## Temperature control of the gain spectrum of fiber optical parametric amplifiers

Optics Express, Vol. 13, Issue 12, pp. 4666-4673 (2005)

http://dx.doi.org/10.1364/OPEX.13.004666

Acrobat PDF (309 KB)

### Abstract

The gain spectrum of a fiber optical parametric amplifier (OPA) can be controlled by imposing a temperature distribution along the fiber, which modulates the local fiber zero-dispersion wavelength *λ*_{0}, and hence the parametric gain coefficient. We present simulations and experimental verification for various binary temperature distributions. The method should be applicable to fibers with realistic longitudinal variations of *λ*_{0}.

© 2005 Optical Society of America

## 1. Introduction

1. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. **21**, 573–575 (1996). [CrossRef] [PubMed]

2. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. **21**, 1354–1356 (1996). [CrossRef] [PubMed]

*λ*

_{0}, which prevent their gain spectra from matching those of ideal fibers with uniform

*λ*

_{0}.

## 2. Theory and simulations

*β*(

*z*)=

*β*

_{2}(

*z*)(Δ

*ω*

_{s})

^{2}+

*β*

_{4}(

*z*)(Δ

*ω*

_{s})

^{4}/12, where:

*z*is the distance along the fiber;

*β*(

_{m}*z*) is the

*m*th derivative of the local wavevector

*β*(

*ω*,

*z*) with respect to the angular frequency

*ω*, evaluated at the pump angular frequency

*ω*, and at

_{p}*z*; Δ

*ω*=

_{s}*ω*-

_{s}*ω*;

_{p}*ω*is the signal angular frequency. Generally fiber OPAs must be operated with a small Δ

_{s}*β*(

*z*), and therefore the pump wavelength

*λ*must be close to the zero-dispersion wavelength

_{p}*λ*

_{0}(

*z*) for all

*z*. For a given fiber we assume that

*β*

_{3}and

*β*

_{4}remain constant along the fiber, so that

*β*(

*z*) can in principle be given an arbitrary shape, by suitably controlling the shape of

*λ*

_{0}(

*z*). One way to do this is to have a corresponding temperature distribution along the fiber, because it is known that

*λ*

_{0}varies approximately linearly with temperature: the rate of change is about 0.03 nm/°C in dispersion-shifted fiber (DSF) [3

3. K. C. Byron, M. A. Bedgood, A. Finney, C. McGauran, S. Savory, and I. Watson, “Shifts in zero dispersion wavelength due to pressure, temperature and strain in dispersion shifted singlemode fibers,” IEE Electron. Lett. **28**, 1712–1714 (1992). [CrossRef]

4. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. **19**, 1691–1697 (2001). [CrossRef]

*β*

_{3}and

*β*

_{4}do not vary with temperature; small variations will not significantly alter the basic reasoning.) In principle, one could use this method to synthesize arbitrary dispersion profiles to control the gain spectra of fiber OPAs. In particular, this method could in principle be used to overcome the presence of random dispersion fluctuations in practical fibers.

*T*

_{1}and

*T*

_{2}, and by placing different regions of a fiber in these two regions. Such regions could for example be: (i) a temperature-controlled oven; (ii) the room at ambient temperature, i.e. about 25°C; (iii) a mixture of water and ice providing a temperature of 0°C. We chose to perform our experiments with (ii) and (iii) for reasons of convenience; the simulations correspond to these conditions.

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

*T*

_{1}and

*T*

_{2}do not overlap.

*N*periods along the fiber. Each period consists of a length

_{p}*L*

_{1}at temperature

*T*

_{1}, followed by a length

*L*

_{2}at

*T*

_{2}.

*N*=1, the overall power gain spectrum is simply obtained as the sum (in decibels) of the individual power gain spectra of the two halves. This can be understood as follows:

_{p}*N*=2, we can view the overall OPA as a cascade of two OPAs with

_{p}*N*=1. The overall power gain spectrum, however, cannot be calculated as the sum of the spectra of the two halves, because these spectra are actually identical, and therefore can strongly interfere. In general pump, signal and idler emerge from the first half with finite amplitudes, and phases governed by the structure of the first half. These phases now affect the power gains in the second half. This situation is similar to that encountered in our previous work on fiber OPAs with periodic dispersion compensation, where each period consisted of two different fiber segments [6

_{p}6. M. E. Marhic, F. S. Yang, M. C. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” IEEE J. Lightwave Technol. **17**, 210–215 (1999). [CrossRef]

*N*increases further, the gain spectrum continues to exhibit a complicated behavior, including rapid modulation. However, when

_{p}*N*becomes very large (in a sense to be defined shortly), we eventually enter a new regime where the spectrum is very simple again. This occurs when the spatial period of the modulation,

_{p}*L*

_{1}+

*L*

_{2}, becomes much shorter than the nonlinear length

*L*=1/(

_{NL}*γP*

_{0}), where

*γ*is the fiber nonlinearity coefficient, and

*P*

_{0}is the pump power. Then the waves essentially experience the local average of the dispersion, and the details of the rapid fluctuations are not important. In this situation, the OPA behaves as if the fiber had a uniform temperature, given by the average

*T*=(

_{av}*L*

_{1}

*T*

_{1}+

*L*

_{2}

*T*

_{2})/(

*L*

_{1}+

*L*

_{2}). Therefore, we expect the spectrum to consist of a single high lobe, shifted by an amount proportional to

*L*

_{1}/

*L*

_{2}. So by varying

*L*

_{1}/

*L*

_{2}it is possible to obtain the same spectra as one would have with a uniform-temperature OPA, but at different effective temperatures.

7. OptSim, distributed by RSoft (http://www.rsoftdesign.com). A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber,” IEEE J. Sel. Areas Commun.15, 751–765 (1997). [CrossRef]

7. OptSim, distributed by RSoft (http://www.rsoftdesign.com). A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber,” IEEE J. Sel. Areas Commun.15, 751–765 (1997). [CrossRef]

*L*=200 m;

*γ*=2.3 W

^{-1}km

^{-1};

*λ*

_{0}=1542.3 nm;

*β*

_{3}=1.14×10

^{-40}s

^{3}m

^{-1};

*β*

_{4}=-5×10

^{-55}s

^{4}m

^{-1};

*λ*

_{p}=1540.43 nm;

*P*

_{0}=10 W;

*T*

_{1}=25°C;

*T*

_{2}=0°C. Figure 1 shows gain spectra calculated for

*N*=1, 2, 4, and 32. For

_{p}*N*=1, 2, 4, the appearance of the spectra is as expected from the previous qualitative description.

_{p}*N*=32 is the minimum value of

_{p}*N*for which the spectrum forms a single smooth peak; the shape of the spectrum remains the same as

_{p}*N*is further increased. This last result shows that all spatial dispersion variations due to temperature variations (and/or other phenomena) that have a period smaller than 1/(32

_{p}*γP*

_{0}), will affect OPA performance only by means of their local average, calculated over a length of the order of 1/(32

*γP*

_{0}).

## 3. Experiments

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

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

**10**, 1133–1141, (2004). [CrossRef]

*y*of the diameter [corresponding to the fraction on

*x*=cos

^{-1}(1-2

*y*)/

*π*of the circumference] could be immersed in ice water.

## 4. Experimental results

*y*of the DSF fiber spool diameter submerged in the ice water.

*λ*

_{p}was 1540.43 nm. The ASE peak is an indication of the OPA gain spectrum. As

*y*increases from 0 to 2/3, the ASE spectrum shifts to the right, the peak wavelength increasing from 1462.98 nm to 1472.99 nm (i.e. Δ

*λ*≈10 nm), consistent with what we have obtained in Ref. [5

**10**, 1133–1141, (2004). [CrossRef]

*λ*

_{0}, in good agreement with what we predicted in previous section.

*λ*=1540.43 nm. The circumference of the spooled fiber was

_{p}*C*=0.518 m, so that

*N*

_{p}=387. We see that there is excellent agreement with the experimental results: the locations of the peaks, as well as their widths at -20 dB match very well. In order to obtain a good match for the peak locations, we had to use the value

*dλ*

_{0}/

*dT*=0.034 nm/°C, which is close to typical values generally used for DSF [3

3. K. C. Byron, M. A. Bedgood, A. Finney, C. McGauran, S. Savory, and I. Watson, “Shifts in zero dispersion wavelength due to pressure, temperature and strain in dispersion shifted singlemode fibers,” IEE Electron. Lett. **28**, 1712–1714 (1992). [CrossRef]

*λ*=1540.43 nm. We see that the match with the experimental ASE spectrum is quite good. In particular the relative heights of the two adjacent Stokes peaks in the two-temperature case are also found by simulation to be uneven; the same is true for the anti-Stokes peaks.

_{p}## 5. Discussion

*λ*

_{0}(

*z*) variations in a typical HNLF; 2) the possibility of flattening the broad gain spectrum in a one-pump fiber OPA.

*λ*

_{0}actually may not be provide the most desirable gain spectrum shape, and one might thus want to obtain some other well-controlled

*λ*

_{0}distribution. The relationship between

*λ*

_{0}(

*z*) and the spectrum shape is a complex one, and to date it has not received much attention. One exception is Ref. [9

9. L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, “Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,” J. Opt. Soc. Am. B **20**, 1532–1537 (2003). [CrossRef]

*λ*

_{0}, it is possible to obtain a gain spectrum which is nearly rectangular, a desirable shape for such applications as wideband optical communication. If we assume that we start from a perfect fiber with uniform

*λ*

_{0}, all we need to do is wind it onto four different spools, and bring them to different temperatures by heating or cooling; this is a simple extension of our setup in Fig. 3(b). A numerical example in Ref. [9

9. L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, “Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,” J. Opt. Soc. Am. B **20**, 1532–1537 (2003). [CrossRef]

*λ*

_{0}span a 5.5 nm range, which corresponds to a 92°C temperature range. This is larger than the range considered above, but is still smaller than the range already demonstrated for SBS suppression [4

4. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. **19**, 1691–1697 (2001). [CrossRef]

*λ*

_{0}variations as severe as in Ref. [8

8. A. Mussot, E. Lantz, T. Sylvestre, H. Maillotte, A. Durecu-Legrand, C. Simonneau, and D. Bayart, “Zero-dispersion wavelength mapping of a highly nonlinear optical fibre-based parametric amplifier,” 30th European Conference on Optical Communication. ECOC 2004, 5–9 Sept. 2004, Stockholm, Sweden; p.190–1vol.2

*λ*

_{0}regions, one would need a distributed temperature control, to counteract the local

*λ*

_{0}variations, and to impose the desired ones. In other words, the system would need to be the same as above. On the other hand, if progress in the manufacture of HNLF succeeds in greatly reducing

*λ*

_{0}fluctuations, then the simple four-spool arrangement should be sufficient to obtain a rectangular OPA gain spectrum as proposed in Ref. [9

9. L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, “Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,” J. Opt. Soc. Am. B **20**, 1532–1537 (2003). [CrossRef]

*λ*

_{0}(

*z*) by means of temperature has a considerable advantage over the alternative method of splicing together different fibers, namely the absence of splicing loss. There is essentially no limit to how many different regions one can have by temperature control, whereas splice loss limits the alternative approach to just a few segments, and modifies the spectrum compared to the ideal lossless case [6

6. M. E. Marhic, F. S. Yang, M. C. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” IEEE J. Lightwave Technol. **17**, 210–215 (1999). [CrossRef]

## 6. Conclusion

## Appendix

*λ*

_{0}along their length exhibit gain when -4

*γP*

_{0}<Δ

*β*<0. Hence we can find the location of the edge of the gain region(s) by solving the equation

*ω*

_{s})

^{2}. The simplest root is (Δ

*ω*

_{sa})

^{2}=0; it corresponds to the wide gain region containing the pump wavelength, 5 which has been studied extensively in recent years. The other root is

*ω*

_{sb}can be increased arbitrarily by moving

*λ*

_{p}away from

*λ*

_{0}; hence we can obtain a second gain region, away from the pump. In Ref. [5

**10**, 1133–1141, (2004). [CrossRef]

*λ*and

_{p}*λ*

_{0}, and therefore to the fiber temperature, as it modifies

*λ*

_{0}. For this reason, in this paper we focus on the effect of temperature on this narrow gain feature, rather than on the usual broader gain region containing

*λ*.

_{p}## Acknowledgments

## References and Links

1. | M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. |

2. | M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. |

3. | K. C. Byron, M. A. Bedgood, A. Finney, C. McGauran, S. Savory, and I. Watson, “Shifts in zero dispersion wavelength due to pressure, temperature and strain in dispersion shifted singlemode fibers,” IEE Electron. Lett. |

4. | J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. |

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

6. | M. E. Marhic, F. S. Yang, M. C. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” IEEE J. Lightwave Technol. |

7. | OptSim, distributed by RSoft (http://www.rsoftdesign.com). A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “Time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber,” IEEE J. Sel. Areas Commun.15, 751–765 (1997). [CrossRef] |

8. | A. Mussot, E. Lantz, T. Sylvestre, H. Maillotte, A. Durecu-Legrand, C. Simonneau, and D. Bayart, “Zero-dispersion wavelength mapping of a highly nonlinear optical fibre-based parametric amplifier,” 30th European Conference on Optical Communication. ECOC 2004, 5–9 Sept. 2004, Stockholm, Sweden; p.190–1vol.2 |

9. | L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, “Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,” J. Opt. Soc. Am. B |

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

(060.2330) Fiber optics and optical communications : Fiber optics communications

(190.4370) Nonlinear optics : Nonlinear optics, fibers

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 9, 2005

Revised Manuscript: June 4, 2005

Published: June 13, 2005

**Citation**

K. K. Y. Wong, M. Marhic, and L. Kazovsky, "Temperature control of the gain spectrum of fiber optical parametric amplifiers," Opt. Express **13**, 4666-4673 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-12-4666

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### References

- M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, �??Broadband fiber optical parametric amplifiers,�?? Opt. Lett. 21, 573-575 (1996). [CrossRef] [PubMed]
- M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, �??Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,�?? Opt. Lett. 21, 1354-1356 (1996). [CrossRef] [PubMed]
- K. C. Byron, M. A. Bedgood, A. Finney, C. McGauran, S. Savory, and I. Watson, �??Shifts in zero dispersion wavelength due to pressure, temperature and strain in dispersion shifted singlemode fibers,�?? IEE Electron. Lett. 28, 1712-1714 (1992). [CrossRef]
- J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, �??Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,�?? J. Lightwave Technol. 19, 1691-1697 (2001). [CrossRef]
- M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky., �??Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,�?? IEEE J. Sel. Top. Quantum. Electron. 10, 1133-1141, (2004). [CrossRef]
- M. E. Marhic, F. S. Yang, M. C. Ho, and L. G. Kazovsky, �??High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,�?? IEEE J. Lightwave Technol. 17, 210-215 (1999). [CrossRef]
- OptSim, distributed by RSoft <a href=�??http://www.rsoftdesign.com�??>(http://www.rsoftdesign.com)</a>. A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, �??Time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber,�?? IEEE J. Sel. Areas Commun. 15, 751-765 (1997). [CrossRef]
- A. Mussot, E. Lantz, T. Sylvestre, H. Maillotte, A. Durecu-Legrand, C. Simonneau, and D. Bayart, �??Zerodispersion wavelength mapping of a highly nonlinear optical fibre-based parametric amplifier,�?? 30th European Conference on Optical Communication. ECOC 2004, 5-9 Sept. 2004, Stockholm, Sweden; p.190-1 vol.2
- L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, �??Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,�?? J. Opt. Soc. Am. B 20, 1532-1537 (2003). [CrossRef]

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