## Wavelength conversion bandwidth in fiber based optical parametric amplifiers

Optics Express, Vol. 11, Issue 9, pp. 1002-1007 (2003)

http://dx.doi.org/10.1364/OE.11.001002

Acrobat PDF (90 KB)

### Abstract

We propose a systematic approach to evaluating and optimising the wavelength conversion bandwidth and gain ripple of four-wave mixing based fiber optical wavelength converters. Truly tunable wavelength conversion in these devices requires a highly tunable pump. For a given fiber dispersion slope, we find an optimum dispersion curvature that maximises the wavelength conversion bandwidth.

© 2003 Optical Society of America

## 1. Introduction

1. T. Yamamoto, T. Imai, Y. Miyajima, and M. Nakazawa, “High speed optical path routing by using four-wave mixing and a wavelength router with fiber gratings and optical circulators,” Opt. Commun. **120**, 245–248 (1995). [CrossRef]

2. N. Antoniades, S. J. B. Yoo, K. Bala, G. Ellinas, and T. E. Stern, “An architecture for a wavelength-interchanging cross-connect utilizing parametric wavelength converters,” IEEE J. Lightwave Tech. **17**, 1113–1125 (1999). [CrossRef]

3. S. Nakamura, Y. Ueno, and K. Tajima, “168-Gb/s All-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch,” IEEE Photonics Tech. Lett. **13**, 1091–1093 (2001). [CrossRef]

4. S. Spälter, H. Y. Hwang, J. Zimmermann, G. Lenz, T. Katsufuji, S.-W. Cheong, and R. E. Slusher, “Strong self-phase modulation in planar chalcogenide glass waveguides,” Opt. Lett. **27**, 363–365 (2002). [CrossRef]

6. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photonics Tech. Lett. **14**, 1506–1508 (2002). [CrossRef]

7. M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. **38**, 85–86 (2002). [CrossRef]

9. J. L. Blows and S. E. French, “Low-noise-figure optical parametric amplifier with a continuous-wave frequency modulated pump,” Opt. Lett. **27**, 491–493 (2002). [CrossRef]

_{s}, to any converted wavelength λ

_{c}, within a wavelength range Δλ, can be represented by a vertical line of length Δλ on Fig. 1(a), which is a plot of λ

_{c}against λ

_{s}. A horizontal line on this diagram represents conversion to a fixed λ

_{c}from any λ

_{s}. Therefore conversion from any λ

_{s}to any λ

_{c}within that range is contained within a solid square with side length Δλ. Because here we are only concerned with conversion within the same band, this square must lie symmetrically about the line λ

_{c}=λ

_{s}, as shown in Fig. 1(c). Furthermore, the conversion efficiency from λ

_{s}to λ

_{c}should ideally be constant, that is independent of both λ

_{s}and λ

_{c}.

_{c}=1/(2/λ

_{p}-1/λ

_{s}), where λ

_{p}is the pump wavelength. Therefore a tunable λ

_{c}is obtained by moving λ

_{p}. Different design considerations apply to fiber parametric amplifiers depending on whether their final application is as wavelength converters (possibly with gain) or as broadband amplifiers. PWCs require a tunable λ

_{c}, and so need a tunable λ

_{p}, whereas parametric amplifiers designed solely for amplification [11] are optimised for gain bandwidth and flatness at a single pump wavelength only.

7. M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. **38**, 85–86 (2002). [CrossRef]

_{s},λ

_{c}) space have appeared previously [7

7. M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. **38**, 85–86 (2002). [CrossRef]

_{s},λ

_{c}) space and systematically investigates methods to maximise the size of the square by tailoring device parameters.

*G*

_{thresh}, and the local maxima are denoted

*G*

_{max}, then the gain ripple is given by

*R*=

*G*

_{max}/

*G*

_{thresh}.

_{s},λ

_{p}). This plot would show the boundaries of the regions for which the converter gain is above

*G*

_{thresh}. The plot is then made compatible with Fig. 1(c) by converting the λ

_{p}axis to λ

_{c}using λ

_{c}=1/(2/λ

_{p}-1/λ

_{s}), as has been done for Fig. 3. Therefore Fig. 3 shows that a PWC is far from an ideal device because it does not map to a square that is similar to Fig. 1(c). However, by fitting the largest possible square within the solid lines on this figure, one defines a region in which the PWC operates close to an ideal device. This square is a contour enclosing the combinations of λ

_{s}and λ

_{c}for which the power of λ

_{c}is above

*G*

_{thresh}. The bandwidth of the PWC is then given by the side length of this inscribed square.

## 2. Theory

_{p}and power

*P*

_{p}. The four-wave mixing process then generates two photons of frequencies ω

_{s}and ω

_{c}that are symmetric around ω

_{p}, from the annihilation of two photons at ω

_{p}. Thus

_{s}(wavelength λ

_{s}), so the frequency of the converted wave ω

_{c}(wavelength λ

_{c}) is then determined by pump frequency from Eq. (1). Thus ω

_{c}can be chosen from a range Δω by varying the pump frequency ω

_{p}over a range Δω/2. The gain,

*G*, of this process is given by

*L*is the fiber length, and the parametric gain,

*g*, is given by

*g*is maximum when Δβ=2γ

*P*

_{p}, and the corresponding value fo

*G*. and the The maximum value of

*g*occurs when Δβ=2γ

*P*

_{p}and the corresponding

*G*is the maximum gain for a parametric amplifier. We choose this maximum gain to be the

*G*

_{max}for PWCs, so therefore

_{c}=λ

_{s}=λ

_{p}, the gain equals

*G*

_{max}and

*G*

_{0}can be considered constant because Eqs. (5) and (6) both depend on the fiber only through γ, which is slowly varying with ω. In fact, as is customary in this field of research, γ is assumed constant over the limited wavelength ranges that we are considering (see Table 1). This is consistent with Fig. 2(a), which shows that, for our parameters, the gain in the central minimum (at Δβ=0) and the maximum gain do not depend on λ

_{p}.

_{2}) vanishes at frequency ω

_{0}and with cubic (β

_{3}) and quartic (β

_{4}) dispersions defined at ω

_{0}. Ignoring higher-order dispersion, Δβ can be rewritten as

*G*

_{thresh})

^{±}. An analytic solution to these equations is possible with careful selection of

*G*

_{thresh}. For

*G*

_{0}<

*G*

_{thresh}<

*G*

_{max}, the gain

*G*

_{0}at λ

_{c}=λ

_{s}is, by assumption, below the minimum acceptable gain and so the requirements described by Fig. 1(c) cannot be met. In contrast, for

*G*

_{thresh}≤

*G*

_{0}, the requirements of Fig. 1(c) can always be satisfied. We choose

*G*

_{thresh}=

*G*

_{0}because this leads to the smallest ripple,

*G*

_{thresh}=

*G*

_{0}, Eq. (3) gives an analytic solution for g and Eq. (7) is then used to give analytic expressions for the contours. When β

_{4}≠0, the contours are:

**Φ**=(β

_{4}/2)(ω

_{p}-ω

_{0})

^{2}+β

_{3}(ω

_{p}-ω

_{0}). The ± sign inside the square-root in Eq. (9) is independent of the one outside it. Applying Eq. (1) then gives the equivalent expression for ω

_{c}. Note that if β

_{3}=0 or β

_{4}=0, then the last of Eqs. (9) simplifies considerably. We have also found similar equations for the case β

_{4}=0.

## 3. Results

_{s}=λ

_{0}. These lines intersect with each other and with the original curve. The other two sides can then be found geometrically. We find that when β

_{3}=0,

_{3}and β

_{4}, however, the critical points and intersections used to find the bandwidth have to be found numerically from Eq. (9).

*G*

_{0},

*G*

_{max}or

*R*can be freely chosen. The remaining device parameters are then completely defined by Eqs. (8) and the appropriate solutions to Eq. (10). Equation (10) shows that doubling the bandwidth requires an eight (β

_{4}=0) or sixteenfold (β

_{3}=0) increase in the γ

*P*

_{p}to dispersion-parameter ratio, making it difficult to increase the bandwidth.We have found a novel way to contribute to a further increase in this bandwidth.

_{4}on the

*G*=

*G*

_{0}contour, and therefore the bandwidth, of a PWC.

_{4}that maximises the conversion bandwidth for a fiber with a β

_{3}given in Table 1 and the corresponding maximum bandwidth square is shown in red. The blue square in Fig. 4(a) is the bandwidth for β

_{4}=0. The black bandwidth contours fall inside this blue square when β

_{4}<0. Therefore only values of β

_{4}>0 contribute to an increase in the conversion bandwidth.

_{3}. Figure 4(b) shows these

_{3}, the values of

_{4}=

_{4}=0, in the wavelength range investigated. The red dashed line on Fig. 4 shows the effect on conversion bandwidth when β

_{4}is perturbed by 10% from

## 4. Discussion and conclusions

*P*

_{p}and decrease with increasing dispersion. However, the bandwidth only grows sub-linearly with these parameters. We have also found this to be true in the general case β

_{3}≠0 and β

_{4}≠0. However, optimisation of fiber dispersion parameters can provide a significant further increase in gain bandwidth. Within the square defining the region of operation, and for the particular choice of

*G*

_{thresh}=

*G*

_{0}, Eq. (8) shows that the gain ripple of these devices depends on γ

*P*

_{p}

*L*. This allows independent selection of ripple and bandwidth because for a given piece of fiber, the bandwidth is selected by choosing

*P*

_{p}and the ripple is fixed by the device length. For other choices of

*G*

_{thresh}, this may not be the case.

## Acknowledgements

## References and links

1. | T. Yamamoto, T. Imai, Y. Miyajima, and M. Nakazawa, “High speed optical path routing by using four-wave mixing and a wavelength router with fiber gratings and optical circulators,” Opt. Commun. |

2. | N. Antoniades, S. J. B. Yoo, K. Bala, G. Ellinas, and T. E. Stern, “An architecture for a wavelength-interchanging cross-connect utilizing parametric wavelength converters,” IEEE J. Lightwave Tech. |

3. | S. Nakamura, Y. Ueno, and K. Tajima, “168-Gb/s All-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch,” IEEE Photonics Tech. Lett. |

4. | S. Spälter, H. Y. Hwang, J. Zimmermann, G. Lenz, T. Katsufuji, S.-W. Cheong, and R. E. Slusher, “Strong self-phase modulation in planar chalcogenide glass waveguides,” Opt. Lett. |

5. | N. Chi, L. Xu, L. Christiansen, K. Yvind, J. Zhang, P. Holm-Nielsen, C. Peucheret, C. Zhang, and P. Jeppesen, “Optical label swapping and packet transmission based on ASK/DPSK orthogonal modulation format in IP-over-WDM networks,” in |

6. | K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photonics Tech. Lett. |

7. | M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. |

8. | J. Hiroishi, N. Kumano, K. Mukasa, R. Sugizaki, R. Miyabe, S.-I. Matsushita, H. Tobioka, S. Namaki, and T. Yagi, “Dispersion slope controlled HNL-DSF with high γ of 25W |

9. | J. L. Blows and S. E. French, “Low-noise-figure optical parametric amplifier with a continuous-wave frequency modulated pump,” Opt. Lett. |

10. | G. P. Agrawal, |

11. | L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, “Broadband and flat parametric gain with a single low-power pump in a multi-section fiber arrangement,” in |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(190.2620) Nonlinear optics : Harmonic generation and mixing

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

**ToC Category:**

Research Papers

**History**

Original Manuscript: March 20, 2003

Revised Manuscript: April 17, 2003

Published: May 5, 2003

**Citation**

Ross McKerracher, Justin Blows, and C. de Sterke, "Wavelength conversion bandwidth in fiber based optical parametric amplifiers," Opt. Express **11**, 1002-1007 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-9-1002

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### References

- T. Yamamoto, T. Imai, Y. Miyajima, and M. Nakazawa, �??High speed optical path routing by using four-wave mixing and a wavelength router with fiber gratings and optical circulators,�?? Opt. Commun. 120, 245�??248 (1995). [CrossRef]
- N. Antoniades, S. J. B. Yoo, K. Bala, G. Ellinas, and T. E. Stern, �??An architecture for a wavelength-interchanging cross-connect utilizing parametric wavelength converters,�?? IEEE J. Lightwave Technol. 17, 1113�??1125 (1999). [CrossRef]
- S. Nakamura, Y. Ueno, and K. Tajima, �??168-Gb/s All-optical wavelength conversion with a symmetric-Mach- Zehnder-type switch,�?? IEEE Photonics Tech. Lett. 13, 1091�??1093 (2001). [CrossRef]
- S. Spälter, H. Y. Hwang, J. Zimmermann, G. Lenz, T. aKatsufuji, S.-W. Cheong, and R. E. Slusher, �??Strong selfphase modulation in planar chalcogenide glass waveguides,�?? Opt. Lett. 27, 363�??365 (2002). [CrossRef]
- N. Chi, L. Xu, L. Christiansen, K. Yvind, J. Zhang, P. Holm-Nielsen, C. Peucheret, C.Zhang and P. Jeppesen, �??Optical label swapping and packet transmission based on ASK/DPSK orthogonal modulation format in IP-over- WDM networks,�?? in Proceedings of OFC 2003, Paper FS2 (2003), pp. 792�??794.
- K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, �??Polarization-independent one-pump fiber-optical parametric amplifier,�?? IEEE Photonics Tech. Lett. 14, 1506�??1508 (2002). [CrossRef]
- M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, �??Transparent wavelength conversion in fibre with 24nm pump tuning range,�?? Electron. Lett. 38, 85�??86 (2002). [CrossRef]
- J. Hiroishi, N. Kumano, K. Mukasa, R. Sugizaki, R. Miyabe, S.-I. Matsushita, H. Tobioka, S. Namaki, and T. Yagi, �??Dispersion slope controlled HNL-DSF with high ã of 25W-1km-1 and band conversion experiment using this fibre,�?? in ECOC 2002 Post deadline proceedings (2002), p. PD1.5.
- J. L. Blows and S. E. French, �??Low-noise-figure optical parametric amplifier with a continuous-wave frequency modulated pump,�?? Opt. Lett. 27, 491�??493 (2002). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995), 2nd edn.
- L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte, �??Broadband and flat parametric gain with a single low-power pump in a multi-section fiber arrangement,�?? in Proceedings of OFC 2002, Paper TuS2 (2002), pp. 125�??126.

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