Abstract

We present a novel configuration for the implementation of subwavelength-based graded-index devices. The proposed concept is based on the etching of one-dimensional subwavelength gratings into a high-index slab waveguide to achieve the desired effective index distribution. A graded-index profile can be achieved by gradually modifying the duty ratio of the grating along the horizontal axis, while the beam is confined in the vertical direction by the slab waveguide. On the basis of this concept, novel graded-index lenses and waveguides are both proposed and characterized numerically by use of finite-difference time-domain and finite-element analysis. The proposed devices can be used for guiding, imaging, optical signal processing, mode matching, coupling, and other applications while offering the intrinsic advantages of on-chip integration such as miniaturization, eliminating the need to align each component separately, and compatibility with standard microfabrication techniques for manufacturability.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  41. M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
    [CrossRef]
  42. D. Keil, E. Anderson, “Characterization of reactive ion etch lag scaling,” J. Vac. Sci. Technol. B 19, 2082–2088 (2001).
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    [CrossRef]

2004

2003

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

S. Panda, R. Ranade, G. S. Mathad, “Etching high aspect ratio silicon trenches,” J. Electrochem. Soc. 150, G612–G616 (2003).
[CrossRef]

W. Lijun, M. Mazilu, T. F. Krauss, “Beam steering in planar-photonic crystals: from superprism to supercollimator,” J. Lightwave Technol. 21, 561–566 (2003).
[CrossRef]

2002

J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[CrossRef]

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

W. Nakagawa, R. Tyan, Y. Fainman, “Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation,” J. Opt. Soc. Am. A 19, 1919–1928 (2002).
[CrossRef]

2001

D. Keil, E. Anderson, “Characterization of reactive ion etch lag scaling,” J. Vac. Sci. Technol. B 19, 2082–2088 (2001).
[CrossRef]

2000

J. N. Mait, A. Scherer, O. Dial, D. W. Prather, X. Gao, “Diffractive lens fabricated with binary features less than 60 nm,” Opt. Lett. 25, 381–383 (2000).
[CrossRef]

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

R. R. Boye, R. K. Kostuk, “Investigation of the effect of finite grating size on the performance of guided-mode resonance filters,” Appl. Opt. 39, 3649–3653 (2000).
[CrossRef]

1999

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by C12 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

1998

C. Giaconia, R. Torrini, S. K. Murad, C. D. W. Wilkinson, “Artificial dielectric optical structures: a challenge for nanofabrication,” J. Vac. Sci. Technol. B 16, 3903–3905 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

D. W. Prather, J. Mait, M. S. Mirotzniki, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

1997

1996

1995

1994

1992

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

1981

1965

1956

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Anderson, E.

D. Keil, E. Anderson, “Characterization of reactive ion etch lag scaling,” J. Vac. Sci. Technol. B 19, 2082–2088 (2001).
[CrossRef]

Arai, Shigehisa

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Avary, K.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Boye, R. R.

Brioude, V.

O. Montalien, V. Brioude, A. Tishchenko, O. M. Parriaux, “Optimization of the strength of a graded-index slab waveguide grating,” in Advances in Optical Thin Films, C. Amra, N. Karsev, H. A. Macleod, eds., Proc. SPIE5250, 609–618 (2004).
[CrossRef]

Brundrett, D. L.

Canning, J.

J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[CrossRef]

Chen, C.

Chen, F. T.

Chen, L.

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

Cheng,

Cheng, C.

Chou, S. Y.

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

Chow, E.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Collins, J. P.

Craighead, H. G.

Dial, O.

Doll, T.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Fainman, Y.

U. Levy, Y. Fainman, “Dispersion properties of inhomogeneous nanostructures,” J. Opt. Soc. Am. A 21, 881–889 (2004).
[CrossRef]

U. Levy, C. H. Tsai, L. Pang, Y. Fainman, “Engineering space-variant inhomogeneous media for polarization control,” Opt. Lett. 29, 1718–1720 (2004).
[CrossRef] [PubMed]

W. Nakagawa, R. Tyan, Y. Fainman, “Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation,” J. Opt. Soc. Am. A 19, 1919–1928 (2002).
[CrossRef]

R. Tyan, A. Salvekar, Cheng, A. Scherer, F. Xu, P. C. Sun, Y. Fainman, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14, 1627–1636 (1997).
[CrossRef]

R. Tyan, P. C. Sun, A. Scherer, Y. Fainman, “Polarizing beam splitter based on the anisotropic spectral reflectivity characteristic of form-birefringent multilayer gratings,” Opt. Lett. 21, 761–763 (1996).
[CrossRef] [PubMed]

F. Xu, R. Tyan, P. C. Sun, Y. Fainman, C. Cheng, A. Scherer, “Form-birefringent computer-generated holograms,” Opt. Lett. 21, 1513–1515 (1996).
[CrossRef] [PubMed]

F. Xu, R. Tyan, P. C. Sun, C. Cheng, A. Scherer, Y. Fainman, “Fabrication, modeling, and characterization of form-birefringent nanostructures,” Opt. Lett. 20, 2457–2459 (1995).
[CrossRef] [PubMed]

I. Richter, P. C. Sun, F. Xu, Y. Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt. 34, 2421–2429 (1995).
[CrossRef] [PubMed]

Forchel, A.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Gao, X.

Gaylord, T. K.

Ge, H.

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

Giaconia, C.

C. Giaconia, R. Torrini, S. K. Murad, C. D. W. Wilkinson, “Artificial dielectric optical structures: a challenge for nanofabrication,” J. Vac. Sci. Technol. B 16, 3903–3905 (1998).
[CrossRef]

Glytsis, E. N.

Gu, C.

Hagness, S.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

Happ, T.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Hasegawa, T.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Iwata, K.

Joannopoulos, J. D.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Johnson, S. G.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Kamp, M.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Kanjo, H.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Keil, D.

D. Keil, E. Anderson, “Characterization of reactive ion etch lag scaling,” J. Vac. Sci. Technol. B 19, 2082–2088 (2001).
[CrossRef]

Kikuta, H.

Kim, H. C.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Klopf, F.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Kogelnik, H.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Kostuk, R. K.

Kotlyar, M. V.

M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
[CrossRef]

Krauss, T. F.

M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
[CrossRef]

W. Lijun, M. Mazilu, T. F. Krauss, “Beam steering in planar-photonic crystals: from superprism to supercollimator,” J. Lightwave Technol. 21, 561–566 (2003).
[CrossRef]

Lalanne, D. L.

Lalanne, P.

Levy, U.

Lijun, W.

Lin, S. Y.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Lohmann, A. W.

Loncar, M.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Magnusson, R.

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

Mait, J.

Mait, J. N.

Mathad, G. S.

S. Panda, R. Ranade, G. S. Mathad, “Etching high aspect ratio silicon trenches,” J. Electrochem. Soc. 150, G612–G616 (2003).
[CrossRef]

Mazilu, M.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Mendlovic, D.

Mirotznik, M. S.

Mirotzniki, M. S.

Moharam, M. G.

Montalien, O.

O. Montalien, V. Brioude, A. Tishchenko, O. M. Parriaux, “Optimization of the strength of a graded-index slab waveguide grating,” in Advances in Optical Thin Films, C. Amra, N. Karsev, H. A. Macleod, eds., Proc. SPIE5250, 609–618 (2004).
[CrossRef]

Murad, S. K.

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[CrossRef]

Murakowski, J.

Nakagawa, W.

Nedeljkovic, D.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

O’Faolain, L.

M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
[CrossRef]

Ohira, Y.

Ozaktas, H. M.

Panda, S.

S. Panda, R. Ranade, G. S. Mathad, “Etching high aspect ratio silicon trenches,” J. Electrochem. Soc. 150, G612–G616 (2003).
[CrossRef]

Pang, L.

Parriaux, O. M.

O. Montalien, V. Brioude, A. Tishchenko, O. M. Parriaux, “Optimization of the strength of a graded-index slab waveguide grating,” in Advances in Optical Thin Films, C. Amra, N. Karsev, H. A. Macleod, eds., Proc. SPIE5250, 609–618 (2004).
[CrossRef]

Parther, D. W.

Paulsen, K. D.

Pearsall, T. P.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Prather, D. W.

Pustai, D. M.

Ranade, R.

S. Panda, R. Ranade, G. S. Mathad, “Etching high aspect ratio silicon trenches,” J. Electrochem. Soc. 150, G612–G616 (2003).
[CrossRef]

Reithmaier, J. P.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Richter, I.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salvekar, A.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

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Schneider, G. J.

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Sun, P. C.

Taflove, A.

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Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Tamura, S.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

Tishchenko, A.

O. Montalien, V. Brioude, A. Tishchenko, O. M. Parriaux, “Optimization of the strength of a graded-index slab waveguide grating,” in Advances in Optical Thin Films, C. Amra, N. Karsev, H. A. Macleod, eds., Proc. SPIE5250, 609–618 (2004).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Torrini, R.

C. Giaconia, R. Torrini, S. K. Murad, C. D. W. Wilkinson, “Artificial dielectric optical structures: a challenge for nanofabrication,” J. Vac. Sci. Technol. B 16, 3903–3905 (1998).
[CrossRef]

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Tyan, R.

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by C12 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Venkataraman, S.

Villeneuve, P. B.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Vuckovic, J.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

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R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

Wendt, J. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by C12 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Wilkinson, C. D. W.

C. Giaconia, R. Torrini, S. K. Murad, C. D. W. Wilkinson, “Artificial dielectric optical structures: a challenge for nanofabrication,” J. Vac. Sci. Technol. B 16, 3903–3905 (1998).
[CrossRef]

Wilson, R.

M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Wu, W.

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

Xu, F.

Yeh, P.

Yu, Z.

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Zubrzycki, W. J.

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by C12 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, Shigehisa Arai, “1.5-μm wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9, 1146–1152 (2003).
[CrossRef]

J. Electrochem. Soc.

S. Panda, R. Ranade, G. S. Mathad, “Etching high aspect ratio silicon trenches,” J. Electrochem. Soc. 150, G612–G616 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

Z. Yu, L. Chen, W. Wu, H. Ge, S. Y. Chou, “Fabrication of nanoscale gratings with reduced line edge roughness using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2089–2092 (2003).
[CrossRef]

M. V. Kotlyar, L. O’Faolain, R. Wilson, T. F. Krauss, “High-aspect-ratio chemically assisted ion beam etching for photonic crystals using a high beam voltage-current ratio,” J. Vac. Sci. Technol. B 22, 1788–1791 (2004).
[CrossRef]

D. Keil, E. Anderson, “Characterization of reactive ion etch lag scaling,” J. Vac. Sci. Technol. B 19, 2082–2088 (2001).
[CrossRef]

C. Giaconia, R. Torrini, S. K. Murad, C. D. W. Wilkinson, “Artificial dielectric optical structures: a challenge for nanofabrication,” J. Vac. Sci. Technol. B 16, 3903–3905 (1998).
[CrossRef]

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by C12 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Microelectron. Eng.

K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, A. Forchel, “Deeply etched two-dimensional photonic crystals fabricated on GaAs/AlGaAs slab waveguides by using chemical assisted ion beam etching,” Microelectron. Eng. 61–62, 875–880 (2002).
[CrossRef]

Nature (London)

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature (London) 407, 983–986 (2000).
[CrossRef]

Opt. Commun.

J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[CrossRef]

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Phys. Rev. B

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[CrossRef]

Sov. Phys. JETP

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

We define the polarization with respect to the periodic structure, i.e., E=Ey^for TE and H=Hy^for TM. This is in opposition to the standard definition used in waveguide theory.

N. I. Petrov, “Focusing of beams into subwavelength area in an inhomogeneous medium,” Opt. Express9, 658–673 (2001), www.opticsexpress.org .
[CrossRef] [PubMed]

O. Montalien, V. Brioude, A. Tishchenko, O. M. Parriaux, “Optimization of the strength of a graded-index slab waveguide grating,” in Advances in Optical Thin Films, C. Amra, N. Karsev, H. A. Macleod, eds., Proc. SPIE5250, 609–618 (2004).
[CrossRef]

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[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Proposed graded-index structure. The beam propagates along the z axis, and the duty ratio is varied along the horizontal axis. Vertical confinement is achieved by the slab waveguide.

Fig. 2
Fig. 2

Duty ratio versus lateral distance from the optical axis for TE polarization: n 0 = 3.2 , α = 0.01 (1/μm2), λ = 1.55   μ m , Λ = 0.3   μ m , n 1 = 3.37 , n 2 = 1 .

Fig. 3
Fig. 3

Effective index of the patterned slab versus duty ratio for TE polarization: Λ = 0.3   μ m , n 1 = 3.37 , n 2 = 1 . Slab thickness is 1 μm.

Fig. 4
Fig. 4

Typical beam cross section traveling along subwavelength-based graded-index media. The structure is composed of a 1-μm GaAs slab layer on top of an aluminum oxide cladding layer. The GaAs layer is patterned with a structure having a period of Λ = 0.3   μ m . The duty ratio is calculated according to Eq. (1a) to achieve an effective index profile with n 0 = 3.1 and α = 0.01 (1/μm2).

Fig. 5
Fig. 5

Effective index of the second slab mode for a quadratic profile optimized for the first mode. Solid curve, obtained index profile; dashed curve, fitting to a modified quadratic profile with n 0 = 2.42 , α = 0.01 (1/μm2). Slab thickness is 0.65 μm, with an effective index of 3.19 and 2.61 for the two modes, respectively.

Fig. 6
Fig. 6

Field propagation through a focusing graded-index lens with n 0 = 3 , α = 0.01 (1/μm2). The initial beam diameter is 6.5 μm. (a) Top view showing the focusing effect. (b) Cross section at the focus. For comparison purposes, the Gaussian beam profile is also displayed.

Fig. 7
Fig. 7

Field propagation through a periodic subwavelength-based lens configuration. Each lens is similar to that shown in Fig. 6. The initial beam diameter is 2.5 μm.

Fig. 8
Fig. 8

Field propagation through a subwavelength-based graded-index waveguide with the effective index parameters n 0 = 3 , α = 0.01 (1/μm2). The beam diameter at the front end of the structure was chosen to be (a) 2.4 μm, (b) 4.5 μm. In (a) a supercollimation characteristic is demonstrated since the diffraction and the focusing power are balanced.

Fig. 9
Fig. 9

Strehl ratio versus relative inaccuracy of the postwidth. Current technology supports an accuracy better than 10 nm, corresponding to a Strehl ratio larger than 0.9.

Fig. 10
Fig. 10

Field propagation through the perturbed focusing graded-index lens with the same parameters as in Fig. 6. (a) Top view still showing a significant focusing effect. (b) Field profile at the focal plane. For comparison purposes, the unperturbed profile and a Gaussian beam profile are also displayed.

Equations (12)

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

[ n TE ( 2 ) ] 2 = [ n TE ( 0 ) ] 2 + 1 3 Λ λ   π f ( 1 - f ) ( n 1 2 - n 2 2 ) 2 ,
[ n TM ( 2 ) ] 2 = [ n TM ( 0 ) ] 2 + 1 3 Λ λ   π f ( 1 - f ) 1 n 1 2 - 1 n 2 2 n TE ( 0 ) [ n TM ( 0 ) ] 3 2
[ n TE ( 0 ) ] 2 = fn 1 2 + ( 1 - f ) n 2 2 ,
[ n TM ( 0 ) ] 2 = ( n 1 n 2 ) 2 fn 2 2 + ( 1 - f ) n 1 2 .
n 2 ( x ) = n 0 2 ( 1 - α x p ) ,
n ( x ) = n 0 1 - 1 2   α x 2 .
max Δ n n = max 1 n d n d x   Δ x 1 2   α Λ ω ,
q out = Aq in + B Cq in + D ,
1 q = 1 R ( z ) + j   λ π ω 2 ( z ) .
A B C D = cos ( rd ) sin ( rd ) r - r   sin ( rd ) cos ( rd ) ,
Re ( q out ) = Re Aq in + B Cq in + D = 0 ,
ω 0 = λ n π α 1 / 2 .

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