## Abstract

Continuous tuning over 80 nm is demonstrated for the anti-Stokes wave generated in an optical parametric oscillator (OPO) based on a birefringent photonic crystal fiber pumped by a CW Ytterbium-doped fiber laser tuned around 1.05 μm (within 4 nm only). An influence of the pump laser linewidth and polarization state on the fiber OPO threshold and efficiency is studied. Slope efficiency of parametric generation at 931 nm reaches 19% for ~0.1 nm linearly polarized pump with threshold power of ~5W. At that, the generated linewidth amounts to about 1 nm.

© 2015 Optical Society of America

## 1. Introduction

Fiber optical parametric oscillators (FOPOs) based on four-wave mixing (FWM) in photonic crystal fibers (PCFs) enable high-efficiency generation of tunable radiation with large frequency shifts. Such laser sources are very attractive for applications in nonlinear microscopy [1]. Recent advances in pulsed fiber lasers lead to development of versatile tools for real-time label-free imaging of living tissues [2]. For example, high-efficiency FOPO for coherent anti-Stokes Raman scattering (CARS) microscopy has been demonstrated recently [3]. At the same time tunable CW FOPOs can be potentially applied in optical coherence tomography [4] and coherent Raman scattering microscopy [5]. However, their output parameters are usually not sufficient: anti-Stokes powers are <0.1 W and shifts are <15 THz [6, 7]. Recently, we have developed CW FOPO based on PCF pumped by conventional unpolarized Yb-doped fiber laser (YDFL) demonstrating tuning within a range of 0.95-1.01 μm (about 30 THz parametric shift) and output power up to 0.46 W at 972 nm [8]. A theory predicts that a polarized pumping is more efficient [9]. Besides a pump laser linewidth is also important for parametric process [10] since we use rather broadband pump with linewidth of up to 0.2 nm. However, experimental studies of CW FOPOs output characteristics on the pump linewidth are not known, because single-frequency pumping is usually explored.

In this paper we compare the CW FOPO schemes with randomly and linearly polarized pumping. We also study variations of the FOPO output characteristics (threshold power, slope efficiency, intensity dynamics, and tuning range) while changing the pump laser linewidth. As a result of the optimization, output characteristics of the <1 μm all-fiber CW FOPO based on the PCF (LMA-PM-5) have been greatly improved, namely the tuning range exceeds 80 nm and the efficiency is nearly doubled in comparison with previous result [8].

## 2. Experimental setup

The experimental setup is shown in Fig. 1. It is similar to the scheme proposed in [8].

The pump wave passes through a polarization controller PC-1 and a 20-dB fiber coupler, a broadband wavelength division multiplexer WDM-1 launching it into a 18-m long polarization maintaining PCF (LMA-PM-5 by NKT Photonics). The PCF structure and dispersion properties as well as potential parametric sidebands have been studied in detail in [11]. Due to the parametric process in the PCF, two pump photons with frequency *ω*_{p} are scattered into two new photons with down-shifted *ω*_{s} (Stokes) and up-shifted *ω*_{a} (anti-Stokes wave) frequencies with parametric shift of *Ω* = *ω*_{p} – *ω*_{s} = *ω*_{а} – *ω*_{р}. The Stokes wave (Signal) is launched back into the PCF through WDM-1, whereas the anti-Stokes wave (Idler) is extracted from the cavity via a wavelength division multiplexer WDM-2. Such a scheme allows accumulating only the Stokes component inside the cavity. 20-dB fiber coupler is used for control of the input and back-scattered (port *C*) pump powers. Wavelength division multiplexers WDM-3 and WDM-4 filter the FOPO output from the residual pump and Stokes components. The polarization controllers PC-1 and PC-2 are used to adjust the polarization state of pump and Stokes waves, respectively. The FOPO output spectrum is measured at port *A* by an optical spectrum analyzer (Yokogawa AQ6370). The anti-Stokes power is detected at port *B*. It is worth noting that in most cases of FOPOs the generated Stokes and anti-Stokes power is removed from the cavity via output coupler. The CW anti-Stokes output power was relatively low because of high output coupling coefficient and therefore high (~7-13 dB) round-trip cavity losses [7, 12] or because of low output coupling [6, 13]. We apply the WDMs in the cavity to minimize the total cavity losses for the Stokes wave and to maximally remove the anti-Stokes wave from the loop. The round-trip cavity losses are decreased to 1.4 dB at 1205 nm including ~1 dB loss for two splices between the PCF and 1060 XP fiber which is used in the FOPO components.

The FOPO is pumped by both randomly and linearly polarized CW light. The source of randomly polarized radiation is the conventional YDFL pumped by multimode laser diodes with linear cavity formed by two fiber Bragg gratings (FBGs) which were placed into separate ovens. Output linewidth Δ*λ*_{p} of the YDFL is proportional to the FBG bandwidth [14]. Thus changing the FBGs temperature and thereby mismatching the FBGs reflection spectra *R*_{1,2}, we manage the spectral bandwidth of the cavity effective reflection *R*_{1} × *R*_{2} and in this way the laser linewidth Δ*λ*_{p}. The YDFL delivers up to 16 W at 1048 nm. For linearly polarized pumping an all-fiber master-oscillator power-amplifier (MOPA) source based on a double-clad Yb-doped fiber has been assembled. It consists of ring-cavity randomly polarized YDFL with a tunable FBG (see [8] for details) operating in 1040 – 1070 nm wavelength range, and two polarization maintaining Yb-doped fiber amplifiers (YDFAs). A fiber polarization beam splitter was set after the YDFL to extract the linearly polarized component of the radiation which is then launched in the YDFAs. Finally, the MOPA generates CW tunable linearly polarized radiation with output power of up to 8 W. Spectral linewidth Δ*λ*_{p} of the MOPA source varies irregularly from 30 to 130 pm while tuning back and forth the YDFL’s FBG in a mechanical setup. We were able to obtain fixed value of Δ*λ*_{p} by a proper adjustment of the FBG near the operating wavelength.

## 3. FOPO tuning range

To realize high-efficiency parametric generation it is necessary to satisfy the phase-matching condition. In the scalar case when all waves have the same polarization it is [15]

*β*

_{2}(

*ω*

_{p}),

*β*

_{4}(

*ω*

_{p}) are the 2-nd and the 4-th order dispersion coefficients of the fiber at

*ω*

_{p},

*P*

_{p}is pump power at the PCF input, γ is the fiber nonlinearity coefficient. The polarization maintaining structure of the LMA-PM-5 fiber supports two polarization modes, so the parametric components can be generated for each of them. Variable values

*β*

_{2}(

*ω*

_{р}) and

*β*

_{4}(

*ω*

_{р}) can be expressed in terms of constants

*β*

_{03}and

*β*

_{04}(the 3-nd and the 4-th order dispersion coefficients at the zero dispersion frequency

*ω*

_{0}): ${\beta}_{2}({\omega}_{p})\approx {\beta}_{03}({\omega}_{p}-{\omega}_{0})+({\beta}_{04}/2){({\omega}_{p}-{\omega}_{0})}^{2}$ and ${\beta}_{4}({\omega}_{p})\approx {\beta}_{04}$ [16]. The scalar phase matching diagrams (parametric wavelength vs. pump wavelength) calculated at

*P*

_{p}= 5 W according to Eq. (1) are shown in Fig. 2(a). Solid and dashed curves correspond to the fast and the slow polarization axes of the PCF. Dotted curves demonstrate the phase matching diagrams at

*P*

_{p}= 13 W. In calculations of parametric wavelengths we use the following parameters of the fiber [11]:

*γ*= 10 (W × km)

^{−1},

*β*

_{03}= 6.755 × 10

^{−2}ps

^{3}/km,

*β*

_{04}= −1.001 × 10

^{−4}ps

^{4}/km,

*λ*

_{0}

^{f}= 1052.95 nm,

*λ*

_{0}

^{s}= 1051.85 nm (

*λ*

_{0}is the zero dispersion wavelength (ZDW)). As seen in Fig. 2(a), parametric shifts near 930 nm are independent of the pump power (at P

_{p}≤ 13 W) and defined only by the dispersion properties and pump wavelength. Points in Fig. 2(a) show the experimental parametric wavelengths dependence on the pump wavelength when the linearly polarized radiation of MOPA is used. Continuous sideband tuning from 923 to 1005 nm (82 nm) and 1100 to 1210 nm (110 nm) is demonstrated by tuning the pump wavelength

*λ*

_{р}between 1047.5 and 1051.4 nm (4 nm only). The theory and experiment are in good agreement. Parametric frequency shift reaches 38 THz that is the largest value obtained to date for CW FOPOs, whereas it was usually comparable with the Raman shift in silica ~15 THz [6, 7].

Figure 2(b) shows the FOPO spectra (port *В*). The OSA resolution is 0.1 nm. The state of polarization for each generated wavelengths was adjusted by PC-1 and PC-2 to achieve maximum output power. Spectral bandwidths of the WDM couplers are quite broad ~135 nm and, consequently, the linewidth of the generated components is determined mainly by the parametric gain bandwidth. Inset in Fig. 2(b) shows that the anti-Stokes FWHM Δ*λ*_{a} changes from 5 to 0.7 nm with decreasing wavelength *λ*_{a}. The generation at *λ*_{a} < 923 nm is not observable. This limitation can be explained by the growing losses at the Stokes wavelength owing to the spectral properties of WDMs. In addition, the pump linewidth and longitudinal inhomogeneity along the PCF strongly influence the ZDW resulting in reduction of the parametric gain amplitude at large parametric shifts [9]. As the gain inside the cavity decreases, the FOPO threshold increases thus limiting the tuning range. On the other hand, the parametric generation has no principal limit at small frequency shifts. However, we don’t consider in this paper the generation spectra above 1005 nm as its FWHM exceeds 5 nm due to the increase of parametric gain bandwidth.

## 4. FOPO properties with randomly and linearly polarized pump radiation

To improve the FOPO output parameters it is necessary to study influence of the pump laser linewidth and polarization state on the FOPO’s threshold, slope efficiency and power fluctuations. Figures 3(a) and 3(b) show oscillograms of the pump (port *A*) and the anti-Stokes generation (port *В*) for randomly and linearly polarized pumping, respectively. Experimental data are recorded simultaneously by 1-GHz photodetectors and a digital oscilloscope (Tektronix TDS 3032B, 300 MHz). The generated wavelength *λ*_{a} is 931 nm (a) and 938 nm (b) in the studied cases. The pump radiation in Fig. 3(a) and 3(b) stochastically fluctuates in the time domain with root mean square (RMS) of 12%. The stochastic noise in the oscillograms is related to the interaction of large number of longitudinal modes of the YDFL. The noise is amplified by the parametric process. In the case of randomly polarized pump (Fig. 3(a)) one can see fluctuations of the power with much higher amplitude (RMS ≈33%). Probably they are related to fluctuations of pump polarization. If we use linearly polarized pump light the RMS of fluctuations decreases down to 19% and parametric generation is stabilized in time domain (Fig. 3(b)).

The FOPO threshold can be estimated from the relation *G*_{p}*T* = 1, where *G*_{p} is the signal power gain in the fiber and *T* is the round-trip transmittance of the signal inside the cavity. The fiber loss of 18-m long LMA-PM-5 is small, α_{L}*L* = 0.021 (attenuation constant *α*_{L} < 5 dB/km in the range of 700 to 1200 nm). The threshold pump power is then [9]

Theoretical value of *P*_{th} calculated from Eq. (2) with parameters *γ* = 10 (km × W)^{−1}, *L* = 18 m, *Т* = 0.72 (*λ*_{a} = 930 nm) and *Т* = 0.68 (*λ*_{a} = 940 nm) is 3.3 and 3.6 W at *λ*_{a} of 930 and 940 nm, respectively. Figure 4 shows experimental dependence of the generated anti-Stokes power (port *B*) on the input pump power for randomly (a) and linearly (b) polarized pumping. Points and solid curves demonstrate experimental data and their linear fit, respectively.

The triangles and squares in Fig. 4(a) correspond to the parametric generation at the wavelength of 931 nm for different pump linewidth. The parametric power reaches 320 mW at the input pump power of 13.5 W. The generated linewidth is 1.5 nm. The FOPO slope efficiency for different values of Δ*λ*_{p} is nearly the same amounting to 15%. The pump power threshold increases from 11.3 to 12 W if the pump linewidth increase from Δ*λ*_{p} = 0.16 to 0.2 nm. Such dependence can be explained as follows: the pump spectrum is rather broad and results in spread of the parametric small signal gain and thereby in reducing the gain maximum [10]. If we fix the Stokes wavelength at 1200 nm and change the pump wavelength in a certain range close to the phase matching condition we can find the fraction of the pump power involved in the parametric process. Using this technique and equation for parametric conversion efficiency in [15] we calculate the spectrum of the pump power corresponding to the highest conversion efficiency near 930 nm (inset in Fig. 4(a)). The required FWHM of the pump spectrum is 0.05 nm i.e. it is by 3-4 times lower of the experimental values. Therefore only a part of the pump spectrum is involved in the parametric process resulting in the increase of FOPO threshold. On the other hand, the experimental pump linewidth Δ*λ*_{p} = 0.1 - 0.14 nm used in [8] was less than the required value of 0.15 nm for parametric generation at 970 nm. Therefore the FOPO threshold was independent on the pump linewidth. Thus the efficient parametric generation at shorter wavelengths requires optimization of the pump linewidth. Figure 4(b) shows the anti-Stokes power at the wavelength of 931 (stars) and 942 (circles) versus input pump power for linearly polarized radiation with Δ*λ*_{p} = 0.09 nm. The graphs demonstrate growth of the FOPO threshold with parametric shifts increasing. That growth and the higher value of the measured threshold power in comparison with the theoretical one can be explain by reduction of the parametric small-signal gain owing to influence of the fiber inhomogeneity and the pump linewidth at large parametric shifts [9]. The generated power reaches 230 mW at 942 nm. Comparing the threshold power for different polarization states of the pump we have found that the linearly polarized pump allows one to decrease the FOPO threshold by two times as the all pump power participates in the parametric conversion, increasing also the FOPO slope efficiency from 15 to 19%.

Finally, let us consider other nonlinear effects that may compete with parametric gain in optical fibers. As discussed above efficient parametric generation at 930 nm can be obtained by reducing the pump linewidth down to 0.05 nm. However, narrowing the MOPA lasing spectrum less than 0.03 nm has resulted in the onset of stimulated Brillouin scattering (SBS) inside the FOPO cavity. In the presence of SBS, the dynamics of pump and anti-Stokes waves become chaotic and their average powers decrease in comparison with the CW mode. So the SBS process prevents the pump linewidth narrowing. However, its influence can be suppressed through careful control of the cavity length (suitable for *L*:2 m or less) [17] or by using the phase modulation of the pump wave. The last technique is mostly applied to single-frequency lasers [6, 18, 19]. Another nonlinear effect competing with parametric gain in the PCF is stimulated Raman scattering (SRS). Here the intracavity loss at SRS Stokes wavelength near 1110 nm is high enough (~8.9 dB) owing to optimization of the spectral properties of WDM-1 and WDM-2. Thus, SRS is strongly suppressed inside the FOPO cavity and not observed in the experiment.

## 5. Conclusion

In this paper, the influence of pump linewidth and polarization state on output characteristics of CW FOPO based on YDFL-pumped PM PCF has been studied. It has been shown experimentally that at large parametric shift the FOPO threshold grows with increasing pump linewidth due to the broadening of parametric small-signal gain. On the other hand, a reduction of the pump linewidth below 0.03 nm leads to the onset of SBS that suppresses parametric process. Thus, the pump linewidth appears to have an optimum. Optimization of cavity losses with rather short PCF (18 m) has also been performed. It has been shown that pumping FOPO by linearly polarized radiation instead of unpolarized one results in 2 times lower threshold, higher efficiency, and better temporal characteristics. The obtained output power for the anti-Stokes wave is limited by the available linearly polarized pump reaching 230(130) mW with 19% slope efficiency at the wavelength of 942(931) nm with linewidth below 1 nm. The continuous tuning range is as large as 82 nm (from 923 to 1005 nm) at the pump wavelength variation by 4 nm only. Thus the parametric shift reaches 38 THz: this value exceeds significantly typical shifts for existing CW FOPOs.

## Acknowledgments

The study is supported by the Russian Science Foundation (project No. 14-22-00118).

## References and links

**1. **C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science **322**(5909), 1857–1861 (2008). [CrossRef] [PubMed]

**2. **C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics **7**(11), 875–882 (2013). [CrossRef] [PubMed]

**3. **T. Gottschall, T. Meyer, M. Baumgartl, B. Dietzek, J. Popp, J. Limpert, and A. Tünnermann, “Fiber-based optical parametric oscillator for high resolution coherent anti-Stokes Raman scattering (CARS) microscopy,” Opt. Express **22**(18), 21921–21928 (2014). [CrossRef] [PubMed]

**4. **D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science **254**(5035), 1178–1181 (1991). [CrossRef] [PubMed]

**5. **C. R. Hu, M. N. Slipchenko, P. Wang, P. Wang, J. D. Lin, G. Simpson, B. Hu, and J. X. Cheng, “Stimulated Raman scattering imaging by continuous-wave laser excitation,” Opt. Lett. **38**(9), 1479–1481 (2013). [CrossRef] [PubMed]

**6. **Y. Q. Xu, S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Raman-assisted continuous-wave tunable all-fiber optical parametric oscillator,” J. Opt. Soc. Am. B **26**(7), 1351–1356 (2009). [CrossRef]

**7. **R. Malik and M. E. Marhic, “Tunable Continuous-Wave Fiber Optical Parametric Oscillator with 1-W Output Power”, in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA18. [CrossRef]

**8. **E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Tunable CW all-fiber optical parametric oscillator operating below 1 μm,” Opt. Express **21**(6), 6777–6782 (2013). [CrossRef] [PubMed]

**9. **M. E. Marhic, *Fiber Optical Parametric Amplifiers, Oscillators and Related Devices* (Cambridge University, 2008).

**10. **R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. **18**(7), 1062–1072 (1982). [CrossRef]

**11. **E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B **29**(8), 1959–1967 (2012). [CrossRef]

**12. **C. J. S. de Matos, J. R. Taylor, and K. P. Hansen, “Continuous-wave, totally fiber integrated optical parametric oscillator using holey fiber,” Opt. Lett. **29**(9), 983–985 (2004). [CrossRef] [PubMed]

**13. **Z. Luo, W.-D. Zhong, M. Tang, Z. Cai, C. Ye, and X. Xiao, “Fiber-optic parametric amplifier and oscillator based on intracavity parametric pump technique,” Opt. Lett. **34**(2), 214–216 (2009). [CrossRef] [PubMed]

**14. **S. I. Kablukov, E. A. Zlobina, E. V. Podivilov, and S. A. Babin, “Output spectrum of Yb-doped fiber lasers,” Opt. Lett. **37**(13), 2508–2510 (2012). [CrossRef] [PubMed]

**15. **G. P. Agrawal, *Nonlinear Fiber Optics*, 3rd ed. (Academic, 2001).

**16. **F. Yaman, Q. Lin, and G. P. Agrawal, “Fiber-optic parametric amplifiers for lightwave systems,” in Guided Wave Optical Components and Devices, B. P. Pal, ed. (Academic, 2005), Chap. 7.

**17. **J. K. Jang and S. G. Murdoch, “Strong Brillouin suppression in a passive fiber ring resonator,” Opt. Lett. **37**(7), 1256–1258 (2012). [CrossRef] [PubMed]

**18. **M. E. Marhic, K. K.-Y. Wong, L. G. Kazovsky, and T.-E. Tsai, “Continuous-wave fiber optical parametric oscillator,” Opt. Lett. **27**(16), 1439–1441 (2002). [CrossRef] [PubMed]

**19. **G. K. P. Lei, L. T. Lim, and M. E. Marhic, “Continuous-wave fiber optical parametric oscillator with sub-MHz linewidth,” Opt. Commun. **306**, 17–20 (2013). [CrossRef]