1. Introduction

Parametric four-wave mixing (FWM) is an attractive process for nonlinear frequency conversion in optical fibers. The process is utilized in fiber optical parametric oscillators (FOPOs) for efficient generation of tunable radiation in new spectral ranges, where conventional fiber lasers are not available. For example, fiber optical parametric oscillators and convertors based on photonic crystal fibers (PCFs) with pumping by Yb-doped fiber lasers (YDFLs) or laser systems based on Yb-doped fibers are used for generation of pulsed tunable radiation at wavelengths below 1 μm [1–4] or around 1.3 μm [5], which are highly attractive for applications in optical nonlinear microscopy, coherent tomography and multi-photon fluorescence microscopy. Frequency shifts up to 164 THz from the pump wave can be achieved at the parametric conversion [6]. Recently developed pulsed FOPOs pumped by 1030-nm YDFL efficiently generate kW-level picosecond radiation near 800 nm, which is successfully used in coherent anti-Stokes Raman scattering (CARS) microscopy providing high-resolution imaging of CH₂ and CH₃ in a tissue [7, 8]. Femtosecond parametric radiation tunable from 840 to 930 nm was also applied in CARS microscopy of lipid droplets and myelin sheaths [9]. Besides, widely tunable continuous wave (CW) FOPOs are known to be attractive for high resolution optical coherence tomography [10] and coherent Raman scattering microscopy [11]. In our previous works, we have demonstrated and studied first CW all-fiber OPOs operating below 1 μm [12, 13]. The tuning range of 0.95 - 1.01 μm (up to 30 THz parametric shift) was obtained in [12] with the maximum output power of 0.46 W at 972 nm. It was further extended at the short-wavelength edge to 923 nm (38 THz) [13]. Moreover, it was demonstrated that the implementation of linearly polarized pumping reduces the time-domain noise of generated radiation thus stabilizing the FOPO output characteristics. However, the cavity of the developed CW FOPOs was assembled from conventional fiber components which do not maintain the polarization state of light. Therefore, an adjustment of the polarization state was necessary to reach maximum power at each parametric wavelength.

Here we present for the first time an all-fiber OPO made of polarization-maintaining (PM) components providing stable adjustment-free operation during the wavelength tuning. The FOPO wavelength can be tuned from 920 to 1000 nm for both the fast and slow polarization modes. The generated power varies from 1.26 W at 960 nm to 0.08 W at 920 nm. The slope efficiency reaches 17%.

2. Experimental setup

The all-PM FOPO setup is shown in Fig. 1(a). The pumping is provided by a CW linearly polarized single-mode all-fiber master-oscillator power-amplifier (MOPA) source. The master oscillator represents a ring-cavity YDFL with a tunable fiber Bragg grating (FBG) operating in a 1040 – 1060 nm wavelength range with depolarized output radiation. A fiber polarization beam splitter is set at the YDFL output to extract one linearly polarized component of radiation, which is then launched into a two-stage polarization-maintaining Yb-doped fiber amplifier (YDFA). As a result, the pump source generates linearly polarized radiation tunable from 1040 to 1060 nm with the output power of up to 15 W and linewidth of <0.2 nm in the entire power range. Since the pump line was relatively broad in the experiment, Stimulated Brillouin Scattering effect was not observed. The pump wave is reflected via a PM filtered wavelength division multiplexer PM FWDM-1 into a 18-m long polarization-maintaining PCF (LMA-PM-5 produced by NKT Photonics). The PCF structure, dispersion properties and corresponding parametric shifts have been studied in detail in [14].

 

Fig. 1 (a) All-PM FOPO scheme: PM FWDM – polarization maintaining filtered wavelength division multiplexer, WDM - wavelength division multiplexer, PM PCF – polarization maintaining photonic crystal fiber; (b) Round-trip cavity transmittance of the PM FOPO at the Stokes wavelength. The upper scale shows corresponding anti-Stokes wavelengths calculated from the phase matching conditions for the PCF slow axis at 10 W input pump power; (c) Estimated transmittance of pathway from the PCF output end to the port 2 for the anti-Stokes wave.

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Inside the PCF, two pump photons with frequency ω_p are scattered through the degenerate FWM process into two new photons at down-shifted frequency ω_s (Stokes wave) and up-shifted frequency ω_a (anti-Stokes wave) with parametric shift Ω = ω_p – ω_s = ω_а – ω_р. Efficient parametric generation takes place when the phase matching condition is satisfied. In the case of degenerate pump waves, the condition can be written as $\Delta \beta ={\beta }_s+{\beta }_a-2{\beta }_p+2\gamma P_p=0$, where β is the propagation constant and subscripts s,a,p refer to Stokes, anti-Stokes and pump waves, correspondingly; γ is the PCF nonlinear coefficient and P_p is the incident pump power. The generated anti-Stokes wave is extracted from the cavity via a PM FWDM-2 and the Stokes wave is launched back into the PCF through the PM FWDM-1,2 multiplexers. The main advantages of this scheme include minimization of the total cavity losses for the Stokes wave and maximization of the anti-Stokes radiation extraction from the cavity in all-PM configuration. Wavelength division multiplexers WDM-3 and WDM-4 provide filtering of the FOPO output radiation from the residual pump radiation. The FOPO output spectrum is detected by an optical spectrum analyzer (Yokogawa AQ6370) at port 1 or port 2, and the anti-Stokes power is measured by power meter at port 2.

Polarization of pump light was aligned along the slow axis of PM FWDMs. Phase matching conditions of the scalar parametric process can be fulfilled for both the slow and fast axes of the PCF. Slow or fast polarization mode of the PCF was changed by splicing the fiber and PM FWDMs major axes at 0 or 90 degrees, correspondingly. We characterize intra-cavity losses at the Stokes wavelength with effective round-trip cavity transmittance coefficient T as shown in Fig. 1(b) for the slow axis. It includes insertion losses at PM FWDM-1, 2 and ~1.2 dB loss for two splices between the PM PCF and PM 980 fiber pigtails. Upper scale shows corresponding anti-Stokes wavelengths calculated from the phase-matching condition at 10 W input pump power. The transmittance amounts to ~60% within wide range of wavelengths and decreases down to 28% in the vicinity of 1.23 μm (corresponding to anti-Stokes wavelength of <920 nm), because of spectral parameters of the used PM FWDMs. The estimated transmittance of fiber components from the PCF output end to the port 2 for the anti-Stokes radiation is shown in Fig. 1(c). It takes into account insertion losses at PM FWDM-2, WDM-3, WDM-4. One can see that the insertion losses are about 30% at the transmission maximum.

3. Results

As was mentioned above, the phase matching condition Δβ = 0 should be satisfied for efficient parametric generation. The phase mismatch Δβ in scalar case, when all the waves have the same polarization state, can be written as [14]

 

Fig. 2 Output spectra of the all-PM FOPO at different pump wavelength: (a) Measured from port 1 in slow polarization mode; (b) Measured from port 2 in fast polarization mode. Numbers in parentheses correspond to the detuning of pump wavelength from the ZDW of corresponding PCF axis; (c) Individual output spectrum in slow polarization mode at pump wavelength of 1047.1 nm; (d) Scalar phase-matching diagrams: theory (solid lines), experiment with 18-m-long PCF in fast (triangles), slow (circles) polarization modes and with 5-m-long PCF in slow polarization mode (squares).

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As the cavity transmittance coefficient at 1.1 μm is large enough (see Fig. 1(b)), the 1st (1100 nm) and the 2nd (1160 nm) order Raman generation with corresponding anti-Stokes lines at 1000 and 950 nm is experimentally observed, see Fig. 2(c). To the contrary, in the non-PM cavity configuration the Raman component was not appeared because of the higher non-PM cavity losses at 1.1 μm resulting in better discrimination of the 1st Stokes wave [13]. The competition of parametric and Raman effects may ultimately lead to reduction of the parametric conversion efficiency. Variation of the parametric wavelength versus the pump wavelength calculated for two fiber axes using Eq. (1) and Δβ = 0 with the fiber parameters γ = 10 W⁻¹km⁻¹, β₀₃ = 6.755 × 10⁻² ps³/km, β₀₄ = −1.001 × 10⁻⁴ ps⁴/km, λ₀^fast = 1052.95 nm, λ₀^slow = 1051.85 nm (according to ZDW evaluation in [14]) and P_p = 12 W is shown by solid lines in Fig. 2(d). The theory is in good agreement with the experimental data shown by points. Parametric frequency shift reaches the value of 40 THz which is comparable with the non-PM CW FOPO configuration [13].

Dependence of the anti-Stokes power on the incident pump power for several anti-Stokes wavelengths in fast polarization mode of the PCF is presented in Fig. 3(a). The anti-Stokes power was obtained as follows. First, the total output power at port 2 was directly measured by the power meter. Then the power fraction in the anti-Stokes line was calculated according to the measured spectra presented in Fig. 2(b). It was found that the anti-Stokes fraction at the output port depends on the parametric shift: it decreases from 97% at 960 nm down to 50% at 920 nm, see circles in Fig. 3(b), due to the increasing contribution of the Raman 2nd-order Stokes line. The threshold pump power in Fig. 3(a) increases with the wavelength shortening: from 5 W at 961 nm up to 11.5 W at 922 nm. The maximum anti-Stokes output power varies from 0.08 W to 1.26 W for different anti-Stokes wavelengths being on the level of several hundreds mWs. The slope efficiency of the FOPO calculated from Fig. 3(a) is presented in Fig. 3(b) by filled squares. It decreases from ~17% to ~6% with the shortening of parametric wavelength. The slope efficiency at the PCF exit estimated using Figs. 3(a) and 1(c) is shown by open symbols in Fig. 3(b). One can see that the FOPO slope efficiency directly at the PCF’s output exceeds 30%. The anti-Stokes power and slope efficiency for the slow polarization mode are nearly the same as those for the fast mode, with maximum difference of about 10%.

 

Fig. 3 (a) Anti-Stokes power at port 2 for output wavelength of 922 nm (squares), 930 nm (circles), 941 nm (triangles), 952 nm (diamonds), and 961 nm (stars) versus incident pump power at phase matching along the fast axis of the PCF; (b) Slope efficiency for the fast fiber axis calculated at the FOPO output, port 2, (filled symbols) and estimated at the exit of the PCF (empty symbols) using the data for insertion losses in PM FWDM-2, WDM-3 and WDM-4. Circles show fraction of the anti-Stokes power at the port 2.

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4. Conclusion

Thus, we have developed for the first time a CW all-PM all-fiber optical parametric oscillator based on photonic crystal fiber pumped by a linearly-polarized Yb-doped fiber laser operating near 1.05 μm. The all-PM configuration provides stable output parameters during the wavelength tuning. The wavelength tuning range obtained by changing the pump wavelength for the fast and slow polarization modes of the fiber ranges from 920 nm to ~1000 nm. The generated power amounts to several hundreds of mW and slope efficiency varies from 17% at 961 nm to 6% at 922 nm. The results demonstrate that the optimization of spectral profile for intra-cavity losses is required in order to obtain higher power level and larger tuning range. The optimization should include a reduction of the losses for the Stokes wave and better suppression of the Raman generation.