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In this paper, we report on cascaded Raman scattering (RS) in a highly germanium-doped silica fiber (HGDF) pumped by a picosecond pulsed master oscillator power amplifier (MOPA) system at 1064 nm in the normal dispersion regime. Benefited by the higher Raman gain of germanium (GeO2) than silica in the core, the length of the HGDF is only several meters. The broadest output spectrum comprises of 10 orders Raman stokes waves and eventually evolves into a supercontinuum (SC) spanning from 1000 to beyond 2100 nm with an output average power up to Watt scale. To the best of our knowledge, this is the first time to obtain such a broad cascaded RS spectrum in a short length of GeO2-doped step index silica fiber. We also numerically investigate the propagation of picosecond pulses in this HGDF based on the generalized nonlinear Schrödinger equation (GNLSE) which includes most of the dispersive and nonlinear effects, and the simulation results are in fairly good agreement with our experiments. It is believed that the numerical approach adopted in this paper is very beneficial for designing customized cascaded Raman fiber lasers before experimental implementations.
©2013 Optical Society of America
1. Introduction
Raman scattering (RS) effect has attracted a lot of attention due to its large potential applications in broadband optical amplifiers, tunable lasers, telecommunications, spectroscopy, metrology and medical imaging. The physical mechanisms underlying RS effect in optical fibers are now generally well understood [1, 2]. As a rule of thumb, RS happens when the optical fiber is pumped by a laser in the normal dispersion regime with a pump power higher than the Raman threshold, resulting in energy transfer from the pump towards a frequency down-shifted Stokes wave [3–6]. With the increasing of the pump power beyond the Raman threshold, what are known as second, third, fourth and even higher-order Stokes waves can be excited [7], called cascaded RS, corresponding to an output RS spectrum with discrete Stokes peaks by 13.2 THz Stokes frequency shift in silica and germanium (GeO2) [8].
There are a lot of studies reported on the cascaded RS effect since Cohen and Lin reported 6 cascaded Raman peaks beyond 1.6 μm in a 176 m long step index silica ðber pumped by a Nd:YAG laser operating at 1064 nm [9]. By using a 1 m length of hydrogen-filled hollow-core photonic crystal fiber a three-octave Raman spectral comb spanning from 325 nm to 2.3 μm was generated where the hollow-core photonic crystal fiber has a transmission window spanning from UV to mid-IR [10]. Despite the highly multimode nature of the pump laser, over two octaves cascaded RS covering from 523 to 1750 nm was acquired in a 1 km long graded-index multimode optical fiber and substantial beam cleanup was observed [3]. An all-normal dispersion all-fiber laser system was built with pump at 1064 nm to provide picosecond pulses at 7 different Stokes orders between 1 and 1.6 μm in a 500 m long Raman fiber [6]. Also an all-fiber laser system was put forward to provide a cascaded Raman wavelength shifting from 1.53 to 2.41 μm in the mid-infrared range using a 50 m long of silica fiber [11]. The cascaded RS effect could also be observed in fibers made of soft glasses, such as chalcogenide [12] and tellurium [13] with Stokes frequency shift of 7.5 and 20 THz, respectively. By using a 1.3 m long highly nonlinear tellurite microstructured fiber pumped by a 1064 nm fiber laser with pulse width of 15 ps, a five-order stimulated RS and supercontinuum (SC) generation covering from 730 to 1700 nm was obtained [13]. In 2010, three-order cascaded RS spectra located at 2092, 2205 and 2330 nm were observed in a 4.5 m long piece of microstructured chalcogenide fiber with the pump wavelength of 1995 nm in the normal dispersion region of the fiber [14]. It is expected that the output spectrum of cascaded RS can be extended far into the mid-infrared wavelength using these soft glasses fibers. From above, we find that the lengths of soft glasses fibers are of only several meters which are much shorter than the silica fibers of tens or hundreds of meters. In a short silica fiber, how to achieve broad cascaded RS spectrum is still fascinating and interesting.
In this paper, firstly we experimentally investigate the generation of up to 10 orders cascaded RS spanning from 1000 to beyond 2100 nm in a 10 m long commercial highly GeO2-doped silica fiber (HGDF) by pumping in the normal-dispersion regime with a picosecond pulsed fiber laser at 1064 nm. Then, we employ the generalized nonlinear Schrödinger equation (GNLSE) [15] to simulate the process of cascaded RS instead of a simplified model [16] based on a rate equation describing only the energy transfer among pump and different Stokes pulses. The GNSLE includes most of the dispersive and nonlinear effects which are indispensable to study rigorously the nonlinear propagation and cascaded RS generation of high peak power pulses in fibers. In the end, we discuss the essential conditions for cascaded RS generation in optical fibers and conclude that the numerical approach adopted in this paper is instructive and helpful for designing a cascaded Raman fiber laser.
2. Experimental setup and results
2.1 Experimental setup
The scheme of the all-fiber experimental setup is shown in Fig. 1(a) which comprises a two-stage fiber master oscillator power amplifier (MOPA) system at 1064 nm and a piece of commercially available HGDF. The seed of the MOPA system has a central wavelength of 1064 nm which is obtained from an Ytterbium-doped ðber laser passively mode-locked by a semiconductor saturable absorber mirror (SESAM). The seed is then amplified by a two-stage Ytterbium-doped fiber amplifier (YDFA). The experiment uses a 6 m length of double clad Ytterbium-doped fiber with core/cladding diameter of 10/130 μm as the gain medium in the second stage YDFA followed by an optical Isolator (ISO), a residual pump stripper and a piece of passive double clad fiber (DCF) which has a core/cladding diameter of 10/125 μm. The HGDF has a core/cladding diameter of 2.5/125 μm together with a deposited inner cladding with diameter of 8 μm designed for ease of splicing. There is an extremely high GeO2 concentration of ~38mol% in the fiber core resulting in an ultra-high core numerical aperture of 0.41. The HGDF is spliced with the passive DCF by using a fusion splicer with a repeated arc discharges to compensate the splicing loss, and finally about ~12% splicing loss is achieved. The propagation loss curve of the HGDF and the cross section of the HGDF are shown in Fig. 1(b).
Fig. 1 (a) The experimental setup and (b) The propagation loss curve of the HGDF, the inset shows the cross section of the HGDF.
Figure 2 plots the calculated chromatic dispersion profile β2 and the effective area Aeff of the fundamental mode in the HGDF via fully-vectorial finite element method [17]. The characteristics of single mode silica fiber (SMF-28) are provided for comparison. The HGDF used in this paper has two remarkable properties that make it particularly suitable for cascaded RS generation [3]. Firstly, the zero dispersion wavelength of the HGDF is beyond 2.8 μm as shown in Fig. 2(a), enabling normal dispersion for the entire near-infrared region [11]. Secondly, the relatively high GeO2 concentration in the fiber core [8, 11, 18] results in a high Raman gain. The Aeff of the HGDF at 1064 nm is only ~5 μm2 which is very small and beneficial for forward RS, and the corresponding calculated pump power threshold for the first order Stokes wave (S1) is only ~20 W for 10 m of HGDF given by Pth = 16Aeff/gRLeff [1, 7], where gR represents the Raman gain coefficient of GeO2 in the fiber core and Leff is the effective length of the HGDF defined by Leff = [1-exp(-αL)]/α, where α represents the fiber loss at the pump wavelength, L is the fiber length.
Fig. 2 (a) The chromatic dispersion profiles and (b) effective areas of the fundamental mode of the HGDF and SMF-28.
The temporal characteristics of the mode-locked picosecond pulses are shown in Fig. 3 (a), where the seed pulses train is measured by a 1.2 GHz InGaAs detector with ~100 ps rise time (DET01CFC/M, Thorlabs) and the signal pulse shape is measured by an autocorrelator (FR-103XL, Femtochrome), both signals are monitored by a sampling digital oscilloscope with 1.5 GHz bandwidth. The seed pulse has a measured single pulse width (FWHM) of ~8.3 ps with repetition rate of 32 MHz. The output power of seed oscillator is ~9 mW, and it is increased to 77.5 mW after the first stage YDFA. In the second stage YDFA the output average power of the pulses is further scaled with a slope efficiency of 36.6% as shown in Fig. 3(b), maximum output power of 2.6 W is obtained with 7.59 W pump power at 976 nm which corresponds to an output pulse peak power of ~10 kW. Considering ~12% splicing loss between the passive DCF and the HGDF, the peak power coupled into the HGDF is ~8 kW.
Fig. 3 (a) Temporal characteristics of the mode-locked seed laser, and the inset shows the measured seed pulses train. (b) The 1064 nm signal power versus the incident 976 nm pump power in the third-stage YDFA. (c) Output spectra of the amplified 1064 nm pulses, and the inset provides the detailed SPM-induced spectral broadening. The value in the legend of (c) means the pump power at 976 nm.
Figure 3(c) shows the output spectra of the amplified 1064 nm picosecond pulses after the pump stripper in the MOPA system examined by an optical spectrum analyzer (OSA) (Yokogawa, AQ6370) with spectral resolution of 1 nm. There is a low ASE pedestal around the signal wavelength when the pump power is less than 3.36 W. Obviously, with the increasing of the pump power self-phase modulation (SPM) induced spectral broadening around the signal wavelength is observed as shown in the inset of Fig. 3(c). Further, when the pump power is higher than 6 W, significant first order Stokes waves (S1) located at 1120 nm are observed. With the increasing of the pump power, both the SPM-induced spectral broadening and the S1 peak intensity are enhanced as shown in Fig. 3(c).
2.2 Cascaded RS generation by different pump peak powers
The cascaded RS experiments are investigated in the HGDF pumping by the amplified pulses. The length of the HGDF is 10 m in our first experiment. It should be pointed out that there are two prerequisites for the efficient cascaded RS generation in the HGDF: firstly, the 1064 nm pump wavelength locates at the normal dispersion region of the HGDF; secondly, the coupled maximum pump peak power of the picosecond pulses is ~8 kW which far exceeds the calculated ~20 W Raman threshold power for S1 generation in the HGDF.
The measured spectral evolution of the cascaded RS in the 10 m HGDF with different pump peak powers are shown in Fig. 4, where the spectra in the range from 0.8 to 1.6 μm are measured with an OSA (Yokogawa, AQ6370) and beyond 1.6 μm are measured with another OSA (Yokogawa, AQ6375). Figure 4(a) shows the measured cascaded RS spectra at pump peak powers of 30, 182, 510, 951, 1400, 1760, 6370 and 8580 W. Clearly, all these spectra asymmetrically broaden to the long wavelength region rigorously dominated by cascaded RS effect. Higher-order Stokes peaks are observed with the increasing of the injected pump power, and the spectral widths of the generated higher-order Stokes waves get wider and wider inevitably [19]. When the pump peak power is 8580 W the long wavelength of the output spectrum has been shifted beyond 2.1 μm, this result corresponds to the generation of 10 orders cascaded Raman Stokes waves.
Fig. 4 (a) Measured spectral evolution of the cascaded RS in 10 m HGDF with different pump peak powers. (b) Measured spectra of cascaded RS by pump peak powers of 951 and 8580 W. Si means the i-th order Stokes wave.
Dips in the output spectrum among the low order Stokes waves are obviously observed at pump peak powers from 182 to 1760 W in our experiments. However, with the increasing of the 976 nm pump power in the experiment, the spectrum of the amplified 1064 nm picosecond pulses undergoes significant SPM (seen in Fig. 3(c)), and the pump itself has been broadened before it is coupled into the HGDF resulting in a flat cascaded RS spectra which makes it a little difficult to identify Stokes peaks. Figure 4(b) plots the generated cascaded Raman spectra at pump peak powers of 951 and 8580 W, which shows that up to 6 orders Stokes peaks (from S1 to S6) are generated at pump peak power of 951 W. When the pump peak power is 8580W, the output Raman spectrum evolves to be an SC covering from 1030 to 2000 nm with spectral flatness better than 10 dB as plotted in Fig. 4(b). It is believed that this is the first time to obtain such a wide range flat cascaded RS spectrum by using a short length of step index silica fiber.
2.3 Cascaded RS generation with different fiber lengths
The HGDF has been demonstrated to be very efficient for the cascaded RS generation in the previous section. However, it is well known that higher concentrations of GeO2 in silica fibers will increase the optical loss of the fiber (seen in Fig. 1(b)), so we investigate the fiber length dependence of cascaded RS.
Figure 5(a) to 5(f) show the cascaded RS generation in the HGDF with different fiber lengths by pump peak powers of 182, 510, 951, 3380, 6885 and 8580 W, respectively. Each figure in Fig. 5 shows that broadened Raman spectra are more accessible in the case of long fibers, which mainly results from the fact that the forward Raman threshold Pth is a function of fiber length L (seen in the section 2.1), Pth decreases while L increases. It is also reasonable that only after one order Raman Stokes wave (Si) has been generated can a higher-order Raman Stokes (Si + 1) wave be generated. So that the use of a single pass pump configuration as shown in our experiment setup asks for a suitable fiber length for obtaining as many higher-order Stokes waves as possible. Figure 5(b) shows the evolution of cascaded RS spectra with different HGDF lengths where the pump peak power is fixed at 510 W. When the fiber length is 0.5 m no Raman Stokes peak is observed, but up to 4 orders Stokes peaks are measured with a HGDF length of 10 m. Similar results are also obtained by other pump peak powers as shown in other figures of Fig. 5.
Fig. 5 Measured spectral evolutions of the cascaded RS in the HGDF with different fiber lengths by pump peak powers of (a) 182 W, (b) 510 W, (c) 951 W, (d) 3380 W, (e) 6885 W and (f) 8580 W. The legend shows the different fiber lengths of the HGDF.
Figure 6 shows the obtained average output power of the cascaded Raman fiber laser for different HGDF lengths. As shown, the output power decreases with the increasing fiber lengths which may be resulted from the higher propagation loss brought by a longer HGDF (seen in Fig. 1(b)). With a fiber length of 10 m, the power conversion efficiency of the cascaded Raman fiber laser is about 48.7% at the pump average power of 2.6 W. Considering the ~12% splicing loss, this corresponds to a Raman conversion efficiency of ~55.3%.
2.4 Cascaded RS generation with different pulse widths
It is also well known that RS processes in optical fibers are affected by the so called walk-off length calculated by [1, 13], where TFWHM is the pump pulse width, Vg is the group velocity, λ1 and λ2 are the wavelengths of the pump and Stokes waves. With a pump pulse width of 8.3 ps, the walk-off lengths LW1 among the pump pulse and Stokes waves are calculated shown in Table 1. Once the pulse propagation distance exceeds these walk-off lengths in the HGDF, the pump and Stokes separate from each other resulting in no energy transferring among these Stokes waves and the pump any more.
Table 1. Walk-off lengths of the pump pulse and Raman peaks in the HGDF.
It is reasonable that this problem can be solved by pumping the Raman fiber with much longer pulses to increase the walk-off lengths. So we further investigate the cascaded RS in the HGDF by using a 35 ps mode-locked pulsed fiber laser at the same pump wavelength of 1064 nm. The coupled pump peak power of this source is nearly 2 kW. As presented in Table 1 the walk-off lengths LW2 calculated with a pump pulse width of 35 ps are about four times of the case of 8.3 ps.
Figure 7 plots the measured spectrum of cascaded RS in a 13.2 m HGDF pumped by the 35 ps pulses with coupled peak power of ~2.05 kW. For comparison we also plot the generated cascaded RS spectrum in a 13 m HGDF pumped by 8.3 ps pulses with a coupled pump peak power of ~2.16 kW. Obviously, the output spectrum pumped by the 35 ps pulse spans from the pump wavelength up to beyond 2100 nm, while the spectrum pumped by the 8.3 ps pulses only broadens to 1600 nm comprising of 6 orders Stokes waves. This result demonstrates that the effect of the cascaded RS will be enhanced significantly with a longer pump pulse under the same pump peak power.
3. Numerical modeling and the simulation results
3.1 Propagation equation
In order to simulate the propagation of picosecond pulses in the HGDF, we employ the GNLSE in which the dispersive and nonlinear effects are considered [15, 20],
where C is related to the Fourier transform of the input field envelope by . The second term on the left side L(ω) represents the linear operator, given by L(ω) = i[β(ω)-β(ω0)-β1(ω0)(ω-ω0)]-α(ω)/2 where β1 is the first-order dispersion coefficient associated with the Taylor series expansion of the propagation constant β about ω0, α(ω) is the frequency dependent propagation loss. γ(ω) is the frequency dependent nonlinear coefficient defined as,where n2 is the nonlinear refractive index [15], n0 is the linear refractive index and R(T) in Eq. (1) represents the Raman response function defined by R(T) = (1-fR)δ(T) + fRh(T). fR represents the fractional contribution of the instantaneous Raman response to the nonlinear refractive index, while h(T) accounts for the delayed Raman response. On one hand, the HGDF has a high GeO2 concentration with fraction as high as ~38mol% in the core; on the other hand, the Raman gain coefficient of GeO2 is expected to be 7.7 times higher than that of silica [18], hence the Raman response term used in the simulation derives from GeO2 instead of silica. In a simple picture, the Raman response function of GeO2 can be fitted to a single damped harmonic oscillator [18],where τs is related to the frequency of the “phonon”, τv is related to the attenuation of the network of vibrating atoms for GeO2, and is the Heaviside step function. The initial injected pulse used in the simulations has a hyperbolic secant field profile the same as that in the experiment,where TFWHM is the pulse width, and P0 represents the peak power of the coupled pump pulse. We also include the input pulse shot noise by adding one photon per mode with random phase into each frequency bin in the simulation [21]. Parameters used in the simulation are listed in Table 2.Table 2. Parameters used in the simulations of the cascaded RS in the HGDF.
3.2 Simulation results of cascaded RS along the HGDF
Figure 8 shows the simulation results of the cascaded RS in the HGDF with P0 of 510 W, corresponding to the experimental results as shown in Fig. 5(b). The spectral evolution of the injected pump pulse along the fiber is sketched in Fig. 8(a) which shows that up to 4 orders Stokes waves are generated in the 10 m HGDF. It is clear to see that Stokes waves S1, S2, S3 and S4 are generated at distances of 2, 2.8, 3.7 and 7.5 m sequentially.
Fig. 8 Simulated results of cascaded RS in the HGDF at a pump peak power of 510 W. (a) Evolution of the spectrum along the fiber. (b) Spectral slices at selected propagation distances.
Figure 8(b) shows the spectral slices of cascaded RS in the HGDF at representative propagation distances of 1, 2, 3, 4 and 10 m. The simulation results can explain intuitively that the dominant nonlinear mechanism for spectral evolution in the HGDF is cascaded RS, which is in good agreement with the experimental results as shown in Fig. 5(b). Actually before the first order Stokes wave S1 is generated the injected picosecond pulse is mainly broadened by SPM effect as shown in Fig. 8(b). No four-wave mixing (FWM) process is observed in both the simulated and the experimental results as we have presented. It can be explained that the phase matching condition for FWM is difficult to satisfy due to the fact that the pump wavelength of 1064 nm is far away from the zero dispersion wavelength of the HGDF, as a result that cascaded RS process in the normal dispersion region dominates the output spectrum.
3.3 Simulation results of cascaded RS by different pump peak powers
Furthermore, we numerically investigate the dependence of the output spectral characteristics on different pump peak powers in the 10 m HGDF. The simulated spectral evolution results are plotted in Fig. 9, which shows the same trend as the experimental results in Fig. 5. With the increasing of P0 more higher-order Stokes waves could be generated, and the required fiber length for the generation of higher-order Raman Stokes waves decreases dramatically. In the simulations we find that up to 10 orders Raman Stokes waves can be generated at pump peak power of 3 kW, which is also observed in the experiment under the situation of pump peak power of about 8580 W as shown in the Fig. 4. The difference of the pump peak powers in the simulation and experiment may originate from the method to estimate the value of the experimental pump peak powers using the unchanged seed pulse width of 8.3 ps. However, with the increasing of the pump power at 976 nm the output spectra from the second stage YDFA have been broadened evidently as we have interpreted in the section 2.1. Due to the combined effects of group-velocity dispersion, SPM and the gain on the seed pulses in the two-stage YDFA, the temporal widths of the output amplified pulses have become wider inevitably at high pump powers [1, 22]. Then the parameters of the pulse used in the simulations do not match the experimental conditions well under high pump powers.
4. Conclusion
To obtain more higher-order Stokes waves in a piece of Raman fiber, some essential conditions must be pre-considered. Firstly, the Raman fiber is expected to have a broad, flattened, and normal dispersion region (all-normal dispersion is not necessary) and the pump wavelength is expected to locate in the normal dispersion region of the Raman fiber, which ensures sufficient interaction length between the pump and the Stokes waves and guarantees as much energy as possible to be transferred from the pump to Stokes waves. Secondly, the pump laser is expected to be pulsed instead of a continuous wave to provide a peak power above the threshold power of RS. Sometimes even flat-topped rectangle pulses are considered for transferring much energy to higher-order Stokes waves [16].
It is believed that despite of these small dips in the spectrum between the lower-order Stokes waves, the demonstrated cascaded RS source in this paper can still be used in spectroscopy, broadband optical communication networks, and multispectral LIDAR [6]. Furthermore, in order to eliminate these dips and acquire a flat cascaded RS spectrum, a multi-wavelength pump scheme would be adopted as an efficient way [23, 24].
We have demonstrated that it is possible to generate over an octave cascaded RS generation in only several meters HGDF which is much shorter compared to earlier implementations. The obtained broadest output spectrum bases on 10 orders Raman Stokes waves spanning from 1000 to beyond 2100 nm together with an output power up to Watt scale. Numerical simulation results through solving the GNLSE have shown fairly good agreement with our experimental results. The results demonstrate that the numerical approach adopted in this paper is reasonable and can be used as an effective way to forecast the performance of cascaded Raman fiber lasers before the corresponding experimental implementations.
Acknowledgments
This work was supported by the Projects of the National Natural Science Foundation of China (Grant No. 61077076) and the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 12JJ1010).
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