Abstract

We analyze the operation of a tunable device that is composed of two channel waveguides that are fabricated on a nonlinear substrate and of two adjacent electrodes, where the evanescent fields of the two guided modes overlap. The optical power-dependent propagation constant of the guided modes is modified locally as the power leaks from one channel waveguide to the other, resulting in a continuous change in the local phase matching. We present a general expression for the operation of the device together with a numerical example that demonstrates that the device acts as an all-optical gate, discriminator, and limiter, having a speed that is limited only by the transit time along the channels and the response time of the material.

© 1982 Optical Society of America

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  1. E. A. Marcatili, “Dielectric rectangular waveguides and directional couplers for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
    [Crossref]
  2. S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).
  3. P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).
  4. A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
    [Crossref]
  5. E. A. J. Marcatili, “Optical subpicosecond gate,” Appl. Opt. 19, 1468–1476 (1980).
    [Crossref] [PubMed]
  6. H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
    [Crossref]
  7. H. F. Taylor, “Frequency selective coupling in parallel dielectric waveguides,” Opt. Common. 8, 421–425 (1973).
    [Crossref]
  8. H. Kogelnik and R. V. Schmidt, “Switched directional coupler with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
    [Crossref]
  9. R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
    [Crossref]
  10. S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
    [Crossref]
  11. H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
    [Crossref]
  12. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
    [Crossref]
  13. S. M. Jensen, “An optical logic element and its use in optical logic circuits,” presented at the workshop on All-Optical Processing Elements in Integrated Optics, September17–18, 1981.
  14. D. Sarid, “Power-dependent refractive-index phenomena in optical waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng.317, 1981 (to be published).
  15. D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
    [Crossref] [PubMed]
  16. See, for example, Tao-yi Fu and Murray Sargent, “Effects of signal detuning on phase conjugation,” Opt. Lett. 4, 366–368 (1979).
    [Crossref] [PubMed]

1981 (3)

S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
[Crossref]

H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
[Crossref]

D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
[Crossref] [PubMed]

1980 (2)

E. A. J. Marcatili, “Optical subpicosecond gate,” Appl. Opt. 19, 1468–1476 (1980).
[Crossref] [PubMed]

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

1979 (2)

A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
[Crossref]

See, for example, Tao-yi Fu and Murray Sargent, “Effects of signal detuning on phase conjugation,” Opt. Lett. 4, 366–368 (1979).
[Crossref] [PubMed]

1978 (2)

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

1976 (2)

H. Kogelnik and R. V. Schmidt, “Switched directional coupler with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
[Crossref]

1973 (1)

H. F. Taylor, “Frequency selective coupling in parallel dielectric waveguides,” Opt. Common. 8, 421–425 (1973).
[Crossref]

1972 (1)

S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).

1969 (1)

E. A. Marcatili, “Dielectric rectangular waveguides and directional couplers for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[Crossref]

Alferness, R. C.

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

Cross, P. S.

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

Fu, Tao-yi

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
[Crossref]

Haus, H. A.

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

Inaba, H.

H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
[Crossref]

Ito, H.

H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
[Crossref]

Iwasaki, K.

S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).

Jensen, S. M.

S. M. Jensen, “An optical logic element and its use in optical logic circuits,” presented at the workshop on All-Optical Processing Elements in Integrated Optics, September17–18, 1981.

Kirsch, S. T.

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

Kogelnik, H.

H. Kogelnik and R. V. Schmidt, “Switched directional coupler with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

Kumagi, N.

S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).

Kurazono, S.

S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).

Leonberger, F. J.

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

Marcatili, E. A.

E. A. Marcatili, “Dielectric rectangular waveguides and directional couplers for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[Crossref]

Marcatili, E. A. J.

Mathyssek, K.

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
[Crossref]

Minakata, M.

S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
[Crossref]

Noda, J.

S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
[Crossref]

Ogawa, Y.

H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
[Crossref]

Papuchon, M.

A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
[Crossref]

Puech, C.

A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
[Crossref]

Sargent, Murray

Sarid, D.

D. Sarid, “Analysis of bistability in a ring-channel waveguide,” Opt. Lett. 6, 552–553 (1981).
[Crossref] [PubMed]

D. Sarid, “Power-dependent refractive-index phenomena in optical waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng.317, 1981 (to be published).

Schmidt, R. V.

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

H. Kogelnik and R. V. Schmidt, “Switched directional coupler with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

Schnapper, A.

A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
[Crossref]

Smith, P. W.

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

Tarucha, S.

S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
[Crossref]

Taylor, H. F.

H. F. Taylor, “Frequency selective coupling in parallel dielectric waveguides,” Opt. Common. 8, 421–425 (1973).
[Crossref]

Thornton, R. L.

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Appl. Phys. Lett. 36, 1135–1138 (1976).
[Crossref]

Bell Syst. Tech. J. (1)

E. A. Marcatili, “Dielectric rectangular waveguides and directional couplers for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[Crossref]

IEEE J Quantum Electron. (1)

H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, “Picosecond optical sampling,” IEEE J Quantum Electron. QE-16, 870–873 (1980).
[Crossref]

IEEE J. Quantum Electron. (4)

S. Tarucha, M. Minakata, and J. Noda, “Complementary optical bistable switching and triode operation using LiNbO3directional coupler,” IEEE J. Quantum Electron. QE-17, 321–324 (1981).
[Crossref]

H. Ito, Y. Ogawa, and H. Inaba, “Analysis and experiments on integrated optical multivibrators using electrooptically controlled bistable optical devices,” IEEE J. Quantum Electron. QE-17, 325–331 (1981).
[Crossref]

P. S. Cross, R. V. Schmidt, R. L. Thornton, and P. W. Smith, “Optically controlled two channel integrated-optical switch,” IEEE J. Quantum Electron. QE-14, 557–580 (1978).

H. Kogelnik and R. V. Schmidt, “Switched directional coupler with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

J. Instr. Electr. Commun. Eng. Jpn. (1)

S. Kurazono, K. Iwasaki, and N. Kumagi, “A new optical modulator consisting of coupled optical waveguides,” J. Instr. Electr. Commun. Eng. Jpn. 55C, 103–105 (1972).

Opt. Common. (1)

H. F. Taylor, “Frequency selective coupling in parallel dielectric waveguides,” Opt. Common. 8, 421–425 (1973).
[Crossref]

Opt. Commun. (1)

A. Schnapper, M. Papuchon, and C. Puech, “Optical bistability using an integrated two arm interferometer,” Opt. Commun. 29, 364–368 (1979).
[Crossref]

Opt. Lett. (2)

Other (2)

S. M. Jensen, “An optical logic element and its use in optical logic circuits,” presented at the workshop on All-Optical Processing Elements in Integrated Optics, September17–18, 1981.

D. Sarid, “Power-dependent refractive-index phenomena in optical waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng.317, 1981 (to be published).

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Figures (6)

Fig. 1
Fig. 1

The geometry of the tunable, nonlinear, directional coupler.

Fig. 2
Fig. 2

|b(z)/a(0)|2 as a function of z with an initial phase matching at z = 0 for the following values of the scaled input power |a(0)|2: 1, 10−6; 2, 10−5; 3, 5 × 10−5, 4 10−4; and 5, 2 × 10−4.

Fig. 3
Fig. 3

|b(L)/a(0)|2 as a function of |a(0)|2 for 1, c2 = 10−4 and L = 5 mm, and 2, c2 = 2 × 10−4K and L = 3.88 mm.

Fig. 4
Fig. 4

Pout(t)/Pin(t) for a phase-matching bias of 10−4 at the peak of the Gaussian pulse which is also 10−4.

Fig. 5
Fig. 5

Same as in Fig. 4 but the input power is 10 times larger.

Fig. 6
Fig. 6

The response of the device to a train of input boxcar pulses.

Equations (17)

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n I = n + n 2 , I P / area ,
K Δ β = ( K β c 2 0 2 / 4 P ) - n ( x , y ) n 2 , I ( x , y ) E 4 d x d y .
K Δ β = K n 2 , I P / λ 2 .
d a 1 * / d z = - ( α 1 * + 2 i δ ) a 1 * + i k 1 A 2 ,
d A 2 / d z = - α 2 A 2 + i k 2 * a 1 * .
a 1 * ( z ) = e - i a 3 z { a 1 * ( 0 ) cosh ( w z ) + [ α a 1 * ( 0 ) + i k 1 A 2 ( 0 ) ] sinh ( w z ) / w } ,
A 2 = e - i a 3 z { A 2 ( 0 ) cosh ( w z ) + [ - α A 2 ( 0 ) + i k 2 * a 1 ( 0 ) ] sinh ( w z ) / w } .
a 3 = ( α 2 + α 1 * + 2 i δ ) / 2 , α = ( α 2 - α 1 * - 2 i δ ) / 2 ,
w = ( α 2 - k 1 k 2 * ) 1 / 2 .
d A 1 ( z ) / d z = i k A 2 ( z ) e 2 i δ z
d A 2 ( z ) / d z = i k A 1 ( z ) e - 2 i δ z .
a 1 * ( z ) = e - i δ z { a 1 * ( 0 ) cos ( k ξ z ) + i [ - δ a 1 * ( 0 ) + k A 2 ( 0 ) ] sin ( k ξ z ) / k ξ }
A 2 ( z ) = e - i δ z { A 2 ( 0 ) cos ( k ξ z ) + i [ δ A 2 ( 0 ) + k a 1 * ( 0 ) ] sin ( k ξ z ) / k ξ } ,
δ ( z ) = K n 2 , I [ P ( z ) A - P ( z ) B - P C ] / λ 2 .
a ( z ) = a 1 * ( z ) ( K n 2 , I / λ 2 ) 1 / 2
b ( z ) = A 2 ( z ) ( K n 2 , I / λ 2 ) 1 / 2 .
δ = a ( z ) 2 - b ( z ) 2 - c 2 ,