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Abstract
We reported the simultaneous generation and selective manipulation of scalar and cross-phase modulation instabilities in a fiber optical parametric oscillator. Numerical and experimental results show independent control of parametric gain by changing the input pump polarization state. The resonant cavity enables power enhancement of 45 dB for the spontaneous sidebands, generating laser pulses tunable from 783 to 791 nm and 896 to 1005 nm due to the combination of four-wave mixing, cascaded Raman scattering and other nonlinear effects. This gain controlled, wavelength tunable, fiber-based laser source may find applications in the fields of nonlinear biomedical imaging and stimulated Raman spectroscopy.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
9 February 2018: A typographical correction was made to the title.
1. Introduction
Nonlinear frequency conversion based on four-wave mixing (FWM) in optical fibers provides an effective way to extend the wavelength coverage of fiber lasers or amplifiers beyond emission bandwidths of rare-earth ions [1–3]. One of the prerequisites for efficient FWM is to satisfy the so-called phase matching condition [4]. The condition strongly depends on the fiber dispersion and birefringence, and can generally be divided into two different ways. The first way is dispersion phase matching, which is referred to as the scalar FWM process or scalar modulation instability (SMI) [5]. In this case, the pump, Stokes and anti-Stokes waves are all polarized along the same axis. The other way of achieving phase matching is polarization phase matching and is referred to as the vector FWM process or vector modulation instability (MI) [6]. Depending on the polarization configurations for the pump and generated waves, there are two different forms of vector MI. One is termed as polarization MI (PMI), where the pump is polarized along one of the axes while Stokes and anti-Stokes waves have the same orthogonal polarization. The other one is known as cross-phase modulation instability (XPMI) [7]. In this case, the pump polarization tilts at an angle to the fiber’s birefringent axes while the Stokes and anti-Stokes polarizations are orthogonal along the two axes.
The orientation of the input pump polarization with respect to the birefringent axes of the fiber is crucial for phase matching conditions in FWM. Generally, only one predominant phase matching condition would be possible once the pump wavelength is fixed and the fiber type is selected [8–10]. One way to overcome this is by using specially designed photonic crystal fibers (PCF) and pumping at a specific spectral region, where different phase matching conditions can be satisfied simultaneously, and generation of multiple frequencies is possible. In 2013, A. Mussot’s group demonstrated experimental observation of both SMI and XPMI in a highly birefringent fiber. By pumping the fiber in the normal dispersion regime at 45° to its principal polarization axis, up to five MI sidebands were observed simultaneously [11]. From an application perspective, not only simultaneous generation of multiple MI sidebands, but also independent control of each new frequency is important for real-world frequency conversion experiment. In 2015, a polarization switch of FWM in large mode area (LMA) hybrid PCFs has been realized, the parametric gains for different phase matching conditions could be selectively turned on and off with the help of polarization manipulation of input pump laser [12]. However, the output power and the wavelength tunability of the simultaneously generated MI sidebands are still limited in the spontaneous FWM scheme, which is not enough for vibrational spectroscopic imaging in biology and medicine, such as coherent anti-Stokes Raman spectroscopy (CARS) [13] and stimulated Raman spectroscopy [14].
In this work, we presented a polarization switch for SMI and XPMI phase matching processes in a fiber optical parametric oscillator (FOPO). Up to three MI sidebands were simultaneously generated and selectively controlled by different phase matching conditions. Although the number of the sidebands was less than the previous work, the resonant cavity provided a large power enhancement of up to 45 dB to the generated XPMI sidebands. The spectral intensities of the generated XPMI sidebands were almost two orders of magnitude larger than the previous results [11]. Moreover, a broad wavelength tuning range of 117 nm was achieved within bands of 783-791 and 896-1005 nm. The parametric gain inside the tuning range could be intraband tuned and interband controlled by changing the intra-cavity optical delay and the input pump polarization. As a result, fine and continuous tuning of the output wavelength could be achieved by changing the optical delay. Meanwhile, fast switching between two largely separated wavelengths could be realized by altering the input pump polarization. Therefore, our presented approach offers additional degree of freedom for users to tune the output wavelength of the FOPO, which could facilitate rapid detection of several separated vibrational bands in CARS applications.
2. Experimental setup
The PCF used in our experiment consists of a fused silica core of 5 μm diameter surrounded by air holes with hexagonal structure (NKT Photonics, LMA-PM-5). The fiber pitch is 3.25 μm and air hole diameter to pitch ratio is 0.44. Due to the endlessly single-mode design, the mode field diameter (MFD) of the PCF is 4.2 μm over a wide spectral range. The fiber is polarization maintained (PM) with a phase birefringence δn = 1.83 × 10−4. Figure 1(a) shows the fiber dispersion calculated for an average refractive index naver. Given the value of fiber birefringence δn, the indexes for the fast and slow axes can be deduced by nslow = naver + δn/2 and nfast = naver - δn/2, which in turn can give corresponding dispersion for two axes. The insert of Fig. 1(a) is the microscope image of the PCF. In our numerical modelling, the free-access CUDOS MOF program was used [15]. The calculated zero dispersion wavelengths (ZDW) were 1051.9 nm and 1053.0 nm for the slow and fast principal axes of the PCF, respectively. The corresponding second- and fourth-order dispersion coefficients at 1030 nm were β2s = 1.09 × 10−3 ps2/m and β4s = −4.45 × 10−8 ps4/m for the slow axis, and β2f = 1.05 × 10−3 ps2/m and β4f = −3.85 × 10−8 ps4/m for the fast axis, respectively.
Fig. 1 (a) Dispersion parameter of LMA-PM-5 fiber simulated by CUDOS MOF program, the inset is the microscope image; (b) Calculated parametric gain spectrum for SMI in the fast (black dash line), slow axes (red solid line) and XPMI phase matching conditions (blue dot line), marked with the arrow in the fiber cross section image.
We calculated the parametric gain for SMI and XPMI phase matching conditions following the simulation methods presented by E. Zlobina [4] and L. Zhang [16]. In the numerical simulation, we used a pump central wavelength of 1030 nm, a nonlinear fiber coefficient γ = 10 W−1km−1 and a peak pump power Pp = 2 kW. The nonlinear efficiency γ is calculated from the formula: γ = 2πn2/(λpAeff), where n2 = 2.3 × 10−20 (m2/W) is the nonlinear refractive index coefficient, Aeff = π(MFD/2)2 is the effective mode area, and λp is the pump wavelength. The calculated parametric gains for various polarization configurations are shown in Fig. 1(b). The black dash line and red solid line correspond to the SMI process obtained by coupling the pump to the fast and slow polarization axes. The blue dot line corresponds to the XPMI process obtained by launching the pump at 45° to the principal axis of the fiber. The calculated results indicate that it is possible to achieve the simultaneous generation of three sidebands with very large frequency shifts relative to the pump wavelength by using appropriate input polarization states of pump.
The theoretical prediction was then experimentally investigated based on a FOPO. The ring cavity provided a versatile platform to realize a tunable and practical laser resonator utilizing SMI and XPMI. As shown in Fig. 2, the FOPO was pumped by a home-made Yb-doped fiber laser. The pump laser was seeded by a SESAM (Semiconductor Saturable Absorber Mirror) mode-locked picosecond oscillator at 1030 nm. The temporal duration and spectral bandwidth of the output pulses from the oscillator were 38 ps and 0.15 nm, respectively. The output power of the oscillator was amplified by a 6/125 single-mode fiber (SMF) pre-amplifier. The gain fiber had a pump absorption of 250 dB/m at 976 nm (PM-YSF-HI, Nufern). The length of the gain fiber was 1.1 m. The pump source for the amplifier was a single-mode diode laser with a maximum output power of 400 mW. With 300-mW pump power, the average power of laser pulses from the oscillator was amplified to 150 mW. An acousto-optic modulator (AOM) based pulse picker was used to change the repetition rate of the pump pulses from 20 MHz to 2 MHz. Due to the all-fiber and polarization maintaining structure, the pump fiber laser was compact and stable.
Fig. 2 Experimental setup of FOPO. LD: laser diode; FBG: fiber Bragg grating; ISO: isolator; PBS: polarization beam splitter; HWP: half-wave plate.
The FOPO included a double-clad Yb-doped fiber amplifier, a 48 cm piece of PCF, an output coupler, a 98 m piece of SMF (SMF-28e, Corning), a fiber delay line (General Photonics, MDL-002-D, delay range: 330 ps) and a fiber wavelength division multiplexer (WDM). The double-clad fiber amplifier was used to boost the average power of pump laser from 5 mW to 1.5 W. A piece of 1.4-m 14/135 double-clad Yb-doped fiber was used as the gain medium. The spectral bandwidth of the pump pulses at maximum output power were 1.0 nm. The output coupler was a polarization dependent beam splitter. The SMF, fiber delay line and WDM were used to build a feedback loop and couple the generated MI sidebands into the PCF again. By optimizing the length of the feedback fiber and tuning the position of the delay line, the corresponding repetition rate of the FOPO cavity could be the same as that of the pump laser.
3. Results and discussion
Compared to the conventional master-oscillator power amplifier chain, the presented scheme where the last stage of fiber amplifier was placed in the main cavity has two advantages: Firstly, the average power of the pump laser acting on the dichroic mirror or WDM is much lower than that in the conventional scheme. Therefore, the risk of optical damage in high power operation can be avoided, even using a coupler without a high-power design. Secondly, in the traditional arrangement the WDM is placed right after the main amplifier, which would inevitably induce unwanted nonlinear effects. These effects could lead to a distortion of the pump spectrum, thus reducing the conversion efficiency of FWM and generating unwanted sidebands. Our presented scheme would be a solution to avoid these detrimental nonlinear effects and should be useful for an all-fiber integrated FOPO.
Figure 3(a) shows the output spectra of the spontaneous FWM measured at the end of the PCF for different input pump powers, which were recorded by an optical spectrum analyzer with a resolution of 0.2 nm (Yokogawa AQ6370C). When the input power is 1.0 W, corresponding to a peak power of 5 kW, there are three spectral regions located at 790, 965 and 990 nm on the left side of the pump wavelength. The first and second one correspond to the SMI and XPMI sidebands respectively, while the 990-nm spectral region corresponds to the anti-Stokes radiation generated from 1st Raman scattering. Actually, the 790-nm spectral region contains two adjacent MI sidebands located at 783 and 787 nm, corresponding to the SMI process in the fast and slow polarization axes, respectively. There are two sharp spectral lines located either side around 790 nm, which might be caused by the cascaded FWM process in the PCF. The spectral peak located in the left side (769 nm) originated from FWM between the two broadened SMI sidebands (780 and 791 nm) while the spectral peak at 813 nm resulted from FWM between 769 nm and 791 nm. The measured wavelengths of SMI and XPMI sidebands agree well with the theoretical calculation although the observed parametric gain is smaller than that in the simulation. The discrepancy might be due to the slight difference of the nonlinear coefficient between the calculation and experiment.
The bandwidths of both the SMI and XPMI sidebands are broadened with the increased pump power. When the pump power is 1.2 W (corresponding to a peak power of 6 kW), the 965-nm XPMI sideband and 990-nm Raman-induced 1st anti-Stokes sideband start to merge with each other due to self-phase modulation (SPM) and cross-phase modulation (XPM). With further increase of the pump power, FWM between the 1030-nm pump and cascaded Raman scattering would give rise to the generation of 2nd and 3rd anti-Stokes signals at 944 and 905 nm. These spectral lines are broadened to form a broadband spectral region from 900 to 1000 nm, which could be used to achieve broadband wavelength tunability when using resonant configuration. Figure 3(a) also shows that the intensity of the spontaneous XPMI sideband is much smaller than that of the SMI sideband, although the former has a faster growth rate than the latter.
The low parametric gain for XPMI sideband can be selectively enhanced by the resonant cavity, once the wavelength of the feedback pulse satisfied the phase matching condition and overlapped with the incoming pump pulse, the generated MI sidebands could be amplified in the FOPO. As shown in Fig. 3(b), the spectral line at 954 nm is relatively weak when the pump power is 1.0 W (corresponding to a peak power of 5 kW). As more power is coupled into the PCF (1.3 W), this XPMI sideband is amplified notably. The spectral intensity is enhanced by 45 dB, which shows large enhancement provided by the feedback loop. It should be noticed that the spectral lines around 790 nm generated by SMI are also amplified with the increased pump power, however, their spectral intensities only enhanced by 10 dB. The 954-nm sideband was resonant due to careful tuning of the delay line, as a contrast, the sidebands around 790 nm were spontaneously amplified. It could be also verified by the different 3-dB spectral widths of the 954-nm (0.8 nm) and 790-nm (5.0 nm) sidebands. Therefore, feedback loop offers large enhancement and narrow gain bandwidth for the selected MI sidebands. Changing the setting of the output half-wave plate would affect the feedback ratio of the FOPO. If the feedback ratio was too low, there would be no resonant output pulses, which showed the threshold characteristic of the FOPO.
The output power of the XPMI sideband was measured with the increase of the pump power. The corresponding conversion efficiency of the pump to the XPMI sideband was calculated, as shown in Fig. 4(a). When the pump power is less than 1.0 W, there is not enough parametric gain for stable resonance. With the increase of the pump power from 1.0 to 1.3 W, the conversion efficiency is increased from 0 to 3.5%. Further increase of the pump power would cause other unwanted nonlinear effects and therefore the conversion efficiency drops dramatically.
Fig. 4 (a) The conversion efficiency of the output XPMI signal relative to the input pump power. Average power evolution of the (b) 1030-nm pump, (c) 783-nm sideband, and (d) 954-nm sideband with respect to the angle of the half-wave plate.
We have also measured the polarization states of the sidebands relative to the pump in spontaneous FWM. In the experiment, dichroic mirrors were used after a half-wave plate and a PBS to separate the pump and the MI sidebands. Then the evolution of average power for each wavelength was measured with respect to the angle of the half-wave plate. The measured power variations for 1030-nm pump and 783-nm signal were the same, as shown in Fig. 4(b) and Fig. 4(c). Therefore, these two lasers had the same polarization state, indicating that the 783-nm sideband was caused by SMI. As for the 954-nm signal, the measured power variations were shown in Fig. 4(d). The angle difference of the half-wave plate for peak position between the pump and 954-nm sideband was about 22.5°, which indicated that the angel for the polarization state of the pump relative to the 954-nm sideband was 45°. Therefore, this sideband originated from XPMI process.
Not only power enhancement, but also wavelength tunability can be improved by the feedback loop. The feedback pulse is broadened due to the dispersion of the SMF, only part of the feedback pulse is overlapped with the next pump pulse and obtains the parametric gain. The different part of the feedback pulse in the temporal domain is resulted from group velocity dispersion, thus changing the length of the fiber delay line would result in continuously tuning of the resonant wavelength of the FOPO, as shown in Fig. 5(a). The output wavelength could be tuned from 783 to 791 nm and from 896 to 1005 nm, respectively. The former lies in the SMI sidebands while the latter lies in the XPMI and Raman-induced anti-Stokes sidebands. The wavelength tuning range of SMI process is smaller than that of XPMI, which is caused by different gain bandwidths of these two processes. The measured wavelength tuning results in resonant scheme are in good agreement with the spontaneous FWM spectrum shown in Fig. 3(a). The output power at each wavelength is shown in Fig. 5(b), the maximum value is 23.2 mW at 787 nm. The input pump power was 1.3 W and the coupling efficiency for PCF was estimated to be 40%, corresponding to a maximum conversion efficiency of 4.5%.
Fig. 5 (a) Wavelength tuning results by changing the optical delay line in steps of 30 ps. (b) Output power of anti-Stokes pulses at different wavelengths.
Currently, the tunability of our FOPO is mainly limited by the transmission characteristics of the intra-cavity components and the gain bandwidths of FWM. The WDM used in our experiment had a flat transmission in the range of 780-1000 nm, which limited the longest wavelength of the signal pulses from the FOPO. By optimizing the transmission wavelength ranges of the elements inside the cavity, signal pulses with higher wavelength could be obtained. The gain bandwidth of FWM is determined by the pump wavelength and fiber parameters. There are two possible ways to improve the tuning range of FOPO. Firstly, the parametric gain could be enhanced by using solid-core liquid-filled [17] or gas-filled hollow-core PCFs [18]. Secondly, increasing the pump power would broaden the gain bandwidth for either SMI or XPMI. These two spectral regions might joint with each other and produce an ultra-broadband parametric gain, just as the XPMI and Raman-induced anti-Stokes sidebands overlapped in Fig. 3(a). As for the improvement of the output power and conversion efficiency, narrower spectral bandwidth of the pump, higher coupling efficiency of the PCF and less transmission loss of the feedback loop would be helpful [19].
The feedback loop offers a fine and continuous wavelength tuning method, as a contrast, rotating the polarization state of the pump laser provides a large and stepped wavelength changing method due to selective switch of the parametric gain. When the angle between the input pump polarization and the fiber birefringent axis was changed, the output spectrum of the FOPO changed periodically. Figure 6(a) illustrates the dynamic evolution of the spectra from 0 to 90° with an interval of 22.5°. In our experiment, the optical delay was set to enable resonance of 920-nm XPMI sidebands. When the angle was set to 0 and 90°, the SMI parametric gains for the slow and fast axes could be switched on individually, generating laser pulses at 787 and 783 nm, respectively. Due to the unmatched optical delay, these two wavelengths were not resonant in the FOPO, resulting in a broad bandwidth of 3 nm. When the angle was set to 45°, the XPMI parametric gain was switched on and the output wavelength was 920 nm with a narrow spectral bandwidth. In contrast, for 22.5 and 67.5° the XPMI sideband was not observed and two SMI sidebands were competing with each other.
Fig. 6 Output spectra of FOPO by pumping the PCF at (a) 0 to 90° with an interval of 22.5 °, (b) 35 to 55° with an interval of 5 °.
To illustrate dynamic behavior around the diagonal polarization of the pump laser, the output spectra of the FOPO for rotation angles from 35 to 55° were measured, as shown in Fig. 6(b). When the angle was set to 40 or 50°, simultaneous generation of two spontaneous SMI sidebands and one resonant XPMI sideband could be observed. As the polarization was set to be further away from 45°, i.e. 35 or 55°, the parametric gain of SMI dominated over that of XPMI, resulting in output wavelengths around 790 nm. It is worth noting that the central wavelength of the XPMI sideband could be tuned by changing the optical delay. The output power for every MI sideband could be optimized to larger than 10 mW, which could be directly used in some vibrational spectroscopic imaging experiment.
4. Conclusions
In conclusion, we have demonstrated a polarization switch in a FOPO. Simultaneous generation and selective manipulation of SMI and XPMI were theoretically predicted and experimentally realized through changing the pump polarization. The resonant cavity provides power amplification and wavelength tunability for the generated MI sidebands. The feedback loop provides intraband continuous tuning of oscillating wavelength of the FOPO while polarization switch enables interband control of different phase matching conditions. Such tuning and switching abilities could provide a flexible tool for CARS applications. For instance, to detect CARS signals of two adjacent vibrational bands, one can simply change the delay line to realize a fine tuning of output wavelength. On the other side, to rapidly detect two largely separated CARS signals such as thymine (667 cm−1) and lipid (2933 cm−1), it is favorable to use the polarization switching method. A fast electronic polarization controller (EPC) would enable a fast wavelength hopping within 1 ms [20]. The output laser pulses can be continuously tuned from 783 to 791 and 896 to 1005 nm with an output power larger than 10 mW. The generated MI sidebands and pump laser are temporally synchronized and spatially overlapped. Their frequency differences match the major vibrational band for Raman spectroscopy (2933-3063 cm−1 for CH3, 242-1452 cm−1 for fingerprint region). Therefore, this parametric gain controlled, wavelength tunable FOPO provides a flexible method to tune the output wavelength, and can be a practical ultrashort laser source for nonlinear microscopy and stimulated Raman spectroscopy.
Funding
National Natural Science Foundation of China (11504235, 11434005, &11404211).
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