Stimulated Raman scattering threshold for partially coherent light in silica fibers

Qinghua Li; Haitao Zhang; Xinglai Shen; Ping Yan; He Hao; Mali Gong

doi:10.1364/OE.23.028438

1. Introduction

The output power keeps growing dramatically with the rapid development of high power fiber lasers and amplifiers. In 2009, IPG Photonics reported a fiber amplifier system achieving single mode 10 kW cw output [1]. In 2014, a new record of the single mode output power was set to 20 kW [2]. For pulsed fiber amplifier systems, the peak power is approaching Mega-Watt order [3, 4 ] and the peak power intensity reaches more than 1 kW/µm² [5, 6 ]. Further power scaling is limited mainly on bulk and end face damage threshold of the fiber as well as the emerge of nonlinear effects like stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS) and self-focusing. Self-focusing depends on power, means that it takes place when the peak power exceeds the critical power. As a contrast, SRS and SBS depend on the power density and the effective interaction length of the signal and the pump light. Therefore, large mode area fibers and highly doped gain fibers can be used to alleviate SRS and SBS effects due to reduced optical intensity and shortened light propagation length. Besides, SBS can also be mitigated by increasing the wavelength bandwidth of signal light or shortening the optical pulse width to 1 ns level, since phonon lifetime is typically several nanoseconds [7]. SRS can be mitigated by increasing the propagation loss of the Raman wave in the micro-structured fibers with designed filter functions [8, 9 ],which however makes the fiber manufacturing process more complicated. It also introduces additional energy loss, which will decrease the system efficiency and feasibility. This makes SRS the most crucial bottleneck limit for achieving high peak power intensity.

However, it was mentioned in the theoretical works of A.T. George [10] and M. Bashkansky [11] that the reduced coherence of light would lead to considerable reduction of Raman gain. Thus it is possible to increase SRS threshold significantly by using partially coherent light. If it works, this method will be a promising scheme to further scale the peak power density to a higher level. In this paper, SRS evolution of partially coherent light is investigated both experimentally and theoretically.

2. Experiments

We performed a series of experiments to measure the SRS threshold of partially coherent light in passive fibers. The experiment setup is shown in Fig. 1 .

Fig. 1 Schematic diagram of the experimental setup for measuring SRS threshold of partially coherent light.

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The three-stage single-mode all-fiber amplifier system is seeded by a directly modulated superluminescent diode (SLD) source, which is partially coherent with central wavelength of 1050 nm and the 3 dB bandwidth of 53 nm. An 8-nm band-pass filter with central wavelength of 1064 nm is placed after SLD to narrow down the signal spectrum. The peak power of the seed is about 20 mW, and the width and repetition rate are tunable. To obtain higher peak power and enough pulse energy (the lower limit of our energy meter is 0.5 µJ), the pulse width is set to 200 ns (6 dB) with 1.5 kHz repetition rate. For each amplifier stage, 2 m Yb³⁺-doped SM fiber (6/125 µm, NA = 0.11) is used as the gain medium. The 976 nm pump LD with SM fiber pigtail is coupled into the Yb³⁺-doped SM fiber by WDM. The isolator is placed after each stage to prevent optical damage by the reflected light. ASE from each amplifier stage is filtered out with an 8-nm band-pass filter centered at 1064 nm except for the last stage. The output spectrum from the last stage shows an ASE suppression ratio of about 30 dB at full pump power, as shown in Fig. 2 . The influence on the SRS threshold measurement of the ASE from the last stage is negligible. A tap is placed between the exit of third stage amplifier and the entrance of the 500-meter-long passive fiber (core diameter 8.2 µm, NA 0.14) to detect the possible backward SRS light.

Fig. 2 Output spectrum from third stage amplifier at full pump power of P3 = 320 mW.

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The peak power P_peak is calculated according to $P_{p e a k} = \max (p (t)) E / \int p (t) d t$ by measuring the pulse shape curve p(t) with oscilloscope and pulse energy E using energy meter.

The output energy is 6 µJ and the peak power is close to 50 W after three stages of amplification. The signal pulse shapes before 500 m fiber (corresponds to position A in Fig. 1) are shown in Fig. 3 . The irregular pulse shape with a 3 dB pulse width of 67 ns and a 6 dB pulse width of 200 ns is due to the irregular electric current modulation of SLD. With higher pump power, another peak located at the front edge becomes notable due to gain saturation.

Fig. 3 Signal pulse shapes before 500 m fiber (position A) at pump power of P3 = 140 mW, 220 mW and 320 mW.

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At different pump powers, the signal pulse energies before and after the 500 m fiber (corresponds to position A and B in Fig. 1) and Raman pulse energy after 500 m fiber (position B) are measured as shown in Fig. 4 . The corresponding pulse shapes and spectra are recorded as shown in Figs. 5 and 6 , respectively. The signal pulse shapes are obtained by placing a 10-nm band pass filter with central wavelength of 1064 nm before the detector, and Raman pulse shapes are obtained by replacing the former filter with a 1100 nm long pass filter to filter out the signal wavelength. It can be seen from Figs. 5 and Fig. 6 that with pump power getting higher, pulse peak power is getting higher and SRS starts to grow quickly. At lower pump power e.g. P3 = 140 mW as shown in Fig. 5(a), no Raman light shows up in the pulse shape nor in the spectrum. At higher pump power, e.g. P3 = 220 mW as shown in Fig. 5(b), the signal pulse peak power is getting higher and reaches the SRS threshold. A dip can be seen on the output signal pulse at the peak power position and Raman pulse grows up. On the spectrum, the first-order SRS is significant, with central wavelength of 1117 nm. By keep increasing the pump power to P3 = 320 mW as shown in Fig. 5(c), the gain saturation leads to the quickly growing of the peak at the front edge, and this peak reaches the SRS threshold, too. Then two dips can be observed on the output signal pulse. And for the Raman pulse two peaks can be detected, which confirms the photon flux conservation during the signal-to-Raman conversion process. On the spectrum, the second-order Raman spectrum is observed, with central wavelength of 1173 nm. No backward SRS was observed on the tap.

Fig. 4 Signal and Raman pulse energies vary with pump power P3. Blue curve is for signal pulse energy before 500 m fiber (position A). Green curve is for signal pulse energy after 500 m fiber (position B). Orange curve is for SRS pulse energy after 500 m fiber (position B).

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Fig. 5 Input signal pulse shapes (purple) at position A, output signal pulse shapes (red) and output Raman pulse shapes (green) at position B at pump powers of (a) P3 = 140 mW, (b) P3 = 220 mW and (c) P3 = 320 mW.

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Fig. 6 Spectra after 500 m fiber (position B) at different pump powers.

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The SRS thresholds in experiments are compared with the classical SRS thresholds predicted by Eq. (1), which is modified from the threshold formula given by R.G. Smith. This modified formula includes in the SRS suppression ratio x, defined as power ratio of signal power to Raman power in dB which can be readily read out from measured spectrum. For example, from Fig. 6 we can see that at pump power of P3 = 180 mW, SRS suppression ratio x is approximately equal to 15.8 dB.

P_{c r} = (16 - \frac{x}{10} \ln (10)) \frac{K A_{e f f}}{g_{R} L_{e f f}} \frac{Δ ν_{R} + Δ ν_{p}}{Δ ν_{R}}

In Eq. (1), K is the polarization factor, i.e. K = 1 for linear polarization and K = 2 for random polarization. In the experiment, the light source from SLD is randomly polarized and all the optical components in the amplifier system are polarization independent. As a consequence, the output light from the third stage amplifier is also randomly polarized, which was confirmed by using a polarization extinction ratio meter. The extinction ratio was about 1 dB and the polarization angle changed rapidly and randomly. Thus K should be set to about 2 here. $A_{e f f}$ is the effective modal area, which can be calculated from formula [7] $A_{e f f} = {(\int \int_{- \infty}^{+ \infty} {| E (x, y) |}^{2} d x d y)}^{2} / \int \int_{- \infty}^{+ \infty} {| E (x, y) |}^{4} d x d y$ . For the 500 m passive fiber, its fundamental mode area is 39.5 µm² for 1064 nm. Effective fiber length L_eff can be calculated by formula $L_{e f f} = [1 - \exp (- α L)] / α$ , where fiber length L is 500 meters in the experiment and fiber loss coefficient α is measured to be 0.964 dB/km. Raman-gain coefficient g_R is 9.2 × 10⁻¹⁴ m/W and Raman gain bandwidth $Δ ν_{R}$ is 7.5 THz. The bandwidth for the 1064 nm Raman pump light $Δ ν_{p}$ and Raman suppression ratio x (dB) can be read out from the output spectrum after 500 m fiber. Then the corresponding theoretical critical power can be calculated by Eq. (1). To best fit with the experimental results, K factor is set to 1.9, which is very close to the random polarization K factor of 2. As shown in Fig. 7 is the SRS critical power P_cr vs. SRS suppression ratio x (dB). Solid circles represent theoretical predictions and solid triangles represent experimental data. The SRS critical power P_cr decreases with increased SRS suppression ratio (dB). It can be seen that for SRS suppression ratio greater than 15 dB, the experiment data agree with the theoretical predictions with maximum relative error of less than 2%. When SRS suppression ratio is less than 10 dB, Eq. (1) failed to give an accurate prediction. This is because Eq. (1) is derived under the assumption that the pump light will not be depleted by Raman light. However, when SRS is getting strong, i.e. SRS suppression is less than 10 dB, pump light depletion cannot be ignored, hence force Eq. (1) is no longer valid for SRS threshold prediction. A better threshold prediction formula can be derived by taking the pump light depletion into consideration.

Fig. 7 SRS critical power P_cr vs. SRS suppression ratio x (dB). Solid circles are for theoretical predictions. Solid triangles are for experimental data.

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The well-matched SRS threshold in experiments and the predictions by Eq. (1) implies that stimulated Raman scattering is independent on the phase status of the light. Therefore, partially coherent light does not help to break through the SRS limit. To understand the physical details, a theoretical model for SRS of partially coherent light in fibers is developed.

3. Theoretical study of SRS for partially coherent light in fibers

Raman process is depicted by nonlinear Schrodinger equations [7], which can be finally rewritten into the form of pump and Raman coupled wave equations. Equation (2) shows the one-dimensional time-dependent pump and Raman coupled wave equations. The instantaneous Raman response is assumed in Eq. (2), which is appropriate for Raman pump light with coherence time much longer than the Raman response time of ~0.1 ps, or in other words, the bandwidth of the partially coherent light is much narrower than 30 nm. A_i is the slowly varying envelope (footnote i = p or s, associating with the pump or Raman pulse), β_2i is GVD parameter, d is the walk-off parameter accounting for the group-velocity mismatch between the pump and Raman pulses and has a typically value of 2–6 ps/m, α_i is the fiber absorption coefficient, ϒ_i is the nonlinearity parameter, δ_R is Raman-induced index changes, f_R represents the fractional Raman contribution and g_i is the Raman-gain coefficient.

\begin{array}{l} \frac{\partial A_{p}}{\partial z} + \frac{i β_{2 p}}{2} \frac{\partial^{2} A_{p}}{\partial t^{2}} + \frac{α_{p}}{2} A_{p} = i γ_{p} [{| A_{p} |}^{2} + (2 + δ_{R} - f_{R}) {| A_{s} |}^{2}] A_{p} - \frac{g_{p}}{2} {| A_{s} |}^{2} A_{p} \\ \frac{\partial A_{s}}{\partial z} - d \frac{\partial A_{s}}{\partial t} + \frac{i β_{2 s}}{2} \frac{\partial^{2} A_{s}}{\partial t^{2}} + \frac{α_{s}}{2} A_{s} = i γ_{s} [{| A_{s} |}^{2} + (2 + δ_{R} - f_{R}) {| A_{p} |}^{2}] A_{s} + \frac{g_{s}}{2} {| A_{p} |}^{2} A_{s} \end{array}

However, in the complex amplitudes A_p and A_s in Eq. (2), the phase information for both pump and Raman pulses is in the form of exp(iφ), where φ is the phase of the light. This form is applicable for depicting the coherent light with certain phase φ rather than for the partially coherent light with only a statistical distribution of phase φ and no determinate phase φ. A.T. George [10] treated incoherent light as a sum of plenty of coherent light with different wavelengths and M. Bashkansky [11] employed mutual coherence function to deal with partially coherent light. Later there are mainly four approaches established to describe partially coherent light propagating in nonlinear media, namely, the propagation equation for the mutual coherence function, the coherent density method, the self-consistent multimode theory and Wigner transform method [12]. In 2003, M. Lisak et al. demonstrated that those four approaches are in fact equivalent [13, 14 ]. Wigner transform method describes the electric field by combining its temporal (or spatial) intensity distribution and temporal (or spatial) mutual coherence distribution, thus can easily describe the temporal (or spatial) coherent properties of the light beam. In this paper, Wigner transform method is used to study the stimulated Raman scattering of partially incoherent light.

Define 1-D Wigner transform function as Eq. (3), where the bracket $〈〉$ denotes taking statistical average to include the coherence properties of the light [15].

ρ_{i} (t, ω, z) = (\frac{1}{2 π}) \int_{- \infty}^{+ \infty} e^{i ω τ} 〈 A_{i}^{*} (t + \frac{τ}{2}, z) A_{i} (t - \frac{τ}{2}, z) 〉 d τ

The Wigner transform function

ρ_{i} (t, ω, z)

and the mutual coherence function

〈 A_{i}^{*} (t + τ / 2, z) A_{i} (t - τ / 2, z) 〉

form a Fourier pair. The distribution of ω describes the coherent properties of the beam in the time domain. For the light wave with the static statistical phase distribution, it satisfies

〈 A_{i}^{*} (t + \frac{τ}{2}, z) A_{i} (t - \frac{τ}{2}, z) 〉 = \sqrt{I_{i} (t + \frac{τ}{2}, z) I_{i} (t - \frac{τ}{2}, z)} \exp (- τ^{2} / τ_{c}^{2})

, where

I_{i} (t, z) = 〈 {| A_{i} (t, z) |}^{2} 〉

is the intensity distribution, τ_c is the coherent time. Therefore the Wigner transform method readily includes the coherence parameter τ_c in the light wave. By tuning this coherence parameter τ_c, we can investigate the dependence of SRS threshold on the coherence level of the pump light.

By utilizing Eq. (3), Eq. (2) can be rewritten as Eq. (4), which is in the Wigner-Moyal formalism. The sine and cosine operators are defined by their series expansions and the arrows indicate that the derivatives act to the left and right, respectively. Light intensity $〈 {| A_{i} |}^{2} 〉$ associates with Wigner transform function $ρ_{i} (t, ω, z)$ by $〈 {| A_{i} |}^{2} 〉 = \int_{- \infty}^{+ \infty} ρ_{i} (t, ω, z) d ω$ according to Eq. (3).

\begin{array}{l} \frac{\partial ρ_{p}}{\partial z} = β_{2 p} ω \frac{\partial ρ_{p}}{\partial t} - α_{p} ρ_{p} - 2 γ_{p} [〈 {| A_{p} |}^{2} 〉 \\ + (2 + δ_{R} - f_{R}) 〈 {| A_{s} |}^{2} 〉] \sin (\frac{1}{2} \frac{\overset{\leftarrow}{\partial}}{\partial t} \frac{\vec{\partial}}{\partial ω}) ρ_{p} - g_{p} 〈 {| A_{s} |}^{2} 〉 \cos (\frac{1}{2} \frac{\overset{\leftarrow}{\partial}}{\partial t} \frac{\vec{\partial}}{\partial ω}) ρ_{p} \\ \frac{\partial ρ_{s}}{\partial z} = (d + β_{2 s} ω) \frac{\partial ρ_{s}}{\partial t} - α_{s} ρ_{s} - 2 γ_{s} [〈 {| A_{s} |}^{2} 〉 \\ + (2 + δ_{R} - f_{R}) 〈 {| A_{p} |}^{2} 〉] \sin (\frac{1}{2} \frac{\overset{\leftarrow}{\partial}}{\partial t} \frac{\vec{\partial}}{\partial ω}) ρ_{s} + g_{s} 〈 {| A_{p} |}^{2} 〉 \cos (\frac{1}{2} \frac{\overset{\leftarrow}{\partial}}{\partial t} \frac{\vec{\partial}}{\partial ω}) ρ_{s} \end{array}

As instantaneous nonlinearity response is assumed, Winger-Moyal formalism is valid under the fundamental assumption of Gaussian statistics of the fields so as to expand higher-order moments into products of second-order moments and achieve a closure of the infinite hierarchy of moments equations inherent to the wave turbulence theory. As a consequence, Eq. (4) is justified in the weakly nonlinear regime, where nonlinear length $L_{n l} = 1 / γ P$ is much longer than dispersion length $L_{d i s p} = τ_{c}^{2} / β_{2}$ [16]. However, we can show that even without the assumption of Gaussian statistics of the fields, Winger-Moyal formalism is still applicable for modeling energy transfer between pump and Raman.

For an SLD-seeded fiber amplifier system, the partially coherent light pulse has a typical duration of sub ns or even longer. In general, the pulse consists of sub-pulses with time scale of $τ_{c}$ (coherent time) due to the random phase distribution. Shapes of the sub-pulses will be changed due to the second order dispersion and the coherent time will be shortened due to self- and cross-phase modulation by nonlinear effects. However, the distortion of sub-pulses does not affect the character of the macro pulse seen by the Raman pulse. There exists group velocity mismatch between Raman and pump light, which is described by the walk-off parameter $d$ with a typical value of 2-6 ps/m in silica fiber. Therefore, a walk-off distance for the sub-pulses defined as $L_{w a l k o f f} = τ_{c} / d$ will be much shorter than the dispersion length $L_{d i s p} = τ_{c}^{2} / β_{2}$ as long as the bandwidth is much narrower than 250 nm, which is already satisfied under the instantaneous Raman response assumption (coherent time is much longer than 0.1 ps). Thus the Raman light has experienced many sub-pulses of pump light before significant sub-pulse distortion shows up. Therefore, the Raman light sees the averaged pump light field in Raman process. As a consequence, Eq. (4) still gives meaningful results for Raman process when $τ_{c}$ is in ps or longer time range.

Equation (4) is complicated transcendental equations and difficult to solve analytically, therefore numerical calculation is used in this study to simulate the pulse evolutions of the linear polarized pump and Raman light in silica fibers. The central wavelength λ_p of the Raman pump light is set to 1064 nm, a typical value for high power fiber amplifier systems. λ_s is around 1117 nm for Raman light. Other parameters are set as β_2p = 23 × 10⁻²⁷ s²/m, β_2s = β_2pλ_p/λ_s, d = 2 × 10⁻¹² ps/m, α_i = 0, ϒ_p = 2πn ₂/λ_p, n ₂ = 2.6 × 10⁻²⁰ m²/W, ϒ_s = ϒ_pλ_p/λ_s, δ_R = 0, f_R = 0.18, g_p = 9.2 × 10⁻¹⁴ m/W and g_s = g_pλ_p/λ_s. Two cases for the Raman pump light are set in the simulations, namely, coherent and partially coherent cases. The Raman pump light in both cases has the same central wavelength, pulse shape and peak power, but different Fourier transform products. For coherent case, the pump light has a Fourier transform limited product in time domain, while for the partially coherent case it has hundreds times Fourier transform limited product. In the simulations, pump pulse is Gaussian-shaped and its pulse width is set to 1 ns defined at 1/e² power. Pulse peak power is 30 W. For the Fourier transform limited condition, the pulse coherent time is about 1 ns, and for the partially coherent case, the pulse coherent time is about 3 ps. In both cases, the light propagates in the same type of single mode (SM) fiber with a length of 300 m and a modal area of 40 µm². Figure 8 shows the simulation results by directly solving Eq. (2) for the coherent case. Figures 8(a)-8(d) are for input pump pulse evolution, Raman pulse evolution, output signal spectrum and output Raman spectrum, respectively. Figure 9 shows partially coherent case solved by Eq. (4). Figures 9(a) and 9(b) are for input pump pulse evolution and Raman pulse evolution, respectively, and subfigures Figs. 9(c), 9(d) and 9(e) are the Wigner transform function (WTF) distributions for input pulse, output signal pulse and output Raman pulse, respectively. By comparing signal and Raman pulse evolutions in Fig. 8 with those in Fig. 9, we can see that for both coherent and partially coherent cases, Raman pulses grow at the same rate (in the numerical accuracy) when the dependence of Raman-gain coefficient on bandwidth is ignored, which means SRS threshold is independent on the coherency of the pump pulse in the regime where Eq. (4) is valid. In a physical picture, it implies that the process of Raman only depends on photon flux, regardless of the relations of their phases, when $τ_{c}$ is in ps or longer time range. It is worth noting that the dispersions shown in Figs. 9(c)-9(e) are much smaller than it should be. This can be explained as it is the macro pulse envelope rather than sub-pulses that contributes to the dispersion term under the Wigner-Moyal formalism. The skewed deformation of the spectrogram along the t-axis is expected if sub-pulses are considered [17].

Fig. 8 Coherent light pulse width of 10 ns, peak power of 30 W evolves in SM fiber with length of 300 m. (a) Input pulse evolution (b) Raman pulse evolution (c) Output signal spectrum (d) Output Raman spectrum.

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Fig. 9 Partially coherent light with coherent time of 3 ps, pulse width of 1 ns, peak power of 30 W evolves in SM fiber with length of 300 m. (a) Input pulse evolution (b) Raman pulse evolution (c) WTF distribution for input pulse (d) WTF distribution for output signal pulse (e) WTF distribution for output Raman pulse.

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Pulse evolutions with other coherent status (still in the range of $τ_{c}$ ) 0.1 ps) are also examined and give the same conclusion that coherency does not affect SRS threshold, except that the spectrum of the pulse is broad enough so that the Raman coefficient decreases significantly by a factor of $(Δ ν_{R} + Δ ν_{p}) / Δ ν_{R}$ . Therefore SRS threshold formula for light with coherent time in ps or longer time range can be expressed by the classical SRS threshold formula Eq. (1), as has been demonstrated in the previous experiments. For light with coherent time in fs range, noninstantaneous response of the nonlinearity should be in included in the theory, and the appropriate description is provided by a weak Langmuir turbulence kinetic equation [16].

4. An illustration for SRS threshold application

Nonlinear effects occur as the peak power is high, leading to detrimental effects in the amplifier. It is common that an initial flat-top pulse evolves into a pulse shape with notable leading edge due to gain saturation, which prevents the further amplification. Here we give an illustration of utilizing SRS threshold to eliminate pulse peak at the leading edge and obtain a flat top pulse suitable for further pulse amplification. By using a proper Raman medium, the energy in the peak at the leading edge will be red-shifted due to the SRS process (which can be easily filtered out), while the main part of the pulse keeps unaffected, leading to a maintained flat-top pulse shape for further amplification. The experiment setup is the same as shown in Fig. 1, whereas the previously used SLD with an irregular pulse shape is replaced by a SLD with flat-top pulse shape and the 500 m fiber is replaced by another proper Raman medium. After the three-stage amplifier system, the pulse shape is distorted and with a notable leading edge due to gain saturation as shown in Fig. 10 (blue curve). The peak power of the leading edge was 4.79 W and the power of the flat-top part is 3.78 W. This pulse was sent into a 5139-meter-long 9/125 communication fiber, where the power at the leading edge will lead to 6 dB SRS suppression and the power of the flat top will lead to 20 dB SRS suppression according to Eq. (1). Figure 10 shows the signal pulse shape before and after leading-edge peak elimination by SRS effect. It can be clearly seen that the peak at the leading edge has been successfully eliminated by SRS effect. The experimental results demonstrated that if Raman threshold is known, stimulated Raman scattering can be used to flatten pulse to benefit further amplification.

Fig. 10 Pulse shapes before and after leading-edge peak elimination by SRS. Blue is for input pulse with a leading-edge peak by gain saturation. Orange is for output pulse after peak elimination by SRS.

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5. Conclusion

The Raman threshold of partially coherent light is explored in both theory and experiments. It is found that the Raman threshold only depends on photon flux, i.e., it does not depend on the phase relation-ship between pump and Stokes waves when $τ_{c}$ is in ps or longer time range. An instantaneous Raman response model based on the Wigner-Moyal formalism is developed to describe the Raman process. For a typical 1 µm partially coherent light with bandwidth much narrower than 30 nm, the instantaneous Raman response assumption is valid. There is significant walk-off between sub-pulses of pump and Raman light, so that the Raman light sees the averaged pump light field during Raman process. Therefore, sub-pulses are neglected in this model, which makes the description of dispersion inaccurate. However, it can give good predictions on Raman threshold, which agrees well with experiment data. As an illustration for SRS threshold application, a practical method for pulse peak elimination by SRS effect is put forward and demonstrated in experiment.

Acknowledgments

This research was supported by the National High Technology Research and Development Program of China, the National Natural Science Foundation of China (NSFC) (Grant No. 61475081), and the State Key Laboratory of Tribology, Tsinghua University (SKLT11B05).

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Stimulated Raman scattering threshold for partially coherent light in silica fibers

Abstract

1. Introduction

2. Experiments

3. Theoretical study of SRS for partially coherent light in fibers

4. An illustration for SRS threshold application

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (10)

Equations (4)

Optics Express