Note: Descriptions are shown in the official language in which they were submitted.
1
ACTIVE LMA OPTICAL FIBER WITH ENHANCED
TRANSVERSE MODE STABILITY
TECHNICAL FIELD
.. The technical field generally relates to active LMA optical fibers and more
particularly concerns fibers having a core configuration mitigating Transverse
Mode Instability effects.
BACKGROUND
Transverse Mode Instability (TMI) is a phenomenon that takes place in active
Large Mode Area (LMA) optical fibers used in optical amplifiers, for example
fibers
having a core doped with rare earths such as ytterbium, once the heat load in
the
fiber exceeds a certain threshold. This heat load is understood to originate
from
the quantum defect of the radiative transition coming from the laser inversion
in
the core material initiated by optical pumping, but also from background
losses and
photodarkening in the fiber. The instability unfolds as a refractive-index
grating is
formed in the fiber core following the spatial intensity pattern caused by the
interference of the fundamental transverse mode (LP01) with the first higher-
order
mode (LPii) and causing the former to shed some energy to the latter. The mode
coupling taking place beyond the given threshold is responsible for beam
distortions and pointing fluctuations in the amplifier output, thus limiting
the use of
these fibers for several applications.
The occurrence of TMI is known in the art as a serious obstacle to attempts at
scaling the power of lasers based on active fibers beyond a few kilowatts, as
shown
in FIG. 1 (PRIOR ART). LMA fibers are known to support higher-order transverse
modes in addition to the fundamental transverse mode. Indeed, LMA fibers with
core diameters as large as 50x the wavelength of the light propagating therein
may
not be considered single-mode, even with the most special designs known in the
art. Such large core diameters are needed to reduce the light intensity in the
fiber
core and to avoid distortions induced by nonlinear effects such as Stimulated
Date Recue/Date Received 2022-06-09
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Raman Scattering. On the other hand, TMI may be prevented by using fibers with
smaller core diameters, such that they may support only the fundamental mode,
if
possible.
Various mitigation strategies to TMI have been reported in the art. Referring
for
example to U.S. Patent No. 9,214,781 (Honea et al), an apparatus and method
for
suppressing modal instabilities in fiber-amplifier systems are disclosed,
involving
a hybrid fiber with a smaller core in the initial length where the thermal
loads are
the highest, followed by a larger-core fiber. U.S. Patent No. 9,972,961 (Sipes
et al)
shows a fiber optic amplifier system including a first core fiber having a
first core
diameter and a first cladding size; a second stage, comprising a second core
fiber
having a second core diameter and a second cladding size; and a double mode
adapter connecting the first stage to the second stage. Active methods to
inhibit
the onset of TMI have also been disclosed in the art, for example in U.S.
Patent
No. 9,235,106 (Jauregui et al) and U.S. Patent Application No. 2017/0299900
(Montoya et al). U.S. Patent No. 9,325,151 (Fini et al) and U.S. Patent No.
10,263,383 (Headley) disclose TMI mitigation methods with specific layouts for
fiber spooling in laser systems.
There remains a need in the art for TMI mitigation strategies that provide
improvements on the prior art.
SUMMARY
In accordance with one aspect, there is provided an active Large-Mode-Area
(LMA) optical fiber for mitigating Transverse Mode Instability (TMI) effects.
The
active LMA optical fiber comprises a core and one or more claddings
surrounding
said core, the core having a refractive index and a temperature coefficient
each
having a radial profile, the core comprising:
- a center core region having a center core glass composition comprising one
or more rare-earth center dopants and one or more center co-dopants, said
rare-earth center dopants and center co-dopants having respective
Date Recue/Date Received 2022-06-09
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concentrations and distributions determining radial profiles of the refractive
index and of the temperature coefficient within said center core region; and
- a peripheral core region contiguously surrounding said center core region,
the peripheral core region having a peripheral core glass composition which
is free of rare-earth dopants and comprises one or more peripheral dopants,
said peripheral dopants having respective concentrations and distributions
determining radial profiles of the refractive index and of the temperature
coefficient within said peripheral core region,
wherein the radial refractive index-profile of the core is generally
continuous across
a boundary between the center core region and the peripheral core region; and
wherein a selection and the concentrations and distributions of the rare-earth
center dopants, the center co-dopants and the peripheral dopants are such that
the temperature coefficient is lower in the peripheral core region than in the
center
core region.
In some implementations, the refractive index of the core has a same uniform
value
across the center core region and the peripheral core region, and the
temperature
coefficient has a first uniform value across the center core region and a
second
uniform value across the peripheral core region.
In some implementations, the radial temperature-coefficient profile in the
core is
linearly graded or parabolic.
In some implementations, the radial temperature-coefficient profile forms a
step
function at the boundary between the center core region and the peripheral
core
region.
In some implementations, the temperature coefficient in the peripheral core
region
is about 5% to about 35% lower than the temperature coefficient in the center
core
region.
Date Recue/Date Received 2022-06-09
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In some implementations, the temperature coefficient in the center core region
is
at least 10% or at least 20% lower than the temperature coefficient in the
peripheral
core region.
In some implementations, the active LMA optical fiber has a TMI threshold that
exceeds by a factor of about 30% or more, about 50% or more, or about 100% or
more, a TMI threshold of an equivalent optical fiber having an equivalent core
having a same core diameter as the active LMA optical fiber and a continuous
radial temperature-coefficient profile across said equivalent core.
In some implementations, a weighted mean of molar refractivities of the one or
more peripheral dopants is about the same as the weighted mean of the molar
refractivities of the rare-earth center dopants and center co-dopants and at
least
one of the peripheral dopants has negative contribution to the temperature
coefficient.
In some implementations, the one or more center co-dopants include at least
one
of phosphorus, aluminum and fluorine. Preferably, the one or more peripheral
dopants include at least one of phosphorus, fluorine and boron.
In some implementations:
- the rare-earth center dopant consists of ytterbium;
- the center co-dopants consist of phosphorus, aluminum and fluorine; and
- the peripheral dopants consist of phosphorus and fluorine;
wherein the peripheral core region has higher concentrations of phosphorus and
fluorine than the center core region.
In some implementations:
the rare-earth center dopant consists of ytterbium;
the center co-dopants consist of phosphorus and aluminum; and
the peripheral dopant consists of phosphorus;
Date Recue/Date Received 2022-06-09
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wherein the center core region and the peripheral core region have about a
same
concentration of phosphorus.
In some implementations, the core has a diameter between about 20 pm and about
60 pm and a core numerical aperture between about 0.06 and 0.10. A ratio of a
diameter of the center core region to the diameter of the core may range from
about 0.5 to about 0.9.
In some implementations, the one or more claddings surrounding the core
comprise:
- an inner cladding configured to confine a light beam in the core; and
- an outer cladding configured to confine a pump light in the inner
cladding.
In some implementations, an output light beam exiting from an end of the
optical
fiber has a beam quality factor M2 less than or equal to about 1.3.
In some implementations, the active LMA optical fiber further comprises stress-
applying members extending longitudinally within at least one of the one or
more
claddings.
Other features and advantages will be better understood upon of reading of
detailed embodiments with reference to the appeded drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 (PRIOR ART) is a graph of the laser slope efficiency beyond the TMI
threshold using a conventional polarization-maintaining 20/400 LMA fiber.
FIGs. 2A, 2B and 2C schematically represent a cross-sectional view, the
refractive
index profile and the temperature coefficient profile, respectively, of the
core of an
active LMA optical fiber according to one embodiment.
Date Recue/Date Received 2022-06-09
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FIGs. 3A and 3B schematically represent the cross-sectional view and
refractive
index profile of the core and claddings of an active LMA optical fiber
according to
one embodiment.
FIGs. 4A and 4B schematically represent the cross-sectional view and
refractive
index profile of the core and claddings of an active LMA optical fiber
according to
one embodiment, where the refractive index of the second cladding is higher
than
the refractive index of the first cladding.
FIGs. 5A to 5C are schematic representations of active LMA optical fibers with
multiple claddings and different core refractive index profiles.
FIGs. 6A and 6B respectively illustrate a uniform core refractive index and a
non-
uniform core temperature coefficient profile that can be obtained using radial
profiles of molar compositions of dopants such as shown in FIGs. 6C and 6D.
FIG. 7A is a graph of the refractive index and FIG. 7B is a graph of the
temperature
coefficient of silica glass compounds vs. dopant concentration.
FIGs. 8A and 8B are ternary diagrams of the refractive index change relative
to
pure silica (8A) and the temperature coefficient (8B) of glass with molar
concentrations of phosphorus and fluorine dopants.
FIGs. 9A and 9B are ternary diagrams of the refractive index change relative
to
pure silica (9A) and the temperature coefficient (9B) of glass with molar
concentrations of phosphorus and aluminum dopants.
DETAILED DESCRIPTION
In accordance with some aspects, there is provided an active LMA optical fiber
which mitigates the effects of TMI when used as the gain medium of a fiber
amplifier or laser system.
Date Recue/Date Received 2022-06-09
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To provide a more concise description, some of the quantitative expressions
given
herein may be qualified with the term "about". It is understood that whether
the
term "about" is used explicitly or not, every quantity given herein is meant
to refer
to an actual given value, and it is also meant to refer to the approximation
to such
given value that would reasonably be inferred based on the ordinary skill in
the art,
including approximations due to the experimental and/or measurement conditions
for such given value.
In the present description, the term "about" means within an acceptable error
range
for the particular value as determined by one of ordinary skill in the art,
which will
depend in part on how the value is measured or determined, i.e. the
limitations of
the measurement system. It is commonly accepted that a 10% precision measure
is acceptable and encompasses the term "about".
In the present description, when a broad range of numerical values is
provided,
any possible narrower range within the boundaries of the broader range is also
contemplated. For example, if a broad range value of from 0 to 1000 is
provided,
any narrower range between 0 and 1000 is also contemplated. If a broad range
value of from 0 to 1 is mentioned, any narrower range between 0 and 1, i.e.
with
decimal value, is also contemplated.
Referring to FIGs. 2A, 2B and 2C, the transverse structure, refractive index
profile
and temperature coefficient profile of a portion of an active LMA optical
fiber 20
according to one implementation are schematically illustrated.
The active LMA optical fiber 20 includes a core 22 and one or more claddings
30,
forming a cladding structure 24 (see FIGs. 3A and 3B), surrounding this core.
In
some embodiments, the active LMA optical fiber 20 may be a multi-clad optical
fiber used to amplify a light beam in devices such as fiber lasers and
amplifiers.
Such devices are used in a wide range of optical applications in fields such
as
medicine and surgery, scientific instrumentation, semiconductor device
Date Recue/Date Received 2022-06-09
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manufacturing, military technology, and industrial material processing. In
some
variants, the active LMA optical fiber may include stress-applying members
extending longitudinally within at least one of the one or more claddings on
each
side of the core so as to maintain the polarization of light in a linear
state, such a
fiber being known in the art as panda or bow-tie polarization-maintaining
fiber.
Such specialty fibers are used in fiber lasers and amplifiers in some of the
fields
listed above, for instance where a specific application requires the light to
be
linearly polarized. The generation of laser frequency harmonics using
nonlinear
optical crystals is a first instance where linearly-polarized light is
required, chirp-
pulse amplification using grating pair pulse compressors in ultrafast lasers
being
another instance.
Parameters of the active LMA optical fiber 20 such as the respective
composition,
size and configuration of the core 22 and of the one or more claddings of the
cladding structure 24 may be selected in view of the intended use of the
fiber. As
known in the art, the core 22 is configured to support the propagation of a
light
beam to be amplified in a fundamental core mode of the typically few-mode
active
LMA optical fiber 20 while the claddings 24 are configured to confine the
light beam
in the core 22. When the active LMA optical fiber is used in a cladding-pumped
implementation, at least one of the claddings 24 may also be configured to
support
and guide the optical pump beam in one or more cladding modes. Examples of
cladding configurations are provided further below. In some implementations,
the
output light beam exiting from the end of the optical fiber has a beam quality
factor
M2 less than or equal to about 1.3.
In accordance with some implementations, the core includes a center core
region
26 and a peripheral core region 28 contiguously surrounding the center core
region
26. The center core region 26 has a center core glass composition comprising
at
least one rare-earth center dopant and one or more center co-dopants. The
peripheral core region 28 has a peripheral core glass composition which is
free of
rare-earth dopants and comprises one or more peripheral dopants.
Date Recue/Date Received 2022-06-09
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As is known in the art, the core has a refractive index and a temperature
coefficient
each having a radial profile along the transverse direction. The refractive
index
profile of a glass material is determined by the composition and distribution
of the
dopants in the glass host. In accordance with one aspect, the core 22 of the
active
LMA optical fiber 20 described herein has a generally continuous refractive
index
profile across a boundary 27 between the center core region 26 and the
peripheral
core region 28. As one skilled in the art will readily understand, the
expression
"generally continuous" allows for some manufacturing artefacts in the
refractive
index profile at the boundary 27, inasmuch as such artefacts have a negligible
impact on the optical modes guided by the fiber for the targeted application.
Furthermore, the temperature coefficient of the peripheral core region 28 is
lower
than the temperature coefficient of the center core region 26. As explained
below,
in some implementations, radially dependent but azimuthally uniform
concentrations of co-dopants over the cross-sectional area of the core 22 may
advantageously be used to lessen the susceptibility of the active LMA optical
fiber
to TMI when the heat load in the fiber becomes considerable.
The susceptibility of optical fibers to TMI under an increasing heat load is
believed
20 to depend on characteristics such as the thermal conductivity, the heat
capacity
and the temperature coefficient of the glass materials of the optical fiber.
The
temperature coefficient is also referred to in the art as the thermo-optic
coefficient.
The temperature coefficient refers to the tendency of the refractive index of
a glass
material to change while the material is heated or cooled. The temperature
coefficient is also symbolized in the literature as the parameter dn/dT, n
being the
refractive index of the material and Tthe temperature. The temperature
coefficient
depends on the glass host composition, with regards to the addition of dopants
(aluminum, phosphorus, fluorine, ...) and their respective concentrations in
the
glass.
Date Recue/Date Received 2022-06-09
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In conjunction with rare-earth dopants provided in the core of an optical
fiber to
generate optical gain, co-dopants are typically included in the fabrication of
active
fibers for several reasons, such as (i) increasing the solubility of rare
earths ions
in the glass host; (ii) controlling the refractive index contrast between the
core and
.. the adjacent cladding; and (iii) reducing the susceptibility of the fiber
to
photodarkening. In accordance with one aspect, the dopants in the core of the
active LMA optical fibers described herein are additionally or alternatively
used to
control the temperature coefficient profile of the glass host.
In some implementations, the center core glass composition includes a glass
host
such as silica glass, and at least one rare-earth center dopant such as
ytterbium
(Yb3+), neodymium (Nd3+), erbium (Er), thulium (Tm3+), praseodymium (Pr3+) and
holmium (Ho3+). The center core glass composition further includes one or more
center co-dopants, which may for example be embodied by aluminum,
phosphorus, fluorine, or combinations thereof. The rare-earth center dopants
and
the center co-dopants have respective concentrations and distributions
determining the radial refractive index profile of the core 22 within the
center core
region 26. The peripheral core glass composition of the peripheral core region
28
also includes a glass host such as silica glass. However, in contrast to the
glass
composition of the center core region 26, it is free of rare-earth dopants.
The
peripheral core glass composition includes one or more peripheral dopants, for
example, phosphorus oxide and/or fluorine, having respective concentrations
and
distributions determining the radial refractive index profile within the
peripheral
core region 28.
In the present description, the dopants and co-dopants can be referred to as
using
the chemical element name of the corresponding active element. For instance,
one
can refer to "aluminum" or "phosphorus" co-dopants, and to "ytterbium" dopant.
One skilled in the art will understand that such elements are present in the
optical
fiber in their oxide form. Hence, the terms "aluminum" and "aluminum oxide" co-
dopant can be used interchangeably. Similarly, the terms "phosphorus" and
Date Recue/Date Received 2022-06-09
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"phosphorus oxide" co-dopant can be used interchangeably. Regarding the rare
earth dopants, such as ytterbium for instance, one will use the terms
"ytterbium",
"Yb31-", "ytterbium oxide", and "Yb203" interchangeably.
In accordance with one aspect, the configuration and composition of the core
22
are designed such that the temperature coefficient of the peripheral core
region is
lower than the temperature coefficient of the center core region. Such a core
22
advantageously combines the following features:
i. The confinement of the rare earth dopants in the center region promotes
the fundamental mode (LP01), while the higher-order modes are deprived
from the gain otherwise needed for the TMI to thrive;
ii. The coupling between the fundamental mode (LPoi ) and the next higher-
order mode (LPii) is reduced as the temperature coefficient is made lower
in the peripheral core region, where the overlap between these two modes
is the greatest, given the heat load in the active fiber.
As will be understood by one skilled in the art, these two complementary
measures
can prevent TMI from taking place in LMA fibers used in fiber lasers and fiber
amplifiers. Beside from the roll-off seen on the output power of fiber lasers
and
amplifiers (see FIG. 1), the TMI onset may also be identified from intensity
fluctuations that will show up on signal samples recorded using a fast
photodiode
on which is directed the laser beam outputted by the active LMA optical fiber.
Distinct frequencies usually stand out from a Fourier analysis performed on
the
signal temporal traces, seen as evidence for the coherent beating between the
fundamental mode (LP0i) and the first higher-order mode (LPi 1 ) which is
taking
place as TMI unfolds. Compared to an equivalent optical fiber having an
equivalent
core with a same core diameter as the active LMA optical fibers described
herein
and a continuous temperature coefficient profile across this equivalent core,
the
threshold for TMI as determined from the aforementioned characteristics is
expected to increase by a significant measure, e.g. in some implementations
the
Date Recue/Date Received 2022-06-09
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threshold may be raised by a factor of about 30% or more, in some other
implementations the threshold may be raised by about 50% or more while in yet
other implementations the threshold may be raised by as much as 100% or more.
Precisely how much is the TMI threshold raised depends on how much lower is
the temperature coefficient in the peripheral core region as compared to the
temperature coefficient in the center core region. By way of example, the
temperature coefficient in the peripheral core region may be about 5% to about
35% lower than the temperature coefficient in the center core region. In some
implementations, the temperature coefficient in the peripheral core region is
about
5% lower than the temperature coefficient in the center core region, in some
other
implementations, the temperature coefficient in the peripheral core region is
at
least 10% lower than the temperature coefficient in the center core region
while in
still other implementations the temperature coefficient in the peripheral core
region
is at least 20% lower than the temperature coefficient in the center core
region.
Still referring to FIGs. 2A, 2B and 2C, and with further reference to FIGs. 6A
to 6D,
in some implementations the core 22 of the active LMA optical fiber 20 is
shown to
consist of two distinct concentric regions, embodying the center core region
26 and
the peripheral core region 28. The center core region 26, which is doped with
active
ions such as rare earth ions, for example Yb3+, and other co-dopants (e.g.,
Al, P,
F, ...), is bounded by the peripheral core region 28. The composition of the
peripheral core region 28 may be chosen so as to produce a refractive index
about
the same as the refractive index of the center core region 26, yet with a
temperature coefficient which is lower than that of the center core region 26.
As
mentioned above, this is preferably achieved by including one or more
peripheral
dopants in the peripheral core region 28. Preferably, at least one peripheral
dopant
is a temperature-coefficient-reducing dopant providing a negative contribution
to
the temperature coefficient, that is, the temperature coefficient of the
peripheral
core region is lower than it would be without the presence of this particular
dopant.
In some variants, the weighted mean of the molar refractivities of the one of
more
peripheral dopants is about the same as the weighted mean of the molar
Date Recue/Date Received 2022-06-09
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refractivities of the rare-earth center dopants and center co-dopants found in
the
center core region. By way of example, Table 1 below provides values of the
molar
refractivity An and temperature coefficient of silica and typical glass
dopants.
Material An dn/dT
(.10-4 mol%-1) (.10-6 K-1)
Si02 10.4
Ge02 13 19.4
A1203 23 10.5
P205 9.3 -13.3
A1PO4 -0.9 N/A
F -8 -1.1
B203 -5 -30
Table 1
Reference can also be made to FIGs. 7A and 7B, respectively showing the
refractive index and temperature coefficient of various silica glasses
including
different dopant compounds as functions of the molar concentrations of the
dopants. Furthermore, ternary diagrams of the refractive index change relative
to
pure silica and the temperature coefficient of glass with molar concentrations
of
dopants are shown in FIGs. 8A and 8B for phosphorus oxide and fluorine
dopants,
and on FIGs. 9A and 9B for phosphorus oxide and aluminum oxide dopants.
By way of example, FIGs. 6C and 6D illustrate the molar compositions of two
active
LMA optical fiber samples producing a same non-uniform temperature coefficient
(FIG. 6B) and a uniform core refractive index (FIG. 6A). For instance, the
phosphorus oxide/fluorine-enriched peripheral core region 28 in the fiber
depicted
in FIG. 6C, with a temperature coefficient lower than that of the center core
region,
will contribute less to the refractive index grating induced by the heat load
and
mode coupling will be reduced accordingly. Phosphorus oxide and fluorine
appear
as a good match as their respective molar refractivities nearly offset each
other.
As an example, if an excess of phosphorus oxide and fluorine is added to the
peripheral core region, the temperature coefficient will then be about 20-40%
lower
Date Recue/Date Received 2022-06-09
14
than the temperature coefficient in the center core region, given the maximum
molar concentrations (i.e., 5-10 mol%) that can be achieved with standard
fabrication means (i.e., vapor deposition and solution doping). Beside
fluorine,
boron oxide may also be used in addition to phosphorus oxide. Boron oxide may
add up to phosphorus oxide, exerting altogether a greater influence on the
temperature coefficient. Nonetheless, boron oxide concentration will differ
from
fluorine concentration as the molar refractivity of boron oxide, unlike
fluorine, does
not nearly offset the contribution of phosphorus. At last, phosphorus oxide
may
yield on its own (i.e., without fluorine) a temperature coefficient of the
peripheral
core region that is lower than the temperature coefficient of the center core
region,
provided that the molar compositions are chosen adequately (see for example
FIG.
6D).
In some implementations, such as for example shown in FIG. 5A, the center core
and peripheral core glass compositions may each be radially uniform. As such,
the
refractive index of the core has a same uniform value across the center core
region
and the peripheral core region, and the temperature coefficient has a first
uniform
value across the center core region and a second uniform value across the
peripheral core region, leading to the temperature coefficient profile forming
a step
function at the boundary between the center core region and the peripheral
core
region. In other variants, a graded radial profile of the temperature
coefficient may
be provided through a varying concentration of the peripheral dopants in the
peripheral core region, assuming that such a radially-varying dopant
concentration
is made possible by the technique chosen for the fabrication of the fiber
preform.
Likewise, the refractive index in the core could assume a graded radial
profile,
without departing from the scope of protection. A linear (see FIG. 5B) or
parabolic
(see FIG. 5C) refractive index profile may be desirable, for instance with the
intent
of minimizing the coupling between the fundamental mode and the higher-order
modes.
Date Recue/Date Received 2022-06-09
15
Referring by way of example to FIGs. 3A, 3B, 4A, 4B and 5A to 5C, there are
shown various configurations for the cladding structure 24 of active LMA
optical
fibers 20 according to various implementations. As mentioned above, the active
LMA optical fiber 20 may feature the presence of several claddings.
Preferably, at
least one of the claddings, typically the first cladding immediately
surrounding the
core 22 and sometimes referred to as the "inner cladding" 30, has a refractive
index
lower than that of the core, providing means to confine the light beam in the
core.
The inner cladding 30 typically consists of fused silica and may sometimes
include
index modifiers such as germanium to raise the refractive index above that of
fused
silica, or fluorine to lower the refractive index. Referring by way of example
to FIGs.
2A and 2C, the inner cladding 30 may have a temperature coefficient which is
higher than the temperature coefficient of the peripheral core region 28.
While this
is not essential, the larger temperature coefficient in the first cladding
relative to
that of the core peripheral region may be beneficial for the filtering of
higher-order
modes as the thermal load increases in the fiber core. For instance, in the
case
where the first cladding has a depressed refractive index with respect to the
subsequent cladding (following the teachings of Pare et al. in U.S. Patent No.
8,731,358), this same cladding could be made such as to have a temperature
coefficient larger than that of the core peripheral region, thereby improving
bending
losses.
An outer cladding 32 typically surrounds the inner cladding, the material of
the
outer cladding 32 often consisting of a low-index acrylate polymer, providing
means to confine the pump light within the inner cladding with a numerical
aperture
(NA) of at least 0.46. One or more intermediate claddings 31 of various
thicknesses
may be provided between the inner 30 and outer 32 claddings, with values for
their
refractive indices ranging from that of the core 22 to that of the outer
cladding 32.
One such intermediate cladding 31b could be made of silica glass doped with
fluorine (e.g., fluosi10) and may be provided immediately inward of the outer
cladding 32, thereby providing means to confine pump light with NA = 0.22. In
addition or alternatively, an intermediate cladding 31a having a refractive
index
Date Recue/Date Received 2022-06-09
16
larger than that of the inner cladding 30 may be provided immediately outwards
of
the inner cladding 30, providing means to modify the waveguide properties in
the
core 22, such as for example taught in U.S. Patent No. 8,731,358 (Pare et al.
By way of example, in the embodiment illustrated in FIGs. 4A and 4B, the
active
LMA optical fiber configuration includes a first cladding 30 featuring a
depressed
refractive index, which may be conducive to a better mode stability. The
active fiber
illustrated in FIGs. 3A and 3B, where each cladding is shown to have a
refractive
index smaller than the previous cladding, may also be used.
The outer diameter of the fiber (by convention without the outermost cladding)
is
preferably in the range from 125 to 600 pm. In some implementations, the
diameters of the claddings could be made to change periodically along the
fiber,
for instance if the fiber is pulled as a taper during fiber drawing (see the
teachings
of Roy et al. in U.S. Patent No. 10,985,519). Finally, the outermost cladding
of the
active LMA optical fiber is typically coated with a polymer layer to provide
means
for protecting the fiber against environmental influences.
Examples and Additional Considerations
The extent of the rare earth doped cross section of the center core region, or
inversely the rare-earth dopant confinement ratio, depends on several
parameters,
including the core and the cladding diameters, the concentration of rare-earth
dopants in the glass host, and the mode field diameter of the light beam in
the core
of the active LMA optical fiber. As known in the art, the mode field diameter
of the
light beam relates to the main purpose of active LMA fibers, i.e., to amplify
laser
beams at high powers and yet avoid distortions induced by the high intensity
of the
mode field in the fiber core leading to the onset of nonlinear effects. The
mode field
tends to be more tightly confined within the core as the core diameter gets
larger,
or if the heat load is increased. For instance, considering a step-index fiber
with
core diameter dcõ, and numerical aperture NA =
Lore ¨ nlac/7 Marcuse
equation yields the mode-field diameter MFD for the fundamental mode LPoi as:
Date Recue/Date Received 2022-06-09
17
MFD = dõõ = (0.65 + 1.619/V3"2 + 2.879/V6) (1)
where V (= ffdõõNAR) is the normalized frequency of the fiber and A is the
wavelength of light in vacuum. The larger the normalized frequency, the
smaller
the mode field diameter relative to the core diameter (i.e., V >> yields MFD
¨> 0.65 =
dcore in equation (1) above). In essence, as the core diameter gets larger,
the more
the rare-earth dopants are to be confined in the center region to achieve the
desired light amplification. On the other hand, too great a confinement
requires
rare earth concentrations exceeding the restrictions set by clustering and
photodarkening in the glass host, both effects causing the laser slope
efficiency to
decrease and the excess heat to be transferred to the laser gain media. The
absorption of pump light in rare-earth-doped double-clad fibers is obtained as
the
product of the absorption cross-section OF
- abs,pump with the density of rare-earth
dopants Nõ, taking into account the overlap i19 of
the pump light propagating in
the cladding (assumed to be evenly distributed) with the cross-sectional area
of
the center core region doped with rare earths:
abs = iipuim, = aabs,pump Nre (2)
where riptimp :7z Are/ Aclad (0C dr2e1(1c2iad), and Are and /lc/ad refer to
the cross-sectional
areas of the rare-earth core dopants (hence of the center core region) and
cladding
respectively. In typical optical fibers, where there is no confinement of rare-
earth
dopants, the extent of the doped region is then considered the same as the
core
diameter (dre = dcore). The absorption cross-section of rare earths in the
glass host
depends on the concentrations of center co-dopants used in the center core
region
to increase the solubility of rare earths ions in the glass host (solutizer
ions). In
fact, the absorption cross-section is known to change more or less given the
specific laser wavelength used for optical pumping (e.g., 915-976 nm for
ytterbium)
Date Recue/Date Received 2022-06-09
18
depending on which solutizer ions are being used in the glass host, for
example
whether it is aluminum, phosphorus, or both. The density of rare-earth dopants
is
generally in the range of about 1025-1026 ions/m3.
In general, LMA fibers with core diameters in the range dcõ, ,-,' 20 ¨ 30 [tm
and
numerical aperture NA ,-,' 0.065 are found to have normalized frequencies in
the
range V ,-,' 4 ¨ 6. LMA fibers drawn as tapers were reported to have dõõ ?, SO
[tm
and normalized frequency V ?, 10 at the distal end (see the teachings of Roy
et al.
in U.S. Patent No. 10,985,519). The active LMA optical fiber described herein
preferably has a core diameter dõõ ,-,' 20 ¨ 60 [tm and core numerical
aperture
NA ,-,' 0.06 ¨ 0.10. The cladding diameter dciad is generally selected from a
few
standard sizes to match the fiber-optic components currently used by laser
system
engineers (i.e., 125, 250, 400 and 600 pm). The latter depends first and
foremost
on the power and brightness of the pump light to be launched in the fiber
cladding
but also the amplifier output power required to meet the user's needs for
specific
applications.
Given the figures mentioned herein, confinement ratios (= dõIdõõ) ranging from
about 0.5 to 0.9 are reasonable for active LMA optical fibers according to
some
embodiments. Too small a confinement ratio may result in excessively low
absorption of pump light due to limitations on concentrations of rare earth
dopants,
which in turn involves long fibers and nonlinear effects showing up at an
early
stage. For instance, a confinement ratio of 0.5 involves a concentration of
rare
earth dopants roughly 4x greater for pump absorption to stay the same as for a
fiber having a core doped with the same rare earths over its full transverse
section.
Fiber preforms for the drawing of active LMA optical fibers as described
herein
may be fabricated using conventional processes, such as modified chemical
vapor
deposition (MCVD) and solution doping, even though additional process steps
may
be required before the fiber preform is completed and made available for fiber
drawing. Chemical vapor-phase deposition process with chelate precursors
Date Recue/Date Received 2022-06-09
19
alleviates some of the complexity as much greater control is provided to
tailor both
the refractive index and the temperature coefficient simultaneously,
especially to
address more complex radial profiles such as the ones illustrated in Figure 5.
In
some implementations the stack-and-draw fabrication technique may also be
used, with even greater precision on the final radial profiles of refractive
index and
temperature coefficient as the procedure of drawing stacked preforms can be
repeated until the desired structure and dimensions are achieved (with the
macroscopic rods/capillaries used in the first place now transformed to
submicron
scale). The molar concentrations of dopants found in the various regions, or
more
precisely their respective oxide compounds, will be added to the fiber preform
during its fabrication in accordance with both the refractive index profile
and the
temperature coefficient profile that are sought, provided that the molar
refractivity
and temperature coefficient of each oxide compound are known. Graded profiles
may be achieved for instance by increasing or decreasing the concentration of
at
least one of the center and peripheral dopants radially outward from the
center of
the core. Optical fibers with varying dopant concentrations along the core
radius
may be fabricated with a vapor-phase doping method using chelate precursors,
as
known in the art, or else from the stack-and-draw method where the final
preform
stack includes glass rods derived from a plurality of preforms.
As mentioned above, the temperature coefficient of silica glass depends on the
nature and concentration of the co-dopants included therein. Some compounds
like germanium oxide (Ge02) will raise the temperature coefficient of silica
glass
while others like phosphorus oxide (P205) will result in a lower temperature
coefficient. Properties of optical glasses such as the refractive index and
temperature coefficient may be described with the additivity model known in
the
art, where the aggregate glass properties are obtained from the weighted mean
of
the individual oxide properties, the weights being the oxide fractional
volumes in
the glass. Conventional fabrication methods (e.g., MCVD) do not necessarily
allow
for the addition of co-dopants with arbitrarily high concentrations in the
silica glass
host. It is, however, possible to make use of various co-dopants with
differing
Date Recue/Date Received 2022-06-09
20
temperature coefficients to lessen the impact of the heat load (symbolized
here as
the temperature elevation ST). First, as mentioned previously, this is done
most
simply through tailored glass compositions including co-dopants with a
negative
contribution to the temperature coefficient such as phosphorus oxide. In
addition,
the use of a core configuration as disclosed herein may further reduce TMI
effects.
The radially decreasing temperature coefficient (11,4 so produced seeks to
minimize
the coupling taking place from the fundamental mode (LPoi ) to the next higher-
order mode (LPii), accounted for by the overlap integral in the equation
below:
C RIG = noksffipol (r , (P)dn(r)'Mr , (P)IPii(r, (P)
dT (3)
where no is the refractive index of the glass host and lc, is the wavenumber
of the
light propagating in the fiber. The TMI threshold is further expected to vary
inversely with the coupling strength cRiG once the index grating is initiated
as the
result of the mode interference pattern at some location along the fiber.
Hence, a
50% decrease in coupling strength cruG should raise the TMI threshold roughly
by
a factor of 2. In some embodiments, active LMA optical fibers as described
herein
have a coupling coefficient less than equivalent fibers without the claimed
core
configuration by at least a factor of 2, which yields a significant advantage
over
conventional LMA fibers.
The molar composition in the peripheral core region largely depends on the
molar
composition in the center core region in order to yield the desired mismatch
between the temperature coefficients of both regions. The concentration of
rare
earth ions, such as ytterbium, in silica glass fibers is limited by adverse
effects
such as crystallization and clustering. As mentioned above, the solubility of
rare-
earth dopants in a glass host depends on the addition of one or more center co-
dopants such as phosphorus oxide (P205) and/or aluminum oxide (A1203). The
addition of both phosphorus and aluminum oxides in the silica host yields a
glass
Date Recue/Date Received 2022-06-09
21
system which is sometimes called alum inophosphosilicate glass (APS in short).
The refractive index of APS glass depends on the concentrations of P and Al
oxides present therein. A P/AI molar ratio of 1:1 is known to yield a slight
decrease
of the refractive index of the glass because of the formation of aluminum
phosphate
(AIP04), having a negative molar refractivity. In practice, it is common for
the glass
host to feature an excess of phosphorus oxide in the region doped with active
ions.
Hence, the refractive index in this region is mostly determined by the
concentration
of excess phosphorus and ytterbium oxides. In some variants, the center core
region of the core may additionally include fluorine as an index-lowering
agent.
In turn, the concentrations of phosphorus and fluorine (if any) in the
peripheral core
region may be chosen so as to level the refractive index with that of the
center core
region while producing a substantial decrease of the temperature coefficient,
as
mentioned above. According to the data listed in Table 1, the molar
refractivities of
phosphorus and fluorine almost offset each other while both have negative
temperature coefficients. In some embodiments, about equal concentrations of
phosphorus and fluorine therefore allow for tailoring the temperature
coefficient of
the peripheral core region in a way such as to mitigate TMI in high power
fiber
lasers and amplifiers. Alternatively, an excess of phosphorus in the
peripheral core
region may be required to produce a uniform refractive index profile in the
core.
The specific concentration of phosphorus and fluorine not only depend on the
rare-
earth concentration in the center core region (e.g., ytterbium), but also on
the P/AI
molar ratio in the center core region and whether the reaction leading to the
formation of aluminum phosphate is complete.
Two distinct examples of active LMA optical fibers according to some
embodiments are discussed hereinafter. In both cases, an active LMA optical
fiber
doped with ytterbium and with a core numerical aperture NA of 0.065 is
considered.
In the first sample, the distribution of dopants over the core cross section
is
.. assumed to be similar to that shown in FIG. 6C. Ytterbium and aluminum are
found
only within the center core region whereas phosphorus and fluorine span the
full
Date Recue/Date Received 2022-06-09
22
extent of the fiber core. The molar composition in the center core region is
0.2Yb203-1.0E-2.8P205-1.4A1203-94.6Si02 while the molar composition in the
peripheral core region is 2.4F-4.2P205-93.4Si02. The number in front of each
chemical species refers to the molar concentration in mol% of the species. A
molar
ratio P/AI about 2:1 is found in the center core region, although the latter
could be
made as low as 3:2 and even 1:1 in the case where the concentration of
ytterbium
is large enough. Fluorine in the center core region is adjusted in accordance
with
the ytterbium concentration and the phosphorus not involved in the formation
of
aluminum phosphate so that the core NA = 0.065. Whether the addition of
fluorine
in the center core region is necessary depends on the P/AI molar ratio and the
core
numerical aperture. The concentrations of phosphorus and fluorine in the
peripheral core region were further adjusted so that the temperature
coefficient in
this region could be made about 20% lower than the temperature coefficient in
the
center core region and yet keep the refractive index uniform over the core
cross
section, as shown schematically in FIGs. 6A and 6B. In this case, the
phosphorus
concentration in the peripheral core region is about three times larger than
the
excess phosphorus in the center core region (i.e., the fraction of phosphorus
not
participating to the formation of aluminum phosphate). Also, the fluorine
concentration in the peripheral core region is about 2.5 times larger than the
fluorine concentration in the center core region.
FIG. 6D shows the distribution of dopants over the core cross section of the
second
fiber sample. Once again, ytterbium and aluminum are found only within the
center
core region, yet with concentrations higher than in the first sample, whereas,
unlike
the first sample, only phosphorus spans the full extent of the fiber core. The
molar
composition in the center core region is 0.3Yb203-4.2P205-2.8A1203-92.7Si02
while the molar composition in the peripheral core region is 4.2P205-95.8Si02.
A
molar ratio P/AI of about 3:2 is then found in the center core region in the
second
fiber sample. The 3:2 P/AI ratio means that more aluminum phosphate will
likely
form after the reaction involving aluminum and phosphorus oxides will take
place
and less excess phosphorus will remain thereafter. The absolute concentration
of
Date Recue/Date Received 2022-06-09
23
phosphorus in the center core region was nonetheless adjusted given the
ytterbium concentration and core numerical aperture so that the refractive
indices
of both the center core region and peripheral core region are nearly equal.
The molar compositions specified for the fiber samples mentioned above are
provided by way of example only and different molar compositions could yield
similar refractive index and temperature coefficient. The specific
realizations are
considered non-limiting and variations to the molar ratios discussed herein
are
considered within the scope of protection. In particular, the concentration
values of
dopants and co-dopants in various implementations will depend on the
concentration of rare earths and, in turn, on the confinement ratio (i.e., the
diameter
of the center core region relative to the core diameter) and the cladding
diameter.
The molar compositions specified hereabove correspond to a fiber with a 30/400
pm core/cladding diameter ratio and having a confinement ratio of about 0.7
(which
yield a cladding absorption near 0.5 dB/m at 915-nm wavelength). The ternary
diagrams for the refractive index and the temperature coefficient illustrated
in FIGs.
8A, 8B, 9A and 9B may serve to determine the concentrations of phosphorus,
fluorine and aluminum required in the distinct core regions to achieve the
desired
effect according to the invention disclosed herein. For instance, from the
ternary
diagram of FIG. 8A it can be seen that the temperature coefficient could be
further
reduced in the peripheral core region. The ranges of molar concentration used
in
the ternary diagrams were limited to molar compositions readily achieved using
conventional fiber fabrication means such as modified chemical vapor
deposition
and solution doping. Fabrication techniques like the molten core method and
the
stack-and-draw method, even if they are much less common, may nonetheless
make possible to produce molar compositions with greater co-dopant
concentrations and further decrease the temperature coefficient in the center
and
peripheral core regions. The molar compositions given herein may then be
adapted to yield fiber samples different from the fiber samples detailed
herein
without departing from the scope of the invention described herein.
Date Recue/Date Received 2022-06-09
24
Beside from the constituents of the core, the molar composition of the inner
cladding 30 may include one or more index-raising or index-lowering co-dopants
depending on the core refractive index and the core numerical aperture. The co-
dopants found in the inner cladding may be chosen so that the temperature
coefficient in that region will be greater than the temperature coefficient in
the
peripheral core region and perhaps even greater than that of the center core
region, as shown in FIG. 6B. While it is not essential, an inner cladding
having a
temperature coefficient larger than the temperature coefficient in the
peripheral
core region will further help in mitigating TMI. For instance, the inner
cladding may
assume the molar composition xF-yGe02-(100-x-y)Si02 where the molar
concentrations x and y will be chosen depending on the molar composition of
the
core. For the fiber samples considered in FIGs. 6A to 6D, the cladding of the
first
fiber sample consists of silica only (x = y = 0, see FIG. 6C) while the
cladding of
the second fiber sample has the molar composition 1.4Ge02-98.6Si02 (x = 0, see
FIG. 6D). Once again, the molar compositions are not unique and other dopants
could produce similar results.
As will be readily understood by one skilled in the art, the examples
described
above are provided for illustrative purposes only, and numerous features may
be
provided and/or combined in variants of the active LMA optical fiber described
herein, such as, for example:
(a) A fiber core including rare-earth dopants (ytterbium, erbium,
thulium and so
on) providing means for amplification of laser beams in several spectral bands
given the appropriate pump light is also available.
(b) Solutizer co-dopants (aluminum, phosphorus, and so on) included in the
core of the fiber and providing means for increasing rare earth solubility and
further
avoid clustering and photodarkening.
(c) Index-raising co-dopants (germanium, titanium) and index-lowering co-
dopants (fluorine, boron) providing means to tailor the refractive indices in
the core
and cladding(s) of the fiber.
Date Recue/Date Received 2022-06-09
25
(d) Multiple claddings surrounding the core and providing means to confine
the
pump light in the fiber. The claddings have thicknesses and refractive indices
appropriate for efficient launching of pump light given its power and
brightness.
(e) Stress-applying members (e.g., boron-doped silica rods) providing means
to maintain the light polarization along a linear axis given the induced
birefringence
in the fiber core.
(f) Frustoconical sections along the fiber with straight sections in-
between,
obtained by tapering the preform glass melt during fiber drawing, and
providing
means for adiabatic changes to the fiber core and resultant mode field.
Advantageously, embodiments of optical fiber as claimed herein could find
widespread use in high-power laser oscillators and/or amplifiers, from as low
as
100 W to as much as 10 kW output power, either with CW beams (single frequency
or multi-longitudinal mode) or light pulses (about 100-fs to 1-ps durations,
from
known chirped pulse amplification and Q-switching techniques). Coherent
combining of output beams from multiple amplification channels, each using
active
LMA optical fibers as disclosed herein, could be performed to scale the power
beyond the limit set by state-of-the-art laser amplifiers nowadays. Nonlinear
optical
crystals could be used with the invention disclosed herein for generating one
or
more laser frequency harmonics (2nd, 3rd, 4th and so on) in the near-infrared,
visible
and ultraviolet spectral bands. Nonlinear pulse compression could also be
performed with the optical fiber disclosed herein to generate high-order
harmonics
in the extreme UV or soft X-ray using a gas jet in a vacuum chamber inserted
downstream the nonlinear pulse compression stage.
Of course, numerous additional modifications could be made to the embodiments
described above without departing from the scope of protection as defined in
the
appended claims.
Date Recue/Date Received 2022-06-09
