference of the lenses is 0.0534 cm. The
beam width i3 6 r~, the Fresnel number i8 ~.S And the r
C parameter ls 0.83,
The phase correction as described with reference
15 to Figures 9A, 9B, 9C and 9D has a primary applicaticn :
to laser systems in which a polarized output beam is
provided and in which Presnel numbers exceed 2 or 3.
The improvement is also applicable to laser ~ystems of
larger apertures (i.e. Fresnel numbers as large as 40)
20 where the bea~ approximates a smooth Gaussian or a "flat
top" profile. In practical ex~mples, corrections have
been achieved for be~ms both under and over a ~ phase ,.
deviation. Phase deviations beyond 2~ appear to repre~ent
1;~5~4~
- 76 - ;~
a practical upper limit for substantial phase correction.
~ he phase compengation, herein provided ~ay be
applied using a fil~r with matched spherical lenses in
the caQe that the phase deviation of the beam has circu-
lar symmetry as in a stable re~onator or ~n unstableresonator. In the event that the reQonator i~ a stable/
unstable resonator, then the phase compensation may
entail separate cylindrical elements for separately
cQmpensating the phase deviation along the stable and
10 unstable axes. While the compensation ha~ been applied
for improvernent o the far field beam, in the typical
case, near field beam conditions are also improved.
The adjustable form of the filter herein disclosed
is useful in that it removes one critical variable in
15 the prescription of the filter and addi flexibility in
a given laser system application.
In far ~ield correction, there are three circum-
stances ln which the beam formed by an optical re~onator
may require phase correction. In the beam formed in an
20 unstable resonator, adjustable ~pherical optics are
appropriate. In the beam formed in a stable/unstable
resona~or, adjustable cylindrical opticq are appropriate.
j3~ Z~;,5~3 L~7
- 7 7 -
In both ca~e~, where formal mode ~truc:ture i8 ab~ent,
~he phase de~iation increase~-signific:antly as the margin
of the ~eam i~ approached. ~h~ third clrcumstance re-
qulring correction i8 where the beam is created in ~n
optic~l re~onator ~n'which th0 fund~m~nt~l mode, while
paramount, i~ accemp~nl~d by ~me contrlbution~ from
other higher order modes. In far field correcti.on, the
phase deviation correction ordinarily need not be zero
on-axis, is generally small and increases as the radial
dl~tance o the beam element incrqases.
In the ne~r field application, where the beam
profile is being modified and the filter is used in
combination with polarizers, the adjustability ~eature
all~ws one to select the distance from the axis at which
the pha~e correction goes through zero changinq from
p~aitive to a negative sense and the tran~mission i0
maximum. In profile modlfication, adjustability i8
a~so lmportant for optimized performance.
The filter 10 amployed ln the stable re~ona~or
of the Figure 3A-3B embodiment use~ ~pherical lenses of
equal center thicknes3 in which the radii of curvature
~LZ~ 3~
- 73 ~
of the ~pherical surfaces are 29.72 cm, the assumed
beam di~meter being 6 ~m. The filter 90 employed
ln the stable/un3table resonator of the Pigure 7A-7B
embodiment h~ radii of cur~ature equal to 82.54 cm,
measured in a horizontal plane alon~ the un~table ~S)
~xis. The filter 90 i~ of an adjustable construction
and accordingly, the adjustment is set for optimum
performance at equal center thicknesses. The larger
~ran9Ver9e dimengion of the beam in the stable/un~table
resonator i9 one cmt
I I ' .
