Abstract

New design of optical waveguides is presented to synthesize Bragg grating waveguides without inducing birefringence. In the design, waveguide core has a thin trench on the top surface of the core and width of the trench is modulated concurrently with width modulation of the waveguide core. Effective refractive index profiles in Bragg grating waveguides are obtained by a differential inverse scattering algorithm and converted to waveguide width profiles by using the new core design. This procedure allows design of non-birefringent Bragg grating waveguides on planar substrate. The method is applied to the design of chromatic dispersion compensators. For characterization of Bragg grating waveguides, analysis based on short-time Fourier transform of Bragg grating response waveforms is presented.

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  1. A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
    [CrossRef]
  2. Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
    [CrossRef]
  3. A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13(4), 233–253 (1977).
    [CrossRef]
  4. M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
    [CrossRef]
  5. A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
    [CrossRef]
  6. T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
    [CrossRef]
  7. J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
    [CrossRef]
  8. T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
    [CrossRef]
  9. T. Segawa, S. Matsuo, Y. Ohiso, and T. Ishii, “An apodized sampled grating using a vertical-groove high-mesa waveguide structure,” in Proceedings of 2004 International Conference on Indium Phosphide and Related Materials (IEEE, 2004), pp. 488–491.
  10. H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IV B Systems and Impairments, eds., I. Kaminow and T. Li, (Academic, San Diego, Calif., 2002) Chap. 15.
  11. R. J. Bozeat, S. Day, F. Hopper, F. P. Payne, S. W. Roberts, and M. Asghari, “Silicon based waveguides,” in Silicon Photonics, L. Pavesi and D. L. Lockwood eds. (Springer, Berlin, Heidelberg, 2004) p. 275.
  12. D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
    [CrossRef] [PubMed]
  13. G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2(11), 1905–1915 (1985).
    [CrossRef]
  14. G. Xiao and K. Yashiro, “An efficient algorithm for solving Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antenn. Propag. 50(6), 807–811 (2002).
    [CrossRef]
  15. S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
    [CrossRef] [PubMed]
  16. Fimmwave, http://www.photond.com/products/fimmwave.htm
  17. C. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
    [CrossRef]
  18. L. Cohen, “Time-frequency distributions - a review,” Proc. IEEE 77(7), 941–981 (1989).
    [CrossRef]
  19. M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
    [CrossRef]

2008

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

2006

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
[CrossRef] [PubMed]

2002

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

G. Xiao and K. Yashiro, “An efficient algorithm for solving Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antenn. Propag. 50(6), 807–811 (2002).
[CrossRef]

2001

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
[CrossRef]

1998

A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
[CrossRef]

C. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[CrossRef]

M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
[CrossRef]

1994

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
[CrossRef]

1990

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[CrossRef]

1989

L. Cohen, “Time-frequency distributions - a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

1985

G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2(11), 1905–1915 (1985).
[CrossRef]

1977

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13(4), 233–253 (1977).
[CrossRef]

Arakawa, Y.

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

Azaña, J.

M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
[CrossRef]

Carballar, A.

M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
[CrossRef]

Chotard, H.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

Chu, T.

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

Cohen, L.

L. Cohen, “Time-frequency distributions - a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

Goodberlet, J. G.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

Greiner, C. M.

D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
[CrossRef] [PubMed]

Hastings, J. T.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
[CrossRef]

Himeno, A.

A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
[CrossRef]

Iazikov, D.

D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
[CrossRef] [PubMed]

Ishida, S.

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

Kato, K.

A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
[CrossRef]

Kawachi, M.

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[CrossRef]

Kwong, D. L.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Lee, X.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
[CrossRef]

Lim, M. H.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

Lo, G. Q.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Mailloux, A.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

Mao, S. C.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Measures, R. M.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
[CrossRef]

Miya, T.

A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
[CrossRef]

Mossberg, T. W.

D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
[CrossRef] [PubMed]

Muriel, M. A.

M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
[CrossRef]

Murphy, T. E.

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
[CrossRef]

Nakamura, M.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13(4), 233–253 (1977).
[CrossRef]

Othonos, A.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
[CrossRef]

Painchaud, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

Shannon, C.

C. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[CrossRef]

Shin, S.-Y.

G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2(11), 1905–1915 (1985).
[CrossRef]

Smith, H. I.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
[CrossRef]

Song, G.-H.

G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2(11), 1905–1915 (1985).
[CrossRef]

Sun, X. W.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Tao, S. H.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Vasseur, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

Xiao, G.

G. Xiao and K. Yashiro, “An efficient algorithm for solving Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antenn. Propag. 50(6), 807–811 (2002).
[CrossRef]

Xu, Y. L.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Yamada, H.

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

Yariv, A.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13(4), 233–253 (1977).
[CrossRef]

Yashiro, K.

G. Xiao and K. Yashiro, “An efficient algorithm for solving Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antenn. Propag. 50(6), 807–811 (2002).
[CrossRef]

Yu, M. B.

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Electron. Lett.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30(23), 1972–1974 (1994).
[CrossRef]

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38(24), 1572–1573 (2002).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13(4), 233–253 (1977).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Himeno, K. Kato, and T. Miya, “Silica-based planar lightwave circuits,” IEEE J. Sel. Top. Quantum Electron. 4(6), 913–924 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Tunable optical add-drop multiplexer based on silicon photonic wire waveguides,” IEEE Photon. Technol. Lett. 18(13), 1409–1411 (2006).
[CrossRef]

IEEE Trans. Antenn. Propag.

G. Xiao and K. Yashiro, “An efficient algorithm for solving Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antenn. Propag. 50(6), 807–811 (2002).
[CrossRef]

J. Lightwave Technol.

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001).
[CrossRef]

J. Opt. Soc. Am. A

G.-H. Song and S.-Y. Shin, “Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2(11), 1905–1915 (1985).
[CrossRef]

J. Vac. Sci. Technol. B

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20(6), 2753–2757 (2002).
[CrossRef]

Opt. Express

D. Iazikov, C. M. Greiner, and T. W. Mossberg, “Integrated holographic filters for flat passband optical multiplexers,” Opt. Express 14(8), 3497–3502 (2006).
[CrossRef] [PubMed]

S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module,” Opt. Express 16(25), 20809–20816 (2008).
[CrossRef] [PubMed]

Opt. Lett.

M. A. Muriel, J. Azaña, and A. Carballar, “Fiber grating synthesis by use of time-frequency representations,” Opt. Lett. 23(19), 1526–1528 (1998).
[CrossRef]

Opt. Quantum Electron.

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[CrossRef]

Proc. IEEE

C. Shannon, “Communication in the presence of noise,” Proc. IEEE 86(2), 447–457 (1998).
[CrossRef]

L. Cohen, “Time-frequency distributions - a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

Other

Fimmwave, http://www.photond.com/products/fimmwave.htm

T. Segawa, S. Matsuo, Y. Ohiso, and T. Ishii, “An apodized sampled grating using a vertical-groove high-mesa waveguide structure,” in Proceedings of 2004 International Conference on Indium Phosphide and Related Materials (IEEE, 2004), pp. 488–491.

H. Kogelnik, R. M. Jopson, and L. E. Nelson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IV B Systems and Impairments, eds., I. Kaminow and T. Li, (Academic, San Diego, Calif., 2002) Chap. 15.

R. J. Bozeat, S. Day, F. Hopper, F. P. Payne, S. W. Roberts, and M. Asghari, “Silicon based waveguides,” in Silicon Photonics, L. Pavesi and D. L. Lockwood eds. (Springer, Berlin, Heidelberg, 2004) p. 275.

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Figures (8)

Fig. 1
Fig. 1

Schematic cross-section of non-birefringent waveguide.

Fig. 2
Fig. 2

Conversion curves from effective refractive index to waveguide parameters: trench width w t (red curve) and core width w c (blue curve).

Fig. 3
Fig. 3

Reflectance spectra required to single-channel chromatic dispersion compensator (required) and calculated using coupled mode equations for synthesized Bragg grating waveguide (realized).

Fig. 4
Fig. 4

Profiles of waveguide widths w t (red dots) and w c (blue dots) with respect to coordinate z in a single-channel dispersion compensator. Insets: w t and w c in expanded z scale around 5.105mm.

Fig. 5
Fig. 5

Grating spectrogram (left) and oscillation component Δn eff vs waveguide coordinate (right) for single-channel chromatic dispersion compensator.

Fig. 6
Fig. 6

Group-delay spectra required to design of 50-channel chromatic dispersion compensator waveguide (required) and calculated for synthesized Bragg grating waveguide (realized).

Fig. 7
Fig. 7

Profile of waveguide width w t (red dots) and w c (blue dots) with respect to coordinate z for 50-channel dispersion compensator.

Fig. 8
Fig. 8

Grating spectrogram (left) and oscillation component vs waveguide coordinate (right) for 50-channel chromatic dispersion compensator.

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