## Optimization of output power in a fiber optical parametric oscillator |

Optics Express, Vol. 21, Issue 19, pp. 22617-22627 (2013)

http://dx.doi.org/10.1364/OE.21.022617

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### Abstract

Fiber optical parametric oscillators (FOPOs) are coherent sources that can provide ultra-broadband tunability and high output power levels and are been considered for applications such as medical imaging and sensing. While most recent literature has focused on advancing the performance of these devices experimentally, theoretical studies are still scarce. In contrast, ordinary laser theory is very mature, has been thoroughly studied and is now well understood from the point of view of fundamental physics. In this work, we present a theoretical study of OPOs and in particular we theoretically discuss the process of gain saturation in optical parametric amplifiers. In order to emphasize the significant difference between the two coherent sources, we compare the optimized coupling ratios for maximum output powers of the ordinary laser and the optical parametric oscillator and demonstrate that in contrast to ordinary lasers, highest output powers in optical parametric oscillators are achieved with output coupling ratios close to 1. We confirm experimentally our theoretical studies by building a narrowband fiber optical parametric oscillator at 1450nm with multi-watt output power. We show that the device is robust to intracavity losses and achieve peak power as high as 2.4W.

© 2013 OSA

## 1. Introduction

2. A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 *μ*m wavelength range based on narrowband optical parametric amplification,” Opt. Lett. **35**(19), 3198–3200 (2010). [CrossRef] [PubMed]

3. A. Gershikov, J. Lasri, Z. Sacks, and G. Eisenstein, “A tunable fiber parametric oscillator for the 2 *μ*m wavelength range employing an intra-cavity thulium doped fiber active filter,” Opt. Commun. **284**(21), 5218–5220 (2011). [CrossRef]

4. Y. Nakazaki and S. Yamashita, “Fast and wide tuning range wavelength-swept fiber laser based on dispersion tuning and its application to dynamic FBG sensing,” Opt. Express **17**(10), 8310–8318 (2009). [CrossRef] [PubMed]

5. Y. Zhou, K. K. Y. Cheung, Q. Li, S. Yang, P. C. Chui, and K. K. Y. Wong, “Fast and wide tuning wavelength-swept source based on dispersion-tuned fiber optical parametric oscillator,” Opt. Lett. **35**(14), 2427–2429 (2010). [CrossRef] [PubMed]

8. Y. F. Chen, S. W. Chen, S. W. Tsai, and Y. P. Lan, “Output optimization of a high-repetition-rate diode-pumped Q-switched intracavity optical parametric oscillator at 1.57 μm,” Appl. Phys. B-Lasers O **77**(5), 505–508 (2003). [CrossRef]

9. A. Salehiomran and M. Rochette, “A nonlinear model for the operation of fiber optical parametric oscillators in the steady state,” IEEE Photon. Technol. Lett. **25**(10), 981–984 (2013). [CrossRef]

10. Y. Q. Xu, K. F. Mak, and S. G. Murdoch, “Multiwatt level output powers from a tunable fiber optical parametric oscillator,” Opt. Lett. **36**(11), 1966–1968 (2011). [CrossRef] [PubMed]

11. Y. Q. Xu and S. G. Murdoch, “High conversion efficiency fiber optical parametric oscillator,” Opt. Lett. **36**(21), 4266–4268 (2011). [CrossRef] [PubMed]

12. Y. Q. Xu and S. Murdoch, “93% conversion efficiency from a fiber optical parametric oscillator,” Conference on Lasers and Electro-Optics (CLEO), CM1J7, Jun. (2012) [CrossRef]

13. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain specture of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. **10**(5), 1133–1141 (2004). [CrossRef]

## 2. Gain saturation in ordinary lasers versus gain saturation in FOPOs

### 2.1 Gain saturation in ordinary lasers

*P*

_{circ}. Using basic laser theory, the gain saturation can be derived. Equation (1) gives the gain,

*G*as a function of the power,

*P*

_{circ}for single pass amplification [14]:Where

*P*

_{sat}is the saturated power, which means the value of signal power passing through the laser medium that will saturate the gain coefficient down to half its small-signal or unsaturated value

*G*

_{unsat}. In Fig. 1(a), we illustrate the single pass saturation properties based on Eq. (1), where we assume the unsaturated gain

*G*

_{unsat}= 100. This means that if we want to extract the maximum power from a laser cavity with such rare-earth doped fiber as gain medium, a work point with low single pass gain is preferable. Assuming that the laser is working in a steady state, the gain G, the output coupling

*T*, and the cavity losses

*δ*, should be balanced so they should follow the following relationship

*G*= 1/(1−

*T*) (1−

*δ*). From Eq. (1), the laser with higher output power should operate at a work point with low gain, which corresponds to a lower output coupling and a lower loss in the cavity. The optimized coupling relation is shown in Fig. 1(b), which can also be calculated by the theory in [14].

### 2.2 Gain saturation in FOPOs

*P*

_{sat}is the power at which there is one photon incident on each atom, within its cross section

*σ*, per recovery time

*τ*

_{eff}. If the incident signal power (i.e. the number of incident signal photons) is high enough, the gain monotonically decreased and saturates toward the limiting

*G*= 0dB. In fiber lasers the power cannot be transferred from the amplified signal back to the gain medium or pump. However, the saturation in a parametric amplifier is fundamentally different and thus far, there has not been a fully physical explanation or a clear definition of the term, saturated power, for FOPOs.

*E*

_{0},

*E*

_{1}, and

*E*

_{2}are the electric field complex amplitudes of the pump power, and two sideband amplitudes, respectively. Δ

*k*=

*k*

_{1}+

*k*

_{2}−2

*k*

_{0},

*γ*, and

*z*are the propagation constant mismatch, third order nonlinear parameter, and propagated distance in the fiber, where

*k*

_{0},

*k*

_{1}, and

*k*

_{2}are the electric field complex amplitudes of the pump power, and two sideband amplitudes, respectively. From theoretical and numerical analysis [16

16. G. Cappellini and S. Trillo, “Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B **8**(4), 824–838 (1991). [CrossRef]

17. L. Jin, B. Xu, and S. Yamashita, “Alleviation of additional phase noise in fiber optical parametric amplifier based signal regenerator,” Opt. Express **20**(24), 27254–27264 (2012). [CrossRef] [PubMed]

*P*

_{sig}= |

*E*

_{1}|

^{2},

*P*

_{idl}= |

*E*

_{2}|

^{2}, and

*P*

_{pump}= |

*E*

_{0}|

^{2}, are the power of signal and pump, respectively. The idler is zero at the input,

*P*

_{idl}(0) = 0. α = (

*P*

_{sig}−

*P*

_{idl})/(

*P*

_{sig}+

*P*

_{idl}+

*P*

_{pump}) is the normalized power difference between the signal and idler.

*ξ*=

*zγ*(

*P*

_{sig}+

*P*

_{idl}+

*P*

_{pump}) is the normalized propagation length. The parameters

*a*,

*b*,

*c*, and

*d*, are the roots of equation d

*η*/d

*ξ*= 0 (Eq. (2a) in [16

16. G. Cappellini and S. Trillo, “Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B **8**(4), 824–838 (1991). [CrossRef]

*a*>

*b*>

*η*(

*z*) ≥

*c*>

*d*. To illustrate the results in a concrete form, we calculated the propagation along a lossless fiber using the following parameters: nonlinear parameter

*γ*= 0.001/W/m, input pump power

*P*

_{pump}= 44.8dBm (30W), input signal power

*P*

_{sig}= 26.2dBm (0.421W). We assume a perfect linear phase matching term Δ

*β*= −2

*γ P*

_{pump}. As shown in Fig. 2, if the fiber is long enough, the power transfers from pump to signal and then from pump back to signal periodically as it propagates through the fiber. The energy transfer between the idler and the pump has the same periodicity.

*L*= 100 m, which is corresponding to the first peak of the signal in Fig. 2, the transmission property of the fiber working as a FOPA is presented in Fig. 3. The output signal power is not a monotone increasing function of input signal power but a periodic increasing function. Under these assumptions and parameters, saturation occurs when the input signal is increased to a power around 26.2dBm, see Fig. 3. At this input signal power level, the output power is limited to 39dBm, marked with a circle in Fig. 3. The FOPA at this work point can be regarded as entering the “saturated state”, and can be used as an amplitude limiter in the field of fiber communication systems. Notice that in Fig. 3, there is a higher order saturation state with 45dBm output at the high input signal power. For a FOPA, in principle, if we increase the input signal power in experiments, this state can be reached. However, in this work, the signal of the FOPO originates from amplified spontaneous emission (ASE). By the optimized coupling ratio design, the FOPA can only work steadily at the lower order saturation state.

*P*

_{sig}/∂

*z*= ∂

*P*

_{sig}/∂

*P*

_{sig}(0) = 0. In physics, this means that the phase matching condition is at a critical point. If the input signal power becomes even higher or the fiber length is even longer, the phase matching condition will change, and the energy will transfer back from the signal and idler to the pump.

*G*=

*P*

_{sig}(

*L*)/

*P*

_{sig}(0). The gain medium in FOPAs is therefore inhomogeneous and the gain of signal should not decrease as a strictly monotonic function of the input signal power. The mathematical solution of the gain in a FOPA can be expressed as a combination of elliptic functions, which can be found in [9

9. A. Salehiomran and M. Rochette, “A nonlinear model for the operation of fiber optical parametric oscillators in the steady state,” IEEE Photon. Technol. Lett. **25**(10), 981–984 (2013). [CrossRef]

13. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain specture of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. **10**(5), 1133–1141 (2004). [CrossRef]

*G*, cavity losses

*δ*, and output coupling

*T*, is satisfied:

*G*= 1/(1−

*T*) (1−

*δ*). This relation indicates that the highest output powers are achieved with larger output coupling ratios. This is inverse to the previous discussion with ordinary lasers that showed that the optimize output power require most of the power to be fed back into the cavity and thus much lower output coupling ratios.

*β*= −2

*γP*

_{pump}is automatically satisfied.

*δ*= 0. Another interesting point is that the FOPO is robust to the loss in the cavity. Even the cavity losses as high as 70%-80%, by choosing a suitable coupling ratio, multi-watt outputs can also be realized.

## 4. Experiment

*λ*

_{ZDW}of 1570 nm, a dispersion slope, d

*D*/d

*λ*of 0.072 ps/nm

^{2}/km, and a nonlinear coefficient

*γ*of 0.001/W/km. A low pass filter was made by rotating a SMF-28 fiber or a DSF, where the bend loss was wavelength dependent. This filter ensured only the anti-Stokes light (signal) returns to the DSF through the coupler, and the Stokes light (idler) and the pump in the last round trip were filtered out. The pump source consisted of an external cavity laser which is tunable between 1520 and 1630 with an output power 5mW. The CW output of the laser was modulated by a MZ modulator with the order of nanoseconds Gaussian pulses and the duty ratio of about 1:40. Then the pump pulses were amplified by two EDFAs, and a band pass filter was placed between the two EDFAs in order to suppress the ASE noise. The repetition frequency was finely tuned to match the cavity fundamental frequency (around 1772.8KHz). A 90/10 coupler was inserted before the cavity to monitor the pump power to confirm that the pump pulses into the cavity were amplified to a peak power about 30W. Figure 8 shows the output spectrum of the FOPO in log and linear scale respectively, where the pump wavelength was fixed at 1547nm. The wavelength of the generated anti-Stokes light was about 1450nm.

10. Y. Q. Xu, K. F. Mak, and S. G. Murdoch, “Multiwatt level output powers from a tunable fiber optical parametric oscillator,” Opt. Lett. **36**(11), 1966–1968 (2011). [CrossRef] [PubMed]

19. C. R. Philips and M. M. Fejer, “Stability of the single resonant optical parametric oscillator,” J. Opt. Soc. Am. B **27**(12), 2687–2699 (2010). [CrossRef]

20. C. R. Phillips and M. M. Fejer, “Adiabatic optical parametric oscillators: steady-state and dynamical behavior,” Opt. Express **20**(3), 2466–2482 (2012). [CrossRef] [PubMed]

## 5. Conclusion

## References and links

1. | B. Kuo, N. Alic, P. Wysocki, and S. Radic, “Simultaneous NIR and SWIR wavelength-swept generation over record 329-nm range using swept-pump fiber optical parametric oscillator,” |

2. | A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 |

3. | A. Gershikov, J. Lasri, Z. Sacks, and G. Eisenstein, “A tunable fiber parametric oscillator for the 2 |

4. | Y. Nakazaki and S. Yamashita, “Fast and wide tuning range wavelength-swept fiber laser based on dispersion tuning and its application to dynamic FBG sensing,” Opt. Express |

5. | Y. Zhou, K. K. Y. Cheung, Q. Li, S. Yang, P. C. Chui, and K. K. Y. Wong, “Fast and wide tuning wavelength-swept source based on dispersion-tuned fiber optical parametric oscillator,” Opt. Lett. |

6. | R. W. Boyd, |

7. | T. W. Tukker, C. Otto, and J. Greve, “Design, optimization, and characterization of a narrow-bandwidth optical parametric oscillator,” J. Opt. Soc. Am. B |

8. | Y. F. Chen, S. W. Chen, S. W. Tsai, and Y. P. Lan, “Output optimization of a high-repetition-rate diode-pumped Q-switched intracavity optical parametric oscillator at 1.57 μm,” Appl. Phys. B-Lasers O |

9. | A. Salehiomran and M. Rochette, “A nonlinear model for the operation of fiber optical parametric oscillators in the steady state,” IEEE Photon. Technol. Lett. |

10. | Y. Q. Xu, K. F. Mak, and S. G. Murdoch, “Multiwatt level output powers from a tunable fiber optical parametric oscillator,” Opt. Lett. |

11. | Y. Q. Xu and S. G. Murdoch, “High conversion efficiency fiber optical parametric oscillator,” Opt. Lett. |

12. | Y. Q. Xu and S. Murdoch, “93% conversion efficiency from a fiber optical parametric oscillator,” Conference on Lasers and Electro-Optics (CLEO), CM1J7, Jun. (2012) [CrossRef] |

13. | M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain specture of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. |

14. | A. E. Siegman, |

15. | G. Agrawal, |

16. | G. Cappellini and S. Trillo, “Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B |

17. | L. Jin, B. Xu, and S. Yamashita, “Alleviation of additional phase noise in fiber optical parametric amplifier based signal regenerator,” Opt. Express |

18. | L. B. Kreuzer, “Single and multi-mode oscillation of the singly resonant optical parametric oscillator,” in |

19. | C. R. Philips and M. M. Fejer, “Stability of the single resonant optical parametric oscillator,” J. Opt. Soc. Am. B |

20. | C. R. Phillips and M. M. Fejer, “Adiabatic optical parametric oscillators: steady-state and dynamical behavior,” Opt. Express |

**OCIS Codes**

(140.3510) Lasers and laser optics : Lasers, fiber

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.4910) Optical devices : Oscillators

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 11, 2013

Revised Manuscript: September 5, 2013

Manuscript Accepted: September 9, 2013

Published: September 18, 2013

**Citation**

Lei Jin, Amos Martinez, and Shinji Yamashita, "Optimization of output power in a fiber optical parametric oscillator," Opt. Express **21**, 22617-22627 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-19-22617

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### References

- B. Kuo, N. Alic, P. Wysocki, and S. Radic, “Simultaneous NIR and SWIR wavelength-swept generation over record 329-nm range using swept-pump fiber optical parametric oscillator,” Optical Fiber Communication Conference (OFC), PDPA9, Mar. (2010).
- A. Gershikov, E. Shumakher, A. Willinger, and G. Eisenstein, “Fiber parametric oscillator for the 2 μm wavelength range based on narrowband optical parametric amplification,” Opt. Lett.35(19), 3198–3200 (2010). [CrossRef] [PubMed]
- A. Gershikov, J. Lasri, Z. Sacks, and G. Eisenstein, “A tunable fiber parametric oscillator for the 2 μm wavelength range employing an intra-cavity thulium doped fiber active filter,” Opt. Commun.284(21), 5218–5220 (2011). [CrossRef]
- Y. Nakazaki and S. Yamashita, “Fast and wide tuning range wavelength-swept fiber laser based on dispersion tuning and its application to dynamic FBG sensing,” Opt. Express17(10), 8310–8318 (2009). [CrossRef] [PubMed]
- Y. Zhou, K. K. Y. Cheung, Q. Li, S. Yang, P. C. Chui, and K. K. Y. Wong, “Fast and wide tuning wavelength-swept source based on dispersion-tuned fiber optical parametric oscillator,” Opt. Lett.35(14), 2427–2429 (2010). [CrossRef] [PubMed]
- R. W. Boyd, Nonlinear Optics (Academic Press, 3rd edition, 2008), Chap 2.
- T. W. Tukker, C. Otto, and J. Greve, “Design, optimization, and characterization of a narrow-bandwidth optical parametric oscillator,” J. Opt. Soc. Am. B16(4), 90–95 (1991).
- Y. F. Chen, S. W. Chen, S. W. Tsai, and Y. P. Lan, “Output optimization of a high-repetition-rate diode-pumped Q-switched intracavity optical parametric oscillator at 1.57 μm,” Appl. Phys. B-Lasers O77(5), 505–508 (2003). [CrossRef]
- A. Salehiomran and M. Rochette, “A nonlinear model for the operation of fiber optical parametric oscillators in the steady state,” IEEE Photon. Technol. Lett.25(10), 981–984 (2013). [CrossRef]
- Y. Q. Xu, K. F. Mak, and S. G. Murdoch, “Multiwatt level output powers from a tunable fiber optical parametric oscillator,” Opt. Lett.36(11), 1966–1968 (2011). [CrossRef] [PubMed]
- Y. Q. Xu and S. G. Murdoch, “High conversion efficiency fiber optical parametric oscillator,” Opt. Lett.36(21), 4266–4268 (2011). [CrossRef] [PubMed]
- Y. Q. Xu and S. Murdoch, “93% conversion efficiency from a fiber optical parametric oscillator,” Conference on Lasers and Electro-Optics (CLEO), CM1J7, Jun. (2012) [CrossRef]
- M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain specture of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004). [CrossRef]
- A. E. Siegman, Lasers (University Science Books, 1986), Chap 12.
- G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Aademic Press, 2007), Chapter 10.
- G. Cappellini and S. Trillo, “Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B8(4), 824–838 (1991). [CrossRef]
- L. Jin, B. Xu, and S. Yamashita, “Alleviation of additional phase noise in fiber optical parametric amplifier based signal regenerator,” Opt. Express20(24), 27254–27264 (2012). [CrossRef] [PubMed]
- L. B. Kreuzer, “Single and multi-mode oscillation of the singly resonant optical parametric oscillator,” in Proceedings of the Joint Conference on Lasers and Opto-Electronics (Institution of Electrical and Radio Engineers, 1969), 52–63.
- C. R. Philips and M. M. Fejer, “Stability of the single resonant optical parametric oscillator,” J. Opt. Soc. Am. B27(12), 2687–2699 (2010). [CrossRef]
- C. R. Phillips and M. M. Fejer, “Adiabatic optical parametric oscillators: steady-state and dynamical behavior,” Opt. Express20(3), 2466–2482 (2012). [CrossRef] [PubMed]

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