Abstract

A ray-tracing program designed for grating couplers has been used for an extensive analysis of production tolerances for a focusing grating coupler. In addition the program permits the calculation of coupler behavior in a wave-optical approach including the effects of transverse and axial intensity variations across the grating. The effects of the lateral and longitudinal source point position, wavelength, and waveguide effective index have been studied. The results indicate clearly that in many applications the laser wavelength is the most critical parameter.

© 1992 Optical Society of America

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References

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  1. M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
    [CrossRef]
  2. T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
    [CrossRef]
  3. M. Miler, M. Skalsky, “Chirped and curved grating coupler focusing both outgoing beam and guided wave,” Opt. Commun. 33, 13–16 (1980).
    [CrossRef]
  4. A. Reule, Program GIKO02, Carl Zeiss Internal Rep. WO-FLab LB 90-3 (Carl Zeiss, Oberkochen, Germany, 1990).
  5. D. Heitmann, C. Ortiz, “Calculation and experimental verification of two-dimensional focusing grating couplers,” IEEE J. Quantum Electron. QE-17, 1257–1263 (1981).
    [CrossRef]
  6. S. Ura, T. Suhara, H. Nishihara, “Aberration characterizations of a focusing grating coupler in an integrated-optic disk pickup device,” Appl. Opt. 26, 4777–4782 (1987).
    [CrossRef] [PubMed]
  7. G. N. Lawrence, P. J. Cronkite, “Physical optics analysis of the focusing grating coupler,” Appl. Opt. 27, 672–678 (1988).
    [CrossRef] [PubMed]
  8. G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, S. Flügge, ed., Vol. XXIX, Optische Instrumente (Springer-Verlag, Berlin, 1967), pp. 426–754.
    [CrossRef]
  9. M. T. Wlodarczyk, S. R. Seshadri, “Analysis of grating couplers in planar waveguides for waves at oblique incidence,” J. Opt. Soc. Am. A 2, 171–185 (1985).
    [CrossRef]
  10. E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
    [CrossRef]
  11. J. Seligson, “Modeling of a focusing grating coupler using vector scattering theory,” Appl. Opt. 27, 684–692 (1988).
    [CrossRef] [PubMed]
  12. L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” IEEE J. Lightwave Technol. 6, 1069–1082 (1988).
    [CrossRef]
  13. N. Fabricius, Entwicklungsgesellschaft für Integrierte Optik mbH, D-6833 Waghäusel-Kirrlach, Germany (personal communication).
  14. S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
    [CrossRef]

1989 (1)

S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
[CrossRef]

1988 (3)

1987 (1)

1985 (2)

1981 (1)

D. Heitmann, C. Ortiz, “Calculation and experimental verification of two-dimensional focusing grating couplers,” IEEE J. Quantum Electron. QE-17, 1257–1263 (1981).
[CrossRef]

1980 (1)

M. Miler, M. Skalsky, “Chirped and curved grating coupler focusing both outgoing beam and guided wave,” Opt. Commun. 33, 13–16 (1980).
[CrossRef]

1976 (1)

T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
[CrossRef]

1970 (1)

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Cronkite, P. J.

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Fabricius, N.

N. Fabricius, Entwicklungsgesellschaft für Integrierte Optik mbH, D-6833 Waghäusel-Kirrlach, Germany (personal communication).

Hall, D. G.

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” IEEE J. Lightwave Technol. 6, 1069–1082 (1988).
[CrossRef]

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Heitmann, D.

D. Heitmann, C. Ortiz, “Calculation and experimental verification of two-dimensional focusing grating couplers,” IEEE J. Quantum Electron. QE-17, 1257–1263 (1981).
[CrossRef]

Koyama, J.

T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
[CrossRef]

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Lawrence, G. N.

Mashev, L.

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Miler, M.

M. Miler, M. Skalsky, “Chirped and curved grating coupler focusing both outgoing beam and guided wave,” Opt. Commun. 33, 13–16 (1980).
[CrossRef]

Nishihara, H.

S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, “Aberration characterizations of a focusing grating coupler in an integrated-optic disk pickup device,” Appl. Opt. 26, 4777–4782 (1987).
[CrossRef] [PubMed]

T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
[CrossRef]

Ortiz, C.

D. Heitmann, C. Ortiz, “Calculation and experimental verification of two-dimensional focusing grating couplers,” IEEE J. Quantum Electron. QE-17, 1257–1263 (1981).
[CrossRef]

Popov, E.

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Reule, A.

A. Reule, Program GIKO02, Carl Zeiss Internal Rep. WO-FLab LB 90-3 (Carl Zeiss, Oberkochen, Germany, 1990).

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Seligson, J.

Seshadri, S. R.

Skalsky, M.

M. Miler, M. Skalsky, “Chirped and curved grating coupler focusing both outgoing beam and guided wave,” Opt. Commun. 33, 13–16 (1980).
[CrossRef]

Stroke, G. W.

G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, S. Flügge, ed., Vol. XXIX, Optische Instrumente (Springer-Verlag, Berlin, 1967), pp. 426–754.
[CrossRef]

Suhara, T.

S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, “Aberration characterizations of a focusing grating coupler in an integrated-optic disk pickup device,” Appl. Opt. 26, 4777–4782 (1987).
[CrossRef] [PubMed]

T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
[CrossRef]

Ura, S.

S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, “Aberration characterizations of a focusing grating coupler in an integrated-optic disk pickup device,” Appl. Opt. 26, 4777–4782 (1987).
[CrossRef] [PubMed]

Weller-Brophy, L. A.

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” IEEE J. Lightwave Technol. 6, 1069–1082 (1988).
[CrossRef]

Wlodarczyk, M. T.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

IEEE J. Lightwave Technol. (2)

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” IEEE J. Lightwave Technol. 6, 1069–1082 (1988).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, “Integrated-optic interferometer position sensor,” IEEE J. Lightwave Technol. 7, 270–273 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Heitmann, C. Ortiz, “Calculation and experimental verification of two-dimensional focusing grating couplers,” IEEE J. Quantum Electron. QE-17, 1257–1263 (1981).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Opt. Commun. (2)

T. Suhara, H. Nishihara, J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353–358 (1976).
[CrossRef]

M. Miler, M. Skalsky, “Chirped and curved grating coupler focusing both outgoing beam and guided wave,” Opt. Commun. 33, 13–16 (1980).
[CrossRef]

Other (3)

A. Reule, Program GIKO02, Carl Zeiss Internal Rep. WO-FLab LB 90-3 (Carl Zeiss, Oberkochen, Germany, 1990).

G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, S. Flügge, ed., Vol. XXIX, Optische Instrumente (Springer-Verlag, Berlin, 1967), pp. 426–754.
[CrossRef]

N. Fabricius, Entwicklungsgesellschaft für Integrierte Optik mbH, D-6833 Waghäusel-Kirrlach, Germany (personal communication).

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Figures (19)

Fig. 1
Fig. 1

Focusing grating coupler design and illustration of the choice of variables used throughout the paper.

Fig. 2
Fig. 2

Behavior of the ideal system for different planes of observation. Left: intensity distribution. The area is a square measuring 0.04 mm × 0.04 mm in this and all similar figures; the x and z coordinates are parallel to those in Fig. 1. Right: corresponding curves of encircled energy plotted against the aperture radius in millimeters. Distance from the waveguide to the plane of observation: (a) 5.0 mm (design value), (b) 5.1 mm, (c) 6.2 mm.

Fig. 3
Fig. 3

Focus movement as a function of wavelength variation.

Fig. 4
Fig. 4

The rms spot radius as a function of the wavelength shift in the geometrical-optics approximation. Sigma is the rms width of the diffraction pattern’s projection onto the corresponding axis.

Fig. 5
Fig. 5

Intensity distribution and encircled energy curve corresponding to the plane of least confusion for a working wavelength that is 10 nm shorter than the design value.

Fig. 6
Fig. 6

Focus movement as a function of the mode-index variation.

Fig. 7
Fig. 7

Intensity distributions and encircled energy curves for different planes of observation and a defocusing of 0.2 mm. The distances between the waveguide and plane of observation are 4.9, 5.0, 5.05, 5.2, and 5.3 mm for (a), (b), (c), (d), and (e), respectively.

Fig. 8
Fig. 8

Focus movement as a function of defocusing. Since both x and z remain constant, the dotted curve for z is hidden by the coincident curve for x.

Fig. 9
Fig. 9

Focus movement as a function of lateral source displacement. Only the z coordinate shows a first-order dependence.

Fig. 10
Fig. 10

Intensity distributions and encircled energy curves for different planes of observation and a lateral source displacement of 0.2 mm. The distances between the grating and plane of observation are 4.9, 5.0, 5.1, and 5.2 mm in (a), (b), (c), and (d), respectively.

Fig. 11
Fig. 11

Intensity distribution and encircled energy curve corresponding to the plane of least confusion for a worst-case situation combining all errors assumed in Figs. 5, 7, 8, and 11.

Fig. 12
Fig. 12

Phase (a) and intensity (b) distribution in the exit pupil (grating plane) for the defocused system with a 7-mm source grating distance for homogeneous illumination. In (c) central cross sections of the phase distribution are shown; pupil coordinates are in millimeters, while the phase is in wavelengths. The phase distribution (d) of the ideal system is shown for comparison.

Fig. 13
Fig. 13

Intensity distribution 1 mm above the exit pupil (grating plane) for the defocused system with a 7-mm source grating distance for lateral apodization.

Fig. 14
Fig. 14

Intensity distribution 1 mm above the exit pupil (grating plane) for the defocused system with a 7-mm source grating distance for axial apodization.

Fig. 15
Fig. 15

Focal-plane intensity distribution and encircled energy curve for lateral apodization of the ideal system.

Fig. 16
Fig. 16

Focal-plane intensity distribution and encircled energy curve for axial apodization of the ideal system.

Fig. 17
Fig. 17

Intensity distributions and encircled energy curves for axial apodization of the ideal system in several planes near the focus. The distance from the grating to the observational plane is 4.9, 5.1, and 5.2 mm for (a), (b), and (c), respectively.

Fig. 18
Fig. 18

Intensity distribution and encircled energy curve for lateral apodization of the defocused system in the plane of least confusion.

Fig. 19
Fig. 19

Intensity distribution and encircled energy curve for axial apodization of the defocused system in the plane of least confusion.

Equations (12)

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b ^ · l ^ = n 1 n 2 ( a ^ · l ^ ) ,
b ^ · g ^ = n 1 n 2 ( a ^ · g ^ ) - m λ n 2 d ,
b ^ · n ^ = ± { 1 - [ n 1 n 2 ( a ^ · l ^ ) ] 2 - [ n 1 n 2 ( a ^ · g ^ ) - m λ n 2 d ] 2 } 1 / 2 .
F ( x , z ) = M + μ ,
F ( x , z ) = 1 m · λ { n 1 [ ( x - x 0 ) 2 + ( z - z 0 ) 2 ] 1 / 2 + n 2 [ ( x - x 1 ) 2 + y 1 2 + ( z - z 1 ) 2 ] 1 / 2 } ,
F x = 1 m · λ { n 1 ( x - x 0 ) [ ( x - x 0 ) 2 + ( z - z 0 ) 2 ] 1 / 2 + n 2 ( x - x 1 ) [ ( x - x 1 ) 2 + y 1 2 + ( z - z 1 ) 2 ] 1 / 2 } ,
F z = 1 m · λ { n 1 ( z - z 0 ) [ ( x - x 0 ) 2 + ( z - z 0 ) 2 ] 1 / 2 + n 2 ( z - z 1 ) [ ( x - x 1 ) 2 + y 1 2 + ( z - z 1 ) 2 ] 1 / 2 } ,
g ^ = F x ( F x 2 + F z 2 ) 1 / 2 e ^ x + F z ( F x 2 + F z 2 ) 1 / 2 e ^ z ,
l ^ = F z ( F x 2 + F z 2 ) 1 / 2 e ^ x + F x ( F x 2 + F z 2 ) 1 / 2 e ^ z
n ^ = e ^ y .
d = 1 ( F x 2 + F z 2 ) 1 / 2 .
Δ S = - [ F ( x , z ) - F 0 ] m λ

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