Abstract

Two important considerations for designing coupling prisms for optical waveguides are (a) coupling the incident wave to the full range of effective indices for the modes in the waveguide and (b) the ability to observe the optically contacted area, the wet spot, between the prism and waveguide. The latter becomes a problem with high-index prisms owing to total internal reflections. Design parameters for prisms satisfying both of these requirements are derived, and numerical examples are presented for both symmetrical and right-angle rutile prisms.

© 1987 Optical Society of America

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References

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  1. P. K. Tien, R. Ulrich, “Theory of Prism–Film Coupler and Thin-Film Light Guides,” J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  2. R. T. Kersten, “The Prism–Film Coupler as a Precision Instrument—Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
    [CrossRef]
  3. D. K. Paul, “Thickness and Refractive Index Measurements by Light Coupling: Design Guidelines of a Prism Coupler,” Proc. Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).
  4. H. Kogelnik, “Theory of Dielectric Waveguides,” in Integrated Optics, T. Tamir, Ed. (Springer Verlag, New York, 1979), p. 21.
  5. J. R. DeVore, “Refractive Indexes of Rutile and Sphalerite,” J. Opt. Soc. Am. 41, 416 (1951).
    [CrossRef]

1982 (1)

D. K. Paul, “Thickness and Refractive Index Measurements by Light Coupling: Design Guidelines of a Prism Coupler,” Proc. Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

1975 (1)

R. T. Kersten, “The Prism–Film Coupler as a Precision Instrument—Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

1970 (1)

1951 (1)

DeVore, J. R.

Kersten, R. T.

R. T. Kersten, “The Prism–Film Coupler as a Precision Instrument—Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Theory of Dielectric Waveguides,” in Integrated Optics, T. Tamir, Ed. (Springer Verlag, New York, 1979), p. 21.

Paul, D. K.

D. K. Paul, “Thickness and Refractive Index Measurements by Light Coupling: Design Guidelines of a Prism Coupler,” Proc. Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

Tien, P. K.

Ulrich, R.

J. Opt. Soc. Am. (2)

Opt. Acta (1)

R. T. Kersten, “The Prism–Film Coupler as a Precision Instrument—Part I. Accuracy and Capabilities of Prism Couplers as Instruments,” Opt. Acta 22, 503 (1975).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. K. Paul, “Thickness and Refractive Index Measurements by Light Coupling: Design Guidelines of a Prism Coupler,” Proc. Soc. Photo-Opt. Instrum. Eng. 342, 100 (1982).

Other (1)

H. Kogelnik, “Theory of Dielectric Waveguides,” in Integrated Optics, T. Tamir, Ed. (Springer Verlag, New York, 1979), p. 21.

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Figures (4)

Fig. 1
Fig. 1

Symmetrical prism on waveguide.

Fig. 2
Fig. 2

Permitted values of prism base angle θp as a function of refractive index nf.

Fig. 3
Fig. 3

Critical angles for prism–air interface and prism–substrate interface.

Fig. 4
Fig. 4

Reflections in a right-angle prism.

Equations (18)

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Θ p = arcsin n eff n p + arcsin ( 1 n p sin Θ i ) .
- π / 2 Θ i , min < Θ i < Θ i , max π / 2.
arcsin n eff n p + arcsin ( 1 n p sin Θ i , min ) < Θ p < arcsin n eff n p + arcsin ( 1 n p sin Θ i , max )
n S < n eff < n f .
arcsin n f n p + arcsin ( 1 n p sin Θ i , min ) < Θ p < arcsin n s n p + arcsin ( 1 n p sin Θ i , max ) .
Θ c , f = arcsin n f n p ,
Θ c , s = arcsin n s n p ,
Θ c , f + arcsin ( 1 n p sin Θ i , min ) < Θ p < Θ c , s + arcsin ( 1 n p sin Θ i , m a x ) .
α = θ p - θ c , a ,
β = θ p - θ c , s ,
arcsin ( 1 n p sin Θ i , min ) < α < arcsin ( 1 n p sin Θ i , max )
arcsin ( 1 n p sin Θ i , min ) < β < arcsin ( 1 n p sin Θ i , max ) .
Θ c , a + arcsin ( 1 n p sin Θ i , min ) < Θ p < Θ c , a + arcsin ( 1 n p sin Θ i , m a x )
Θ c , s + arcsin ( 1 n p sin Θ i , min ) < Θ p < Θ c , s + arcsin ( 1 n p sin Θ i , max ) .
Θ c , a + arcsin ( 1 n p sin Θ i , min ) < Θ p < Θ c , s + arcsin ( 1 n p sin Θ i , max ) .
γ = 90 ° - ( 2 θ p - θ c , a ) ,
δ = 90 ° - ( 2 θ p - θ c , s ) .
45 ° + 1 2 Θ c , a - 1 2 arcsin ( 1 n p sin ψ i , max ) < Θ p < 45 ° + 1 2 Θ c , s - 1 2 arcsin ( 1 n p sin ψ i , min ) .

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