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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 10 — May. 7, 2012
  • pp: 11407–11422
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Origin of thermal modal instabilities in large mode area fiber amplifiers

B. Ward, C. Robin, and I. Dajani  »View Author Affiliations


Optics Express, Vol. 20, Issue 10, pp. 11407-11422 (2012)
http://dx.doi.org/10.1364/OE.20.011407


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Abstract

We present a dynamic model of thermal modal instability in large mode area fiber amplifiers. This model allows the pump and signal optical intensity distributions to apply a time-varying heat load distribution within the fiber. This influences the temperature distribution that modifies the optical distributions through the thermo-optic effect thus creating a feedback loop that gives rise to time-dependent modal instability. We describe different regimes of operation for a representative fiber design. We find qualitative agreement between simulation results and experimental results obtained with a different fiber including the time-dependent behavior of the instability and the effects of different cooling configurations on the threshold. We describe the physical processes responsible for the onset of the instability and suggest possible mitigation approaches.

© 2012 OSA

1. Introduction

To investigate this possibility we introduce a model wherein the optical intensity field is governed by the propagation and interference of two transverse modes under the perturbing influence of the thermal index variation and gain distribution throughout the fiber. The thermal distribution evolves according to the time dependent heat equation while the gain distribution is determined using two-level rate equations. We assessed this to be the simplest reasonable scheme for investigating the plausibility of this mechanism. A description of this model follows after which some example calculations are presented. We then qualitatively compare the predictions of the model with experimental observations. Finally we comment on possible mitigation techniques revealed by our results.

2. Model

Our model begins with the scalar paraxial optical wave equation valid for weakly-guiding large mode area fibers given by Eq. (1):
iψz=12k[t2k2+n(x,y)2k02]ψ
(1)
where ψis the scalar field amplitude, kis a suitably chosen wave vector magnitude, t2 is the transverse Laplacian operator, n(x,y)is the refractive index distribution, and k0=2πν/cis the vacuum optical wave vector magnitude. If we now set ψ/z=0the solution of the eigenproblem given by Eq. (2)
[t2β02+n(x,y)2k02]ϕ0(x,y)=0
(2)
yields the stationary mode field profile ϕ0(x,y)and propagation constant β0. Additionally we impose the normalization condition on ϕ0 given by Eq. (3)
Ω|ϕ0|2dxdyϕ0|ϕ0=1
(3)
where Ω represents the fiber cross section. We now look for a higher-order mode ϕ1(x,y),β1satisfying Eq. (4) such that

12β0[t2β02+n(x,y)2k02]ϕ1(x,y)=Δβϕ1.
(4)

Substituting β02=β12+(β02β12)and invoking Eq. (2) modified to describe ϕ1(x,y) andβ1 reveals that β12=β022β0Δβwhich constitutes a somewhat non-standard yet deliberate definition of Δβ. The field evolution along the fiber is then given by Eq. (5)
ψ(x,y,z)=c1ϕ1(x,y)exp[iΔβz]
(5)
where we have introduced the complex field amplitude c1. Allowing slow variation of the field amplitudes with zwe arrive at a general expression for the scalar field representing the propagation of two transverse modes given by Eq. (6):

ψ(x,y,z)=c0(z)ϕ0(x,y)+c1(z)ϕ1(x,y)exp[iΔβz]
(6)

The coefficients ciare normalized such that the signal optical intensity field is given by Is=|ψ|2in which case the power in the modes is given by Pi=|ci|2. To study the effect of thermally induced index variations on the evolution of the coefficients we introduce them perturbatively such that n(x,y,z)=n0(x,y)+T(x,y,z)(dn/dT). Furthermore, laser gain is introduced locally so as to increase the optical intensity according to the usual two-level rate equations. We neglect resonantly-induced refractive index changes [9

9. A. A. Fotiadi, O. L. Antipov, and P. M’egret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (Intec, 2010), 209–234.

] since we are focusing on operating regimes for which these changes are much smaller than the thermally-induced ones. Invoking Eq. (1), Eq. (2), Eq. (4) and Eq. (6) leads to the equation for the evolution of the field
iψz[n0(x,y,z)T(x,y,z)k02β0dndT+ig(x,y,z)2]ψc1Δβϕ1exp(iΔβz)
(7)
where the higher order term in the index perturbation has been neglected. Substituting Eq. (6) into Eq. (7) yields
ic0zϕ0+ic1zϕ1exp[iΔβz][k0TdndT+ig2][c0ϕ0+c1ϕ1exp(iΔβz)]
(8)
where we have further approximated k0n0(x,y,z)β0. This approximation is valid for weakly guiding fibers with little index variation across the core. Multiplying Eq. (8) by each mode profile ϕi, integrating both sides of the equation over the fiber cross-section and invoking the orthogonality of the two modes yields a coupled set of differential equations for the amplitudes
ic0z=ϕ0|δH|ϕ0c0+ϕ0|δH|ϕ1exp(iΔβz)c1
(9a)
ic1z=ϕ1|δH|ϕ1c1+ϕ1|δH|ϕ0exp(iΔβz)c0
(9b)
where the expression forδHis given by Eq. (10)

δHk0T(x,y,z)dndT+ig(x,y,z)2.
(10)

This model thus accounts for both intra and intermodal non-linear phase modulation and gain. The first term on the right hand side of Eq. (9a)-(9b) represents the change in optical length of the fiber as its temperature changes as well as the optical gain of the modes. The second term represents the resonant energy transfer between the two as well as inter-modal laser gain. The choice of β0as the reference wavevector for the slowly varying envelope approximation may lead to a breakdown in the accuracy of the solutions of Eq. (9a)-(9b) in the presence of a large thermal gradient. To mitigate this possibility we apply a variable transformation given by Eq. (11)
ci(z)=c˜i(z)exp[i0zκ(z)dz]
(11)
to Eq. (9a)-(9b) leading to the equations for the transformed amplitudes
ic˜0z=[ϕ0|δH|ϕ0κ(z)]c˜0+ϕ0|δH|ϕ1exp(iΔβz)c˜1
(12a)
ic˜1z=[ϕ1|δH|ϕ1κ(z)]c˜1+ϕ1|δH|ϕ0exp(iΔβz)c˜0
(12b)
where κ(z)is chosen to minimize the local self-phase modulation along the fiber taking into account the thermal gradient. Alternatively we could have decreased the longitudinal grid spacing to accurately approximate the increasing strength of the phase fluctuations. This transformation effectively locally optimizes the reference wavevector throughout the fiber length in the presence of thermal gradients.

The deliberate choice to include only two modes in the description of the optical field limits the ability of the model to treat cases where the index profile changes appreciably over the length of the fiber. An arbitrary number of modes may be added to our model in the future to treat such cases. Including the LP02 mode in particular would enable the model to treat fibers with a thermally-induced shrinking mode field diameter [10

10. F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997. [CrossRef] [PubMed]

]. No power loss results from this limitation however because the resonant coupling terms in Eq. (12a)-(12b) conserve total power.

To solve E Eq. (12a)-(12b) both the temperature and gain distributions throughout the fiber must be known. The thermal distribution evolves according to the time dependent heat equation given by Eq. (13)
Tt=KCρ2T+QCρ
(13)
with appropriate boundary conditions. Quantum defect heating is assumed to be the sole contributor to the heat load Q. The gain within the doped region of the fiber is given by
g=N2σesN1σas
(14)
where the population densities Niin Eq. (14) are determined by the equilibrium solution to the two level rate equations and the quantum defect heating is given by Eq. (15)

Q=N2σes(νpνs1)Is.
(15)

It is important to note that the population densities and therefore the gain, heating, and temperature vary throughout the fiber as well as in time. We have neglected laser dynamics in our treatment on the grounds that we are primarily considering optical pump and signal intensities far above their respective saturation intensities such that the populations are assumed to reach equilibrium on a time scale smaller than that describing the thermal variations within the fiber.

3. Modeling results

We model a large mode area photonic crystal fiber (PCF) with a pump cladding diameter of 170 µm, an outer cladding diameter of 400 µm, and doping concentration of 3.5 × 1025 m−1 which results in a device length of approximately 1.6 meters. This type of fiber is comparable in mode area and device length to some studied previously [4

4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218. [CrossRef] [PubMed]

,5

5. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258. [CrossRef] [PubMed]

,7

7. C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440. [CrossRef] [PubMed]

,8

8. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965. [CrossRef] [PubMed]

]. The large mode area results in a relatively long beat length between the two transverse modes. The beat length is the primary length scale that drives the longitudinal grid resolution requirement. The modeled fiber has a 7-cell core design resulting in a doped area that is somewhat smaller than the overall core area. The fiber has a pitch of 25 µm and an air hole diameter of 5.2 µm resulting in a mode field area of 2773 µm2 for the fundamental LP01 mode and 2939 µm2 for the LP11 mode as shown in Fig. 1
Fig. 1 Photonic crystal fiber design (a), LP01 mode field profile (b) and LP11 field profile (c).
. The beat length between these two modes in the absence of thermally induced index change is 22.6 mm.

Our model describes a wide range of amplifier configurations. In this initial work we consider only counter-pumped configurations with 47.5 Watts of input power in the LP01 mode and 2.5 Watts of input power in the LP11 mode both inputs being monochromatic. To save the need to time-step throughout the entire warm up period, which can be several seconds, we first solve the time-independent heat equation for the thermal distribution assuming all of the power is in the LP01 mode before adding in the LP11 power and allowing time to evolve. We have established that this method of initiating the simulation gives the most rapid approach to conditions conducive to equilibrium. Figure 2
Fig. 2 Propagation distance dependence of the powers of the LP01 and LP11 modes after a time of 60 ms (a, c, e) and the output power in each mode as a function of time (b, d, f) for pump powers of 380, 636, and 952 Watts for a convectively-cooled amplifier. The media show the evolution over time from 0 to 60 ms (a [Media 1], c [Media 2], e [Media3]).
shows results for three different pump powers with convective cooling at the boundary at a uniform 200 W/m2K. The time step used was 40 µs and the spatial grid spacing was 111 µm in the longitudinal direction and 5.5 µm in the transverse direction. These were varied to ensure the numerical convergence of representative simulations. These values resulted in a spatial numerical grid with 7.9 × 107 points.

Figure 2(a)-2(b) describe the behavior of the amplifier when pumped with 380 Watts. As shown in the embedded movie (Media 1), during the initial transient behavior power transfers from the LP01 to the LP11 mode. This coupling requires the phase of the optical intensity to lag the phase of the temperature variations in a particular region of the fiber [6

6. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180. [CrossRef] [PubMed]

]. This is made possible by the fact that the optical phase can change much faster than the temperature phase. The optical phase shift at a given point in the fiber relative to the phase at the fiber entrance is accumulated throughout the fiber length. Therefore the relative phase change, and hence the coupling behavior, is strongest at the output end of the amplifier. The direction of the power transfer depends on the size of the phase shift. For shifts less than π radians, power couples from the LP11 to the LP01 mode while for shifts greater than π radians, power couples in the reverse direction. Thus for a monotonically increasing optical phase shift, power transfers back and forth between the modes as the local phase passes multiples of π as the signals propagate down the amplifier. According to this picture, once the temperature distribution reaches equilibrium with the optical phase, no coupling will be possible and the LP01 mode will dominate the output as shown in Fig. 2(a)-2(b).

An additional feature is rapid temporary coupling of power between the modes at a spatial frequency corresponding to the inter-modal beat length. This rapid temporary coupling occurs because the effect of the local optical intensity on the temperature is mediated through the heat equation and the laser rate equations rather directly through the intensity. This leads to a coupling constant that reverses sign within one period of the induced grating. Previously published work has shown that no such temporary coupling exists where the index changed is caused purely by the non-linear refractive index [5

5. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258. [CrossRef] [PubMed]

]. Another important feature of this rapid coupling is that it apparently does not depend on a particular thermo-optic phase shift because it remains present even for amplifiers below the instability threshold that reach equilibrium as shown in Fig. 2(a) and Fig. 4(a)
Fig. 4 Propagation distance dependence of the powers of the LP01 and LP11 modes after a time of 60 ms (a, c, e) and the output power in each mode as a function of time (b, d, f) for pump powers of 500, 1060, and 1750 Watts for a conductively-cooled amplifier. The media show the evolution over time from 0 to 60 ms (a [Media 4], c [Media 5], e [Media6]).
.

Figure 2(e)-2(f) describe the amplifier with 952 Watts of pump. Very interestingly, the amplifier appears to reach equilibrium with most of the power in the LP11 mode. We chose these power levels to demonstrate three different behavior regimes. To accurately determine the rapidity of the onset of the instability we would need to run the simulation for longer times. For all configurations the total amplifier output is steady in time in agreement with experimental observations [4

4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218. [CrossRef] [PubMed]

]. We did not study the convectively-cooled amplifier at pump powers higher than 952 Watts because the maximum temperature of the fiber in this last case approached 500 °C which is probably as high as and perhaps higher than such amplifiers should sustain. We have indeed observed instability in simulations of convectively cooled amplifiers at higher powers that exhibited intolerable fiber core temperatures. Figure 3
Fig. 3 Temperature profiles at the end of the 60 ms simulation for the convectively-cooled amplifier with 952 Watts pump within planes passing through the center of the fiber core. Temperature is in °C with respect to the temperature of the cooling medium.
shows the temperature profile at the end of the 60 ms simulation for the 952 Watt pump case. We observe that the variation in the profile due to the inter-modal beating is small compared to the overall temperature profile.

Figure 4(c)-4(d) describe the behavior of a conductively-cooled amplifier pumped at 1060 Watts. One of the interesting features of this simulation is the presence of an apparent temporary equilibrium with most of the power in the LP11 mode at the amplifier output followed by a rapid transition to an oscillatory behavior with most of the power in the LP01 mode. As the pump power is increased, these oscillations increase in amplitude until they cause a transition to dynamic full-depth oscillation between the modes at the output shown in Fig. 4(e)-4(f) which describe the amplifier when pumped with 1750 Watts.

4. Experimental results

Figure 7
Fig. 7 Experimental setup of counter-pumped PCF amplifier. A three stage amplifier system was utilized to provide approximately 30 Watts of seed power. An image of the beam was captured using a commercial M2 beam analyzer. The phase modulator was not utilized in the single-frequency experiments.
depicts the experimental setup. The NPRO provided 10 mW of continuous wave seed power with a nominal linewidth of a few kHz that was subsequently amplified using a four stage amplifier chain the final stage of which consisted of the counter-pumped PCF amplifier. For the single-frequency studies, the phase modulator shown in the Fig. 7 was not used. Our measurements indicated that ~30 W of the 50 W of third-stage output power was coupled into the PCF core. We used fiber-coupled diode stacks to launch up to about 1 kW of ~976 nm pump into the 10 meter length of PCF. Investigation into the thermal dependence of the phenomena was prompted by a comparison this fiber design to commercially available fibers used in high power fiber amplifiers. The 976 nm pump absorption of this fiber is at least twice that of 25/400 step index or 40/400 photonic crystal fibers. As such, the heat deposition per unit length is much higher in the fiber discussed here relative to other fiber designs.

A comparison of M2 as a function of signal output power was performed for a fiber amplifier under a second cooling condition. The fiber was conductively cooled with an aluminum ring, as shown in Fig. 8
Fig. 8 Conductively cooled fiber amplifier setup. The seed laser is input from the left, where the fiber is held in a water-cooled chuck. The output end of the fiber departs the aluminum ring on the right and is held in a water-cooled chuck.
. Water-cooled plates were affixed to the aluminum ring to improve cooling of the fiber. Approximately 2.5 meters of fiber, near the seed input end, was taken off the ring and suspended in air.

Finally, we conducted a study to capture the time-dependent behavior of the output signal. It is known that low-speed cameras such as the one used for the M2 studies presented above are not fast enough to capture the time dynamics of the energy transfer between the LP01 and LP11 modes [12

12. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572. [CrossRef] [PubMed]

]. To increase the time resolution we focused a sample of the output beam into a single-mode fiber and monitored the output using a fast photodiode detector. The output from the fiber is proportional to the power in the fundamental mode. The trace of the output power in time is shown in Fig. 11
Fig. 11 Time series output (a) and frequency spectrum (b) of the fiber-coupled fast photodetector measuring the output of the PCF amplifier showing periodic oscillatory behavior. The output power was 500 Watts.
exhibiting oscillations with frequencies on the order of several kHz. This trace was obtained near the threshold of 500 Watts and indicates that the amplifier was operating in the intermediate instability regime.

5. Mitigation strategies

6. Conclusion

Acknowledgments

This work was supported in part by a grant of computer time from the DoD High Performance Computing Modernization Program at Air Force Research Laboratory DoD Supercomputing Resource Center, Wright-Patterson Air Force Base, OH. The authors gratefully acknowledge the High Energy Laser Joint Technology Office, the Air Force Research Laboratory and the Laser and Optics Research Center at the United States Air Force Academy for support. The views expressed in this article are those of the authors and do not reflect the official policy or position of the US government or the Department of Defense.

References and links

1.

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240.

2.

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656. [CrossRef] [PubMed]

3.

M. Laurila, M. M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability,” Opt. Express 20(5), 5742–5753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742. [CrossRef] [PubMed]

4.

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218. [CrossRef] [PubMed]

5.

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258. [CrossRef] [PubMed]

6.

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180. [CrossRef] [PubMed]

7.

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440. [CrossRef] [PubMed]

8.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965. [CrossRef] [PubMed]

9.

A. A. Fotiadi, O. L. Antipov, and P. M’egret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (Intec, 2010), 209–234.

10.

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997. [CrossRef] [PubMed]

11.

C. Robin and I. Dajani, “Acoustically segmented photonic crystal fiber for single-frequency high-power laser applications,” Opt. Lett. 36(14), 2641–2643 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-14-2641. [CrossRef] [PubMed]

12.

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572. [CrossRef] [PubMed]

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4480) Lasers and laser optics : Optical amplifiers
(140.6810) Lasers and laser optics : Thermal effects
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 19, 2012
Revised Manuscript: April 26, 2012
Manuscript Accepted: April 26, 2012
Published: May 3, 2012

Virtual Issues
June 11, 2012 Spotlight on Optics

Citation
B. Ward, C. Robin, and I. Dajani, "Origin of thermal modal instabilities in large mode area fiber amplifiers," Opt. Express 20, 11407-11422 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11407


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References

  1. C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .
  2. T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 . [CrossRef] [PubMed]
  3. M. Laurila, M. M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability,” Opt. Express 20(5), 5742–5753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742 . [CrossRef] [PubMed]
  4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 . [CrossRef] [PubMed]
  5. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 . [CrossRef] [PubMed]
  6. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180 . [CrossRef] [PubMed]
  7. C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 . [CrossRef] [PubMed]
  8. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965 . [CrossRef] [PubMed]
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