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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 24 — Aug. 20, 2009
  • pp: 4801–4813

Conditions for primitive-lattice-vector-direction equal contrasts in four-beam-interference lithography

Justin L. Stay and Thomas K. Gaylord  »View Author Affiliations


Applied Optics, Vol. 48, Issue 24, pp. 4801-4813 (2009)
http://dx.doi.org/10.1364/AO.48.004801


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Abstract

Four distinct conditions for primitive-lattice-vector-direction equal contrasts in four-beam interference are introduced and described. By maximizing the absolute contrast subject to an equal contrast condition, lithographically useful interference patterns are found. Each condition is described in terms of the corresponding constraints on the plane wave wave vectors, polarizations, and intensities. The resulting locations of global intensity maxima, minima, and saddle points are presented. Subordinate conditions for unity absolute contrast are also developed. Three lattices are treated for each condition: simple cubic, face-centered cubic, and body-centered cubic.

© 2009 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(110.3960) Imaging systems : Microlithography
(220.3740) Optical design and fabrication : Lithography
(110.4235) Imaging systems : Nanolithography
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: April 9, 2009
Manuscript Accepted: July 28, 2009
Published: August 19, 2009

Citation
Justin L. Stay and Thomas K. Gaylord, "Conditions for primitive-lattice-vector-direction equal contrasts in four-beam-interference lithography," Appl. Opt. 48, 4801-4813 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-24-4801


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References

  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).
  2. A. Di Falco, C. Conti, and G. Assanto, “Three-dimensional superprism effect in photonic-crystal slabs,” J. Lightwave Technol. 22, 1748-1753 (2004). [CrossRef]
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032-2038 (1999). [CrossRef]
  4. T. Matsumoto and T. Baba, “Photonic crystal k-vector superprism,” J. Lightwave Technol. 22, 917-922 (2004). [CrossRef]
  5. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Discrete negative refraction in photonic crystal waveguide arrays,” Opt. Lett. 31, 1343-1345 (2006). [CrossRef] [PubMed]
  6. M. Qiu, L. Thylen, M. Swillo, and B. Jaskorzynska, “Wave propagation through a photonic crystal in a negative phase refractive-index region,” IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003). [CrossRef]
  7. J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E 71, 026604 (2005). [CrossRef]
  8. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768-10783 (2005). [CrossRef] [PubMed]
  9. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413-2422(2006). [CrossRef] [PubMed]
  10. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, “Properties of the slab modes in photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1554-1564 (2000). [CrossRef]
  11. A. Jafarpour, E. Chow, C. M. Reinke, J. Huang, A. Adibi, A. Grot, L. W. Mirkarimi, G. Girolami, R. K. Lee, and Y. Xu, “Large-bandwidth ultra-low-loss guiding in bi-periodic photonic crystal waveguides,” Appl. Phys. B 79, 409-414(2004). [CrossRef]
  12. M. M. Beaky, J. B. Burk, H. O. Everitt, M. A. Haider, and S. Venakides, “Two-dimensional photonic crystal Fabry-Perot resonators with lossy dielectrics,” IEEE Trans. Microwave Theory Tech. 47, 2085-2091 (1999). [CrossRef]
  13. P. Kramper, A. Birner, M. Agio, C. M. Soukoulis, F. Muller, U. Gosele, J. Mlynek, and V. Sandoghdar, “Direct spectroscopy of a deep two-dimensional photonic crystal microresonator,” Phys. Rev. B 64, 233102-1-233102-4 (2001). [CrossRef]
  14. P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Muller, U. Gosele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, “Near-field visualization of light confinement in a photonic crystal microresonator,” Opt. Lett. 29, 174-176 (2004). [CrossRef] [PubMed]
  15. T. Kim and C. Seo, “A novel photonic bandgap structure for low-pass filter of wide stopband,” IEEE Microwave Guid. Wave Lett. 10, 13-15 (2000). [CrossRef]
  16. R. C. Rumpf, A. Mehta, P. Srinivasan, and E. G. Johnson, “Design and optimization of space-variant photonic crystal filters,” Appl. Opt. 46, 5755-5761 (2007). [CrossRef] [PubMed]
  17. A. Mehta, R. Rumpf, Z. Roth, and E. G. Johnson, “Simplified fabrication process of 3-D photonic crystal optical transmission filter,” Proc. SPIE 6462, 64621D (2007). [CrossRef]
  18. B. Z. Steinberg, A. Boag, and R. Lisitsin, “Sensitivity analysis of narrowband photonic crystal filters and waveguides to structure variations and inaccuracy,” J. Opt. Soc. Am. A 20, 138-146 (2003). [CrossRef]
  19. T. Kamalakis and T. Sphicopoulos, “Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory,” IEEE J. Quantum Electron. 41, 863-871 (2005). [CrossRef]
  20. C.-Y. Liu and L.-W. Chen, “Tunable photonic crystal waveguide coupler with nematic liquid crystals,” IEEE Photon. Technol. Lett. 16, 1849-1851 (2004). [CrossRef]
  21. A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861-865 (2001). [CrossRef]
  22. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76-84 (2005). [CrossRef]
  23. M. Thorhauge, L. H. Frandsen, and P. I. Borel, “Efficient photonic crystal directional couplers,” Opt. Lett. 28, 1525-1527 (2003). [CrossRef] [PubMed]
  24. B. Momeni and A. Adibi, “Demultiplexers harness photonic-crystal dispersion properties,” Laser Focus World 42, 125-128 (2006).
  25. C. Caloz, A. K. Skrivervik, and F. E. Gardiol, “An efficient method to determine Green's functions of a two-dimensional photonic crystal excited by a line source--the phased-array method,” IEEE Trans. Microwave Theory Tech. 50, 1380-1391(2002). [CrossRef]
  26. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005). [CrossRef]
  27. S. Chakravarty, J. Topol'ancik, P. Bhattacharya, S. Chakrabarti, Y. Kang, and M. E. Meyerhoff, “Ion detection with photonic crystal microcavities,” Opt. Lett. 30, 2578-2580(2005). [CrossRef] [PubMed]
  28. J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12, 5221-5228 (2004). [CrossRef] [PubMed]
  29. S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001). [CrossRef] [PubMed]
  30. S. Cabrini, L. Businaro, M. Prasciolu, A. Carpentiro, D. Gerace, M. Galli, L. C. Andreani, F. Riboli, L. Pavesi, and E. Di Fabrizio, “Focused ion beam fabrication of one-dimensional photonic crystals on Si3N4/SiO2 channel waveguides,” J. Opt. A: Pure Appl. Opt. 8, 550-553 (2006). [CrossRef]
  31. A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. Van Blaaderen, “Self-assembly route for photonic crystals with a bandgap in the visible region,” Nat. Mater. 6, 202-205 (2007). [CrossRef] [PubMed]
  32. A. J. Danner, B. Wang, S.-J. Chua, and J.-K. Hwang, “Fabrication of efficient light-emitting diodes with a self-assembled photonic crystal array of polystyrene nanoparticles,” IEEE Photon. Technol. Lett. 20, 48-50 (2008). [CrossRef]
  33. T. Prasad, R. Rengarajan, D. M. Mittleman, and V. L. Colvin, “Advanced photonic crystal architectures from colloidal self-assembly techniques,” Opt. Mater. 27, 1250-1254 (2005). [CrossRef]
  34. U. Gruning, V. Lehmann, and C. M. Engelhardt, “Two-dimensional infrared photonic band gap structure based on porous silicon,” Appl. Phys. Lett. 66, 3254-3256 (1995). [CrossRef]
  35. S. Rowson, A. Chelnokov, and J. M. Lourtioz, “Two-dimensional photonic crystals in macroporous silicon: from mid-infrared (10 μm) to telecommunication wavelengths (1.3-1.5 μm),” J. Lightwave Technol. 17, 1989-1995 (1999). [CrossRef]
  36. A. Birner, A. P. Li, F. Mueller, U. Goesele, P. Kramper, V. Sandoghdar, J. Mlynek, K. Busch, and V. Lehmann, “Transmission of a microcavity structure in a two-dimensional photonic crystal based on macroporous silicon,” Mater. Sci. Semicond. Process. 3, 487-491 (2000). [CrossRef]
  37. T. Zijlstra, E. Van Der Drift, M. J. A. De Dood, E. Snoeks, and A. Polman, “Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching,” J. Vac. Sci. Technol. B 17, 2734-2739 (1999). [CrossRef]
  38. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402-1411 (2000). [CrossRef]
  39. A. Chelnokov, S. David, K. Wang, F. Marty, and J. M. Lourtioz, “Fabrication of 2-D and 3-D silicon photonic crystals by deep etching,” IEEE J. Sel. Top. Quantum Electron. 8, 919-927(2002). [CrossRef]
  40. R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A 21, 1703-1713 (2004). [CrossRef]
  41. V. Berger, O. Gauthier-Lafaye, and E. Costard, “Fabrication of a 2D photonic bandgap by a holographic method,” Electron. Lett. 33, 425-426 (1997). [CrossRef]
  42. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56 (2000). [CrossRef] [PubMed]
  43. L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27, 900-902 (2002). [CrossRef]
  44. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238-2244(2002). [CrossRef]
  45. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858-1860 (2001). [CrossRef]
  46. J. L. Stay and T. K. Gaylord, “Three-beam-interference lithography: contrast and crystallography,” Appl. Opt. 47, 3221-3230 (2008). [CrossRef] [PubMed]
  47. J. L. Stay and T. K. Gaylord, “Contrast in four-beam-interference lithography,” Opt. Lett. 33, 1434-1436(2008). [CrossRef] [PubMed]

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