Abstract

A technique was developed to couple near-field evanescent waves into observable diffraction orders in the far-field region. This investigation was of two gratings that have a 1.0μm grating period in glass and 1.1μm in silicon and are individually subwavelength, but when coupled together yield an 11.0μm effective grating period. This effective grating period is not subwavelength to a 1.550μm infrared incident source and exhibits higher diffraction orders. Optimum evanescent wave coupling efficiency was simulated by varying the grating thickness and the grating separation between the subwavelength gratings. This proposed evanescent wave coupling concept is being investigated for use in a bulk silicon MEMS accelerometer.

© 2009 Optical Society of America

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References

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  1. M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. R. Hull, Properties of Crystalline Silicon (Institution of Engineering and Technology, 1999).
  15. R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
    [CrossRef]

2007 (1)

2006 (1)

2005 (4)

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

K. Taniguchi and Y. Kanemitsu, “Development of an apertureless near-field optical microscope for nanoscale optical imaging at low temperatures,” Jpn. J. Appl. Phys. 44, 575-577 (2005).
[CrossRef]

B. E. Keeler, G. R. Bogart, and D. W. Carr, “Laterally deformable optical NEMS grating transducers for inertial sensing applications,” Proc. SPIE 5592, 306-312 (2005).
[CrossRef]

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

2004 (1)

2002 (4)

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

1966 (1)

K. Yee, “Numerical solutions of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Barbara, A.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Bogart, G. R.

B. E. Keeler, G. R. Bogart, and D. W. Carr, “Laterally deformable optical NEMS grating transducers for inertial sensing applications,” Proc. SPIE 5592, 306-312 (2005).
[CrossRef]

Bustarret, E.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Cao, H.

Carr, D. W.

B. E. Keeler, G. R. Bogart, and D. W. Carr, “Laterally deformable optical NEMS grating transducers for inertial sensing applications,” Proc. SPIE 5592, 306-312 (2005).
[CrossRef]

Cheben, P.

Chen, H. T.

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Chen, Y.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Cho, G. C.

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Csúcs, G.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

De Paul, S. M.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Densmore, A.

Dereux, A.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

Girard, C.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2004).

Hane, K.

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

Hesthaven, J. S.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Horvath, R.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Hull, R.

R. Hull, Properties of Crystalline Silicon (Institution of Engineering and Technology, 1999).

Ishimori, M.

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

Janz, S.

Johansen, P. M.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Kanamori, Y.

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

Kanemitsu, Y.

K. Taniguchi and Y. Kanemitsu, “Development of an apertureless near-field optical microscope for nanoscale optical imaging at low temperatures,” Jpn. J. Appl. Phys. 44, 575-577 (2005).
[CrossRef]

Karpowicz, N.

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Keeler, B. E.

B. E. Keeler, G. R. Bogart, and D. W. Carr, “Laterally deformable optical NEMS grating transducers for inertial sensing applications,” Proc. SPIE 5592, 306-312 (2005).
[CrossRef]

Kersting, R.

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Kim, S. H.

Kraatz, S.

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Lee, H. S.

Lee, K. D.

Lee, S. S.

Lopez-Rios, T.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Nahata, A.

Pedersen, H. C.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Peyrade, D.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Quemerais, P.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Quidant, R.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Ramsden, J. J.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Sasaki, M.

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

Skivesen, N.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Spencer, N. D.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Szendro, I.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Taniguchi, K.

K. Taniguchi and Y. Kanemitsu, “Development of an apertureless near-field optical microscope for nanoscale optical imaging at low temperatures,” Jpn. J. Appl. Phys. 44, 575-577 (2005).
[CrossRef]

Textor, M.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Vörös, J.

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Weeber, J. C.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

Wilcox, L. C.

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Xu, D.

Yee, K.

K. Yee, “Numerical solutions of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Yoon, Y. T.

Appl. Phys. B: Lasers Opt. (1)

R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,” Appl. Phys. B: Lasers Opt. 81, 65-73 (2005).
[CrossRef]

Biomaterials (1)

J. Vörös, J. J. Ramsden, G. Csúcs, I. Szendrō, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23, 3699-3710 (2002).
[CrossRef] [PubMed]

Europhys. Lett. (1)

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, “Near-field observation of evanescent light wave coupling in subwavelength optical waveguides,” Europhys. Lett. 57, 191-197 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. Yee, “Numerical solutions of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Jpn. J. Appl. Phys. (2)

M. Ishimori, Y. Kanamori, M. Sasaki, and K. Hane, “Subwavelength antireflection gratings for light emitting diodes and photodiodes fabricated by fast atom beam etching,” Jpn. J. Appl. Phys. 41, 4346-4349 (2002).
[CrossRef]

K. Taniguchi and Y. Kanemitsu, “Development of an apertureless near-field optical microscope for nanoscale optical imaging at low temperatures,” Jpn. J. Appl. Phys. 44, 575-577 (2005).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (1)

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Proc. SPIE (1)

B. E. Keeler, G. R. Bogart, and D. W. Carr, “Laterally deformable optical NEMS grating transducers for inertial sensing applications,” Proc. SPIE 5592, 306-312 (2005).
[CrossRef]

Semicond. Sci. Technol. (1)

G. C. Cho, H. T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol. 20, S286-S292 (2005).
[CrossRef]

Other (3)

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2004).

R. Hull, Properties of Crystalline Silicon (Institution of Engineering and Technology, 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Coupled gratings drawn to scale: light (yellow online), Λ = 1.1 μ m ; dark (blue online), Λ = 1.0 μ m , illustrating the 11.0 μ m effective grating. (b) Two sinusoidal gratings ( K 1 and K 2 ) in the time domain and their Fourier transform spatial frequency components surrounded by the LPF region. (c) Convolved frequency domain of grating-modulated waves showing coupling ( K 1 + K 2 and K 1 K 2 ) in the LPF region.

Fig. 2
Fig. 2

Optiwave simulation layout. The 1.550 μ m Gaussian input is indicated by the vertical (red online) line in the glass medium of n = 1.57 with 1.0 μ m grating. There is an air grating separation before the EWs recouple with the 1.1 μ m grating in silicon. For clarity, only a portion of the 120 μ m width x dimension is shown.

Fig. 3
Fig. 3

(a) Output intensity of the coupled EWs for 1.0 μ m and 1.1 μ m coupled SW gratings in glass and silicon at the first diffraction order of 8.1005°. (b) Maximum output intensity as a function of grating separation from 0.0 to 600 nm in 100 nm increments.

Equations (12)

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E 0 ( z ) = A 0 exp ( j k z ) ,
m Λ = λ sin ( θ ) θ = sin 1 ( m Λ λ ) .
t 1 ( x ) = 1 + b 1 cos ( K 1 x ) ,
E 0 + ( x ) = A 0 [ 1 + b 1 cos ( K 1 x ) ] .
P 0 + ( k x ) = E 0 + ( x ) exp ( j k x x ) d x = A 0 δ ( k x ) + A 0 b 1 2 δ ( k x K 1 ) + A 0 b 1 2 δ ( k x + K 1 ) .
k z = ± ( k 2 k x 2 ) 1 2 .
F z ( k x ) = A 0 δ ( k x ) + A 0 b 1 2 δ ( k x K 1 ) + A 0 b 1 2 δ ( k x + K 1 ) exp { ± j z [ ( k 2 k x 2 ) 1 2 ] } .
E z ( x , z ) = F z ( k x ) exp ( j k x x ) d k x = A 0 exp ( j k z ) + A 0 b 1 2 exp [ ± j z ( k 2 K 1 2 ) 1 2 ] exp ( j K 1 x ) + A 0 b 1 2 exp [ ± j z ( k 2 K 1 2 ) 1 2 ] exp ( j K 1 x ) .
= A 0 exp ( j k z ) + A 0 b 1 2 exp [ z ( K 1 2 k 2 ) 1 2 ] exp ( j K 1 x ) + A 0 b 1 2 exp [ z ( K 1 2 k 2 ) 1 2 ] exp ( j K 1 x ) .
t 2 ( x ) = 1 + b 2 cos ( K 2 x ) ,
P 0 + + ( k x ) = [ E 0 + ( x ) t 2 ( x ) ] exp ( j k x x ) d x = A 0 δ ( k x ) + A 0 b 1 2 [ δ ( k x K 1 ) + δ ( k x + K 1 ) ] + A 0 b 2 2 [ δ ( k x K 2 ) + δ ( k x + K 2 ) ] + A 0 b 1 b 2 4 { δ [ k x ( K 1 + K 2 ) ] + δ [ k x + ( K 1 + K 2 ) ] + δ [ k x ( K 1 K 2 ) ] + δ [ k x + ( K 1 K 2 ) ] } .
E z ( x , z ) = P 0 + + ( k x ) exp ( j k x x ) d x x = A 0 [ exp ( j z k z ) ] + A 0 b 1 2 [ exp ( j x K 1 ) exp [ ± j z ( k 2 K 1 2 ) 1 2 ] ] + exp ( j x K 1 ) exp [ ± j z ( k 2 K 1 2 ) 1 2 ] + A 0 b 2 2 [ exp ( j x K 2 ) exp [ ± j z ( k 2 K 2 2 ) 1 2 ] + exp ( j x K 2 ) exp [ ± j z ( k 2 K 2 2 ) 1 2 ] ] + A 0 b 1 b 2 4 [ exp [ j x ( K 1 + K 2 ) ] exp { ± j z [ k 2 ( K 1 + K 2 ) 2 ] 1 2 } + exp ( j x ( K 1 + K 2 ) ) exp { ± j z [ k 2 ( K 1 + K 2 ) 2 ] 1 2 } + exp [ j x ( K 1 K 2 ) ] exp { ± j z [ k 2 ( K 1 K 2 ) 2 ] 1 2 } + exp ( j x ( K 1 K 2 ) ) exp { ± j z [ k 2 ( K 1 + K 2 ) 2 ] 1 2 } ] .

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