Abstract

We report a theoretical study and a numerical analysis of the coupling efficiency of a grating coupler in a slab waveguide with a nonlinear guiding medium characterized by a saturable index of refraction. A phenomenological relationship is assumed for the saturation of the nonlinearity.

© 1990 Optical Society of America

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References

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  1. G. I. Stegeman, C. T. Seaton, “Nonlinear Integrated Optics,” J. Appl. Phys. 58, R57–R78 (1985).
    [CrossRef]
  2. R. Moshrefzadeh, X. Mai, C. T. Seaton, G. I. Stegeman, “Efficient Grating Couplers for Polymer Waveguides,” Appl. Opt. 26, 2501 (1987).
    [CrossRef]
  3. C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, “Nonlinear Distributed Waveguide Couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
    [CrossRef]
  4. W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
    [CrossRef]
  5. R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
    [CrossRef]
  6. M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.
  7. Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
    [CrossRef]
  8. P. Vincent, N. Paraire, M. Neviere, A. Koster, R. Reinisch, “Gratings in Nonlinear Optics and Optical Bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
    [CrossRef]
  9. H. G. Winful, G. I. Stegeman, “Applications of Nonlinear Periodic Structures in Guided Wave Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214–218 (1985).
  10. M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).
  11. G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).
  12. P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
    [CrossRef]
  13. V. Briguet, P. Pirani, W. Lukosz, “Self-Pulsing in Prism Coupling into Planar Waveguides,” Opt. Lett. 12, 525–527 (1987).
    [CrossRef] [PubMed]
  14. R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, G. I. Stegeman, “Pulsed Excitation of Nonlinear Distributed Coupling into Zinc Oxide Optical Guides,” J. Opt. Soc. Am. B 5, 425–431 (1988).
    [CrossRef]
  15. G. Assanto, R. M. Fortenberry, C. T. Seaton, G. I. Stegeman, “Theory of Pulsed Excitation of Nonlinear Distributed Prism Couplers,” J. Opt. Soc. Am. B 5, 432–442 (1988).
    [CrossRef]
  16. R. Moshrefzadeh, B. Svensson, M. Xu, C. T. Seaton, G. I. Stegeman, “Chirped Gratings for Efficient Coupling into Nonlinear Waveguides,” Appl. Phys. Lett. 51, 390–391 (1987).
    [CrossRef]

1988 (5)

W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
[CrossRef]

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
[CrossRef]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, G. I. Stegeman, “Pulsed Excitation of Nonlinear Distributed Coupling into Zinc Oxide Optical Guides,” J. Opt. Soc. Am. B 5, 425–431 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, G. I. Stegeman, “Theory of Pulsed Excitation of Nonlinear Distributed Prism Couplers,” J. Opt. Soc. Am. B 5, 432–442 (1988).
[CrossRef]

1987 (3)

1986 (1)

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

1985 (5)

P. Vincent, N. Paraire, M. Neviere, A. Koster, R. Reinisch, “Gratings in Nonlinear Optics and Optical Bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

H. G. Winful, G. I. Stegeman, “Applications of Nonlinear Periodic Structures in Guided Wave Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214–218 (1985).

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, “Nonlinear Distributed Waveguide Couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

G. I. Stegeman, C. T. Seaton, “Nonlinear Integrated Optics,” J. Appl. Phys. 58, R57–R78 (1985).
[CrossRef]

G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).

1984 (1)

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Assanto, G.

Ballantyne, J. M.

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

Bennion, I.

M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.

Briguet, V.

W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
[CrossRef]

V. Briguet, P. Pirani, W. Lukosz, “Self-Pulsing in Prism Coupling into Planar Waveguides,” Opt. Lett. 12, 525–527 (1987).
[CrossRef] [PubMed]

Burzynski, R.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Carter, G. M.

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).

Chen, Y. J.

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).

Fortenberry, R. M.

Goodwin, M. J.

M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.

Koster, A.

Kramer, J.

W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
[CrossRef]

Liao, C.

Lukosz, W.

W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
[CrossRef]

P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
[CrossRef]

V. Briguet, P. Pirani, W. Lukosz, “Self-Pulsing in Prism Coupling into Planar Waveguides,” Opt. Lett. 12, 525–527 (1987).
[CrossRef] [PubMed]

Mai, X.

Moshrefzadeh, R.

Nellen, P. M.

P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
[CrossRef]

Neviere, M.

P. Vincent, N. Paraire, M. Neviere, A. Koster, R. Reinisch, “Gratings in Nonlinear Optics and Optical Bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Paraine, N.

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Paraire, N.

Pirani, P.

Prasad, P. N.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Reinisch, R.

P. Vincent, N. Paraire, M. Neviere, A. Koster, R. Reinisch, “Gratings in Nonlinear Optics and Optical Bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Rowe, C. J.

M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.

Seaton, C. T.

Shoemaker, R. L.

Singh, B. P.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Sonek, G. J.

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

Stegeman, G. I.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, G. I. Stegeman, “Theory of Pulsed Excitation of Nonlinear Distributed Prism Couplers,” J. Opt. Soc. Am. B 5, 432–442 (1988).
[CrossRef]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, G. I. Stegeman, “Pulsed Excitation of Nonlinear Distributed Coupling into Zinc Oxide Optical Guides,” J. Opt. Soc. Am. B 5, 425–431 (1988).
[CrossRef]

R. Moshrefzadeh, B. Svensson, M. Xu, C. T. Seaton, G. I. Stegeman, “Chirped Gratings for Efficient Coupling into Nonlinear Waveguides,” Appl. Phys. Lett. 51, 390–391 (1987).
[CrossRef]

R. Moshrefzadeh, X. Mai, C. T. Seaton, G. I. Stegeman, “Efficient Grating Couplers for Polymer Waveguides,” Appl. Opt. 26, 2501 (1987).
[CrossRef]

G. I. Stegeman, C. T. Seaton, “Nonlinear Integrated Optics,” J. Appl. Phys. 58, R57–R78 (1985).
[CrossRef]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, “Nonlinear Distributed Waveguide Couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

H. G. Winful, G. I. Stegeman, “Applications of Nonlinear Periodic Structures in Guided Wave Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214–218 (1985).

Svensson, B.

R. Moshrefzadeh, B. Svensson, M. Xu, C. T. Seaton, G. I. Stegeman, “Chirped Gratings for Efficient Coupling into Nonlinear Waveguides,” Appl. Phys. Lett. 51, 390–391 (1987).
[CrossRef]

Tiefenthaler, K.

P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
[CrossRef]

Tripathy, S. K.

G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).

Trundle, C.

M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.

Valera, J. D.

Vincent, P.

P. Vincent, N. Paraire, M. Neviere, A. Koster, R. Reinisch, “Gratings in Nonlinear Optics and Optical Bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Winful, H. G.

H. G. Winful, G. I. Stegeman, “Applications of Nonlinear Periodic Structures in Guided Wave Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214–218 (1985).

Xu, M.

R. Moshrefzadeh, B. Svensson, M. Xu, C. T. Seaton, G. I. Stegeman, “Chirped Gratings for Efficient Coupling into Nonlinear Waveguides,” Appl. Phys. Lett. 51, 390–391 (1987).
[CrossRef]

Zanoni, R.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, G. I. Stegeman, “Nonlinear Optical Processes in a Polymer Waveguide: Grating Coupler Measurements of Electronic and Thermal Nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Y. J. Chen, G. M. Carter, G. J. Sonek, J. M. Ballantyne, “Nonlinear Optical Coupling to Planar GaAs, AlGaAs Wave guides,” Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

R. Moshrefzadeh, B. Svensson, M. Xu, C. T. Seaton, G. I. Stegeman, “Chirped Gratings for Efficient Coupling into Nonlinear Waveguides,” Appl. Phys. Lett. 51, 390–391 (1987).
[CrossRef]

J. Appl. Phys. (1)

G. I. Stegeman, C. T. Seaton, “Nonlinear Integrated Optics,” J. Appl. Phys. 58, R57–R78 (1985).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

W. Lukosz, V. Briguet, J. Kramer, “External Grating Couplers on Planar Waveguides: Linear and Nonlinear Coupling and Optical Bistability,” Opt. Commun. 69, 121–127 (1988).
[CrossRef]

Opt. Eng. (1)

G. M. Carter, Y. J. Chen, S. K. Tripathy, “Intensity Dependent Index of Refraction in Organic Materials,” Opt. Eng. 24, 609–612 (1985).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

H. G. Winful, G. I. Stegeman, “Applications of Nonlinear Periodic Structures in Guided Wave Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 214–218 (1985).

M. Neviere, P. Vincent, N. Paraine, R. Reinisch, “A New Use of Gratings: Bistable Components,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 216–223 (1984).

Sensors and Actuators (1)

P. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated Optical Input Grating Couplers as Biochemical Sensors,” Sensors and Actuators 15, 285–295 (1988).
[CrossRef]

Other (1)

M. J. Goodwin, C. J. Rowe, I. Bennion, C. Trundle, “Periodic Grating Structures in Nonlinear Optical Waveguides,” in Proc. of the 4th European Conference on Integrated Optics, Glasgow, UK (1987), p. 182.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the slab waveguide used for the numerical analysis.

Fig. 2
Fig. 2

Coupling efficiency vs incident power for the linear grating, as well as nonlinear grating with different values of saturation.

Fig. 3
Fig. 3

Schematic representation of a saturable index (arbitrary units on both axes).

Fig. 4
Fig. 4

Coupling efficiency vs incident power for the same saturation value and three values of third order nonlinearity.

Fig. 5
Fig. 5

Coupling efficiency vs incident power for different values of chirp rate for an unsaturable nonlinear index.

Fig. 6
Fig. 6

Coupling efficiency vs incident power for the same chirp rate and three different values of saturation.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

β 0 = k o sin θ + κ .
d d x a g w ( x ) = t a i n ( x ) exp { i [ Δ β ( x ) - Δ κ x ] x } - ( α + 1 l c ) a g w ( x ) ,
Δ β ( x ) = Δ β 0 P g w ( x ) .
Δ β ( x ) = Δ β max { 1 - exp [ - Δ β 0 P g w ( x ) / Δ β max ] } ,
Δ β ( x ) Δ β max ,

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