## Optical frequency comb generation based on repeated frequency shifting using two Mach-Zehnder modulators and an asymmetric Mach-Zehnder interferometer

Optics Express, Vol. 17, Issue 26, pp. 23712-23718 (2009)

http://dx.doi.org/10.1364/OE.17.023712

Acrobat PDF (191 KB)

### Abstract

A novel approach to generating an optical frequency comb based on repeated frequency shifting is proposed and experimentally demonstrated. The frequency shifting is implemented via optical carrier suppression and single-sideband modulation using two Mach-Zehnder modulators in conjunction with a bidirectional asymmetric Mach-Zehnder interferometer with wavelength-shifted transmission spectra along the opposite directions. A theoretical analysis is performed, which is confirmed by a proof-of-concept experiment. A stable optical comb covering a spectral range of 0.18 THz is generated.

© 2009 OSA

## 1. Introduction

1. P. J. Delfyett, F. Quinlan, S. Ozharar, and W. Lee, “Stabilized optical frequency combs from diode lasers–applications in optical communications, signal processing and instrumentation,” in *Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference*, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThN6.

3. Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral line-by-line pulse shaping on an optical frequency comb generator,” IEEE J. Quantum Electron. **43**(12), 1163–1174 (2007). [CrossRef]

4. K. P. Ho and J. M. Kahn, “Optical frequency comb generator using phase modulation in amplified circulating loop,” IEEE Photon. Technol. Lett. **5**(6), 721–725 (1993). [CrossRef]

6. P. Shen, N. J. Gomes, P. A. Davies, P. G. Huggard, and B. N. Ellison, “Analysis and demonstration of a fast tunable fiber-ring based optical frequency comb generator,” J. Lightwave Technol. **25**(11), 3257–3264 (2007). [CrossRef]

4. K. P. Ho and J. M. Kahn, “Optical frequency comb generator using phase modulation in amplified circulating loop,” IEEE Photon. Technol. Lett. **5**(6), 721–725 (1993). [CrossRef]

5. S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. **11**(5), 551–553 (1999). [CrossRef]

6. P. Shen, N. J. Gomes, P. A. Davies, P. G. Huggard, and B. N. Ellison, “Analysis and demonstration of a fast tunable fiber-ring based optical frequency comb generator,” J. Lightwave Technol. **25**(11), 3257–3264 (2007). [CrossRef]

7. M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. **29**(10), 2693–2701 (1993). [CrossRef]

6. P. Shen, N. J. Gomes, P. A. Davies, P. G. Huggard, and B. N. Ellison, “Analysis and demonstration of a fast tunable fiber-ring based optical frequency comb generator,” J. Lightwave Technol. **25**(11), 3257–3264 (2007). [CrossRef]

7. M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. **29**(10), 2693–2701 (1993). [CrossRef]

8. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. **32**(11), 1515–1517 (2007). [CrossRef] [PubMed]

9. S. Ozharar, F. Quinlan, I. Ozdur, S. Gee, and P. J. Delfyett, “Ultraflat optical comb generation by phase-only modulation of continuous-wave light,” IEEE Photon. Technol. Lett. **20**(1), 36–38 (2008). [CrossRef]

10. K. Imai, M. Kourogi, and M. Ohtsu, “30-THz span optical frequency comb generation by self-phase modulation in an optical fiber,” IEEE J. Quantum Electron. **34**(1), 54–60 (1998). [CrossRef]

11. R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in *Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference*, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OWJ3.

12. T. Kawanishi, T. Sakamoto, S. Shinada, and M. Izutsu, “Optical frequency comb generator using optical fiber loops with single sideband modulation,” IEICE Electron. Express **1**(8), 217–221 (2004). [CrossRef]

13. T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett. **16**(6), 1534–1536 (2004). [CrossRef]

**25**(11), 3257–3264 (2007). [CrossRef]

11. R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in *Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference*, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OWJ3.

**25**(11), 3257–3264 (2007). [CrossRef]

7. M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. **29**(10), 2693–2701 (1993). [CrossRef]

8. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. **32**(11), 1515–1517 (2007). [CrossRef] [PubMed]

10. K. Imai, M. Kourogi, and M. Ohtsu, “30-THz span optical frequency comb generation by self-phase modulation in an optical fiber,” IEEE J. Quantum Electron. **34**(1), 54–60 (1998). [CrossRef]

11. R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in *Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference*, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OWJ3.

## 2. Principle

*f*

_{e1}and

*f*

_{e2}(assume

*f*

_{e1}<

*f*

_{e2}). Thank to the OCS, the MZM would only generate odd-order sidebands. Since the phase modulation index of the MZM is small, only the first-order sidebands are considered and the higher-order sidebands can be ignored. The free spectral range (FSR) of the BOCF is

*f*

_{FSR}, and the two transmission spectra of the AMZI along the two opposite directions are shifted by

*f*

_{shift}, as shown in Fig. 1(b). The process of the frequency up-shifting in the optical spectral domain is illustrated in Fig. 1(b). The incident light wave at frequency

*f*

_{o}is sent to the first MZM (MZM1) and only two sidebands

*f*

_{o}±

*f*

_{e1}are generated thanks to the OCS. After going through the AMZI, the sideband

*f*

_{o}–

*f*

_{e1}is removed and the sideband

*f*

_{o}+

*f*

_{e1}is kept if

*f*

_{o}is tuned at the rising edge of a transmission window of the AMZI, and

*f*

_{e1}<

*f*

_{FSR}/2. The sideband

*f*

_{o}+

*f*

_{e1}is then modulated by the second MZM (MZM2) and the generated two new sidebands

*f*

_{o}+

*f*

_{e1}±

*f*

_{e2}are then sent to the AMZI along the opposite direction. When the transmission spectrum along the opposite direction is shifted by a proper

*f*

_{shift}, we have

*f*

_{o}+

*f*

_{e1}–

*f*

_{e2}is removed while the

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}is kept and then amplified by the EDFA. The 10% output of the EDFA is sent to an optical spectrum analyzer (OSA) via the 1:9 coupler, and the 90% is routed to MZM1 via the 1:1 optical combiner. After the first circulation, the frequency of the incident lightwave

*f*

_{o}is up-converted to

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}. Ifthe relative position of

*f*

_{o}to a transmission window of the AMZI will be the same as that of

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}=

*f*

_{o}+

*f*

_{FSR}. Once the sideband

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}is routed back to MZM1, it will also be up-shifted to

*f*

_{o}+ 2(

*f*

_{e1}+

*f*

_{e2}) after the second circulation and such frequency up-shifting repeats as the circulation continues. If

*f*

_{o}is located at the falling edge of a transmission window and

*f*

_{e1}>

*f*

_{FSR}/2, to realize the frequency up-shifting, Eq. (1) will be replaced by

*f*

_{o}is located at the rising or falling edge of a transmission window, Eq. (1) will be replaced by

*f*

_{FSR}. The frequency shifting process will become stable until the EDFA is saturated. The spacing between two adjacent comb lines is equal to the FSR of the transmission spectra of the AMZI. Under a steady-state operation, we assume that the optical comb at the input port of MZM1 has a power distribution of

*P*(

*n*) which represents the power of the incident light wave, and

*n*= 0, 1, 2, …, refers to the

*n*

^{th}comb line except for

*n*= 0. With frequency shifting, the power distribution of the new comb at the input port of the EDFA iswhere

*η*is the power efficiency of the frequency shifting. The total input power

*P*

_{in}to the EDFA is given by

*G*of the EDFA is a function of the input power

*P*

_{in}given by [14

14. X. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. **12**(1), 28–30 (2000). [CrossRef]

*G*

_{max}is the unsaturated, small-signal gain,

*P*

_{sat}is an internal saturation power and

*α*is a characteristic parameter of the EDFA. Therefore, after amplified by the EDFA, the power distribution of the optical comb becomes

*GP*′(

*n*+ 1). The amplified comb is then routed back to MZM1 via the two optical couplers with a total coupling coefficient of

*κ*. Since the system is under steady-state, the power distribution of the optical comb must satisfy

*κGη*will be less than 1. Equation (7) is rewritten as

*W*is given by

*η*and

*κ*,

*G*can be calculated by solving Eq. (8) and Eq. (11), and so is the

*P*(

*n*). Figure 2 shows a theoretically calculated comb envelope of the power distribution

*P*(

*n*) for three different values of

*κGη.*From Fig. 2, it is obvious that the power of the comb line is decreasing as

*n*is increasing, and the comb envelope becomes flatter and wider as the value of

*κGη*is greater.

*κGη*increases to unity,

*P*

_{in}will increase significantly, which would lead to a decrease of the value of

*G*. Due to the tradeoff between the gain of the EDFA and

*P*

_{in}, increasing the value of

*κGη*up to unity is difficult. To further flatten the profile of the generated comb, a chirped fiber Bragg grating (FBG) filter or simply an optical notch filter can be incorporated in the loop, as shown in Fig. 1, to intentionally discontinue the frequency shifting process and limit the number of the comb lines to a finite number,

*N*. In such a case, the total input power

*P′*

_{in}to the EDFA is given by

*N*there is an upper limit to the value of

*P*

_{in}. Thus, the value of

*κGη*can be increased to unity to generate a flat comb [13]. The number of the comb lines will be decided by the spectrum width of the chirped FBG filter or the spacing between the wavelength of the input light wave and the centre wavelength of the optical notch filter.

*G*(

*n*) depends on the frequency of the comb line, namely, the value of

*n*.

*P*(

*n*) becomes

*P*

_{FBG}(

*n*). Equation (10) is rewritten as

*G*(

*n*)/

*G*(1) is decided by the reflection spectrum of the chirped FBG. The first term in the right-hand side of Eq. (15) is the power distribution of the comb given the value of

*κG*(1)

*η*without the FBG; the second term is the modification term introduced by the chirped FBG to modify the profile of the generated comb. From Eq. (15), for a desired

*P*

_{FBG}(

*n*),

*G*(

*i*) is calculated by

*G*(

*n*).

4. K. P. Ho and J. M. Kahn, “Optical frequency comb generator using phase modulation in amplified circulating loop,” IEEE Photon. Technol. Lett. **5**(6), 721–725 (1993). [CrossRef]

**25**(11), 3257–3264 (2007). [CrossRef]

*κ*,

*G*and

*η*. In the previous methods, however, the power distribution of the optical comb is also dependent on the dispersion, since the resonant conditions must be met [4

**5**(6), 721–725 (1993). [CrossRef]

*f*

_{e1}and

*f*

_{e2}. Once

*f*

_{e1}and

*f*

_{e2}are set, the comb spacing is determined. Any variation of the FSR of the AMZI and

*f*

_{shift}due to the instability of the AMZI would degrade the SSB modulation and to reduce the frequency shifting efficiency

*η*. In addition, the variations of these parameters will also cause the generation of undesired sidebands which may not be perfectly removed by the AMZI.

## 3. Experimental results and discussion

_{3}electro-optical modulators. Three PCs are used to adjust the polarization of the input light waves to minimize the polarization dependent loss. The AMZI is implemented using a polarization-maintaining fiber (PMF) in conjunction with two optical circulators (OCs) and two polarization analyzers (PAs), as shown in Fig. 3(a) . Since the light waves with orthogonal polarizations are traveling in the same fiber, the AMZI has a better stability compared to an AMZI with a structure having two physically separated arms. The two PAs are actually the two MZMs since the waveguides inside the MZMs support only the TE mode. The transmission spectra of the AMZI along the two opposite directions are measured and shown in Fig. 3(b). The FSR is approximately 26.8 GHz and the isolation depth is more than 30 dB. The frequency shift

*f*

_{shift}is adjusted to make it be equal to one quarter of

*f*

_{FSR}, which is 6.7 GHz, and

*f*

_{o}is located at the falling edge of one transmission window. According to Eqs. (2) and (3), we have

*f*

_{e1}= 20.1 GHz,

*f*

_{e2}= 6.7 GHz.

*P*(0), the value of

*κGη*can be increased. The optical spectrum at the output of the 10% port of the 1: 9 optical coupler is observed by the OSA. Figure 4 shows the recorded optical spectra of the generated optical frequency comb. The comb line spacing is 26.8 GHz, which is equal to the FSR of the AMZI. From Fig. 4, it can be clearly seen that as the gain of the EDFA is increased, more and more comb lines are generated and the comb envelope becomes flatter. Due to the large insertion loss in the loop and SSB modulation loss, the power efficiency of the frequency shifting is very low, an optical comb with comb lines up to seven spanning a spectral range over approximately 0.18 THz is generated. But the results have clearly demonstrated the capability of the proposed approach in optical comb generation. It is believed that more comb lines with a much flatter envelope would be obtained with a much greater

*κGη*. The comb line spacing can be tuned by changing the FSR of the AMZI and

*f*

_{e1}and

*f*

_{e2。}

*f*

_{e1}and

*f*

_{e2}is not exactly equal to

*f*

_{FSR}; 2) the wavelength shift of the AMZI spectra does not exactly satisfy Eq. (3); and 3) the two MZMs are not biased perfectly at the OCS.

_{3}electro-optical modulators can be replaced by two polarization modulators (PolMs) [15

15. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE **5577**, 133–143 (2004). [CrossRef]

16. S. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett. **21**(13), 929–931 (2009). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | P. J. Delfyett, F. Quinlan, S. Ozharar, and W. Lee, “Stabilized optical frequency combs from diode lasers–applications in optical communications, signal processing and instrumentation,” in |

2. | A. J. Seeds, C. C. Renaud, M. Pantouvaki, M. Robertson, I. Lealman, D. Rogers, R. Firth, P. J. Cannard, R. Moore, and R. Gwilliam, “Photonic synthesis of THz signals,” in |

3. | Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral line-by-line pulse shaping on an optical frequency comb generator,” IEEE J. Quantum Electron. |

4. | K. P. Ho and J. M. Kahn, “Optical frequency comb generator using phase modulation in amplified circulating loop,” IEEE Photon. Technol. Lett. |

5. | S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. |

6. | P. Shen, N. J. Gomes, P. A. Davies, P. G. Huggard, and B. N. Ellison, “Analysis and demonstration of a fast tunable fiber-ring based optical frequency comb generator,” J. Lightwave Technol. |

7. | M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. |

8. | T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. |

9. | S. Ozharar, F. Quinlan, I. Ozdur, S. Gee, and P. J. Delfyett, “Ultraflat optical comb generation by phase-only modulation of continuous-wave light,” IEEE Photon. Technol. Lett. |

10. | K. Imai, M. Kourogi, and M. Ohtsu, “30-THz span optical frequency comb generation by self-phase modulation in an optical fiber,” IEEE J. Quantum Electron. |

11. | R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in |

12. | T. Kawanishi, T. Sakamoto, S. Shinada, and M. Izutsu, “Optical frequency comb generator using optical fiber loops with single sideband modulation,” IEICE Electron. Express |

13. | T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett. |

14. | X. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. |

15. | D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE |

16. | S. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(350.4010) Other areas of optics : Microwaves

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 23, 2009

Revised Manuscript: November 26, 2009

Manuscript Accepted: December 7, 2009

Published: December 11, 2009

**Citation**

Wangzhe Li and Jianping Yao, "Optical frequency comb generation based on repeated frequency shifting using two Mach-Zehnder modulators and an asymmetric Mach-Zehnder interferometer," Opt. Express **17**, 23712-23718 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23712

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### References

- P. J. Delfyett, F. Quinlan, S. Ozharar, and W. Lee, “Stabilized optical frequency combs from diode lasers–applications in optical communications, signal processing and instrumentation,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThN6.
- A. J. Seeds, C. C. Renaud, M. Pantouvaki, M. Robertson, I. Lealman, D. Rogers, R. Firth, P. J. Cannard, R. Moore, and R. Gwilliam, “Photonic synthesis of THz signals,” in Proceedings of the 36th European Microwave Conf. (2006), pp. 1107–1110.
- Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral line-by-line pulse shaping on an optical frequency comb generator,” IEEE J. Quantum Electron. 43(12), 1163–1174 (2007). [CrossRef]
- K. P. Ho and J. M. Kahn, “Optical frequency comb generator using phase modulation in amplified circulating loop,” IEEE Photon. Technol. Lett. 5(6), 721–725 (1993). [CrossRef]
- S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. 11(5), 551–553 (1999). [CrossRef]
- P. Shen, N. J. Gomes, P. A. Davies, P. G. Huggard, and B. N. Ellison, “Analysis and demonstration of a fast tunable fiber-ring based optical frequency comb generator,” J. Lightwave Technol. 25(11), 3257–3264 (2007). [CrossRef]
- M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29(10), 2693–2701 (1993). [CrossRef]
- T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. 32(11), 1515–1517 (2007). [CrossRef] [PubMed]
- S. Ozharar, F. Quinlan, I. Ozdur, S. Gee, and P. J. Delfyett, “Ultraflat optical comb generation by phase-only modulation of continuous-wave light,” IEEE Photon. Technol. Lett. 20(1), 36–38 (2008). [CrossRef]
- K. Imai, M. Kourogi, and M. Ohtsu, “30-THz span optical frequency comb generation by self-phase modulation in an optical fiber,” IEEE J. Quantum Electron. 34(1), 54–60 (1998). [CrossRef]
- R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OWJ3.
- T. Kawanishi, T. Sakamoto, S. Shinada, and M. Izutsu, “Optical frequency comb generator using optical fiber loops with single sideband modulation,” IEICE Electron. Express 1(8), 217–221 (2004). [CrossRef]
- T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett. 16(6), 1534–1536 (2004). [CrossRef]
- X. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 12(1), 28–30 (2000). [CrossRef]
- D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE 5577, 133–143 (2004). [CrossRef]
- S. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett. 21(13), 929–931 (2009). [CrossRef]

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