Abstract

The optical power spectrum of a signal externally modulated using a Mach-Zehnder modulator is calculated analytically. Optical power spectra are calculated for binary signals for which the drive signal has either raised-cosine or Bessel-filtered pulse shape as well as for duobinary signals created by Bessel filtering. While the optical power spectrum is often approximated by the electrical power spectrum of the drive signal, this approximation usually underestimates the spectral spreading of the optical signal. Differences between the optical spectrum and the drive-signal electrical spectrum are most significant for drive signals having longer rise and fall times. Modulator chirp also broadens the optical spectrum. Chirp-induced spectral broadening is more significant for drive signals having longer rise and fall times.

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  1. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien and D. E. Bossi, "A review of Lithium Niobate modulators for fiber-optic communications systems", IEEE J. Select. Topics Quantum Electron. , vol. 6, pp. 69-82, Jan.-Feb. 2000.
  2. M. Erman, P. Jarry, R. Gamonal, P. Autier, J.-P. Chane and P. Frijlink, "Mach-Zehnder modulators and optical switches on III--V semiconductors", J. Lightwave Technol., vol. 6, pp. 837-846, June 1988.
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  4. F. J. Leonberger and J. P. Donnelly, "Semiconductor integrated optic devices," in Guided-Wave Optoelectronics, T. Tamir, Ed. Berlin: Germany: Springer-Verlag, 1990, pp. 317-396.
  5. J. Yu, C. Rolland, A. Somani, S. Bradshaw and D. Yevick, "Phase-engineered III--V MQW Mach-Zehnder modulator", IEEE Photon. Technol. Lett., vol. 8, pp. 1018-1020, Aug. 1996.
  6. Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape", Science, vol. 288, pp. 119-122, Apr. 2000.
  7. F. Koyama and K. Oga, "Frequency chirping in external modulators", J. Lightwave Technol., vol. 6, pp. 87-93, Jan. 1988.
  8. A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford and D. T. Moser, "Dispersion penalty reduction using an optical modulator with adjustable chirp", IEEE Photon. Technol. Lett., vol. 3, pp. 916-918, Oct. 1991.
  9. M. Schiess and H. Carlden, "Evaluation of the chirp parameter of a Mach-Zehnder intensity modulator", Electron. Lett., vol. 30, pp. 1524-1525, 1994.
  10. H. Kim and A. H. Gnauck, "Chirp characteristics of dual-drive, Mach-Zehnder modulator with a finite DC extinction ratio", IEEE Photon. Technol. Lett., vol. 12, pp. 298-300, Mar. 2002.
  11. S. Walklin and J. Conradi, "Effect of Mach-Zehnder modulator DC extinction ratio on residual chirp-induced dispersion in 10-Gb/s binary and AM-PSK duobinary lightwave systems", IEEE Photon. Technol. Lett., vol. 9, pp. 1400-1402, Oct. 1997.
  12. K.-P. Ho, "Spectral density of cross-phase modulation induced phase noise", Opt. Commun., vol. 169, pp. 63-68, 1999.
  13. K.-P. Ho, E. Kong, L. Y. Chan, L.-K. Chen and F. Tong, "Analysis and measurement of root-mean-squared bandwidth of cross-phase modulation induced spectral broadening", IEEE Photon. Technol. Lett., vol. 11, pp. 1126-1128, Sept. 1999.
  14. J. G. Proakis, Digital Communications, 4 ed. Boston, MA: McGraw-Hill, 2000, pp. 559-561.
  15. A. J. Price and N. L. Mercier, "Reduced bandwidth optical digital intensity modulation with improved chromatic dispersion tolerance", Electron. Lett., vol. 31, pp. 58-59, 1995.
  16. T. Ono, Y. Yano, K. Fukuchi, T. Ito, H. Yamazaki, M. Yamaguchi and K. Emura, "Characteristics of optical duobinary signals in terabits/s capacity, high-spectral efficiency WDM systems", J. Lightwave Technol., vol. 16, pp. 788-797, May 1998.
  17. H. Kim and C. X. Yu, "Optical duobinary transmission system featuring improved receiver sensitivity and reduced optical bandwidth", IEEE Photon. Technol. Lett., vol. 14, pp. 1205-1207, Aug. 2002.

J. Lightwave Technol.

F. Koyama and K. Oga, "Frequency chirping in external modulators", J. Lightwave Technol., vol. 6, pp. 87-93, Jan. 1988.

M. Erman, P. Jarry, R. Gamonal, P. Autier, J.-P. Chane and P. Frijlink, "Mach-Zehnder modulators and optical switches on III--V semiconductors", J. Lightwave Technol., vol. 6, pp. 837-846, June 1988.

T. Ono, Y. Yano, K. Fukuchi, T. Ito, H. Yamazaki, M. Yamaguchi and K. Emura, "Characteristics of optical duobinary signals in terabits/s capacity, high-spectral efficiency WDM systems", J. Lightwave Technol., vol. 16, pp. 788-797, May 1998.

Other

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien and D. E. Bossi, "A review of Lithium Niobate modulators for fiber-optic communications systems", IEEE J. Select. Topics Quantum Electron. , vol. 6, pp. 69-82, Jan.-Feb. 2000.

R. C. Alferness, "Titanium-diffused Lithium Noibate waveguide devices," in Guided-Wave Optoelectronics, T. Tamir, Ed. Berlin: Germany: Springer-Verlag, 1990, pp. 145-210.

F. J. Leonberger and J. P. Donnelly, "Semiconductor integrated optic devices," in Guided-Wave Optoelectronics, T. Tamir, Ed. Berlin: Germany: Springer-Verlag, 1990, pp. 317-396.

J. Yu, C. Rolland, A. Somani, S. Bradshaw and D. Yevick, "Phase-engineered III--V MQW Mach-Zehnder modulator", IEEE Photon. Technol. Lett., vol. 8, pp. 1018-1020, Aug. 1996.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape", Science, vol. 288, pp. 119-122, Apr. 2000.

A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford and D. T. Moser, "Dispersion penalty reduction using an optical modulator with adjustable chirp", IEEE Photon. Technol. Lett., vol. 3, pp. 916-918, Oct. 1991.

M. Schiess and H. Carlden, "Evaluation of the chirp parameter of a Mach-Zehnder intensity modulator", Electron. Lett., vol. 30, pp. 1524-1525, 1994.

H. Kim and A. H. Gnauck, "Chirp characteristics of dual-drive, Mach-Zehnder modulator with a finite DC extinction ratio", IEEE Photon. Technol. Lett., vol. 12, pp. 298-300, Mar. 2002.

S. Walklin and J. Conradi, "Effect of Mach-Zehnder modulator DC extinction ratio on residual chirp-induced dispersion in 10-Gb/s binary and AM-PSK duobinary lightwave systems", IEEE Photon. Technol. Lett., vol. 9, pp. 1400-1402, Oct. 1997.

K.-P. Ho, "Spectral density of cross-phase modulation induced phase noise", Opt. Commun., vol. 169, pp. 63-68, 1999.

K.-P. Ho, E. Kong, L. Y. Chan, L.-K. Chen and F. Tong, "Analysis and measurement of root-mean-squared bandwidth of cross-phase modulation induced spectral broadening", IEEE Photon. Technol. Lett., vol. 11, pp. 1126-1128, Sept. 1999.

J. G. Proakis, Digital Communications, 4 ed. Boston, MA: McGraw-Hill, 2000, pp. 559-561.

A. J. Price and N. L. Mercier, "Reduced bandwidth optical digital intensity modulation with improved chromatic dispersion tolerance", Electron. Lett., vol. 31, pp. 58-59, 1995.

H. Kim and C. X. Yu, "Optical duobinary transmission system featuring improved receiver sensitivity and reduced optical bandwidth", IEEE Photon. Technol. Lett., vol. 14, pp. 1205-1207, Aug. 2002.

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