Abstract

We theoretically prove that a conventional Mach–Zehnder modulator can generate an optical frequency comb with excellent spectral flatness. The modulator is asymmetrically dual driven by large amplitude sinusoidal signals with different amplitudes. The driving condition to obtain spectral flatness is analytically derived and optimized, yielding a simple formula. This formula also predicts the conversion efficiency and bandwidth of the generated frequency comb.

© 2007 Optical Society of America

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References

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  1. T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
    [CrossRef]
  2. K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
    [CrossRef]
  3. M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
    [CrossRef]
  4. T. Sakamoto, T. Kawanishi, and M. Izutsu, Opt. Lett. 31, 811 (2006).
    [CrossRef] [PubMed]
  5. M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.
  6. J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
    [CrossRef]
  7. M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
    [CrossRef]
  8. Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

2006 (1)

2005 (1)

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

1999 (1)

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

1994 (1)

M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
[CrossRef]

1993 (1)

T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
[CrossRef]

1977 (1)

M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
[CrossRef]

Aoki, K.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Doi, M.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

Ejiri, T.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Enami, T.

M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
[CrossRef]

Futami, F.

Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

Goh, T.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Hamajima, A.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Imaeda, M.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Iwata, Y.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Izutsu, M.

T. Sakamoto, T. Kawanishi, and M. Izutsu, Opt. Lett. 31, 811 (2006).
[CrossRef] [PubMed]

M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
[CrossRef]

Kawanishi, T.

Kominato, T.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Kondo, A.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Kondo, J.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Kourogi, M.

M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
[CrossRef]

Kozuka, Y.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Minakata, M.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Mitomi, O.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Mizuno, Y.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Mori, K.

T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
[CrossRef]

Mori, T.

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

Morioka, T.

T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
[CrossRef]

Nakazawa, T.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

Ohtsu, M.

M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
[CrossRef]

Okamoto, K.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Onaka, H.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

Sakamoto, T.

Saruwatari, M.

T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
[CrossRef]

Sueta, T.

M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
[CrossRef]

Sugiyama, M.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

Takita, Y.

Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

Taniguchi, S.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

Watanabe, S.

Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

Yamada, H.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Yamane, Y.

M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
[CrossRef]

Electron. Lett. (2)

T. Morioka, K. Mori, and M. Saruwatari, Electron. Lett. 29, 862 (1993).
[CrossRef]

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Izutsu, Y. Yamane, and T. Sueta, IEEE J. Quantum Electron. 13, 287 (1977).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. Kondo, K. Aoki, A. Kondo, T. Ejiri, Y. Iwata, A. Hamajima, T. Mori, Y. Mizuno, M. Imaeda, Y. Kozuka, O. Mitomi, and M. Minakata, IEEE Photon. Technol. Lett. 17, 2077 (2005).
[CrossRef]

M. Kourogi, T. Enami, and M. Ohtsu, IEEE Photon. Technol. Lett. 6, 214 (1994).
[CrossRef]

Opt. Lett. (1)

Other (2)

Y. Takita, F. Futami, M. Doi, and S. Watanabe, in Conference on Laser and Electro-Optics (CLEO'04) (OSA, 2004), Paper CTuN1.

M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, in Optical Fiber Communication Conference (OFC' 02) (OSA, 2002), pp. 854-856.

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Figures (4)

Fig. 1
Fig. 1

Concept of ultraflat optical frequency comb generation using a conventional MZM.

Fig. 2
Fig. 2

Numerically calculated spectra: (a) Single-arm driven ( A ¯ = 6 π , Δ A = 3 π , Δ θ = π 4 ), and (b) dual-arm driven ( A ¯ = 6 π , Δ A = π 4 , and Δ θ = π 4 ).

Fig. 3
Fig. 3

Normalized conversion efficiency, η k η k , max , versus dc bias, 2 Δ θ ; theoretically (asymptotically) (solid curve) and numerically (dashed lines) calculated average conversion efficiency within 0.5 Δ ω bandwidth ( A ¯ = 6 π ) .

Fig. 4
Fig. 4

(a) Maximum conversion efficiency, η k , max versus induced phase shift A ¯ ; theoretically (asymptotically) (solid curve) and numerically averaged conversion efficiency within 0.5 Δ ω (squares), and (b) bandwidth, Δ ω , versus A ¯ ; theoretically (asymptotically) ( Δ ω ) (solid curve), number of cw components within 3 dB drop of η k (squares), and fitted curve ( 0.67 Δ ω ) (dashed line).

Equations (6)

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E out = 1 2 E in k = [ J k ( A 1 ) e j ( k ω t + θ 1 ) + J k ( A 2 ) e j ( k ω t + θ 2 ) ] ,
η k P k P in 1 2 π A ¯ [ 1 + cos ( 2 Δ θ ) cos ( 2 Δ A ) + { cos ( 2 Δ θ ) + cos ( 2 Δ A ) } cos { 2 A ¯ ( 2 k + 1 ) π 2 } ] ,
Δ A ± Δ θ = π 2 ,
η k = 1 cos 4 Δ θ 4 π A ¯ ,
η k , max = 1 2 π A ¯ , when Δ A = Δ θ = π 4 .
Δ ω = P out ¯ ω η k P in = 2 π A ¯ ω 1 cos ( 2 Δ A ) J 0 ( 2 Δ A ) 1 cos ( 4 Δ A ) π A ¯ ω ( for small Δ A ) ,

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