Abstract

The reflection sidelobes of a corrugated optical waveguide filter are shown to be suppressed when the corrugation depth is tapered with a function that has low, Fourier-transform sidelobes. Several specific taper functions are considered, and sidelobe levels lower than −70 dB are shown to be feasible. A simple rule for estimating the 3-dB reflection bandwidth of a tapered corrugation is also presented.

© 1977 Optical Society of America

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References

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  1. D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
    [CrossRef]
  2. R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
    [CrossRef]
  3. P. S. Cross, H. Kogelnik, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.
  4. H. Kogelnik in Topics in Applied Physics, Vol. 7, T. Tamir, ed. (Springer-Verlag, New York, 1975); D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974); A. Yariv, IEEE J. Quantum. Electron. QE-9, 919 (1973).
    [CrossRef]
  5. H. Kogelnik, Bell Syst. Tech. J. 55, 109–126 (1976).
  6. M. Matsuhara, K. O. Hill, A. Watanabe, J. Opt. Soc. Am. 65, 804–809 (1975).
    [CrossRef]
  7. See, for example, A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 239–250.
  8. See, for example, R. M. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  9. E. A. J. Marcatili, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.
  10. P. S. Cross, to be published.

1976 (1)

H. Kogelnik, Bell Syst. Tech. J. 55, 109–126 (1976).

1975 (1)

1974 (2)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

Bracewell, R. M.

See, for example, R. M. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Cross, P. S.

P. S. Cross, to be published.

P. S. Cross, H. Kogelnik, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.

Flanders, D. C.

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

Hill, K. O.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 55, 109–126 (1976).

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

P. S. Cross, H. Kogelnik, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.

H. Kogelnik in Topics in Applied Physics, Vol. 7, T. Tamir, ed. (Springer-Verlag, New York, 1975); D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974); A. Yariv, IEEE J. Quantum. Electron. QE-9, 919 (1973).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.

Matsuhara, M.

Oppenheim, A. V.

See, for example, A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 239–250.

Schafer, R. W.

See, for example, A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 239–250.

Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

Standley, R. D.

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

Watanabe, A.

Appl. Phys. Lett. (2)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

R. V. Schmidt, D. C. Flanders, C. V. Shank, R. D. Standley, Appl. Phys. Lett. 25, 651–652 (1974).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 55, 109–126 (1976).

J. Opt. Soc. Am. (1)

Other (6)

See, for example, A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 239–250.

See, for example, R. M. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

E. A. J. Marcatili, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.

P. S. Cross, to be published.

P. S. Cross, H. Kogelnik, to be presented at the 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, July 18–20, 1977.

H. Kogelnik in Topics in Applied Physics, Vol. 7, T. Tamir, ed. (Springer-Verlag, New York, 1975); D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974); A. Yariv, IEEE J. Quantum. Electron. QE-9, 919 (1973).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a typical optical corrugated-waveguide filter.

Fig. 2
Fig. 2

Fourier transforms and calculated-reflectivity spectra for four different taper functions: (a) Hamming, (b) raised-cosine, (c) Blackman, and (d) Kaiser. The shaded region on each taper function is the rectangular distribution with the same peak reflectivity and 3-dB bandwidth as the taper function. The minima between the sidelobes of the transform and reflectivity spectra actually go to zero (−∞ dB).

Fig. 3
Fig. 3

(a) Plots of the taper functions in Eqs. (3)(6), normalized to the same peak and integrated values. (b) Expanded plots of the tail regions of the taper functions. The heavy bars on the abscissa indicate the end points of the various functions.

Equations (9)

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R peak = tanh 2 ( s ) ,
s = - L / 2 L / 2 κ ( z ) d z .
w ( z ) = 1 + 0.852 cos ( 2 π z / L ) .
w ( z ) = 1 + cos ( 2 π z / L ) .
w ( z ) = 1 + 1.19 cos ( 2 π z / L ) + 0.19 cos ( 4 π z / L ) .
w ( z ) = ( β / sinh β ) I 0 { β [ 1 - ( 2 z / L ) 2 ] 1 / 2 } ,
- L / 2 L / 2 w ( z ) d z = L .
κ ( z ) = s w ( z ) / L .
L eff = L - L / 2 L / 2 z w ( z ) d z - L / 2 L / 2 z d z ,

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