Note: Descriptions are shown in the official language in which they were submitted.
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Photonic Signal Frequency Conversion Using a Photonic
Band Gap Structure
Background of tke Invention
Statement as to Rights to Inventions Made Under
Federally Sponsored Research and Development
This invention was made with Government support under Contract
DAAHO1-96-P-RO10 awarded by the U.S. Army Missile Command. The
Government has certain rights in the invention.
Field of the Invention
This invention relates to the generation of photonic signals at frequencies
other than the input signal. In particular, it relates to second or higher
harmonic
generation, sum, and difference frequency conversion, Raman processes and
generic parametric amplification near the photonic band edge.
Related Art
In recent years, advances in photonic technology have generated a trend
toward.the integration of electronic and photonic devices. These devices offer
an
array of advantages over conventional electronic devices. For example, they
can
provide enhanced speed of operation, reduced size, robustness to environmental
changes, such as rapid temperature variations, and increased lifetime and
ability
to handle high repetition rates. These structures can be made of metals,
semiconductor materials, ordinary dielectrics, or any combination of these
materials.
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The theoretical and experimental investigations of photonic band gap
(PBG) structures is evidence of the widely recognized potential that these new
materials offer. In such materials, electromagnetic field propagation is
forbidden
for a range of frequencies, and allowed for others. The nearly complete
absence
of some frequencies in the transmitted spectrum is referred to as a photonic
band
gap {PBG), in analogy to semiconductor band gaps. This phenomenon is based
on the interference of light; for frequencies inside the band gap, forward-
and
backward-propagating components can cancel destructively inside the structure,
leading to complete reflection.
For example, recent advancements in PBG structures have been made in
the development of a photonic band edge nonlinear optical limiter and switch.
See, "Optical Limiting and Switching of Ultrashort Pulses in Nonlinear
Photonic
Band-Gap Materials", M. Scalora, et al. , Physical Review Letters 73:1368 (
1994)
(incorporated by reference herein in its entirety). Also, advancements in
photonic
technology have been achieved with the development of the nonlinear optical
diode. See, "The Photonic Band-Edge Optical Diode", M. Scalora, et al.,
Journal
ofApplied Physics 76:2023 (1994), which is incorporated by reference herein in
its entirety. In addition, the physical processes involved in the photonic
signal
delay imparted by a uniform PBG structure are described in detail in Scalora,
et
- 20 al., "Ultrashort pulse propagation at the photonic band edge: large
tunable group
delay with minimal distortion and loss," Phys. Rev. E Rapid Comm. 54(2), R
1078-
81081 (August 1996), which is incorporated by reference herein in its
entirety.
The frequency conversion of coherent light sources, such as lasers, has
been investigated for many years, because of the desirability to expand the
ranges
of available output wavelengths. Many different processes have been utilized,
including Raman-shifting, harmonic generation, and quasi-phase-matching
techniques. Also important are frequency up-and down-conversion, and the more
general issue of obtaining laser radiation at frequencies generally not
accessible
with a more direct process.
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Harmonic generation involves the non-linear interactions between light and
matter using a suitable non-linear material that can generate harmonics at
multiples
of the pump signal frequency. Conventional non-linear materials include
potassium dihydrogen phosphate (KDP), ~i-barium borate (BBO), lithium
triborate
(LBO), lithium niobate (LiNb03), and the like. However, the utility of these
types
of non-linear crystals for efficient frequency conversion often depends on
proper
adjustment of parameters such as non-linear coefficients, phasematching
capabilities, walkoff angle, and angular acceptance.
For example, lithium niobate is conventionally used for second harmonic
(SH) generation because its nonlinear x~2y coefficient is larger than most
other
materials. In addition, the effective magnitude of x~2~ can be enhanced
further by
a process called polling. Typically, a certain length of LiNb03 material,
ordinarily
a few millimeters to a few centimeters, is subdivided in sections each on the
order
of a few microns in thickness. Then, a strong, static electric field is
applied to the
material such that the direction of the electric field is reversed in each
successive
section. In effect then, the field leaves a permanent impression behind,
similar to
the impression that visible light leaves on a photographic plate, which causes
the
sign of the x~2~ to reverse in a predetermined way in each successive section
throughout the length of the material. As a consequence of alternating the
sign
of the nonlinear index of refraction, a technique that is also referred to as
quasi-
phase-matching (QPM), SH generation from a similar length of material that is
not
quasi-phase-matched can be orders of magnitude smaller than the phase-matched
case.
The reason for this kind of material processing can be explained as follows.
For SH generation, a field at twice the original frequency is generated. In
addition
to its dependence on field strength, the index of refraction of any material
also
depends on frequency. For typical SH up-conversion, the indices of refraction
may differ by as much as 10% or more; this means that the speed of light in
the
material may differ by that amount, causing the two waves, the fundamental and
the SH, to get out of phase. As it turns out, by modulating the x~2~, the
waves tend
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to remain in phase, which defines the QPM phenomenon, thus yielding enhanced
SH generation.
However, QPM devices utilized in frequency conversion are typically on
the order of a 1-2 centimeters (cm) in length. What is needed is a device that
performs frequency conversion of a light source that is compact in size, has
sufficient conversion efficiency, and can be manufactured by conventional
techniques.
Summary of the Invention
The present invention provides a new device and method to produce
photonic signals at frequencies other than the frequency of the incident pump
beam or pulse. The photonic band gap (PBG) device comprises a plurality of
first
and second material layers. 'The first and second material layers are arranged
such
that the PBG device exhibits a photonic band gap structure. The photonic band
gap structure exhibits a transmission band edge corresponding to the pump
signal
frequency. A second photonic signal at a second frequency is generated by an
interaction of the input photonic signal with the arrangement of layers. The
second
photonic signal is an harmonic of the pump signal and can be either
transmitted
through the device or reflected out the input region of the PBG device.
According to one embodiment of the present invention, the first and
second layers are arranged in a periodically alternating manner. In addition,
the
PBG device can further comprise one or more periodicity defects in order to
produce other harmonics of the pump signal.
According to the present invention, a method for the frequency conversion
of a pump pulse comprises selecting a desired frequency for the pump signal to
produce a second signal at a desired harmonic frequency. Next, a PBG structure
is provided, wherein the arrangement of layers comprising the PBG structure is
similar to the structure described above. The method further comprises
inputting
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the desired pump signal into the PBG structure in order to produce an ouput
signal at a desired harmonic of the pump signal frequency.
The generated signals can be in the form of either a continuous wave (cw)
signal, if the pump beam is a cw signal, or a pulsed signal, if the pump beam
is
pulsed. The frequency conversion process for the PBG device is orders of
magnitude more efficient than any other ordinary QPM device of comparable
size.
This conversion efficiency can be achieved with the utilization of a photonic
band
gap (PBG) structure. An incident pump beam or pulse is applied to the PBG
device near the photonic band edge transmission resonance, in close proximity
to
the photonic band gap. The output signal (of different frequency or
wavelength)
that is generated in the PBG device is also tuned at a transmission resonance.
A frequency conversion device of compact size can be designed to perform
a wide range of applications including harmonic generation and parametric
oscillation by using a model of a one-dimensional structure. These PBG devices
can also be fabricated by straightforward techniques to satisfy current
technology
needs.
Further features and advantages of the present invention, as well as the
structure and operation of various embodiments of the present invention, are
described in detail below with reference to the accompanying drawings.
Brief Description of tke Figures
The present invention is described with reference to the accompanying
drawings. In the drawings, like reference numbers indicate identical or
functionally similar elements. Additionally, the left-most digits) of a
reference
number identifies the drawing in which the reference number first appears.
FIG. 1 A is a schematic representation of one embodiment of the present
invention, a quarter-wave frequency conversion device with a uniform PBG
structure.
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FIG.1 B is a diagram of the characteristic index of refraction profile of the
uniform PBG structure shown in FIG. lA.
FIG. 2 is a schematic diagram of one embodiment of the present invention,
a mixed quarter-half wave PBG device.
FIG. 3 shows a characteristic transmission profile for a PBG device for
third harmonic generation according to the present invention.
FIG. 4 shows group index versus normalized, dimensionless frequency
profile according to the present invention.
FIG. S shows one embodiment ofthe present invention, a PBG device with
a periodicity defect region.
FIG. 6 is a diagram of the characteristic index of refraction profile of the
PBG structure shown in FIG. 5.
FIG. 7 shows a transmission versus normalized, dimensionless frequency
for a 20-period, half quarter-wave stack.
FIG. 8 shows maximum energy output versus index of refraction.
FIG. 9 shows the pump field eigenmode distribution inside a PBG
structure of the present invention, at the instant that the peak of the pulse
reaches
the PBG structure.
FIG. 10 shows a second-harmonic eigenmode for the case of FIG. 9.
FIG. 11 shows comparison between the SH energy output from the PBG
(solid line) and a phase-matched bulk material (dotted line), as a function of
pulse
width.
FIG. 12 shows spontaneously generated SH pulses.
FIG. 13 shows SH conversion efficiency versus incident pulse peak field
strength.
FIG. 14 is a flowchart illustrating a method of generating frequency
conversion according to the present invention.
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Detailed Description of the Preferred Embodiments
1. Overview of the Present Invention
The present invention provides a frequency conversion device that utilizes
a photoriic band gap (PBG) structure. The enhancement mechanism demonstrated
in these PBG structures in the linear regime leads to frequency up- (or down-)
conversion rates nearly three orders of magnitude better than conversion rates
achieved with ordinary phase matched materials, or in conventional fiber
grating
geometries. The geometrical properties and the periodicity of the PBG
structure
can act to significantly modify the density of electromagnetic field modes
near the
band edge, thus facilitating the emission of the second harmonic (SH) signal
at a
much-enhanced rate. More importantly perhaps, this means that current
fabrication issues that arise in ordinary quasi-phase-matched structures can
be
avoided altogether by utilizing current technology for deposition of
semiconductor
or dielectric thin films and combinations thereof.
The present invention is described in terms of this example environment.
Description in these terms is provided for convenience only. It is not
intended that
the invention be limited to application in this example environment. In fact,
after
reading the following description, it will become apparent to a person skilled
in the
relevant art how to implement the invention in alternative environments.
2. Nonlinear Interaction of Light with Matter
The nonlinear interaction of light with matter is important for applications
in the field of light generation at frequencies that are usually not
accessible by a
more direct laser process. At a qualitative level, all materials found in
nature are
nonlinear to some degree. This means that the characteristic properties of
ordinary materials, such as the dielectric susceptibility, change if an
applied
electromagnetic field intensity is strong enough.
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This dependence of the susceptibility (which ultimately is a statement of
the index of refraction of the material) on the electric field strength can be
exemplified in the following way:
x - x~o + x~2~ E + x~3~ E2 +...xu~ Ee - ~... +...
where j is an integer, x~'~ is the medium susceptibility for low incident
fields, xti)
is the jth nonlinear coefficient whose magnitude decreases rapidly as (j)
increases,
and E is the applied field. Therefore, contributions from the jth term become
significant if the field strength is gradually increased. Typically, the x~~
can be
two to four orders of magnitude greater than each successive x~+'~
coefficient,
depending on the material. On the other hand, all the coefficients with odd or
even (j) greater than one may vanish, depending on the characteristics of the
material at the molecular level. For example, all the even coefficients vanish
if the
molecule has a geometrical center of symmetry, as in a gas.
Because of the nonlinear contributions to the dielectric susceptibility, the
I S application of a strong external optical field at frequency w is capable
of
generating light at frequency 2w, 3w, 4w, and so on. By the same token, if two
strong fields of different frequencies w, and w~ are applied to the nonlinear
material, light at frequencies (w, +w~ and (w,-w2) (i.e., sum and difference
frequencies) can also be generated in addition to the individual harmonics.
For
example, a x~2~ medium, which means that the first order nonlinear coefficient
dominates the dynamics, is capable of SH generation, and sum and difference
frequency conversion; a x~3~ medium is capable of third harmonic generation,
and
so on.
For example, a type of nonlinear frequency conversion that is typically
sought in nonlinear media is SH generation. However, the present description
is
also applicable for nonlinear frequency conversion to higher or lower
frequencies,
such as third harmonic generation, and so on.
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Conventional nonlinear materials used for frequency conversion processes,
such as LiNb03, are processed in such a way that the nonlinear contribution to
the
index of refraction alternates sign every few tens of microns. However, the
linear
index of refraction of the LiNb03 host material is not modified in any way
(i.e.,
$ it is spatially uniform).
The method of forming a device designed to perform frequency
conversion, according to the present invention, is completely different: a
spatial
modulation is imparted to the linear part of the refractive index. In other
words,
the linear index of refraction of the structure alternates between a high and
a low
value. This is accomplished by alternating at least two materials, such as
GaAs
(Gallium Arsenide) and AIAs (Aluminum Arsenide), whose indices of refraction
are approximately 3.4 and 2.9 respectively, resulting in a structure that is 5
to 10
microns in length. The consequence of alternating different materials with
different refractive indices as indicated above is the creation of a photonic
band
gap (PBG) structure.
The physical processes that are exploited in the present invention are
different from conventional frequency conversion techniques in that photonic
band
edge effects are utilized. Photonic band edge effects cause strong overlap of
the
pump and SH signals, significant reduction of the respective propagation
velocities, and therefore, increased interaction times. As described below,
some
of the advantages of the present invention include: ( 1 ) the structure can be
100 to
1000 time shorter than typical QPM structures, with comparable conversion
efficiencies; (2) ordinary semiconductor materials can be used in forming the
PBG
structure, leading to a reduction of production costs; and (3) the PBG device
is
compatible with integrated circuit environments due to its size and
composition.
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3. Frequency Conversion using a PBG Structure
In one dimension, a photonic band gap structure comprises a plurality of
layers, as shown in FIG.1 A, where the plurality of layers alternates between
a low
and a high index of refraction. PBG structure 102 comprises a stack of
alternating
layers 108 and 110 of refractive materials having predetermined indices of
refraction n, and n2 (for low incident pump powers), and predetermined
thicknesses a and b, respectively. In particular, the first type of layer 108
can be
chosen such that it is a high index layer n,. The second type of layer 110 can
be
chosen to be a low index layer n2. The widths of the layers can be chosen such
that they are both a fraction of the size of the incident pump wavelength.
For example, first layer 108 can be designed to have a thickness (a)
corresponding to the wavelength of an incoming photonic signal (~,),
determined
by the equation a = ~, / 4n,. Similarly, second layer 110 can have an index of
refraction n2, and a thickness (b), where b = ~. / 4n2. This pattern can be
repeated
for N periods 122, where a period is equal to one set of alternating layers
112.
This type of structure is also referred to as a quarter-wave structure. As
would
be apparent to one of ordinary skill in the art based on the present
description,
other arrangements of alternating layers can also be made, depending on the
particular frequency conversion application.
Adj usting the width of the layers causes a shift of the location of the band
gap to a different frequency. This property is a beneficial one, which adds
flexibility when the options of input and output laser frequencies are being
considered.
FIG. 1B is a diagram of a characteristic index of refraction square-wave
pattern profile of PBG structure 102 for N periods. Diagram 150 plots the
index
of refraction (n) 152 of a uniform PBG structure as a function of distance (z)
154,
which is limited by the number of periods 156 in the device. Diagram 150
illustrates the periodic nature of the abrupt refractive index changes
occurring in
the material.
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In general, large index modulation PBG structures are not as easily
susceptible to band-structure shifts due to nonlinear index changes because
index
variations are a small perturbation on the linear index modulation depth. As
described below, for ultrashort pulses tuned near the photonic band edge, a
choice
of materials with suitable indices of refraction, thicknesses, and periodicity
can
lead to low group velocities, enhanced field intensity, and conversion
efficiencies
nearly three orders of magnitude larger than conventional bulk up-conversion
rates. Conversion efficiencies greater than 10-3 can be achieved for
structures only
a few micrometers in length, with a single pump pass, and at realistic pump
intensities. Plane-wave conversion rates can be approximated by utilizing
pulses
whose frequency bandwidth is smaller than the transmission resonance
bandwidth,
such as for pump signals of only a few picoseconds (ps) in duration.
A preferred embodiment of the present invention is shown in FIG. 2. PBG
structure 200 is formed in such a way that a single period comprises two
layers:
a quarter-wave layer 202 and a half wave layer 204, to form a periodic, mixed
quarter-half wave structure. This particular choice causes the first and
second
order band edges to be approximately a factor of two apart from each other, as
indicated in FIG. 4, described in detail below. Then, both the pump and SH
fields
are tuned to their respective photonic band edges. This coincidence of the
band
edges leads to strong overlap of the fields, significant reduction of the wave
velocities by several orders of magnitude below the speed of light in either
medium, and increased interaction times. See, e.g., "Pulsed second harmonic
generation in one-dimensional, periodic structures", Phys. Rev. A, October
1997,
by Scalora et al. (incorporated by reference herein in its entirety). These
factors
result in an increase in the SH energy output that significantly exceeds
conventional QPM devices.
The types of structures discussed above result in a PBG structure in which
a range of frequencies about some reference frequency cannot propagate inside
a
PBG device. On the other hand, the structure may be transparent to other
frequencies away from the band gap. For example, a representative photonic
band
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gap structure is shown in FIG. 3, which shows a characteristic transmission
profile
for structure 301. At higher frequencies, higher order gaps may also appear to
create a series of gaps. Usually, however, the higher order gaps are ignored.
In
FIG. 3, both the first order band gap 302 and second order band gap 304 are
depicted. Typically, a uniform PBG structure, such as that shown in FIG. lA,
exhibits an infinite number of photonic band gaps and band edges. In FIG. 3,
transmission profile 306 is obtained by plotting the optical transmission 308
as a
function of normalized frequency (S2) 310, where ~ = c.~/c~o. The maximum
possible transmission is 1. Therefore, it is the absence of those frequencies
from
I 0 the transmitted spectrum that gives rise to the name "band gap", in
analogy to the
electronic band gap of semiconductors where electrons having a specific range
of
energies cannot propagate inside a semiconductor crystal.
At frequencies outside the photonic band gap, the properties of the
structures are such that a series of transmission resonances are obtained. The
number of such resonances is equal to the number of periods that make up the
structure. The bandwidth of said resonances is a sensitive function of the
total
number of periods, the indices n, and n2, and their difference 8n=~nz-n,~,
also
known as index modulation depth.
In regard to SH generation, a PBG structure can be formed where
nonlinear gain, or the production of SH signal, is maximized. Using the
calculations described in detail below, the equations that describe the
propagation
of electromagnetic waves in PBG structures can be solved. The results of the
calculations show that if a pulse of light interacts with a nonlinear x~Z~
medium to
produce a SH signal, then the SH energy output from the PBG structure is
approximately three orders of magnitude greater than the energy output of a
simple bulk nonlinear medium of approximately the same length.
One embodiment of the present invention is a PBG structure that
comprises 20 periods (or 40 layers) of alternating layers of GaAs and AIAs.
Alternatively, the PBG structure can also comprise different sets of
materials, for
example, air and GaAs, glass and AIAs, a combination of other dielectric
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materials, as well as with materials that would not conventionally be
considered
as nonlinear materials. In addition, the PBG structure may also be created in
an
optical fiber, in the form of a fiber grating. This illustrates that this
frequency
conversion capability is not specific to any one material, and that some
flexibility
exists according to the specific needs of a particular application.
Accordingly, the
structure of the present invention should not be limited solely to the
embodiments
described herein.
According to the present invention, a pulse of light of about one
picosecond or more in duration can be tuned to the frequency corresponding to
the maximum of the first transmission resonance away from the low frequency
band edge. This is shown schematically in FIG. 4, which plots group index as a
function of normalized frequency. The total energy of a signal produced at
twice
the frequency of a pump (i.e., at the SH frequency) is about 1000 times
greater
than the energy output of a QPM device of similar nonlinear properties and
1 S dimensions, but that does not exhibit a photonic band gap structure.
Accordingly,
the signal generated at the second harmonic frequency is tuned to the second
transmission resonance of the low frequency band edge of the second order gap,
as shown in FIG. 4.
According to the present invention, if the enhancement of any other
frequency is desired, for example, a difference or sum frequency, it will be
apparent to one of skill in the art based on the present description to devise
a PBG
structure such both the pump and the desired frequency are both tuned to a
photonic band transmission resonance. If higher conversion efficiencies are
sought, the calculations explained in detail below indicate that such
conversion
efficiency increases can be accomplished by only modest increases in the
number
of periods that comprise the structure. The reason for this is that the
conversion
efficiency in a typical PBG structure is very sensitive to the length of the
structure.
For example, ifN is the number of periods comprising the device, then the
energy
output is approximately proportional to the N6. As would be apparent to one of
skill in the art based on the present description, an optimization procedure
can
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then be employed to produce the ideal parameters for the up- or down-
conversion
process for a particular application.
For example, in the case of third harmonic generation, a PBG structure
comprises a quarter-wave periodic structure with a "defect" layer one half
wavelength thick at the center of the structure. This embodiment is shown
schematically in FIG. 5. Device 502 comprises at least two stacks (or regions)
504 and 506 of alternating layers of refractive materials similar to those
described
above in connection with FIG. 1 A. In the center of device 502, a periodicity
defect region 508 is interposed (or placed) between stacks 504 and 506, with
each
stack having an equal number of alternating layers of refractive material.
Defect
region 508 is also a refractive material that can have an index of refraction
(n) that
is equivalent to either n, or n2, and with the same x~2~ nonlinear
coefficient. For
example, if individual layer thicknesses in the uniform stacks 504 and 506 are
taken to be one quarter-wavelength long, then the thickness of periodicity
defect
region 508 can be one half or one wavelength in thickness. However, other
thicknesses for periodicity defect region 508 can also be utilized. The term
"defect", in this context, simply means a break in the periodicity of the
structure.
This defect layer breaks the periodicity in such a way that it generates a
transmission resonance in the middle of every gap, as shown in FIG. 6. Here,
the
distance between the center of the first and second order gap is exactly a
factor
of three. Therefore, tuning the pump signal to the center of the first order
gap will
enhance the generation of light at the third harmonic. For example, using a
pump
signal wavelength of approximately 1550 nm, such as found in conventional
communications laser diodes, a third harmonic signal will be output from the
PBG
device at a wavelength of approximately 516 nanometers (nm). Therefore, by
selecting the proper set of parameters, such as material type, material
parameters,
and the exact geometrical properties of the materials (i.e., layer thickness),
a
person of skill in the art can arrive at a device with the desired properties.
Another embodiment ofthe present invention is a PBG device comprising
a plurality of periodicity "defects." In other words, several defects of
varying
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thicknesses can be placed in a PBG device. The placement of these multiple
defects between stacks of alternating layers forms an a-periodic structure,
that also
exhibits a photonic band gap structure. This a-periodic structure can be
utilized
to perform any of the frequency conversion techniques described herein, as
would
be apparent to one of skill in the art based on the present description.
According to the present invention, conversion efficiencies can be even
higher for structures with an increased number of periods. For example, by
increasing the structure length by 50% (from 20 to 30 periods), the energy
output
can increase by a factor of 5. However, it should be noted that: ( 1 ) the
transmission resonance bandwidth decreases as 1/N?, where N is the number of
periods, so that the pulse duration needs to be increased in order to ensure
large
pump enhancement inside the structure; and (2) a material breakdown may occur
because of excessive electric-field buildup, or enhancement, inside the PBG
structure.
Consideration of nonlinear effects highlight even more dramatic differences
between the PBG structures of the present invention and conventional nonlinear
materials used for frequency conversion. Typical nonlinear index changes in
GaAs
or AIAs layers can be of order BnN~ =10-3. This implies that nonlinear index
shifts
can be larger than the linear index modulation depth. Consequently, the
location
- 20 of the gap on the frequency axis can shift dramatically to higher or
lower
frequencies, and its bandwidth can increase or decrease significantly,
depending
on the sign of the nonlinearity.
In contrast, the frequency bandwidth of an ultrashort pulse of only a few
hundred optical cycles in duration (i.e., in the femto-second regime) can be
smaller
(depending on the wavelength) than the bandwidth of the PBG's first
transmission
resonance peak, where the group velocity is a minimum. Here, ultrashort pulse
propagation can be nondispersive. In addition, the nonlinear index change
remains
orders of magnitude smaller than the index modulation depth, which for PBG
structures can be of order unity or larger. Thus, gap and transmission
resonance
bandwidths, and their locations, are only marginally altered, although changes
may
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be sufficient for the onset of optical limiting and switching, optical diode
behavior,
and strong pulse reshaping.
The stability of the band structure in the frequency domain is also
important in parametric optical up- and down-conversion, and harmonic
generation. This result highlights the fact that a new generation of compact
and
efficient high gain optical amplifiers and optical parametric oscillators
based on
photonic band-edge effects can be achieved according to the present invention.
The enhancement of gain in these PBG structures is understood by
recalling that the density of accessible field modes in the vicinity of
dielectric
boundaries is modified by the boundary. This means that if a linear or
nonlinear
gain medium is introduced with in a PBG structure, the stimulated and
spontaneous emission rates are modified according to Fermi's golden rule (see
below). In QPM structures, a minimization of the phase difference between the
waves is desirable in order to avoid a phase mismatch in the continuous wave
case.
I 5 For QPM devices, this minimization of phase difference is typically
achieved by
poling the active material, which is uniform in its composition and contains
no
linear index discontinuities. Accordingly, the nonlinear coefficient only
alternates
sign in the longitudinal direction every few tens of micrometers (p,m).
For the PBG structures of the present invention, the unusually strong
confinement of both the pump and the SH signal that occurs near the photonic
band edges is relied on. Where the density of electromagnetic field modes is
large,
the group velocity is low, the field amplitude may be enhanced over bulk
values
by one order of magnitude or more, and strong pump and SH mode overlap
occurs. In this regime, the material is not poled in the usual manner; it is
the
geometrical properties of the structure that cause strong mode overlap, co-
propagation, and larger interaction times, the combination of which is
ultimately
responsible for the enhanced gain of these PBG structures.
The PBG structures discussed above can be manufactured by conventional
techniques. Other suitable modifications and adaptations of the variety of
reaction
conditions and parameters normally encountered in preparing photonic and
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semiconductor devices will be apparent to those skilled in the art. without
departing form the spirit and scope of the invention.
As discussed above, the invention can be implemented in group III-V or
II-VI material systems, as well as with dielectric materials. For purposes of
explanation. the above examples are described in GaAs/AIAs material systems,
but
it will be understood by those skilled in the art that the invention described
herein
can also be implemented with other III-V or II-VI systems.
Further, background material concerning semiconductor solid-state physics
may be found in a number of references including two books by S.M. Sze,
titled:
Physics ofSemiconductor Devices, John Wiley and Sons, Inc., New York (1981 ),
and Semiconductor Devices, Physics and Technology, John Wiley and Sons, Inc.,
New York (1985), both of which are incorporated herein by reference. Those
skilled in the art can readily manufacture the layered devices disclosed
according
to conventional processing techniques without undue experimentation.
4. Example Applications
The PBG structures of the present invention can be utilized to perform a
variety of frequency conversion techniques. As described above, a mixed
quarter-
half wave structure can be utilized to perform SH generation of a variety of
- coherent light sources, including tunable solid state lasers, gas lasers and
semiconductor diode lasers. For example, a PBG structure can be placed at the
output facet of a conventional AIGaAs diode laser that emits a laser beam at a
wavelength of approximately 810 nm. Diode lasers ofvarious output wavelengths
are commercially available from a number of commercial vendors, including
Spectra Diode Labs, Inc. and Coherent Inc., both of California. By choosing
the
proper set of alternating layer materials, by selecting an appropriate set of
layer
thicknesses, and by choosing an appropriate number of periods for the PBG
device, an output at approximately 405 nm can be achieved from the PBG device.
This type of device would be outputting "blue" laser emission, which is
extremely
valuable for communications and optical storage applications. In addition,
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because of the compact size and angular independence of the PBG device (as
opposed to conventional non-linear materials such as potassium dihydrogen
phosphate (KDP), ~3-barium borate (BBO), lithium triborate (LBO), which are
extremely dependent upon angular alignment), SH generation optical cavity
arrangements (e.g., external cavity and infra-cavity designs) would be very
straightforward to design. Typical optical layouts for harmonic generation are
well known. See e.g., W. Koechner, "Solid-State Laser Engineering," Springer-
Verlag, 2"~ Ed. (1988), especially Chapter 10, which is incorporated by
reference
herein. Known anti-reflection coatings can also be utilized to reduce spurious
reflections, as would be apparent to one of skill in the art.
In addition, the PBG structures ofthe present invention can also be utilized
in parametric oscillation techniques where, for example, output wavelengths
greater than the pump pulse wavelengths can be generated. Based on the known
methods of optical parametric oscillation, such as those described in the
Koechner
reference, it would be apparent to one of skill in the art to design a
parametric
device utilizing the PBG structure of the present invention to achieve
frequency
conversion at lower frequencies (i.e., longer wavelengths).
Further, optical fiber gratings can be designed similar to the types of PBG
structures described above. Optical fiber gratings are also periodic
structures.
The index of refraction for a fiber grating can achieve an index modulation
depth
(i.e., a high and low value) similar to that of high index contrast
semiconductor
structures. However, fiber gratings are structures with a smaller index
discontinuity than that associated with a semiconductor PBG structure: for a
fiber
grating an index modulation along its core is typically on the order of 8n=10-
' to
104, as opposed to a semiconductor PBG structure with an index modulation
approaching unity. Since the bandwidth of transmission resonances and band
gaps are proportional to 8n (the index modulation depth), fiber grating
frequency
conversion devices are preferred for use with optical pulses of longer (i.e.,
nanosecond) duration in order to preserve their shape.
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A fiber grating can be created on an optical fiber by well-known fabrication
techniques. For example, see the fiber grating applications and fabrication
techniques described in "Continuously tunable single-mode erbium fiber laser,"
by
G. Ball and W. Morey, Optics Letters, Vol. 17, No. 6, p.420 (1992) and
S "Spatially-multiplexed fiber-optic bragg grating strain and temperature-
sensor
system based on interferometric wavelength shift," by Y. Rao, et al.,
Electronics
Letters, Vol. 31, No. 12, p. 1009 (1995), which are both incorporated by
reference in their entirety.
For example, f ber grating fabrication can be accomplished by placing an
optical "mask" over a photo-sensitive fiber core and then by illuminating the
mask-
fiber assembly with a high intensity ultraviolet light beam, such as an
Excimer
laser. The resulting grating, referred to as a fiber grating, displays much
the same
properties of a high index contrast semiconductor PBG structure, especially
with
respect to band gaps and transmission resonances. In addition, a mask can be
I S designed to create a grating that imparts either a band-edge effect or a
transmission resonance similar to the one shown above in FIG. S. Based on the
present description, it would be apparent to one of skill in the art to design
a fiber
grating capable of frequency conversion. For example, a fiber grating device
designed according to the parameters discussed above can be coupled to the
output of a laser diode to produce a compact source capable of output
emissions
in the blue wavelength range.
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S. Model
a. Equations
According to the present invention, a model can be utilized to allow one
of ordinary skill in the art to design a PBG structure to perform optical
frequency
conversion for a desired application. For example, shown here is an analysis
describing the dynamics associated with ultrashort pulses (about 1 ps or less)
in
one-dimensional systems. This model extends the analysis of SH generation and
enhancement to arbitrarily deep PBG gratings in the pulsed regime by directly
integrating Maxwell's equations in the time domain.
I 0 Consider the following simple one-dimensional system similar to device
200 shown in FIG. 2. The example device comprises 40 dielectric layers (20
periods in all, roughly 12 ~m thick for a reference wavelength of 1 Vim), and
the
index of refraction alternates between a high and a low value, n2 = 1.42857
and
n, = 1. A small value of x~2~ ~0.1 pm/V (roughly 3 x 10-9 cm/statvolt in
Gaussian
units) is chosen and it is assumed that the nonlinear material is distributed
uniformly throughout the PBG structure. Then, for a reference wavelength ~.a,
the
layers have thicknesses a=.lo l(4n,) and b = ~,~/(2nz), respectively. This
forms a
mixed half quarter-wave stack for wavelength Jlro. A range of frequencies is
reflected, as shown in FIG. 7, where the transmission coefficient for this
structure
- 20 is plotted as a function of the scaled frequency ~2 = c~/ coo, where coo
= 2 nc/~,o.
FIG. 7 indicates that this choice of parameters causes the location of the
second-
order gap to be removed from the first-order gap by approximately a factor of
2.
For an ordinary quarter-wave structure, such as the device shown in FIG. 1, a
factor of 3 separates the first- and second-order band edges. Utilizing these
two
edges is more suitable for third-harmonic generation.
The equations of motion can be derived beginning with Maxwell's equation
for the total field, in Gaussian units, and can be written as:
a2~ E(Z~ t) _ nz a 2 E(z~ t) - 4~ a 2 pNC ~ (I)
aZ - ~ ar ~- at
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Here, P,,,~ is the total nonlinear polarization. Without loss of generality,
the fields
can arbitrarily and conveniently be decomposed as follows:
E~z, t) - s",~z, t~ ei("'-w'~ + c. c. + ~2~ ~z, t) e2'(w°'r) + c. c.
, (2)
i( ~-tut ) 2i( lc-mt )
PN~ {z, t) = p~ ~z, t) a + c. c. + pew ~z, t) a + c. c. (3)
S This decomposition highlights the fundamental and second-harmonic angular
frequencies. The nonlinear polarization can be expanded in powers of the
electromagnetic field strength as follows:
pNL(Z't~ x(2)E2(Z't~ 2x(2)~m(Z~t)~2m(Z~t)el(~ art)
+ c. c. + x ~2~E~ ~z, t)e2'1'~-~') + c. c. (4)
While one can assume an initial left- or right-propagating pump pulse, the SH
signal is initially zero everywhere. The direction of propagation of the
spontaneously generated SH field and the exact nature of the quasi-standing
wave
inside the structure are dynamically determined by (a) the nature of the
initial and
- boundary conditions, (b) pump-frequency tuning with respect to the band
edge,
and (c) the distribution of nonlinear dipoles inside the structure. This
nonlinear
dipole distribution can significantly affect the results. SH generation is a
phase-
sensitive process. The field and its phase at any point inside the structure
are a
superposition of all fields originating everywhere else inside the structure.
Thus,
the phase is important element that should be included in the integration of
the
equations of motion. However, dipole distribution is important to the extent
that
it is modified in the layers where the fields happen to be localized. For
example,
near the Iow-frequency band edges, the fields are localized in the high-index
layers. Modifying the nonlinear medium distribution in the low-index layers
will
have little effect, although some mode overlap between layers always occurs.
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For this model, ultrashort incident pulses propagating in the presence of
large index discontinuities are considered. Therefore, all second-order
spatial
derivatives should be retained in order to properly include boundary
conditions.
However, it can be assumed that pulse envelopes have a duration that is always
S much greater than the optical cycle, thus allowing the application of the
slowly
varying envelope approximation in time (SVEAT) only. For a general description
of SVEAT, see Scalora, M., et al., Phys. Rev. Lett. 73:1368 (1994), which is
incorporated by reference herein in its entirety. The equations of motion for
the
fundamental and the second-harmonic fields can be derived as follows. First,
substituting Eq. (2) into Eq. ( 1 ) yields:
a2c~' + 2ik ac~' - k2c - n~ a2c~ + 2i~n2 as~,
aZ2 aZ w c2 ate C2 at
w 2 _ _4~c a z _a _ (5)
+ c2 n~~~ c2 ate P~ - 2i~ - at p°' ~2P~ '
2 2 2
a ~2~ + 4ik a~2~ - 4k2E2~ - n22 a ~Zr~
az az C al
4i ~
+ c2 nz~ at + 4 c2 n2~~2~
z
- cz~ atz P2~ - 4i~ a PZW - 4tv 2P2~
o~
where k = ~c, and the SVEAT is made. This choice of wave vector is simply an
initial condition consistent with a pump field of frequency w initially
propagating
in free space, located away from any structure. Any phase modulation effects
that
ensue from propagation (i.e., reflections and nonlinear interactions) are
accounted
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for in the dynamics of the field envelopes. The inclusion of all second-order
spatial derivatives in the equations of motion means that reflections are
accounted
for to all orders, without any approximations. Therefore, assuming that pulses
never become so short as to violate SVEAT (usually this means a few tens of
optical cycles if propagation distances are on the order of pulse width),
neglecting
all but the lowest order temporal contributions to the dynamics, and using the
nonlinear polarization expansions of Eqs. (4), Eqs. (5) and (6) become:
2 ~ __ ~ a2~~ _ a~~ 2
n~ ~ ~' ~~' T ~ 452 a~2 a~ + i~(n~ -1)S2~
()
+~s~ 2~x c2'~~~2~
a2~ _ a~
2
n2~ ~2~ (~~ Z) - g~S2 a~2~ a~ + ~n(n2u -1~2SZE2~ 8
()
+i 8~ 2 SZx c2) En .
Here ~ z/.Io, and z= ctli~,. Equation (8) describes the rate of change of the
SH
field, whereas equation (7) describes the pump (or fundamental) signal. The
spatial coordinate z has been conveniently scaled in units of ~.o; the time is
then
expressed in units of the corresponding optical period. Thus, by knowing the
indices of refraction for the layers of the PBG device, the pump signal
frequency
I 5 and bandwidth, and the pump signal intensity, one can design a PBG
structure to
yield a desired output signal having a frequency different from the pump
signal.
As discussed, both forward and backward SH generation can occur. In
other words, a frequency conversion device can either transmit or reflect the
output harmonic signal. Additionally, assuming that the medium is
dispersionless,
and the pump signal is tuned at the low-frequency band-edge transmission
resonance, then the SH frequency is found well away from the second-order band
edge: it is tuned in the middle of the pass band, as indicated in FIG. 7. In
order
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to properly tune the SH signal frequency near the band edge, material
dispersion
is introduced. This causes changes in the band structure. Specifically, all
higher
order gaps tend to move down in frequency, causing the SH signal to be tuned
closer to the low-frequency, second-order band edge, where the electromagnetic
density of states is largest.
From a calculational standpoint, varying the amount of dispersion is
strightforward to undertake. From a fabrication standpoint, obtaining the same
conditions can be more difficult. However, the inventors find that the band
structure and its features are strongly influenced by (a) the number of
periods, (b)
layer thickness, and (c) material dispersion. For example, increasing (or
decreasing} the number of layers sharpens the band edges, and increases (or
decreases) the number of transmission resonances between gaps, causing an
effective shift of each resonance. Changing layer thickness away from the
quarter-
or half wave conditions (in units of ~.o) can also cause frequency shifts in
the
location of the band gaps and transmission resonances. A structure with the
desired properties can be realized when these frequency shifts are coupled
with
material dispersion.
In order to find the optimal parameters for SH generation, i.e., tuning with
respect to the band edge, the index of refraction of the high-index layer is
varied
from nz(2S2) =1.42857 to n2 (2i~) = 1.65. The higher-index value corresponds
to
SH generation just inside the second-order gap, where its suppression is
expected.
For intermediate values of the index, SH generation also occurs at frequencies
where the density of modes is a maximum. The degree of dispersion assumed is
typical of the degree of dispersion found in both dielectric or semiconductor
materials, 5 - 10% in this case.
Recall that FIG. 4 shows the group index, defined as N ~ = cdkldtv, for a
preferred PBG sample, similar to that shown in FIG. 2. Note that the maximum
group index is also a sensitive function of 8n, the index modulation depth,
and the
number of periods. The maximum value of the group index for this mixed half
quarter-wave structure is similar in magnitude to that of a quarter-wave, 20-
period
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structure with the same index modulation depth. In this case, n, (SZ) =
1.42857,
and n, (2SZ) = 1.519. Note also that the magnitude of this function is largest
near
the high-and low-frequency band edges.
b. Picosecond input pulse model
In this example, the pump pulse frequency is chosen to correspond to the
iow-frequency band edge, where the transmission resonance is approximately
unity
and the group index is a maximum (S2 = 0.591 in Fig. 2). A high pump index
implies that a dramatic increase in the field intensities inside the structure
occurs
at that frequency. This is important, since SH gain is nonlinear in the field,
as Eq.
(8) suggests. By choosing the index of refraction such that nz (2i~) = 1.519,
the
SH frequency coincides with the second density of modes maximum on the low-
frequency side of the second-order band gap (see FIG. 4). Here, the total-
energy
output from the PBG device with respect to the index-matched bulk, which
includes forward and backward SH generation, varies from one order of
1 S magnitude for a pump pulse only 60 optical cycles in duration ( 1 /e width
of the
intensity envelope is about 200 femto-seconds (fs) if ~.o =1 p,m), to
approximately
500 times for pulses about 1 ps long. For sub-picosecond pulses, the
enhancement
is. reduced due to the broad frequency content of the pulse.
- SH generation is not at a maximum when the SH signal is tuned at the
density of the mode maximum, because the fields do not have the right phase
for
this to occur. As an example, using the known matrix transfer method, it can
be
found that the phase of the transmitted, plane-wave field undergoes a n phase
shift
across the gap, and a phase shift of 2n between consecutive resonances on the
same side of any gap. Therefore, the number of periods chosen can have an
impact on the overall phase of the SH field inside the structure. For short
pulses,
the circumstances are much more complicated, because of their broadband
frequency makeup.
Fig. 8 shows the calculated SH energy output for a 1 ps pulse, as a
function of nz(2~), i.e., dispersion. The maximum energy output occurs when
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n~(2S2) = 1.519, which corresponds to the second transmission or group index
maximum. The band structure for nz =1.519 is illustrated in Fig. 4. Evidence
of
the curvature of the band structure near the band edge is rather weak away
from
the second transmission resonance. These results demonstrate that the dipole
distribution is also an important factor. In this case, the SH field is
generated
inside the structure from a continuous distribution of nonlinear dipoles; the
nonlinearity is in both the high and low index layers. This dipole
distribution
determines the form of the propagating eigenmode, and the manner in which the
generated signal leaves the structure. Therefore, as would be apparent to one
of
skill in the art based on the present description, one can likely find a
nonlinear
dipole distribution that will maximize or further improve SH conversion
efficiency.
The above calculations also highlight the importance of pulse width.
Pulses whose spectral widths are larger than the band-edge transmission
resonance ,
tend to couple poorly with the structure. This situation leads to dispersive
propagation, and to only slightly enhanced field intensities inside the PBG
structure. On the other hand, a pulse whose frequency band-width is smaller
than
the band-edge resonance bandwidth has fewer frequency components, experiences
little or no dispersion, and allows the field to build up inside the structure
by about
one order of magnitude or more with respect to its free space or bulk values,
where the field amplitude is in general proportional to Ef~~/n.
For example, FIG. 9 plots the pump-field intensity inside the structure, at
the instant the peak of the 1-ps pulse reaches the structure. As the pulse
slows
down dramatically, the maximum field intensity is amplified by more than one
order of magnitude (compared to its peak value outside the structure) by
linear
interference effects of backward- and forward- traveling components. FIG. 10,
on the other hand, represents the SH field intensity quasistanding-wave
pattern at
the same instant in time as FIG. 9. Both eigenmodes overlap to a large extent
inside the high index layers, and the fields propagate in this configuration
for the
entire duration of the pump pulse. This mode overlap, combined with the
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dramatic group velocity reduction for both fields, allows efficient energy
exchange
between the pump and the SH signal.
Fig. l l shows the total-energy output (forward and backward included) as
a function of incident pulse width, expressed in optical cycles, for a 20-
period,
12-um-thick device (solid line), and a 12-pm bulk sample coated with anti
reflection layers at both ends to minimize pump reflections (dotted line). Low
input field intensities are considered that yield conversion efficiencies on
the order
of 10'''-, although this trend persists as long as pump depletion is not
significant.
For clarity, the abscissa is plotted on a logarithmic scale. FIG. 11 shows
that the
total-energy output (and therefore power output) becomes about 500 times
greater for the PBG sample than for index-matched bulk material when an input
pulse width approaches 300 optical cycles, or about 1 ps. The results indicate
that at these length scales the energy output for the bulk sample increases
linearly
with incident pulse width. Thus, this figure clearly demonstrates that
suitable
output energies can be obtained from the PBG devices of the present invention
when continuous wave input pulses are applied.
In contrast, an early exponential increase characterizes energy growth in
the PBG case, giving way to linear growth only when pulse width approaches 1
ps. This implies that the pump field eigenmode intensity (and hence SH gain)
increases rapidly with pulse width, saturating when a quasimonochromatic limit
is reached, in this case, when pulse frequency bandwidth is somewhat less than
band-edge resonance bandwidth.
Also, both the amplitude and the width of the generated SH pulses increase
with increasing incident pulse width. FIG. 12 shows the SH field propagating
away from the structure. While the pump was incident from the left, note that
the
structure radiates significantly in both directions, and that the SH pulses
generated
have the same width as incident pump pulses. It would be difficult to predict
this
overall behavior a priori, especially in the absence of analytical results in
this
regime. Further, tuning the pump away from the band edge, tuning to the high-
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frequency band edge, or modifying the nonlinear dipole distribution can
significantly alter the pattern of FIG. 12.
FIG. 13 is a plot of the conversion efficiency vs. peak field intensity in
Gaussian units, for a pulse of 1 ps duration, where IEF of 109 in these units
S corresponds to roughly 10 GW/cm2 in free space. The free-space value of the
energy flow is to be distinguished from energy flow inside the structure.
Here,
efficiency is defined as the ratio between the final total SH energy and the
total
initial pump energy. This ratio is also representative of the ratio between
the
corresponding peak field intensities, respectively. FIG. 13 indicates that for
this
simple PBG structure only 12 pm in length, a conversion efficiency of order 10-
Z
can be achieved with pump intensity of 10 GW/cm2 , yielding a SH signal
intensity
of approximately 10 GW/cm'-. This is quite remarkable, considering that the
PBG
structure is only a few micrometers in length, only a single pump pass occurs,
and
that a very modest value of x~2~ ~0.1 pm/V is used. Note that a x~2~ value of
0.1
pm/V is a conservative value. Clearly, materials chosen with even higher x~2~
values can be incorporated into the PBG structure of the present invention,
resulting in conversion efficiencies approaching 10-'. Considering the
extremely
compact nature of the PBG device of the present invention, and that the pump
traverses the sample only once, the gain-to-device length ratio undergoes
several
orders of magnitude improvement over current state of the art devices.
Such large enhancements with respect to phase-matched up-conversion
can be explained as follows. According to Fermi's golden rule, the power
radiating from an oscillating dipole is given by P( c.>) = p(c~) IE (cv)~,
where p(c~)
is the density of modes and I E (c~)~ is the eigenmode intensity. The average
energy
output can be obtained by multiplying the power output by i, the interaction
time.
As pointed out above, all these quantities increase by nearly one order of
magnitude for the PBG structure. In fact, since (E (cv)F and z are both
proportional to p(c.~), then the total energy emitted is generally
proportional to
p(ca)3. Hence the significant increase in the total energy output that is
shown in
FIG. 11.
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Higher conversion efficiencies can readily be achieved by increasing pump
power, or, as mentioned earlier, by increasing the length of the structure by
only
modest amounts. For example, calculations show that by increasing the total
number of periods to 30, thus increasing the length of the device by 50%, the
SH
output energy (and power level) increases by a factor of 5 for a 1 ps pulse,
enhancing the conversion efficiency by the same factor. This occurs because
the
maximum group index increases approximately as NZ , where Nis the number of
periods. The field eigenmode intensity is also proportional to lVi , thus
enhancing
energy output in a nonlinear fashion with respect to device length.
Calculations also indicate that in the linear, undepleted-pump regime, the
conversion efficiency is proportional to the free-space peak field value, as
illustrated in FIG. 13. Here, any small deviation in the actual x~2~ value,
tuning
with respect to the band edge, and input pulse width can significantly affect
comparison with experimental results. For this reason, the model presented
above
is of great value in order to determine the overall behavior of a PBG
structure, and
it can be used in the determination of x~2~. Therefore, exercising reasonable
care
in the design process of a PBG device based on the present invention can
produce
a very efficient SH generator, provided absorption at the SH wavelength is
minimized. Note that a similar model can also be used to design an efficient
third
- 20 harmonic generator, and the like.
In another embodiment of the present invention, a structure comprises a
series of alternating layers, where n, {~2,2~) = l and n2 02,252) = 1.42857.
For
added simplicity, it is assumed that the material is not dispersive. For this
example, layer thicknesses are chosen such that the width of the low index
layer
is a = 0.65 ~.°ln, (the low index layer is now the active layer because
of the shift in
localization of the field), and the width of the high index layer is such that
b =
0.089,°/n,. Then, tuning the pump at the first resonance of the first-
order, high-
frequency band edge causes the SH signal to be tuned at the second resonance
of
the second-order high-frequency band edge, in analogy to what was accomplished
above for the low-frequency band edge. However, the conversion efficiency for
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the high frequency band edge example can increase up to about a factor of two
for
a 1 ps pulse, compared to the low-frequency band-edge conversion efficiency.
Tuning the pump at the high-frequency band edge causes a shift of the pump
field
localization in the low index layer. This shift increases the field eigenmode
intensity in that layer. Also, the width of the active layer increases by
about 30%,
from 0.5~.° to 0.65.°. This combination can account for the
increase in overall
nonlinear gain for a device length of approximately 12 pm in length.
c. GaAslAIAs half quarter-wave stack for SHgeneration
This section describes a numerical model of a mixed half quarter-wave
structure comprising 20 periods of GaAs/AIAs material. It was assumed that
x~z>
1 pm/V for both materials, the index of refraction alternated between n,(S~) _
2.868 and n2(f~) = 3.31, n,(21~) = 2.9 and n2 (2~) = 3.35, and that absorption
could be ignored. These indices correspond to a pump wavelength of 3 pm, and
a second-harmonic signal at 1.5 pm. For a pump intensity of 10 GW/cm2 , the
mixed half quarter-wave GaAs/AIAs structure produced conversion efficiencies
on the order 10-2 - 10'3 for this 20-period structure. The model equations
described above for nonlinear SH gain (which from Eq. (6) is defined as the
product x~2~ eZQ) indicate that this high conversion efficiency is due to the
order-of
magnitude increase in x~'-~ and the order-of magnitude decrease in the field
eigenmode intensity (due to the substantial increase in the index for GaAs).
In
addition, a significant increase in conversion efficiency can be achieved with
increasing number of periods in the PBG structure. These results also indicate
that different materials, such as II-VI based semiconductors, would be ideal
for
up-converting at higher frequencies.
6. Method of Frequency Conversion
A method for performing frequency conversion of an input photonic signal
is shown in FIG. 14. The input photonic signal has an input photonic signal
frequency and an input photonic signal bandwith. In step 1402, the frequency
of
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the input photonic signal is selected so as to correspond to a second signal
at a
desired harmonic frequency. In addition, the type of input signal (e.g.,
continuous
wave or pulsed operation) should also be considered. Next a device is provided
in step 1404, where the device comprises an arrangement of material layers
that
exhibits a photonic bandgap structure. Various types of material layer
arrangements are discussed above. The specific type of an:angement (and hence
the type of frequency conversion to be performed) depends upon factors that
include, but are not limited to: (1) the absorption and transmission
properties of
the materials selected; (2) the indices of refraction of the materials forming
the
structure, which affects such parameters as the index discontinuity; (3) the
thicknesses of the material layers; and (4) the number of periods of
alternating
layers. The combination of parameters results in a PBG structure that
preferably
exhibits a transmission band edge corresponding to the input photonic signal
frequency. Finally, the input photonic signal is delivered into the device in
order
to generate a second photonic signal at an harmonic frequency ofthe pump
signal.
An interaction of the input photonic signal with the arrangement of layers
generates the second photonic signal at a second frequency, where the second
frequency is different than the first frequency. It will be apparent to one of
skill
in the art to use this method to perform such frequency conversion techniques
as,
for example, harmonic generation and optical par3lnetric oscillation.
7. Conclusions
While various embodiments of the present invention have been described
above, it should be understood that they have been presented by way of example
only, and not limitation. Thus, the breadth and scope of the present invention
should not be limited by any of the above-described exemplary embodiments, but
should be defined only in accordance with the following claims and their
equivalents. Additionally, all articles and patent documents mentioned above
are
incorporated by reference herein.
