Abstract

Planar waveguide-grating couplers are analyzed to determine the effects of grating length, the incident beam size, and the coupling length of the grating on the input-coupling efficiency. The emphasis is to examine the effects of these finite lengths on the range of angles over which input coupling occurs and the shape of the efficiency curve. A general formula for normalized input-coupling efficiency is given to relate these lengths. When any one of these characteristic lengths is much smaller than the other two, both the angular width and angular dependence of the coupling efficiency for a scan of the incident beam angle will be mainly determined by that characteristic length. This is demonstrated experimentally for two cases: one has a relatively short grating length, and the other has a short coupling length.

© 1995 Optical Society of America

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References

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  1. S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
    [CrossRef]
  2. Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
    [CrossRef]
  3. H. F. Taylor, “Application of guided-wave optics in signal processing and sensing,” Proc. IEEE 75, 1524–1535 (1987).
    [CrossRef]
  4. T. Tamir, “Beam and waveguide couplers,” in Integrated Optics, T. Tamir, ed. (Springer, New York, 1975), pp. 83–137.
    [CrossRef]
  5. M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
    [CrossRef]
  6. L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
    [CrossRef] [PubMed]
  7. M. C. Gupta, L. Li, “Achromatic compensation for integrated optic grating couplers with focused beams,” Appl. Opt. 30, 1461–1463 (1991).
    [CrossRef] [PubMed]
  8. K. E. Spaulding, G. M. Morris, “Achromatic waveguide input–output coupler design,” Appl. Opt. 30, 1096–1112 (1991).
    [CrossRef] [PubMed]
  9. K. E. Spaulding, G. M. Morris, “Achromatic waveguide couplers,” submitted to J. Lightwave Technol.
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    [CrossRef] [PubMed]
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  13. M. Long, J. Newman, “Image reversal techniques with standard positive photoresist,” in Advances in Resist Technology, C. G. Willson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.469, 189–193 (1984).
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  15. J. Brazas, “Vacuum-coated organic recording media,” J. Imag. Sci. 32, 56–59 (1988).
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    [CrossRef] [PubMed]
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    [CrossRef]

1992 (1)

1991 (2)

1990 (1)

1988 (2)

Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
[CrossRef]

J. Brazas, “Vacuum-coated organic recording media,” J. Imag. Sci. 32, 56–59 (1988).

1987 (1)

H. F. Taylor, “Application of guided-wave optics in signal processing and sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

1986 (1)

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

1977 (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

1976 (1)

1970 (1)

Alling, E.

E. Alling, C. Stauffer, “Image reversal of positive photoresist,” in Advances in Resist Technology and Processing II, L. F. Thompson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.539, 194–213 (1985).

Austin, S.

Beesley, M. J.

Brazas, J.

Casteldine, J. G.

Gupta, M. C.

Kohnke, G.

Koyama, J.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

Li, L.

M. C. Gupta, L. Li, “Achromatic compensation for integrated optic grating couplers with focused beams,” Appl. Opt. 30, 1461–1463 (1991).
[CrossRef] [PubMed]

L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
[CrossRef] [PubMed]

L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 72–82 (1988).

Long, M.

M. Long, J. Newman, “Image reversal techniques with standard positive photoresist,” in Advances in Resist Technology, C. G. Willson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.469, 189–193 (1984).

Lukosz, W.

Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
[CrossRef]

McMullen, J.

Morris, G. M.

K. E. Spaulding, G. M. Morris, “Achromatic waveguide input–output coupler design,” Appl. Opt. 30, 1096–1112 (1991).
[CrossRef] [PubMed]

K. E. Spaulding, G. M. Morris, “Achromatic waveguide couplers,” submitted to J. Lightwave Technol.

Nellen, Ph. M.

Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
[CrossRef]

Neviere, M.

M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

Newman, J.

M. Long, J. Newman, “Image reversal techniques with standard positive photoresist,” in Advances in Resist Technology, C. G. Willson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.469, 189–193 (1984).

Nishihara, H.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

Peng, S. T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Seaton, C. T.

L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 72–82 (1988).

Spaulding, K. E.

K. E. Spaulding, G. M. Morris, “Achromatic waveguide input–output coupler design,” Appl. Opt. 30, 1096–1112 (1991).
[CrossRef] [PubMed]

K. E. Spaulding, G. M. Morris, “Achromatic waveguide couplers,” submitted to J. Lightwave Technol.

Stauffer, C.

E. Alling, C. Stauffer, “Image reversal of positive photoresist,” in Advances in Resist Technology and Processing II, L. F. Thompson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.539, 194–213 (1985).

Stegeman, G. I.

L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 72–82 (1988).

Stone, F. T.

Suhara, T.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

Tamir, T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

T. Tamir, “Beam and waveguide couplers,” in Integrated Optics, T. Tamir, ed. (Springer, New York, 1975), pp. 83–137.
[CrossRef]

Taylor, H. F.

H. F. Taylor, “Application of guided-wave optics in signal processing and sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

Tiefenthaler, K.

Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
[CrossRef]

Ura, S.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

Xu, M.

L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 72–82 (1988).

Appl. Opt. (6)

Appl. Phys. (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

J. Imag. Sci. (1)

J. Brazas, “Vacuum-coated organic recording media,” J. Imag. Sci. 32, 56–59 (1988).

J. Lightwave Technol. (1)

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An integrated optical pickup device,” J. Lightwave Technol. LT-4, 913–918 (1986).
[CrossRef]

Proc. IEEE (1)

H. F. Taylor, “Application of guided-wave optics in signal processing and sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

Sens. Actuat. (1)

Ph. M. Nellen, K. Tiefenthaler, W. Lukosz, “Integrated optical input grating couplers as biochemical sensors,” Sens. Actuat. 15, 285–295 (1988).
[CrossRef]

Other (6)

K. E. Spaulding, G. M. Morris, “Achromatic waveguide couplers,” submitted to J. Lightwave Technol.

T. Tamir, “Beam and waveguide couplers,” in Integrated Optics, T. Tamir, ed. (Springer, New York, 1975), pp. 83–137.
[CrossRef]

M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 72–82 (1988).

M. Long, J. Newman, “Image reversal techniques with standard positive photoresist,” in Advances in Resist Technology, C. G. Willson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.469, 189–193 (1984).

E. Alling, C. Stauffer, “Image reversal of positive photoresist,” in Advances in Resist Technology and Processing II, L. F. Thompson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.539, 194–213 (1985).

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Figures (10)

Fig. 1
Fig. 1

Geometry and coordinate system of a grating coupler of finite length, Lg.

Fig. 2
Fig. 2

SEM of the grating used in the experiments, with the waveguide removed.

Fig. 3
Fig. 3

Optical beams that exist in an input-grating and output-grating coupler pair for the measurement of input-coupling efficiency.

Fig. 4
Fig. 4

Experimental setup for measuring the coupling efficiency for a range of incident angles, using a He–Ne laser (λ = 0.6328 μm).

Fig. 5
Fig. 5

Representative reflection and transmission results for coupling efficiency measurements that use TE polarization (set A: Lg = 1 mm, Lc = 1.2 mm, and ω0 = 3.28 mm).

Fig. 6
Fig. 6

Experimental input-coupling efficiency for the TE0 mode (set A: Lg = 1 mm, Lc = 1.2 mm, and ω0 = 3.28 mm), using the transmission and reflection data from Fig. 5 in Eq. (18).

Fig. 7
Fig. 7

Theoretical normalized coupling efficiency and experimental normalized throughput for detuning of the nominal incident angle for the TE0 mode (set A: Lg = 1 mm, Lc = 1.2 mm, and ω0 = 3.28 mm), corresponding to case 3 in the text.

Fig. 8
Fig. 8

Theoretical normalized coupling efficiency and experimental normalized throughput for detuning of the nominal incident angle in which LcLg for the TE0 mode (Set B: Lg = 1 mm, Lc = 0.07 mm, and ω0 = 3.28 mm), corresponding to case 2 in the text.

Fig. 9
Fig. 9

Results for the measurement of angular width Δϴ for grating sets A(●) and B (♦) and their theoretical results (−), using Lc values of 1.2 and 0.07 mm, respectively.

Fig. 10
Fig. 10

Experimental coupling efficiencies for gratings of set A and theoretical results, assuming a groove depth of 35 nm.

Equations (19)

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A ( z ) = a ( z ) exp [ i ( 2 π λ n c sin θ + m 2 π Λ ) z ] ,
η = C | a ( 0 ) | 2 ,
d a ( z ) d z = ( α + i Δ β ) a ( z ) + cq ( z ) ,
Δ β = 2 π λ n c ( sin θ sin θ ) ,
Δ β = 2 π λ n c cos θ Δ θ .
a ( z ) = c exp [ ( α + i Δ β ) z ] L g z exp [ ( α + i Δ β ) z ] q ( z ) d z .
η = C | L g 0 exp [ ( α + i Δ β ) z ] q ( z ) d z | 2 ,
η = C | [ rect ( z L g ) exp ( α z ) q ( z ) ] exp ( i Δ β z ) d z | 2 ,
rect ( x ) = { 1 , 0 < x < 1 0 , otherwise ,
L c = 1 / α .
η 0 = exp ( ½ Δ β 2 ω 0 2 ) ,
Δ ϴ = 2 ln 2 π λ ω 0 n c cos θ ,
η 0 = α 2 α 2 + Δ β 2 ,
Δ ϴ = 1 π λ L c n c cos θ .
η 0 = sinc 2 ( Δ β L g 2 ) ,
Δ ϴ = 2 x 0 π λ L g n c cos θ ,
Δ β = 2 π λ n c cos θ d θ d λ Δ λ .
η = I i ( I r + I t ) I i ,
η = D 1 ( D 3 + D 2 ) D 1 .

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