Abstract

Input-grating coupling characteristics have been studied for narrow Gaussian beam incidence and finite-length grating coupler with an electromagnetic full-vector field model based on the finite-difference time domain (FDTD) method. Analytic analysis based on perturbation theory has been compared to the FDTD technique. The influences of the variation in grating period, modulation depth, corrugation, and beam size have been investigated. Certain aspects of the calculated results have been confirmed with experiments.

© 2004 Optical Society of America

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References

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Appl. Opt. (4)

Appl. Phys. (1)

T. Tamir and S. T. Peng, �??Analysis and design of grating couplers,�?? Appl. Phys. 14, 235-254 (1977)
[CrossRef]

Appl. Phys. Lett . (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, �??Near-field optical storage using a solid immersion lens,�?? Appl. Phys. Lett . 65, 388-390 (1994)
[CrossRef]

Appl. Phys. Lett. (3)

F. Issiki, K. Ito, K. Etoh, and S. Hosaka, �??1.5-Mbit/s direct readout of line-and-space patters using a scanning near-field optical microscope probe slider with air-bearing control,�?? Appl. Phys. Lett. 76, 804-806 (2000).
[CrossRef]

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

A. Gruss, K. T. Tam, and T. Tamir, �??Blazed dielectric gratings with high beam-coupling efficiencies,�?? Appl. Phys. Lett. 36, 523-525 (1980)
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, �??A theoretical analysis of etched grating couplers for integrated optics,�?? IEEE J. Quantum Electron. QE-9, 29-73 (1973)
[CrossRef]

J. Computational Phys. (1)

J. S. Hesthaven, P. G. Dinesen, and J. P. Lynov, �??Spectral collocation time-domain modeling of diffractive optical elements,�?? J. Computational Phys. 155, 287-306 (1999)
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

B. Lichtenberg and N. C. Gallagher, �??Numerical modeling of diffractive device using the finite element method,�?? Opt. Eng. 33, 1592-1598 (1994)
[CrossRef]

Optical and Quantum Electron. (1)

H. J. W. M. Hoekstra, �??Coupled mode theory for resonant excitation of waveguiding structures,�?? Optical and Quantum Electron. 32, 735-758 (2000)
[CrossRef]

Optics Communications (1)

M. Neviere, R. Petit, and M. Cadilhac, �??About the theory of optical coupler-waveguide systems,�?? Optics Communications 8, 113-245 (1973)
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, �??Analysis and applications of optical diffraction by gratings,�?? Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. A. Kiselev, �??Diffraction coupling of radiation into a thin-film waveguide,�?? Sov. J. Quantum Electron. 4, 872-875 (1975)
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram showing a waveguide and a grating coupler. The beam of light is incident on and coupled into the waveguide with a periodical grating of finite length. θ is the angle of incidence, and zc is the lateral offset of the beam center from the edge of the grating. XYZ is a coordinate system. The arrow in the core layer represents the direction of mode beam propagation. In (a), the grating on the surface of film, surface-corrugation; in (b) the grating on substrate.

Fig. 2.
Fig. 2.

Calculated coupling efficiency as a function of angle of incidence at various groove depths marked on each curve for grating period (a) Λ=0.68 µm and (b) Λ=0.36 µm in the configuration of surface-corrugation.

Fig. 3.
Fig. 3.

Calculated efficiency as a function of groove depth. a: substrate-corrugation, groove period Λ=0.36 µm; b: surface-corrugation, groove period Λ=0.36 µm; c: surface-corrugation, groove period Λ=0.68 µm.

Fig. 4.
Fig. 4.

Calculated attenuation coefficient α vs. groove depth as TE0 mode propagates in the grating region. The grating has a rectangular groove profile with period Λ=0.36 µm and a 50% duty cycle.

Fig. 5.
Fig. 5.

Radiation of guided mode into free space and substrate, based on ray optics.

Fig. 6.
Fig. 6.

Calculated efficiency as a function of beam position zc relative to groove edge at the groove depths of 30 nm and 70 nm.

Fig. 7.
Fig. 7.

(a) Calculated efficiency vs. groove depth (b) normalized coupling efficiency vs. angle of incidence detuning for three beam sizes in the configuration of surface-corrugation. In (b) the groove depth is 30 nm for 2w0=79λ, 40 nm for 2w0=40λ, and 60 nm for 2w0=20λ.

Fig. 8.
Fig. 8.

Topography of grooved surface and groove profile normal to the groove, obtained by an atomic-force-microscope.

Fig. 9.
Fig. 9.

Schematic diagram showing the setup for the characterization of the grating coupler. The incident beam is s-polarized. A photodiode measures the light propagated in the waveguide.

Fig. 10.
Fig. 10.

In-put coupling efficiency vs. groove depth. The individual data points represent the experimental data while the solid curve is theoretically calculated.

Fig. 11.
Fig. 11.

Angle of incidence θ0 for optimal coupling at various grooved depths. The individual data points represent the experimental data while the solid curve is theoretically obtained. Inset is sin(θ0) vs. d for those grooves having a nearly 50% duty cycle. The gating period is 0.48 µm.

Fig. 12.
Fig. 12.

Normalized coupling efficiency vs. angle of incidence detuning for a groove depth of 30 nm. The solid line a plot of the experimental data while the individual data points are theoretical.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

n eff = sin θ + m λ Λ ,
η = f c 2 π ( α w 1 2 ) exp { 2 [ ( α w 1 2 ) 2 α z c ] } [ 1 + erf ( z c w 1 α w 1 2 ) ] 2 .
α w 1 0.68 and α z c 0.5 ,
ϕ k 0 2 d c cos θ c ( n c sin θ c n s sin θ s ) + ϕ gh

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