Abstract

Periodic structures that vary spatially in coupling strength, period, and gain/loss are analyzed using a perturbation technique to determine their response as Bragg reflectors or filters. A formula for the response, accurate to first order in the perturbation, is given. Results obtained by evaluating the formula are presented graphically. It is also shown analytically that antisymmetric variations in coupling and/or periodicity have a negligible effect on response (to first order) when neither gain nor loss is present.

© 1976 Optical Society of America

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  1. H. Kogelnik and C. V. Shank, "Stimulated Emission in a Periodic Structure," Appl. Phys. Lett. 18, 152–154 (1971).
  2. A. Yariv, "Coupled Mode Theory for Guided-Wave Optics," IEEE J. Quantum Electron. QE-9, 919–933 (1973).
  3. D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).
  4. F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).
  5. W-T. Tsang and S. Wang, "GaAs-Ga1-xAlxAs Double Heterostructure Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 28, 596–598 (1976).
  6. D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).
  7. R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).
  8. K. O. Hill, "A Periodic Distributed Parameter Waveguide for Integrated Optics," Appl. Opt. 13, 1853–1856 (1974).
  9. M. Matsuhara and K. O. Hill, "Optical-Waveguide Band-Rejection Filters: Design," Appl. Opt. 13, 2886–2888 (1974).
  10. M. Matsuhara, K. O. Hill, and A. Watanabe, "Optical-Waveguide Filters: Synthesis," J. Opt. Soc. Am. 65, 804–809 (1975).
  11. H. Kogelnik, "Filter Response of Nonuniform Almost-Periodic Structures," Bell. Syst. Tech. J. 55, 109–126 (1976).

1976 (2)

W-T. Tsang and S. Wang, "GaAs-Ga1-xAlxAs Double Heterostructure Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 28, 596–598 (1976).

H. Kogelnik, "Filter Response of Nonuniform Almost-Periodic Structures," Bell. Syst. Tech. J. 55, 109–126 (1976).

1975 (2)

M. Matsuhara, K. O. Hill, and A. Watanabe, "Optical-Waveguide Filters: Synthesis," J. Opt. Soc. Am. 65, 804–809 (1975).

F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).

1974 (5)

D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

K. O. Hill, "A Periodic Distributed Parameter Waveguide for Integrated Optics," Appl. Opt. 13, 1853–1856 (1974).

M. Matsuhara and K. O. Hill, "Optical-Waveguide Band-Rejection Filters: Design," Appl. Opt. 13, 2886–2888 (1974).

1973 (1)

A. Yariv, "Coupled Mode Theory for Guided-Wave Optics," IEEE J. Quantum Electron. QE-9, 919–933 (1973).

1971 (1)

H. Kogelnik and C. V. Shank, "Stimulated Emission in a Periodic Structure," Appl. Phys. Lett. 18, 152–154 (1971).

Burnham, R. D.

D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

Hill, K. O.

Kogelnik, H.

H. Kogelnik, "Filter Response of Nonuniform Almost-Periodic Structures," Bell. Syst. Tech. J. 55, 109–126 (1976).

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

H. Kogelnik and C. V. Shank, "Stimulated Emission in a Periodic Structure," Appl. Phys. Lett. 18, 152–154 (1971).

Logan, R. A.

F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).

Matsuhara, M.

Reinhart, F. K.

F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).

Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

Scifres, D. R.

D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).

Shank, C. V.

F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

H. Kogelnik and C. V. Shank, "Stimulated Emission in a Periodic Structure," Appl. Phys. Lett. 18, 152–154 (1971).

Standley, R. D.

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

Streifer, W.

D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).

Tsang, W-T.

W-T. Tsang and S. Wang, "GaAs-Ga1-xAlxAs Double Heterostructure Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 28, 596–598 (1976).

Wang, S.

W-T. Tsang and S. Wang, "GaAs-Ga1-xAlxAs Double Heterostructure Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 28, 596–598 (1976).

Watanabe, A.

Yariv, A.

A. Yariv, "Coupled Mode Theory for Guided-Wave Optics," IEEE J. Quantum Electron. QE-9, 919–933 (1973).

Appl. Opt. (2)

Appl. Phys. Lett. (6)

H. Kogelnik and C. V. Shank, "Stimulated Emission in a Periodic Structure," Appl. Phys. Lett. 18, 152–154 (1971).

D. R. Scifres, R. D. Burnham, and W. Streifer, "Distributed Feedback Single-Heterostructure GaAs Diode Laser," Appl. Phys. Lett. 25, 203–206 (1974).

F. K. Reinhart, R. A. Logan, and C. V. Shank, "GaAs- AlxGai1-xAs Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 27, 45–48 (1975).

W-T. Tsang and S. Wang, "GaAs-Ga1-xAlxAs Double Heterostructure Injection Lasers with Distributed Bragg Reflectors," Appl. Phys. Lett. 28, 596–598 (1976).

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, "Grating Filters for Thin-Film Optical Waveguide," Appl. Phys. Lett. 24, 194–196 (1974).

R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, "Narrow-Band Grating Filters for Thin-Film Optical Waveguides," Appl. Phys. Lett. 25, 651–652 (1974).

Bell. Syst. Tech. J. (1)

H. Kogelnik, "Filter Response of Nonuniform Almost-Periodic Structures," Bell. Syst. Tech. J. 55, 109–126 (1976).

IEEE J. Quantum Electron. (1)

A. Yariv, "Coupled Mode Theory for Guided-Wave Optics," IEEE J. Quantum Electron. QE-9, 919–933 (1973).

J. Opt. Soc. Am. (1)

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