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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23712–23718
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Optical frequency comb generation based on repeated frequency shifting using two Mach-Zehnder modulators and an asymmetric Mach-Zehnder interferometer

Wangzhe Li and Jianping Yao  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23712-23718 (2009)
http://dx.doi.org/10.1364/OE.17.023712


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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

Optical frequency comb generation (OFCG) is an important technique that can find numerous applications, such as dense-wavelength-division multiplexing, optical signal processing [1

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.

], millimeter- and terahertz wave generation [2

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 Proceedings of the 36th European Microwave Conf. (2006), pp. 1107–1110.

] and arbitrary waveform generation [3

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]

]. A number of techniques have been reported to generate an optical comb. An optical comb can be generated using a sinusoidally driven phase modulator placed in a fiber loop with a loop gain slightly less than unity [4

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

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]

]. Once the loop resonance frequency is an integral subharmonic of the modulation frequency and of the input optical frequency [4

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]

], a wide optical comb can be obtained [5

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]

]. The major difficulty associated with this technique is the poor stability. To ensure a stable operation, a feedback control is required [6

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]

]. The incorporation of an optical resonant structure (e.g., a Fabry-Perot cavity) can also improve the resonance stability [7

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]

]. The improvement in [6

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]

] and [7

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]

] was achieved at the cost of a higher complexity and a lower tunability. External modulation, using a dual-electrode Mach-Zehnder modulator (MZM) driven by two sinusoidal signals, has been proposed to generate a flexible, yet stable optical comb [8

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

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]

]. The major limitation of this approach is that the RF power has to be as high as several Watts to generate a wide comb, which limits the suitability for practical applications. To eliminate the requirement for a high RF power while maintaining other advantages, optical nonlinear effects in an optical fiber have been used in combination with the external modulation approach to generate a stable and flexibly tunable comb [10

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

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.

], but a high power erbium-doped fiber amplifier (EDFA) and a highly nonlinear fiber should be used. An optical comb can also be generated using a single-sideband modulator based on repeated frequency shifting [12

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]

]. As an input light wave is circulating in the loop, after each circulation, a new comb line is generated thanks to the frequency shifting. The single-sideband modulator is a specially designed integrated device that consists of three sub-MZMs [13

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]

]. Since the operation of the single-sideband (SSB) modulator requires three DC bias controls, an extra care must be made to minimize the bias drifting, to avoid the generation of undesired optical sidebands, which would generate positive feedback in the loop, further deteriorating the stability.

2. Principle

The schematic of the proposed optical comb generator is shown in Fig. 1(a)
Fig. 1 (a) Schematic diagram of the proposed optical comb generator based on repeated frequency shifting; (b) wavelength-shifted transmission spectra of the AMZI along the opposite directions.
. The system consists of a continuous-wave laser source, a 1:1 and a 1:9 optical coupler, three polarization controllers (PCs), a bidirectional AMZI serving as a bidirectional optical comb filter (BOCF), two MZMs and an EDFA. The two MZMs are biased at the optical carrier suppression (OCS) mode and driven by two microwave signals with frequencies 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 of 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

fo+fe1fe2=fofe1fshift
(1)

The sideband f o + f e1f 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. If
fe1+fe2=fFSR
(2)
the 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

fo+fe1fe2=fofe1+fFSRfshift
(3)

For frequency down-shifting, if f o is located at the rising or falling edge of a transmission window, Eq. (1) will be replaced by

fofe1+fe2=fo+fe1fFSRfshift
(4)
or  fofe1+fe2=fo+fe1+fFSRfshift
(5)

Pin=n=0P'(n+1)=n=0ηP(n)
(7)

The gain 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=G(Pin)=Gmax1+(Pin/Psat)α
(8)
where 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

κGP'(n+1)=κGηP(n)=P(n+1)
(9)

Therefore, we have

P(n)=(κGη)nP(0)
(10)

Due to the gain saturation in the EDFA, the value of κGη will be less than 1. Equation (7) is rewritten as

Pin=n=1η(κGη)n1P(0)=ηP(0)1κGη
(11)

From Eq. (10), the 3-dB comb width W is given by

W=nfFSR=3fFSR10log(1/κGη)
(12)

For a given EDFA and the values of η and κ, G can be calculated by solving Eq. (8) and Eq. (11), and so is the P(n). Figure 2
Fig. 2 Theoretically calculated envelope of the optical comb, in which the power distribution P(n) versus n for three different values of κGη is shown.
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.

According to Eq. (11), as the value of 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

Pin=n=1Nη(κGη)n1P(0)={ηP(0)[1(κGη)N1]/(1κGη)κGη<1NηP(0)κGη=1
(13)

It can be seen from Eq. (13) that for a given 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.

A chirped FBG can also be used to modify the profile of the comb, by reshaping the gain curve of the EDFA. In such a case, the gain of the EDFA 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

PFBG(n)=(κη)ni=1nG(i)P(0)=[κG(1)η]ni=1nG(i)G(1)P(0)
(14)
or  10log10PFBG(n)P(0)=10log10[κG(1)η]n+i=1n10log10G(i)G(1)
(15)

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)=PFBG(n)κηPFBG(n1)(n>1)
(16)

The chirped FBG with the corresponding reflection spectrum can by designed based on G(n).

3. Experimental results and discussion

A proof-of-concept experiment is performed based on the setup shown in Fig. 1(a). The two MZMs are two polarization dependent LiNbO3 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)
Fig. 3 (a) The configuration of the AMZI; (b) The measured transmission spectra of the AMZI along the two opposite directions.
. 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.

By either gradually increasing the gain of the EDFA or decreasing the input power 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
Fig. 4 The measured optical spectra of the generated optical frequency comb. From (a) to (f), the gain of the EDFA is gradually increased.
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。

In Fig. 4, some small peaks between dominant comb lines are observed. The generation of these small peaks can be caused by the following reasons: 1) the sum of 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.

The stability of the comb generator mainly depends on the stability of the AMZI and the OCS of the two MZMs. The long-term stability of the system could be affected by the bias drift of the MZMs and the transmission spectra shift of the AMZI. To improve the stability and to simplify the system, the two LiNbO3 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]

]. It was demonstrated that a PolM with a polarization analyser (PA) can operate eqiuvelently as a MZM, but free from bias drift [16

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

A novel approach to generating an optical frequency comb based on repeated frequency shifting has been proposed and experimentally demonstrated. The frequency shifting was implemented via OCS and SSB generation using two MZMs in conjunction with a bidirectional AMZI with wavelength-shifted transmission spectra along the opposite directions. The proposed technique enables the generation of a flexible and stable optical comb with a simple and compact configuration. A theoretical analysis was presented, which was verified by a proof-of-concept experiment. An optical comb covering a spectral range of 0.18 THz was obtained. With a higher frequency shifting efficiency, an optical comb with a wider width and a flatter envelope can be generated. A chirped FBG filter or an optical notch FBG filter can also be incorporated in the loop to flatten or modify the profile of the optical comb.

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through its strategic project grants program.

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 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThN6.

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 Proceedings of the 36th European Microwave Conf. (2006), pp. 1107–1110.

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]

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]

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]

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]

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]

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

  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.
  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 Proceedings of the 36th European Microwave Conf. (2006), pp. 1107–1110.
  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]
  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]
  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]
  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]
  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]

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