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Abstract
We conducted comprehensive theoretical research on rotational stimulated Raman scattering (SRS) of hydrogen molecules in hollow-core fibers. A reliable model for describing the steady-state rotational SRS of hydrogen was established and the influences of various factors was investigated. To verify the theoretical model, a single-pass fiber gas Raman laser (FGRL) based on hydrogen-filled hollow-core photonic crystal fibers pumped by a 1.5 µm nanosecond-pulsed fiber amplifier was constructed. Experimental results were congruent with simulation results. As the output powers and pulse shapes can be well calculated, the model can offer guidance for FGRL investigation, particularly for achieving high-efficiency and high-power FGRLs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Gas stimulated Raman scattering (SRS) has been studied extensively since it was initially reported in 1963 [1]. As gas SRS exhibits characteristics such as high gain coefficient, large Raman frequency shift, and flexible selection of the gain medium, it has been proven to be effective in obtaining a tunable, narrow linewidth and new wavelength laser emission [2,3]. Historically, gas SRS in free space has been beset by problems such as short interaction distance and low interaction intensity, which lead to a very high pump power. Moreover, gas SRS generates multiple Raman lines, resulting in a low conversion efficiency of the required wavelength. However, hollow-core fibers (HCFs) can provide a near-ideal environment for gas SRS [4–10]. The pump light is bound in the micron-scale fiber core, which improves the energy density substantially, and the interaction distance can be expanded by increasing the length of the HCFs. Furthermore, the wavelength-dependent fiber loss can be reasonably designed to control the gain spectrum. Since gas SRS in HCFs was first demonstrated in 2002 [11], fiber gas Raman lasers (FGRLs) based on HCFs have undergone rapid development [12–25], in which hydrogen is the most widely used gain gas medium. At present, various wavelengths over a very broad range can be achieved with hydrogen, such as the 1 µm band [12,13], 2 µm band [15], and 4 µm band [22,25]. In recent years, subwatt 1.7 µm FGRLs using H2-filled hollow-core photonic crystal fibers (HC–PCFs) pumped with a 1.5 µm pulsed fiber amplifier have been reported mainly in experiments [24], providing an effective and novel method for 1.7 µm fiber lasers, which offer extensive applications in biological imaging, laser medical treatment, material processing and detection, and mid-infrared laser generation. To achieve high-efficiency and high-power 1.7 µm FGRLs, further theoretical study is necessary. Although some published studies deal with the theories of gas SRS in HCFs [11–14], none of them can calculate suitably the output Stokes powers, residual pump power and pulse shapes.
In this study, we conducted comprehensive theoretical research on the rotational SRS of hydrogen in HCFs pumped with 1.5 µm nanosecond pulses, and established a reliable model for describing the steady-state H2 rotational SRS in HCFs. To approach the actual experimental conditions more closely, the generation of high-order Stokes light, pump pulse shape, continuous wave (CW) ratio of total pump power, and coupling efficiency were considered in the model. Moreover, the influences of the Raman gain and linewidth, pump pulse repetition frequency and width, and fiber transmission loss and length on the output power and pulse shape were simulated in detail. Thereafter, a 1.7 µm FGRL based on H2-filled HC-PCFs was established to verify the theoretical model, which was pumped by a 1.5 µm tunable fiber pulse amplifier. Because the pump power was too low to generate second-order Stokes light, we further improved the amplifier output power. All of the low- and high-power experimental results were in good agreement with the simulation results, thereby proving that the model can calculate suitably the output Stokes and residual pump powers and pulse shapes, which is helpful when choosing proper parameters for achieving high-efficiency and high-power FGRLs.
2. Theory and simulations
2.1 Energy level transition of hydrogen molecules in SRS
From a quantum mechanics viewpoint, molecules have structures comprising vibrational and rotational energy levels owing to the existence of vibrational and rotational motion states. The following is an example of a hydrogen molecule, for which the expression of the intrinsic energy value is as follows [26]:
In Eq. (1), the first term is the potential energy of the molecule in the equilibrium state, the second term is the vibrational energy level, and the third term is the rotational energy level. For hydrogen molecules, hνe is approximately 0.5 eV and hB is approximately 0.008 eV [26]. Therefore, eight rotational energy levels exist between the vibrational energy levels of V = 0 and V = 1. When considering nuclear spin, ortho- and para-hydrogen molecules exist. The ortho-hydrogen levels are J = 1, 3, 5, and 7 and exist in the symmetric nuclear spin state, whereas the para-hydrogen levels are J = 0, 2, 4, and 6 and exist in the antisymmetric nuclear spin state. No energy level transition occurs between ortho- and para-hydrogen during the SRS process. Figure 1 presents the common energy level transition process.It can be observed that the Raman frequency shift of the hydrogen molecule vibration SRS is 4155 cm-1. For ortho-hydrogen energy levels from J = 1 to J = 3, para-hydrogen energy levels from J = 0 to J = 2, and para-hydrogen energy levels from J = 2 to J = 4, the corresponding Raman frequency shifts are 587, 354, and 814 cm-1, respectively [27]. The relationship among the pump frequency υp, Stokes frequency υS, and Raman frequency shift Δω is as follows:
where c is the speed of light.2.2 Theoretical model of hydrogen rotational SRS in HC–PCFs
In our experiment, because the pump pulse width is substantially larger than the normal dephasing time of hydrogen molecules (<1 ns) [28], it is classified as steady-state SRS and the steady-state coupled wave equation can be used to build a theoretical model. Furthermore, as only first- and second-order Stokes light are generated when pumping at high power, we introduce an equation of the second-order Raman conversion in the coupled wave equation. Therefore, the basic model of our experiment can be expressed as follows:
2.3 Simulation results and discussion
The calculation curves of the output power with the fiber length are obtained using Eqs. (3) and (4), as illustrated in Fig. 2(a). It can be observed that, in the first half of the HCF, because the initial intensity of the Stokes light is excessively small, the increase in the Raman power is not obvious. However, when the light is transmitted to a certain “conversion point,” the pump power decreases rapidly and the process of the pump light being completely converted into first-order Stokes light only takes place with a short fiber length. In the second half of the HCF, the first-order Stokes light is completely converted into second-order Stokes light.
Fig. 2. (a) Calculation curves of output power with HCF length; (b) calculation curves of the output power with pump power after considering pulse shape; (c) coupling efficiency; and (d) CW component proportion of pump light based on steady-state SRS model in HCFs.
We also consider the influence of the pulse shape on the output power. The calculation curves of the output power with the pump power are presented in Fig. 2(b). It can be observed that the first- and second-order Raman thresholds of the Gaussian pulse are larger than those of the rectangular pulse; thus, higher pump power is required for the Gaussian pulse for Raman conversion to occur. Furthermore, the residual pump power of the Gaussian pulse is not completely converted into Raman power because only the center part of the Gaussian pump pulse is converted into Stokes light, as demonstrated by the pulse shape changes in Figs. 6(a) and 6(b).
Moreover, we consider the influence of the coupling efficiency on the output power based on the Gaussian pulse shape; the calculation results are plotted in Fig. 2(c). It can be observed that the first- and second-order Raman thresholds decrease with the increase in the coupling efficiency. Therefore, in the actual experiment, we should attempt to improve the coupling efficiency, which is conducive to increasing the Raman conversion efficiency and achieving a higher power output. Figure 2(d) presents the calculation curves of the output power with the pump power at different CW ratios when the pulse shape is Gaussian and the coupling efficiency is 98%. It can be observed that, as the CW ratio declines, both the first- and second-order Raman thresholds decrease. When the CW ratio is reduced to 0%, the residual pump power begins to decrease continuously once the pump power exceeds the first-order Raman threshold. In contrast, with a high CW ratio, the residual pump power gradually increases following a short decline. Thus, we can evaluate the CW ratio of the pump power by observing the changes in the residual pump power in the actual experiment.
Subsequently, based on the above simulation model, considering the shape of the pump pulses as a Gaussian type, we explored the influences of the Raman gain and linewidth, pump pulse repetition frequency and width, and fiber loss and length on the output Raman power. Moreover, the changes in the pulse shape were simulated. The main simulation parameters are displayed in Table 1.
Table 1. Main simulation parameters
2.3.1 Influence of Raman gain and linewidth
The Raman gain and linewidth are two important parameters in the H2 SRS process, and both can be adjusted by the gas pressure. The first-order steady-state Raman gain coefficient is expressed as follows [29]:
Fig. 3. Simulation curves of output Raman power with coupled pump power at different (a) first-order Raman gain coefficients and (b) Raman linewidths.
Simulation curves of the output Raman power with the coupled pump power at different Raman linewidths are presented in Fig. 3(b). The first- and second-order Raman thresholds also decline with the increase in the Raman linewidth, but the change range of the second-order Raman threshold is larger, which means that the increase in the Raman linewidth is more conducive to second-order Raman conversion. Therefore, to achieve a higher first-order Raman power output, it is necessary to adjust the first- and second-order Raman thresholds using the gas pressure, which means that there may be an optimal gas pressure in the actual experiment.
2.3.2 Influence of repetition frequency and width of pump pulses
When the Raman threshold is constant, the key to achieving higher first-order Raman power is to adjust the pulse repetition frequency and width to obtain an appropriate pump pulse peak power. Figure 4 presents simulation curves of the output Raman power with the coupled pump power at different pump pulse repetition frequencies and widths. It can be observed that, as the pulse repetition frequency and width decline, the first- and second-order Raman thresholds are also reduced. This is because the reduction in these two parameters leads to higher pulse peak power, causing gas SRS to occur more easily. However, it can also be observed that, when the pulse repetition frequency and width are excessively small, as the coupled pump power increases, the first-order Raman power declines after reaching a peak. This is because the peak power is very high and exceeds the second-order Raman threshold, leading to the conversion of first-order Stokes light into second-order Stokes light. Furthermore, it is worth noting that when the repetition frequency and pulse width become too large, the maximum first-order Raman power also declines. This is because the peak power is very low and only a small amount of pump light is converted into Stokes light. Therefore, to achieve higher first-order Raman power output, the pulse repetition frequency and width need to be adjusted so that the peak power is at an optimal value, which is substantially larger than the first-order Raman threshold, but does not exceed the second-order Raman threshold.
Fig. 4. Simulation curves of output Raman power with coupled pump power at different (a) pump pulse repetition frequencies and (b) pulse widths.
2.3.3 Influence of HCF transmission losses and length
Figure 5 presents simulation curves of the output Raman power with the coupled pump power at different pump light losses, first-order Stokes light losses, second-order Stokes light losses, and fiber lengths. As can be observed from Fig. 5(a), when the pump light loss increases, both the first- and second-order Raman thresholds increase, and the slope efficiency of the first-order Raman power hardly changes. In Fig. 5(b), it can be observed that, when the loss of the first-order Stokes light increases, the first-order Raman threshold does not change significantly, but the second-order Raman threshold increases and the slope efficiency of the first-order Raman declines. It can be observed from Fig. 5(c) that the increase in the second-order Stokes light loss inhibits the generation of second-order Stokes light. Therefore, to improve the first-order Raman power, the pump light and first-order Stokes light losses should be as small as possible, but the second-order Stokes light loss should be increased. It can be observed from Fig. 5(d) that the first- and second-order Raman thresholds decrease with the increase in the fiber length. However, if the fiber is excessively long, the transmission loss will increase and second-order Raman conversion is more likely to occur, resulting in a decrease in the first-order Raman power. Therefore, an optimal fiber length exists for obtaining the maximum first-order Raman power.
Fig. 5. Simulation curves of output Raman power with coupled pump power at different (a) pump light losses, (b) first-order Stokes light losses, (c) second-order Stokes light losses, and (d) fiber lengths.
2.3.4 Residual pump and Stokes pulse shapes
Figures 6(a) and 6(b) present the simulation shapes of the rectangular and Gaussian pump pulses, with first-order Raman and residual pump pulses, respectively, when the repetition frequency is 3 MHz and the pump power is 10 W. It can be observed that, when the pump pulse is rectangular, all of the pump light is converted into Stokes light. In contrast, for the Gaussian pump pulse, only the center part that is higher than the first-order Raman threshold is converted into Stokes light, leaving a dip in the center of the residual pump pulse. Figure 6(c) presents the pulse shape change when the repetition frequency is 2 MHz and the pump power is 10 W. Because part of the first-order Stokes light is converted into second-order Stokes light, a dip also appears in the center of the first-order Raman pulse.
Fig. 6. Shape changes of (a) rectangular pulse and (b) Gaussian pulse when only first-order Raman conversion occurs; (c) shape change of Gaussian pulse when second-order Raman conversion occurs.
3. Experiments and results
3.1 Experimental setup
Figure 7(a) depicts the experimental setup, which is similar to that of our previous experiments [24], except for the pump source and changing fiber lengths. The pump source is a home-made tunable 1.5 µm pulse fiber amplifier that can output Gaussian pulses with a pulse width of approximately 12 ns, and a pulse repetition frequency tuning range from 500 kHz to 4 MHz. In the low-power experiment, the maximum average power of the pump source was approximately 1.8 W, with a wavelength tuning range of 1535 to 1565 nm. Because the pump power was too low for second-order Raman conversion to occur, we further optimized the pump source performance to increase its maximum average output power to approximately 7.5 W, but the effective wavelength tuning range was only 1540 to 1550 nm at high power.
Fig. 7. (a) Experimental setup: W: coated output windows, L: convex-plane lens, FM: silver mirror on flip mounts, LPF: long-pass filter, PM: power meter, OSA: optical spectrum analyzer; (b) measured transmission spectrum of used HC–PCF. Inset: schematic cross-section of HC–PCF from product manual.
A fiber coupler with a coupling ratio of 99:1 was used to monitor the real-time pump power, the main output fiber (SMF-28e) of which was spliced directly to the HC–PCF (NKT Photonics, HC-1550-02) owing to the similar mode field area and numerical aperture, and the coupling efficiency was found to be approximately 70% by subtracting the fiber loss from the system transmission. The other end of the HC–PCF was sealed in a gas cavity. The gas cavity can be used to vacuum the HC-PCF and fill the HC-PCF with H2, and it takes more than eight hours for the gas pressure to balance between the HC-PCF and the gas cavity after filling with gas [30]. The Stokes light and residual pump light transmitted from the output window (transmission: approximately 95% at both pump and Stokes light) were collimated by a plano-convex lens and then sent to an optical spectrum analyzer (OSA) (Yokogawa AQ6370D) or power meter by means of a silver mirror on flip mounts. The long-pass filter (transmission: approximately 95% > 1600 nm) placed in front of the power meter was used to filter the residual pump laser. Figure 7(b) presents the measured transmission spectrum of the HC–PCF, which has a transmission range of approximately 1415 to 1740nm. The actual HC–PCF loss, as measured by the cut-off method, is higher than the loss provided in the product manual. The fiber losses at the pump light (approximately 1540 nm) and first-order Stokes light (approximately 1700 nm) are approximately 0.04 and 0.11 dB/m, respectively.
3.2 Low-power experimental results and discussion
Figure 8(a) depicts the output spectrum of the different pump wavelengths when the pump power is approximately 1.8 W and the HC–PCF length is 20 m. It can be observed that each pump line corresponds to only one Stokes line (ortho-hydrogen Raman frequency shift of 587 cm-1 from rotational energy levels J = 1 to J = 3). Other Raman lines outside the transmission band are suppressed owing to high loss, such as the vibrational SRS (Raman frequency shift of 4155 cm-1). Figures 8(b) to 8(g) present the fine spectra of the lines with an OSA resolution of 0.02 nm. The 3 dB linewidth of the pump and Raman lines are less than 0.2 nm.
Fig. 8. (a) Output spectrum of different pump wavelengths; (b) to (g) corresponding fine spectra with OSA resolution of 0.02 nm when pump power is 1.8 W and HC–PCF length is 20 m.
Figure 9(a) displays the evolution of the output Raman power and residual pump power with the coupled pump power at different pump wavelengths when the gas pressure is 16 bar and the pump pulse repetition frequency is 500 kHz. It can be observed that the maximum first-order Raman power decreases with the increase in the pump wavelength, which is attributed to the performance of the pump source, the maximum output power of which declines towards a long wavelength. It can also be observed that, once the coupled pump power exceeds the first-order Raman threshold, the residual pump power increases gradually following a short decline, which implies that the pump light contains CW light according to the simulation results in Fig. 2(d). By comparing the ratio of the pulse shape area in Fig. 10 and the output power ratio, the CW ratio of the pump power is estimated to be 7%.
Fig. 9. Evolution of output Raman power and residual pump power with coupled pump power at different (a) pump wavelengths, (c) gas pressures, and (e) pump pulse repetition frequencies; and corresponding simulation results in (b), (d), and (f), respectively, when HC–PCF length is 20 m and pump power is relatively low.
Fig. 10. (a), (b), and (c) Pulse shapes of first-order Stokes light and residual pump light at different pump powers; and (d), (e), and (f) corresponding simulation pulse shapes, respectively, when pump wavelength is 1540 nm, gas pressure is 16 bar, and repetition frequency is 500 kHz.
Figure 9(b) presents the simulation curves of the 1550 nm pump wavelength. In the calculation of the curves, the Raman gain coefficients gS1 = 0.25 cm/GW and gS2 = 0.17 cm/GW at 16 bar pressure are estimated according to [24,29], and are slightly adjusted to match the experimental results. Figure 9(c) depicts the evolution of the output Raman power and residual pump power with the coupled pump power at different gas pressures when the pump wavelength is 1540 nm and the pump pulse repetition frequency is 500 kHz. It can be observed that, when the gas pressure is adjusted from 4 to 16 bar, the first-order Raman threshold is reduced and the maximum first-order Raman power increases, which can be explained by the increase in the Raman gain. When the gas pressure increases further to 23 bar, the Raman thresholds are basically unchanged owing to Raman gain saturation at high gas pressure, but the maximum first-order Raman power is reduced. This is because the Raman linewidth still increases with the increase of gas pressure, which is conducive to the decrease of the second-order Raman threshold, a part of the first-order Stokes light is converted to second-order Stokes light. Thus, an optimal gas pressure exists, which is consistent with the conclusion drawn from the simulation results in Fig. 3.
Figure 9(d) presents the simulation curves for the 16 bar gas pressure. In the calculation of the curves, with the exception of the pump wavelength and power values, the simulation parameters are the same as those in Fig. 9(b). It can be observed that the simulation curves are also in strong agreement with the experimental results. Figure 9(e) depicts the evolution of the output Raman power and residual pump power with the coupled pump power at different repetition frequencies when the pump wavelength is 1540 nm and the gas pressure is 16 bar. It can be observed that, as the repetition frequency declines, the first-order Raman threshold is reduced and the maximum first-order Raman power increases, but no second-order Raman conversion occurs. Only the value of the repetition frequency is changed in the calculation. The simulation curves for the 1 MHz repetition frequency are presented in Fig. 9(f). It can be observed that the simulation results are basically the same as the experimental results.
Figures 10(a), 10(b), and 10(c) present the pulse shapes of the first-order Stokes light and residual pump light at different pump powers when the pump wavelength is 1540 nm, the gas pressure is 16 bar, and the repetition frequency is 500 kHz. The corresponding simulation pulse shapes are presented in Figs. 10(d), 10(e), and 10(f), respectively. It can be observed that, when the pump power is increased from 0.6 to 1.8 W, the Raman pulse width increases because more pump light is converted into Stokes light. It can also be observed that the simulation pulse shapes basically reproduce the experimental results.
3.3 High-power experimental results and discussion
Figure 11(a) presents the output spectrum of different pump wavelengths when the pump power is 7.5 W and the HC–PCF length is 20 m; the pump source wavelength tuning range is limited to 1540 to 1550 nm at high power. It can be observed that, similar to Fig. 8(a), each pump line corresponds to only one Stokes line (ortho-hydrogen Raman frequency shift of 587 cm-1 from rotational energy levels J = 1 to J = 3). Figures 11(b) to 11(g) display the fine spectra of the lines with an OSA resolution of 0.02 nm. The 3 dB linewidth of the pump and Raman lines are still less than 0.2 nm.
Fig. 11. (a) Output spectrum of different pump wavelengths; (b) to (g) corresponding fine spectra with OSA resolution of 0.02 nm when pump power is 7.5 W and HC–PCF length is 20 m.
Figure 12(a) displays the evolution of the output Raman power and residual pump power with the coupled pump power at different pump wavelengths when the gas pressure is 16 bar and the pump pulse repetition frequency is 2 MHz. It can be observed that the maximum first-order Raman power still declines with the increase in the pump wavelength owing to the performance of the pump source. The simulation curves for the 1550 nm pump wavelength are presented in Fig. 12(b), where the Raman gain coefficients are the same as those in Fig. 9. It can be observed that the simulation curves still agree well with the experimental results. Figure 12(c) presents the evolution of the output Raman power and residual pump power with the coupled pump power at different gas pressures when the pump wavelength is 1540 nm and the pump pulse repetition frequency is 2 MHz. It can be observed that, compared with the experimental results in Fig. 9(c), the first-order Raman thresholds of the different gas pressures are almost the same because the Raman gain reaches saturation at a high gas pressure, but the output powers still change with the gas pressure, and the maximum first-order Raman power is still obtained when the gas pressure is 16 bar. Figure 12(d) displays the simulation curves for the 16 bar gas pressure. The simulation curves are in strong agreement with the experimental results.
Fig. 12. Evolution of output Raman power and residual pump power with coupled pump power at different (a) pump wavelengths, (c) gas pressures, and (e) pump pulse repetition frequencies; and (b), (d), and (f) corresponding simulation results, respectively, when HC–PCF length is 20 m and pump power is relatively high.
Figure 12(e) depicts the evolution of the output Raman power and residual pump power with the coupled pump power at different repetition frequencies when the pump wavelength is 1540 nm and the gas pressure is 16 bar. It can be observed that, when the repetition frequency is lower than 2 MHz, because the peak power of the pulse exceeds the second-order Raman threshold, conversion from first-order Stokes light into second-order Stokes light occurs, but the second-order Stokes line lies outside the low-loss transmission band of ∼1415 to ∼1740nm. It is transmitted with an excessively high fiber loss, which makes its light intensity at the output very weak and cannot be measured by a power meter. It can be observed by a high-sensitivity optical spectrum analyzer (OSA), so a spectrum is measured for verification, as illustrated in Fig. 13(d). Thus, an optimal repetition frequency exists, which demonstrates the conclusion drawn from the simulation results in Fig. 4. Figure 12(f) presents the simulation curves for the 1 MHz repetition frequency. It can be observed that the simulation curves are still consistent with the experimental results when second-order Raman conversion occurs, indicating that the simulation model is fairly reliable.
Fig. 13. (a) and (d) Output spectrum at maximum pump power; (b) and (e) pulse shapes of pump light: first-order Stokes light and residual pump light; and (c) and (f) corresponding simulation pulse shapes when repetition frequency is 2 and 1 MHz, respectively.
We measure the spectrum at the maximum pump power when the repetition frequency is 2 MHz, as illustrated in Fig. 13(a). Moreover, the pulse shapes of the pump light, first-order Stokes light, and residual pump light are measured, as indicated in Fig. 13(b). Figure 13(c) presents the corresponding simulation results of the pulse shapes. It can be observed from Fig. 13(a) that only one Raman line is generated. Figure 13(b) indicates that only the center part of the pump pulse that is higher than the first-order Raman threshold is transformed, thereby leaving a dip in the middle of the residual pump pulse, whereas the Raman pulse is whole. In Fig. 13(c), the simulation pulse shapes accurately reproduce the experiments. The experimental and simulation results when the repetition frequency is 1 MHz are displayed in Figs. 13(d), 13(e), and 13(f). It can be observed from Fig. 13(d) that three lines exist in the spectrum because the first-order Stokes light is converted into second-order Stokes light. In addition to the lines indicated in Fig. 13(a), (a) second-order Stokes line of 1801 nm is transformed from the first-order Stokes line of 1693 nm (para-hydrogen Raman frequency shift of 354 cm-1 from rotational energy levels J = 0 to J = 2). Thus, it can be observed from Fig. 13(e) that a dip also appears in the middle of the Raman pulse, which is approximately split into two pulses, where one is wider and higher than the other. However, the simulation pulse shapes in Fig. 13(f) are slightly different, and the Raman pulse is split into two parts with the same intensity and energy. This is because the pump light modulates the refractive index of the optical medium near the Raman resonances, resulting in a dispersion change around the Stokes wavelength and a detectable pulse delay in the actual SRS process.
The evolution of the output Raman power and residual pump power with the coupled pump power at different HC–PCF lengths when the pump wavelength is 1540 nm, the gas pressure is 16 bar, and the pump pulse repetition frequency is 2 MHz, with repeated cut-back of a 20 m-long HC–PCF, is presented in Figs. 14(a) and 14(b). It can be observed that, as the HC–PCF length is reduced, the Raman threshold and maximum first-order Raman power also increase. Figure 14(c) presents the simulation curves when the fiber length is 10 m and the other simulation parameters are the same as those in Fig. 12(d). It can be observed that the simulation curves still agree well with the experimental results. To determine the optimal fiber length under the current pump parameters and gas pressure, the simulation curves of the output Raman power with the fiber length at the maximum pump power were calculated, as illustrated in Fig. 14(d). Because the output power of the pump source fluctuates, we performed simulations at pump powers of 7.5 and 7.1 W, and filled in a shadow between the resulting curves. It can be observed that the experimental results are all in the shadow. The simulation curves demonstrate that the optimal fiber length is approximately 10 m, which indicates that this simulation model can provide guidance for achieving high Raman power output.
Fig. 14. Evolution of (a) output Raman power and (b) residual pump power with coupled pump power at different HC–PCF lengths; (c) simulation curves of output power with coupled pump power in 10 m-long HC–PCF; and (d) simulation curves of maximum output Raman power with HC–PCF length at maximum pump power when pump is at 1540 nm, gas pressure is 16 bar, and repetition frequency is 2 MHz.
Using the above simulation parameters and model, the simulation curves of the first-order Raman threshold with the fiber length and gas pressure are plotted in Figs. 15(a) and 15(b), respectively. It can be observed from Fig. 15(a) that the Raman threshold declines obviously with the increase in the fiber length, but Fig. 15(b) indicates that the Raman threshold basically remains unchanged with the increase in the gas pressure owing to the Raman gain saturation at a high gas pressure.
Fig. 15. (a) Evolution of first-order Raman threshold with HC–PCF length when gas pressure is 16 bar; and (b) evolution of first-order Raman threshold with gas pressure when HC–PCF length is 20 m.
4. Conclusions
We have conducted comprehensive theoretical research on the rotational SRS of hydrogen in HCFs when pumped with 1.5 µm nanosecond pulses. Taking into account several practical factors, including the generation of high-order Stokes light, pump pulse shape, CW ratio of the total pump power, and coupling efficiency, a relatively accurate and reliable steady-state SRS model has been established. Moreover, the influences of the Raman gain and linewidth, pump pulse repetition frequency and width, and fiber loss and length on the output power and pulse shape have been simulated in detail. Further, a 1.7 µm FGRL based on hydrogen-filled HC–PCFs pumped by 1.5 µm nanosecond pulses was constructed, and the test results agree well with the calculations. The good calculation of this model is very useful in choosing proper parameters for achieving high Stokes power output in FGRLs. The theoretical model can be further improved by considering different pump pulse shapes and vibrational SRS that may occur in different gas-filled HCFs. This work is significant for investigations into FGRLs.
Funding
National Natural Science Foundation of China (11974427); Natural Science Foundation of Hunan Province (2019JJ20023).
Disclosures
The authors declare no conflicts of interest.
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