Abstract

The principle that the coupling of light between two fiber waveguides can be controlled by the resonant interference of a third waveguide has been developed [Attard, Appl. Opt. 37, 2296–2302 (1998)]. Here significant details concerning the operation of a photonic switch are obtained, and a more complete analysis is presented. Multiple-resonant conditions are identified for slab and fiber control waveguides at large indices of refraction. Thus a selection of materials with an appropriate refractive index and a Kerr coefficient is rendered more easily. Furthermore it is shown that the light used to control the index of refraction in the control waveguide does not enter the output of the photonic switch but remains confined to the control waveguide, for either a slab or a multimode fiber control waveguide. Spatial fluctuations of the control light beam in the control waveguide do not affect the operation of the photonic switch. Tolerances have been determined for the spacing between the control waveguide and the photonic coupler and also for the index of refraction of the control waveguide.

© 1999 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 matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
    [CrossRef]
  4. R. R. McLeod, K-Y. Wu, K. Wagner, R. T. Weverka, “Acousto-optic photonic crossbar switch. Part 1: Design,” Appl. Opt. 35, 6331–6353 (1996).
    [CrossRef] [PubMed]
  5. T. A. Birks, D. O. Culverson, S. G. Farwell, P. St. J. Russel, “2 × 2 single-mode fiber routing switch,” Opt. Lett. 21, 722–724 (1996).
    [CrossRef] [PubMed]
  6. M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
    [CrossRef]
  7. M. Asobe, H. Kobayashi, H. Itoh, “Laser-driven ultrafast all-optical switching by using highly nonlinear chalcogenide glass fiber,” Opt. Lett. 18, 1056–1058 (1993).
    [CrossRef]
  8. A. E. Attard, “Modulation of coupling in a photonic switch by resonant coupling,” Appl. Opt. 37, 2296–2302 (1998).
    [CrossRef]
  9. D. Marcuse, “Investigation of coupling between a fiber and an infinite slab,” J. Lightwave Technol. 7, 122–130 (1989).
    [CrossRef]
  10. The simulation software, BeamPROP, was obtained from RSoft Inc., Montrose, N.Y.
  11. B. E. A. Saleh, M. C. Teich, Principles of Photonics (Wiley, New York, 1994).
  12. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).
  13. J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

1998 (2)

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

A. E. Attard, “Modulation of coupling in a photonic switch by resonant coupling,” Appl. Opt. 37, 2296–2302 (1998).
[CrossRef]

1996 (2)

1994 (1)

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

1993 (3)

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[CrossRef]

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

M. Asobe, H. Kobayashi, H. Itoh, “Laser-driven ultrafast all-optical switching by using highly nonlinear chalcogenide glass fiber,” Opt. Lett. 18, 1056–1058 (1993).
[CrossRef]

1989 (1)

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

Agrawal, G. P.

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

Alferness, R. C.

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

Appelbaum, I.

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

Asobe, M.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

M. Asobe, H. Kobayashi, H. Itoh, “Laser-driven ultrafast all-optical switching by using highly nonlinear chalcogenide glass fiber,” Opt. Lett. 18, 1056–1058 (1993).
[CrossRef]

Attard, A. E.

Birks, T. A.

Culverson, D. O.

Farwell, S. G.

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 matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[CrossRef]

Haus, J. W.

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

Itoh, H.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

M. Asobe, H. Kobayashi, H. Itoh, “Laser-driven ultrafast all-optical switching by using highly nonlinear chalcogenide glass fiber,” Opt. Lett. 18, 1056–1058 (1993).
[CrossRef]

Kaminow, I.

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

Kanamori, T.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

Kitamura, M.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[CrossRef]

Kobayashi, H.

Komatsu, K.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[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.

Miyazawa, T.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

Persans, P. D.

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

Russel, P. St. J.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Principles of Photonics (Wiley, New York, 1994).

Sugou, S.

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Principles of Photonics (Wiley, New York, 1994).

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]

Wu, K-Y.

Yuan, Z.

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

Appl. Opt. (2)

Bull. Am. Phys. Soc. Ser. 2 (1)

J. W. Haus, Z. Yuan, I. Appelbaum, P. D. Persans, “Silver-coated CdS nanoparticles for nonlinear optical applications,” Bull. Am. Phys. Soc. Ser. 2 43(1), 382 (1998).

Electron. Lett. (2)

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, “Efficient and ultrafast all-optical switching using high Δn, small core chalcogenided glass fiber,” Electron. Lett. 29, 1966–1968 (1993).
[CrossRef]

K. Hamamoto, S. Sugou, K. Komatsu, M. Kitamura, “Extremely low loss 4 × 4 GaAs/AlGaAs optical matrix switch,” Electron. Lett. 29, 1580–1582 (1993).
[CrossRef]

J. Lightwave Technol. (2)

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

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

Opt. Lett. (2)

Other (4)

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

The simulation software, BeamPROP, was obtained from RSoft Inc., Montrose, N.Y.

B. E. A. Saleh, M. C. Teich, Principles of Photonics (Wiley, New York, 1994).

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

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Figures (18)

Fig. 1
Fig. 1

Arrangement of coupling between two fiber waveguides. The control fiber waveguide is a slab waveguide whose dimensions are a µm thick and 50 µm wide, where a varies between 4 and 14 µm. The spacing between the fiber waveguide and the slab waveguide C is g. This parameter is more significant than the distance between the centers of the waveguides. Thus it is possible to compare the effect of spacing g as a parameter independent from slab thickness.

Fig. 2
Fig. 2

Beam propagation simulation for coupling between two fiber waveguides. The control fiber waveguide is a slab waveguide whose dimensions are 9 µm thick and 50 µm wide. The index of refraction of the slab waveguide is 1.484 and is a β-resonant case. Waveguide A has the initial power and retains the optical power. Note the appearance of four small mode maxima in the optical field in the slab waveguide.

Fig. 3
Fig. 3

Beam propagation simulation for coupling between two fiber waveguides. The control slab waveguide has an index of refraction of the slab waveguide of 1.480. Note that this is not a case of resonance between the slab waveguide and the fiber waveguide; the optical switch is on. There are three maxima in the optical field in the slab. Note that the difference in the index of refraction between the two cases in Figs. 2 and 3 is 0.004.

Fig. 4
Fig. 4

Beam propagation simulation of the optical field in the three waveguides where waveguide B has the power initially. Note that power exchange occurs mainly between the waveguides that are more closely coupled together, B and C, and this intense interchange indicates the resonance between waveguides B and C.

Fig. 5
Fig. 5

Beam propagation simulation of the optical field in the three waveguides for coupling between two fiber waveguides where the control waveguide is a slab waveguide. Slab waveguide C is illuminated from the end by a Gaussian beam. Note that the optical field is confined to the slab.

Fig. 6
Fig. 6

Transverse section of the contour map of the optical field corresponding to the three-fiber waveguide case in which the initial optical power is in waveguide A. Fiber A is centered at -17.00 µm. Fiber B is centered at 0.00 µm. The slab is centered at +12.00 µm.

Fig. 7
Fig. 7

Transverse section of the contour map of the optical field corresponding to the case in which the initial optical power is in slab waveguide C. These cases represent two of the alternative modes taken at different positions along the interaction length.

Fig. 8
Fig. 8

Square of the propagation vector displayed as a linear function of the square of the slab index of refraction in the vicinity of a resonance. At point P there is little overlap of the fields of the slab and the fiber. This is representative of the nonresonant condition shown in Fig. 3. At point Q the overlap is at a maximum due to the increase in mode number s. At point R there is a match between the propagation vector in the slab waveguide and the propagation vector in the fiber waveguide. This is the condition of β resonance, corresponding to Fig. 2.

Fig. 9
Fig. 9

Plot of A versus 1/a 2, where a is the slab thickness. The linear regression coefficient is 0.999. This plot demonstrates the formal scaling of the A parameter with the thickness of the slab waveguide.

Fig. 10
Fig. 10

Transverse field profile for the β resonance of the fiber control waveguide at an index of 1.561 showing the l, m = 2, 3 mode.

Fig. 11
Fig. 11

Plot of the correlation of the index of refraction for a control fiber 9 µm in diameter versus (m + 1/2)2. The regression coefficient is 0.9998. Note that the HE11 mode (l, m = 0, 1) has been excluded from the linear regression calculation, since it is outside the range of Eq. (1). V < 2.405 for a single-mode fiber. The l, m coefficients are indicated near each point. Note the systematic progression of the l, m coefficients.

Fig. 12
Fig. 12

Simulation of the case in which the index of the slab control waveguide varies between 1.484 and 1.485 periodically for a total of 10 cycles across the interaction distance. The switch is in the off condition.

Fig. 13
Fig. 13

Simulation of the case in which the index of the slab control waveguide varies between 1.480 and 1.481 periodically for a total of 10 cycles across the interaction distance. The switch is in the on condition.

Fig. 14
Fig. 14

Propagation simulation obtained for coupling between two fiber waveguides. The index of refraction of the slab waveguide varies between 1.521 and 1.523 periodically for a total of 10 cycles across the interaction length. The photonic switch is in the off condition.

Fig. 15
Fig. 15

Beam propagation simulation for coupling between two fiber waveguides. The index of refraction of the fiber control waveguide is 1.471, and the photonic switch is on.

Fig. 16
Fig. 16

Simulation of the case in which the index of the fiber control waveguide varies between 1.471 and 1.472 periodically for a total of 10 cycles over the interaction distance. The switch is still in the on condition.

Fig. 17
Fig. 17

Beam propagation simulation for the case of a fiber control waveguide. The index of refraction of the fiber waveguide is 1.476, and the photonic switch is off and is a β-resonant case.

Fig. 18
Fig. 18

Simulation of the case in which the index of the fiber control waveguide varies between 1.476 and 1.477 periodically for a total of 10 cycles across the interaction distance. The switch is still in the off condition.

Tables (4)

Tables Icon

Table 1 β Resonances of the Slab Waveguides with 9-µm fibera

Tables Icon

Table 2 Slab Indices of Refraction of the Photonic Switch with 9-µm Fibera

Tables Icon

Table 3 β Resonances of the Fiber Waveguides with the 9-µm Fibera

Tables Icon

Table 4 Degenerate Combinations of l, m for Particular Values of m + l/2 for a Fiber Waveguide a

Equations (4)

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

L=π/2C,
βlm2=nlm2k02-m+l22π2a2,
V=2πaλnf2-nc21/2,
nlm=Am+l22+B, for m+l2π/a  β.

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