## Raman amplifier design using geometry compensation technique

Optics Express, Vol. 12, Issue 3, pp. 436-441 (2004)

http://dx.doi.org/10.1364/OPEX.12.000436

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### Abstract

We propose a simple technique to optimize a multi-wavelength backward-pumped fiber Raman amplifier. Based on the geometric characteristics of Raman gain profile, we approximate it using several straight lines and utilize slope compensation technique to achieve flat and wideband gain profile. Good simulation results are obtained.

© 2004 Optical Society of America

## 1. Introduction

1. X Zhou and C Lu, et al, “A simple model and optimal design of a multi-wavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. **13**, 945–947 (2001). [CrossRef]

2. V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” IEEE J. Lightwave Technol. **20**, 250–254 (2002). [CrossRef]

2. V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” IEEE J. Lightwave Technol. **20**, 250–254 (2002). [CrossRef]

## 2. Theoretical model and design method

2. V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” IEEE J. Lightwave Technol. **20**, 250–254 (2002). [CrossRef]

_{th}signal channel in dB can be described as a linear superposition of the gain spectra of individual pump wavelengths with respective weighting factors given by the correspending pump integrals, as shown in Eq. (1).

_{jk}=g

_{υj}(υ

_{j}-υ

_{k})/(K

_{eff}A

_{eff}) for υ

_{j}>υ

_{k}and g

_{jk}=-g

_{υk}(υ

_{k}-υ

_{j}) υ

_{k}/(υ

_{j}K

_{eff}A

_{eff}) for υ

_{j}<υ

_{k}, the gain coefficient at pump frequency υ

_{i}are given by g

_{υi}(Δυ)=gR(Δυ). υ

_{j}/υ

_{0}, where g

_{R}(Δυ) is the Raman gain spectrum measured at a reference pump frequency υ

_{0}, A

_{eff}is the effective area of the fibre and K

_{eff}is the polarization factor. k represents one of the m signal channels, j represents one of the n pump wavelengths. g

_{jk}and I

_{j}correspond to the gain profile and the power integral (the area below the power distribution curve of pump lights along the fiber) of different pump and signal waves. α and L are the loss coefficient of fiber at the signal wavelength and the length of the fiber respectively.

_{j0}a

_{j1}a

_{j2}a

_{j3}a

_{j4}a

_{j5}a

_{j6}a

_{j7}a

_{j8}as shown in Fig. 1. For simplicity, frequency rather than wavelength is used for the gain spectrum representation. For silica fiber the frequency intervals are a

_{j1}a

_{j2}=a

_{j3}a

_{j4}=a

_{j4}a

_{j5}=a

_{j5}a

_{j6}=a

_{j6}a

_{j7}=a

_{j7}a

_{j8}=1.7THz and a

_{j2}a

_{j3}=3.4THz respectively. In Fig. 2, S

_{1}is used to represent the gain spectrum of the longest wavelength pump, S

_{2}, S

_{3}, S

_{4}… and S

_{n}are used to represent the gain spectra of the other pump wavelengths. Typically the integral of the longest wavelength pump light S

_{1}is much larger than those from the other pump wavelengths due to strong stimulated Raman interaction of pumps. As a result, we may neglect the contribution of a

_{j0}a

_{j1}and represent the gain spectra of all the other pump wavelengths with a

_{j1}a

_{j2}a

_{j3}a

_{j4}a

_{j5}a

_{j6}a

_{j7}a

_{j8}(j=2,3…n). Since the portion of gain spectrum of a

_{12}a

_{13}can be considered flat, it is possible to equalize the rest of the gain spectrum of S

_{1}, using contributions from the a

_{j1}a

_{j2}(j=2…n) portion of the gain spectra of all the other pump sources to achieve flat gain spectrum. The range of the gain spectrum to be equalized will decide the number of pump wavelengths required.

_{1}and the two other pumps are S

_{2}and S

_{3}as indicated in Fig. 2. The loss of the fibre is considered to be wavelength independent at first. The flat gain profile can be achieved for the signal channels over a frequency region Δf in the gain profile produced by the longest wavelength pump light. After the gain bandwidth region for the amplifier has been decided, the frequency of the longest wavelenght pump light is decided accordingly. We can then use a

_{j1}a

_{j2}(j=2,3) in the gain profile of the two other pump lights to compensate a portion of the gain profile of S

_{1}to obtain a flat gain spectrum. To compensate the slope of a

_{13}a

_{14}in S

_{1}with the slope of a

_{21}a

_{22}in S

_{2}, we should let the frequency of point a

_{21}be equal to that of point a

_{13}, thus the frequency of the second pump light should be shifted 5.1Thz (about 37.5nm) from that of the longest wavelenghth pump light. The pump integral I

_{2}of S

_{2}should be such that the slope of a

_{21}a

_{22}is the same as the slope of a

_{13}a

_{14}but with opposite sign. Similarly to compensate a

_{14}a

_{15}using a

_{31}a

_{32}of S

_{3}, we should let the frequency of point a

_{31}be equal to that of point a

_{22}. Thus the frequency of the third pump light should be shifted 1.7Thz(about 12.75nm) from the frequency of S

_{2}. The pump integral I

_{3}of S

_{3}should be such that the slope of a

_{31}a

_{32}is the same as the slope of a

_{14}a

_{15}but with opposite sign. When wider amplifier bandwidth is needed, we can use more pump wavelengths and compensate the other part of S

_{1}in the same way. The frequencies of all the pump lights can be determined accordingly. However, when deciding the pump integrals, the contributions to the slope of S

_{1}from S

_{2}and S

_{3}should be considered. From the above discussions and with wavelength independent considered, we can obtain following relationship

_{1}is the pump integral of S

_{1}and I

_{j}is pump integral of S

_{j}. ν

_{ai,j}is the frequency corresponding to point a

_{i,j}and g(ν

_{ai,j}) is the Raman gain at frequency ν

_{ai,j}.

_{1}is also represented by multi-segment lines α

_{3}α

_{4}α

_{5}with 1.7THz per segment as shown in Fig.3, where the solid lines highlight the parts in the geometrical compensation model. We can then use it to modify the slope of S

_{1}. Eq. (2) can thus be modified as:

## 3. Numerical example and discussions

3. Howard Kidorf and Karsten Rottitt, et al, “Pump interaction in a 100-nm bandwidth Raman amplifier,” IEEE Photon. Technol. Lett. **11**, 530–533 (1999). [CrossRef]

_{1}in the design process before the compensation procedure is carried out. After the amplification condition is established, the newly obtained inter-channel Raman interaction value is then used to modify the slope of S

_{1}before a new compensation procedure is carried out. Very few iterations are required since the Raman tilt hardly changes after the signal distribution in the presence of the pump is more or less established. The obtained new result is plotted in Fig. 4(b). The modified pump powers are 682mW, 370mW and 254mW respectively. Clearly, this allow flat net gain spectrum to be achieved even if inter-channel Raman interaction is taken into consideration.

## 4. Conclusions

## References and links

1. | X Zhou and C Lu, et al, “A simple model and optimal design of a multi-wavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. |

2. | V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” IEEE J. Lightwave Technol. |

3. | Howard Kidorf and Karsten Rottitt, et al, “Pump interaction in a 100-nm bandwidth Raman amplifier,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

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

(190.5650) Nonlinear optics : Raman effect

(290.5910) Scattering : Scattering, stimulated Raman

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 2, 2003

Revised Manuscript: December 27, 2003

Published: February 9, 2004

**Citation**

Zhaohui Li, Chao Lu, Jian Chen, and Chunliu Zhao, "Raman amplifier design using geometry compensation technique," Opt. Express **12**, 436-441 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-3-436

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### References

- X Zhou, C Lu, et al, �??A simple model and optimal design of a multi-wavelength backward-pumped fiber Raman amplifier,�?? IEEE Photon. Technol. Lett. 13, 945-947 (2001). [CrossRef]
- V. E. Perlin, H. G. Winful, �??Optimal design of flat-gain wide-band fiber Raman amplifiers,�?? IEEE J. Lightwave Technol. 20, 250-254 (2002). [CrossRef]
- Howard Kidorf, Karsten Rottitt, et al, �??Pump interaction in a 100-nm bandwidth Raman amplifier,�?? IEEE Photon. Technol. Lett. 11, 530-533 (1999). [CrossRef]

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