Abstract

A novel photonic switch structure is described in which the coupling of light between two fiber waveguides is controlled by the resonant interference of a third waveguide. The switching action is controlled by a small variation of the index of refraction of the control waveguide by the application of either photo-optical (Kerr) techniques or electro-optical (Pockels) techniques. The control waveguide can be either a fiber waveguide or a slab waveguide. The equations for the waveguide coupling were obtained by analytical approximations from coupled-mode theory. A beam-propagation simulation was also used. The results of the two models were compared. Multiple resonant interferences were observed in the case of a slab waveguide.

© 1998 Optical Society of America

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References

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  1. B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
    [CrossRef]
  2. R. C. Alferness, “Titanium-diffused LiNbO3 waveguide devices,” in Guided Wave Optoelectronics, T. Tamir ed. (Springer-Verlag, Berlin, 1988).
  3. K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.
  4. R. R. McLeod, K.-Y. Wu, K. Wagner, R. T. Weverka, “Acousto-optic photonic crossbar switch. 1. Design,” Appl. Opt. 35, 6331–6353 (1996).
    [CrossRef] [PubMed]
  5. T. A. Birks, D. O. Culverson, S. G. Farwell, P. St. J. Russell, “2 × 2 Single-mode fiber routing switch,” Opt. Lett. 21, 722–724 (1996).
    [CrossRef] [PubMed]
  6. S. Srivasta, E. K. Sharma, “Analytic expressions for power exchange in multiwaveguide systems,” J. Opt. Soc. Am. A 13, 1683–1688 (1996).
    [CrossRef]
  7. M. D. Feit, J. A. Fleck, “Propagating beam theory of optical fiber cross coupling,” J. Opt. Soc. Am. A 71, 1361–1372 (1981),The simulation software, BeamPROP, was obtained from RSoft, Inc., Montrose, N.Y.
  8. M. J. F. Digonnet, H. J. Shaw, “Analysis of a tunable single mode optical fiber coupler,” IEEE J. Quantum Electron. QE-18, 746–754 (1982).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).
  10. D. Marcuse, “Investigation of coupling between a fiber and an infinite slab,” J. Lightwave Technol. 7, 122–130 (1989).
    [CrossRef]
  11. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  12. H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
    [CrossRef]

1996

1994

B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

1989

D. Marcuse, “Investigation of coupling between a fiber and an infinite slab,” J. Lightwave Technol. 7, 122–130 (1989).
[CrossRef]

1982

M. J. F. Digonnet, H. J. Shaw, “Analysis of a tunable single mode optical fiber coupler,” IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

1981

M. D. Feit, J. A. Fleck, “Propagating beam theory of optical fiber cross coupling,” J. Opt. Soc. Am. A 71, 1361–1372 (1981),The simulation software, BeamPROP, was obtained from RSoft, Inc., Montrose, N.Y.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).

Alferness, R. C.

R. C. Alferness, “Titanium-diffused LiNbO3 waveguide devices,” in Guided Wave Optoelectronics, T. Tamir ed. (Springer-Verlag, Berlin, 1988).

Birks, T. A.

Culverson, D. O.

Digonnet, M. J. F.

M. J. F. Digonnet, H. J. Shaw, “Analysis of a tunable single mode optical fiber coupler,” IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

Farwell, S. G.

Feit, M. D.

M. D. Feit, J. A. Fleck, “Propagating beam theory of optical fiber cross coupling,” J. Opt. Soc. Am. A 71, 1361–1372 (1981),The simulation software, BeamPROP, was obtained from RSoft, Inc., Montrose, N.Y.

Fleck, J. A.

M. D. Feit, J. A. Fleck, “Propagating beam theory of optical fiber cross coupling,” J. Opt. Soc. Am. A 71, 1361–1372 (1981),The simulation software, BeamPROP, was obtained from RSoft, Inc., Montrose, N.Y.

Glance, B.

B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Hamamoto, K.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.

Haus, J. W.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Honma, I.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Kaminow, I.

B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Kim, K. H.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Kitamura, M.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.

Komatsu, K.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.

Komiyama, H.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Marcuse, D.

D. Marcuse, “Investigation of coupling between a fiber and an infinite slab,” J. Lightwave Technol. 7, 122–130 (1989).
[CrossRef]

McLeod, R. R.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Sasabe, H.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Sharma, E. K.

Shaw, H. J.

M. J. F. Digonnet, H. J. Shaw, “Analysis of a tunable single mode optical fiber coupler,” IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

Srivasta, S.

St. J. Russell, P.

Sugou, S.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.

Wagner, K.

Weverka, R. T.

Wilson, R.

B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Wu, K.-Y.

Zhou, H. S.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

M. J. F. Digonnet, H. J. Shaw, “Analysis of a tunable single mode optical fiber coupler,” IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

J. Lightwave Technol.

B. Glance, I. Kaminow, R. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

D. Marcuse, “Investigation of coupling between a fiber and an infinite slab,” J. Lightwave Technol. 7, 122–130 (1989).
[CrossRef]

J. Opt. Soc. Am. A

S. Srivasta, E. K. Sharma, “Analytic expressions for power exchange in multiwaveguide systems,” J. Opt. Soc. Am. A 13, 1683–1688 (1996).
[CrossRef]

M. D. Feit, J. A. Fleck, “Propagating beam theory of optical fiber cross coupling,” J. Opt. Soc. Am. A 71, 1361–1372 (1981),The simulation software, BeamPROP, was obtained from RSoft, Inc., Montrose, N.Y.

Opt. Lett.

Surf. Rev. Lett.

H. S. Zhou, I. Honma, K. H. Kim, H. Komiyama, H. Sasabe, J. W. Haus, “Quantum confinement in coated nanoparticles,” Surf. Rev. Lett. 3, 133–136 (1996).
[CrossRef]

Other

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

R. C. Alferness, “Titanium-diffused LiNbO3 waveguide devices,” in Guided Wave Optoelectronics, T. Tamir ed. (Springer-Verlag, Berlin, 1988).

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical switch matrix,” in Integrated Photonics Research, Vol. 10 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper 1TuA2.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).

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Figures (12)

Fig. 1
Fig. 1

Arrangement of three fiber waveguides over a limited coupling region. The fibers are 9 μm in diameter. The refractive index of the cladding is 1.456. Fibers A and B have a refractive index of 1.460. Fiber C has a variable index. Optical power is initially in fiber A. Fiber B is the pickup fiber. Fiber C is the control fiber.

Fig. 2
Fig. 2

Coupled-mode model calculations for the three-fiber-waveguide shown in Fig. 1. All waveguides have the same index and the same diameter. The calculations are based on Eqs. (5)–(7). Note the inhibition of coupling between waveguides A and B. The coefficients were obtained from Eq. (4).

Fig. 3
Fig. 3

Beam-propagation simulation for coupling in the three-fiber-waveguide system shown in Fig. 1 and corresponding to Fig. 2. All three fibers have the same index of refraction, 1.460. We observe the resonance inhibition of coupling between fiber waveguides A and B.

Fig. 4
Fig. 4

Coupled-mode model calculations for the three-fiber-waveguide case shown in Fig. 1 for the off-resonance condition. The calculations are based on Eqs. (9)–(11).

Fig. 5
Fig. 5

Beam-propagation simulation for coupling in the three-fiber-waveguide system. The index is 1.460 in fiber A (left) and in fiber B (center). The index in control fiber waveguide C (right) is 1.462. The control waveguide is in the nonresonant condition.

Fig. 6
Fig. 6

Arrangement of coupling between two fiber waveguides, where the control fiber waveguide is replaced by a slab waveguide whose dimensions are 9 μm thick and 50 μm wide.

Fig. 7
Fig. 7

Beam-propagation simulation for coupling between two fiber waveguides, where the control fiber waveguide is replaced by a slab waveguide whose dimensions are 9 μm thick and 50 μm wide. The index of refraction of the slab waveguide is 1.460. Note that this is not a case of resonance between the slab waveguide and the fiber waveguide. There is one maximum in the optical field in the slab.

Fig. 8
Fig. 8

Beam-propagation simulation for coupling between two fiber waveguides, where the control fiber waveguide is replaced by a slab waveguide whose dimensions are 9 μm thick and 50 μm wide. The index of refraction of the slab waveguide is 1.462. This is the β-resonant case corresponding to Fig. 3 for three fiber waveguides. Note the appearance of two maxima in the optical field in the slab waveguide.

Fig. 9
Fig. 9

Index of refraction of the slab waveguide is 1.468. Note that this is not a case of resonance between the slab waveguide and the fiber waveguide. There are two maxima in the optical field in the slab. The control waveguide is in the nonresonant condition, corresponding to Fig. 5 for three fiber waveguides.

Fig. 10
Fig. 10

Beam-propagation simulation for coupling between two fiber waveguides, where the control fiber waveguide is replaced by a slab waveguide. The index of refraction of the slab waveguide is 1.471. This is the β-resonant case corresponding to Fig. 3 for three fiber waveguides. Note the appearance of three optical field maxima in the slab waveguide.

Fig. 11
Fig. 11

Index of refraction of the slab waveguide is 1.484. This is the β-resonant case. There are four mode maxima in optical field in the slab.

Fig. 12
Fig. 12

Geometry of the slab waveguide and the corresponding coordinate system. The thickness of the slab is a.

Tables (1)

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Table 1 Slab β Resonances with 9-μm Fibera

Equations (24)

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d A d z = - i β 1 A + bB + cC ,
d B d z = - i bA + β 2 B + aC ,
d C d z = - i cA + aB + β 3 C .
c h = λ 2 π n 1 κ 2 V 2 K 0 r γ h / r K 1 2 r γ ,
a = 1148.3   m - 1 , b = 279.6   m - 1 , c = 24.0   m - 1 .
A z = A 0 a 2 + b 2 cos γ z γ 2 exp - i β z ,
B z = - iA 0 b γ sin γ z exp - i β z ,
C z = A 0 ab γ 2 1 - cos γ z exp - i β z ,
γ 2 = a 2 + b 2 .
A z = A 0 cos bz exp i β z ,
B z = - iA 0 sin bz exp i β z ,
C z = A 0 a b 1 - cos bz exp - i β z .
× 1 ε r   × H r = ω c 2 H r .
H k r = h x exp ik ρ .
H k y , n r = exp ik z z ϕ n x ŷ ;
d d x 1 ε x d ϕ s x d x = k z 2 ε x - ω 2 c 2 ϕ s x .
ϕ s x = exp ik x x = exp is π x / a ,
ω c 2 = k z 2 ε + s 2 π 2 ε a 2 .
β 2 = k z 2 = ω c 2 n s 2 - s 2 π 2 a 2 .
ω c 2 = β s 2 ε + s 2 π 2 ε a 2 = β s 2 n s 2 1 + s 2 π 2 β s 2 a 2 .
ω c = β s n s 1 + s 2 π 2 2 β s 2 a 2 .
n s + 1 n s = 2 β 2 a 2 + s + 1 2 π 2 2 β 2 a 2 + s 2 π 2 .
n s = As 2 + B .
y = Ax + B ,     x = s 2 ,     y = n s .

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