Abstract

It is demonstrated that bent dielectric waveguides can convert incident radiation into guided-mode power. A beam-propagation method simulation of the effect in a slab single-moded weakly guiding waveguide is shown to be in accordance with a theoretical formulation of the process. I establish a simple analytical approximation for power captured by a curved slab guide from an incident Gaussian-shaped beam. The results demonstrate general agreement with the reciprocity principle: the most efficient radiator is the best receiver, and radiation incident from outside the bend couples most efficiently into the guide.

© 1993 Optical Society of America

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References

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  1. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), Chaps. 1 and 2.
  2. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 11 and 23.
  3. A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).
  4. D. Marcuse, J. Opt. Soc. Am. 66, 311 (1976).
  5. W. L. Kath, G. A. Kriegsmann, IMA J. Appl. Math. 41, 85 (1988).
  6. H. F. Taylor, Appl. Opt. 13, 642 (1974).
  7. D. Yap, L. M. Johnson, Appl. Opt. 23, 2991 (1984).
  8. L. Lerner, “Calculation and minimization of transition losses in arbitrarily curved waveguides,” Opt. Commun. (to be published).
  9. C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 10.
  10. L. Lerner, Electron. Lett. 29, 733 (1993).

1993 (1)

L. Lerner, Electron. Lett. 29, 733 (1993).

1988 (1)

W. L. Kath, G. A. Kriegsmann, IMA J. Appl. Math. 41, 85 (1988).

1984 (1)

1976 (1)

1975 (1)

A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).

1974 (1)

Bender, C. M.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 10.

Johnson, L. M.

Kath, W. L.

W. L. Kath, G. A. Kriegsmann, IMA J. Appl. Math. 41, 85 (1988).

Kriegsmann, G. A.

W. L. Kath, G. A. Kriegsmann, IMA J. Appl. Math. 41, 85 (1988).

Lerner, L.

L. Lerner, Electron. Lett. 29, 733 (1993).

L. Lerner, “Calculation and minimization of transition losses in arbitrarily curved waveguides,” Opt. Commun. (to be published).

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 11 and 23.

Marcuse, D.

D. Marcuse, J. Opt. Soc. Am. 66, 311 (1976).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), Chaps. 1 and 2.

Mitchell, D. J.

A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).

Orszag, S. A.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 10.

Snyder, A. W.

A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 11 and 23.

Taylor, H. F.

White, I. A.

A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).

Yap, D.

Appl. Opt. (2)

Electron. Lett. (2)

A. W. Snyder, I. A. White, D. J. Mitchell, Electron. Lett. 11, 332 (1975).

L. Lerner, Electron. Lett. 29, 733 (1993).

IMA J. Appl. Math. (1)

W. L. Kath, G. A. Kriegsmann, IMA J. Appl. Math. 41, 85 (1988).

J. Opt. Soc. Am. (1)

Other (4)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), Chaps. 1 and 2.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 11 and 23.

L. Lerner, “Calculation and minimization of transition losses in arbitrarily curved waveguides,” Opt. Commun. (to be published).

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 10.

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Figures (3)

Fig. 1
Fig. 1

(a) Beam (dark arrow) grazing the outside of a bend, with radius R. Coordinate axes are drawn for three distinct stages of the guide–beam interaction. (b) Field amplitude distribution at the three interaction stages of (a) for the optimum angle of the incident beam, derived from a beam-propagation method simulation in Slab geometry (normalized frequency V = 1.4, profile height Δ = 0.003, R/ρ = 2700).

Fig. 2
Fig. 2

Fraction of incident power in the leaky mode (dashed curve) and guided mode (solid curve) as a function of longitudinal distance s. The parameters are the same as in Fig. 1(b).

Fig. 3
Fig. 3

Fraction of power in the guided mode at the end of interaction as a function of the x component of the beam-propagation constant βr obtained numerically from Eq. (2) (symbols) and analytically from relation (7) (solid curve). The parameters are the same as in Fig. 1(b), with σ/ρ = 2.3 and a/ρ = 11.

Equations (7)

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d 2 E ( x ) d x 2 + Q ( x ) E ( x ) = 0 , Q ( x ) = k 2 n 2 ( x ) β 2 ( 1 + κ x ) 2 ,
| E 0 * ( x , s ) E ( x ) d x | = | E rad * ( x , 0 ) E ( x ) d x | .
E ( x ) { N exp W ( x + ρ δ ) / ρ x ρ + δ N sec U cos U ( x δ ) / ρ ρ + δ x ρ + δ = x c ,
E ( x ) N ( x r x c x r x ) 1 / 4 × exp { 2 3 2 κ β [ ( x r x c ) 3 / 2 ( x r x ) 3 / 2 ] } , x c < x < x r ,
E ( x ) N [ 2 κ β 2 ( x r x c ) Q ( x ) ] 1 / 4 × exp [ 2 3 2 κ β ( x r x c ) 3 / 2 + i x Q ( x ) d x ] , x > x r + ,
E ( x , 0 ) = 1 π 1 / 4 σ exp [ i β r x ( x a ) 2 / 2 σ 2 ]
| E ( x ) E * ( x , 0 ) d x | 2 σ N 2 [ 8 π κ β 2 ( x r x c ) Q ( a ) ( 1 + 4 γ 2 σ 4 ) ] 1 / 2 × exp [ 4 3 2 κ β ( x r x c ) 3 / 2 ] exp ( Δ 2 σ 2 ) ,

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