Abstract

The beam-propagation characteristics of the total internal reflection (TIR) induced by the thermo-optic effect are investigated. Based on the Fourier heat-transmission principle and the variable separation method, we derive an analytical transient expression of the thermal field for general thermo-optic devices. With the analytical expression, the time response and steady-state temperature distribution of thermo-optic devices are presented. The beam expansion rule of TIR in the thermal field is developed mathematically, and a quantitative calculation is given as well. To illustrate the application of the rule, an X-junction 2 × 2 TIR switch with high reflection efficiency is designed through theoretical calculation. The simulation shows that the structure exhibits a high reflection coefficient; the reflection loss is only −0.76 dB. The simulation results agree well with the theoretical calculation.

© 2005 Optical Society of America

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References

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  1. S. K. Sheem, “Total internal reflection integrated-optics switch: a theoretical evaluation,” Appl. Opt. 17, 3679–3687 (1978).
    [CrossRef] [PubMed]
  2. K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
    [CrossRef]
  3. J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
    [CrossRef]
  4. X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
    [CrossRef]
  5. H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).
  6. Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
    [CrossRef]
  7. RSoft Design Group, Ossining, N.Y., RSoft Photonics CAD Suite, Version 5.1 (1993–2003).
  8. N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
    [CrossRef]
  9. M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

2004 (1)

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

2003 (1)

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

2002 (1)

J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
[CrossRef]

1996 (1)

N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
[CrossRef]

1993 (1)

Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
[CrossRef]

1990 (1)

K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
[CrossRef]

1978 (1)

Adams, M. J.

M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

Arai, S.

K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
[CrossRef]

Chen, K.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

Chen, R. T.

J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
[CrossRef]

Hida, Y.

Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
[CrossRef]

Imamura, S.

Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
[CrossRef]

Jiang, X.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

Keil, N.

N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
[CrossRef]

Li, X.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

Onose, H.

Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
[CrossRef]

Sheem, S. K.

Shimomura, K.

K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
[CrossRef]

Suematsu, Y.

K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
[CrossRef]

Tang, Y.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

Wang, M.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

Yang, J.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
[CrossRef]

Yao, H. H.

N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
[CrossRef]

Zawadzki, C.

N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
[CrossRef]

Zhan, H.

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

Zhou, Q.

J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
[CrossRef]

Acta Opt. Sin. (1)

H. Zhan, X. Jiang, K. Chen, M. Wang, “Analysis of Y branch switch based on total internal reflection of multimodes waveguide,” Acta Opt. Sin. 23, 1187–1190 (2003).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Yang, Q. Zhou, R. T. Chen, “Polyimide-waveguide-based thermal optical switch using the total-internal-reflection effect,” Appl. Phys. Lett. 81, 2947–2949 (2002).
[CrossRef]

Electron. Lett. (1)

N. Keil, H. H. Yao, C. Zawadzki, “Polymer waveguide optical switch with −40 dB polarization independent crosstalk,” Electron. Lett. 32, 655–657 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Y. Hida, H. Onose, S. Imamura, “Polymer waveguide thermooptic switch with low electric power consumption at 1.3 μm,” IEEE Photon. Technol. Lett. 5, 782–784 (1993).
[CrossRef]

X. Jiang, J. Yang, H. Zhan, K. Chen, Y. Tang, X. Li, M. Wang, “Photon-induced total-internal-reflection all-optical switches,” IEEE Photon. Technol. Lett. 16, 443–445 (2004).
[CrossRef]

J. Quantum Electron. (1)

K. Shimomura, Y. Suematsu, S. Arai, “Analysis of semiconductor intersectional waveguide optical switch-modulator,” J. Quantum Electron. 26, 883–892 (1990).
[CrossRef]

Other (2)

RSoft Design Group, Ossining, N.Y., RSoft Photonics CAD Suite, Version 5.1 (1993–2003).

M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

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Figures (12)

Fig. 1
Fig. 1

(a) Schematic diagram of the improved TIR optical switch. (b) Cross section and thermo model of the polymeric TO device. The waveguide is of the channel type. Both the cladding and the core are polymers, with a subtle refractive-index difference. An electrode is deposited on the top of the upper cladding.

Fig. 2
Fig. 2

Contour maps of (a) temperature distribution and (b) amplitude. Parameters are l = 90 μm, L = 3600 μm, Q = 0.12 W, k = 0.177 (W/m)/K, a = 5 (W/m2)/K, ρ = 1200 kg/m3, c = 1300 (J/kg)/K, h = 37 μm, w = 5 μm, λ = 1.55 μm, Ncore = 1.534, and Nclad = 1.526.

Fig. 3
Fig. 3

Influence of parameter l on temperature rise θ(0, h).

Fig. 4
Fig. 4

Time responses to (a) different electrode widths and (b) different total device thicknesses. Relative parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Temperature distribution in meridian planes y = 11 μm and y = 18 μm.

Fig. 6
Fig. 6

Reflection of a ray in the thermal field. Dashed curve, axial line of input and output waveguides; solid and dashed–dotted curves, reflection traces. Shaded area, electrode with width 2w.

Fig. 7
Fig. 7

Relation between meridian plane position y and caustic coordinates xc. Relative parameters are the same as in Fig. 2.

Fig. 8
Fig. 8

Field distribution in the widened waveguide. Widened values are p1 and p2 for the two sides.

Fig. 9
Fig. 9

Influence of widened waveguide width Wt on switch behavior in the bar state.

Fig. 10
Fig. 10

Influence of width D of the enlarged area on switch behavior in the bar state. Widened waveguide width Wt is 35 μm.

Fig. 11
Fig. 11

Influence of the core position (vertical distance between the bottom surface of the core and the substrate) on switch behavior in the bar state. D = 98 μm, Wt = 35 μm.

Fig. 12
Fig. 12

Switching characteristics of the TIR switch. D = 98 μm, Wt = 35 μm.

Equations (20)

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k ( 2 T x 2 + 2 T y 2 ) = ρ c T t .
k T y = Q 2 w L - a ( T - T ) , x < w , k T y = - a ( T - T ) , w < x < l ,
k ( 2 θ x 2 + 2 θ y 2 ) = ρ c θ t ,
{ k θ y = - a θ , y = h , x > w , k θ y = g - a θ , y - h , x < w , θ x = 0 , 0 < y < h , x = ± l , θ = 0 , y = 0 , x < l , θ = 0 , t = 0.
θ = g w l ( k + a h ) y + n = 1 C n cos n π l x sinh n π l y + n = 0 A n [ m = 1 B m n sin μ m y exp ( - k μ m 2 t ρ c ) ] × cos n π l x exp ( - k n 2 π 2 ρ c l 2 t ) .
C n = ( 1 - a sinh n π l h n π k l cosh n π l h + a sinh n π l h ) 2 g l sin n π w l k n 2 π 2 cosh n π h l ,
A 0 B m 0 = - g w l ( k + a h ) ( sin μ m h μ m 2 - h cos μ m h μ m ) 1 2 h - sin 2 μ m h 4 μ m ,
A n B m n = - C n n π l μ m cos n π l h sin μ m h - sinh n π l h cos μ m h ( μ m - n 2 π 2 l 2 μ m ) ( 1 2 h - sin 2 μ m h 4 μ m ) ,             n 0.
k μ = - a tan μ h .
μ m ( m + 1 / 2 ) π / h ,             m = 0 , 1 , 2 , 3 .
θ = g w l ( k + a h ) y + n = 1 C n cos n π l × sinh n π l y .
d z d x = N 1 cos γ [ N 2 ( x ) - N 1 2 cos 2 γ ] 1 / 2 ,
N ( x ) = N 1 + Δ N = N 1 + η θ ( x , y ) ,             - l x l ,
N 1 + η θ ( x c , y ) = N 1 cos γ .
d = l - x c ,
f = 2 - l x c N 1 cos γ [ N 2 ( x ) - N 1 2 cos 2 γ ] 1 / 2 d x .
r = 2 l / tan γ .
p 1 = ( r - f 1 ) sin γ ,             p 2 = ( f 2 - r ) sin γ .
f 2 = 3675.7 μ m , f 1 = 3178.7 μ m , r = 3434.6 μ m , p 1 p 2 = 13.5 μ m , D = 81 μ m .
W t = p 1 + p 2 + 7 μ m = 34 μ m .

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