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Applied Optics

Applied Optics


  • Vol. 44, Iss. 18 — Jun. 20, 2005
  • pp: 3774–3783

Fourier analysis of harmonic frequency transmission dielectric structures

María del Mar Sánchez-López, Joaquín Cos, Jeffrey A. Davis, Darren A. Miller, and Ignacio Moreno  »View Author Affiliations

Applied Optics, Vol. 44, Issue 18, pp. 3774-3783 (2005)

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We use an analytical calculation based on the Fourier-transform method to study the transmission spectra of multilayer dielectric optical structures as a function of the relative widths of the layers that constitute the unit cell. We can select which harmonics of the fundamental design frequency are transmitted. The results of this Fourier-transform approach are compared with the exact transmission calculated by means of the transfer matrix method and provide a more intuitive understanding of the transmission spectrum. A simple phasor diagram is derived from this Fourier-transform analysis for this purpose. Inasmuch as it is difficult for us to perform experiments in the optical region, we fabricate rf analogs of these structures, using coaxial cables that have different impedances. Experimental results agree with theory.

© 2005 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.4790) Fourier optics and signal processing : Spectrum analysis
(190.4160) Nonlinear optics : Multiharmonic generation
(310.1620) Thin films : Interference coatings
(310.6860) Thin films : Thin films, optical properties

Original Manuscript: June 14, 2004
Revised Manuscript: December 23, 2004
Manuscript Accepted: January 28, 2005
Published: June 20, 2005

María del Mar Sánchez-López, Joaquín Cos, Jeffrey A. Davis, Darren A. Miller, and Ignacio Moreno, "Fourier analysis of harmonic frequency transmission dielectric structures," Appl. Opt. 44, 3774-3783 (2005)

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  1. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 1986), Chap. 6, pp. 248–255.
  2. P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 5 and 6.
  3. H. Taniyama, “Waveguide structures using one-dimensional photonic crystal,” J. Appl. Phys. 91, 3511–3515 (2002). [CrossRef]
  4. M. Deopura, C. K. Ullal, B. Temelkuran, Y. Fink, “Dielectric omnidirectional visible reflector,” Opt. Lett. 26, 1197–1199 (2001). [CrossRef]
  5. A. Thelen, “Multilayer filters with wide transmittance bands,” J. Opt. Soc. Am. 53, 1266–1270 (1963). [CrossRef]
  6. W. E. Johnson, R. L. Crane, “Introduction to rugate filter technology,” in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 88–108 (1993). [CrossRef]
  7. W. H. Southwell, “Extended-bandwidth reflector designs by using wavelets,” Appl. Opt. 36, 314–318 (1997). [CrossRef] [PubMed]
  8. P. L. Swart, P. V. Bulkin, B. M. Lacquet, “Rugate filter manufacturing by electron cyclotron resonance plasma-enhanced chemical vapor deposition of SiNx,” Opt. Eng. 36, 1214–1219 (1997). [CrossRef]
  9. P. G. Verly, J. A. Dobrowolski, W. J. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989). [CrossRef] [PubMed]
  10. B. E. Perilloux, Thin-Film Design: Modulated Thickness and Other Stopband Design Methods (SPIE Press, 2002), Chaps. 1 and 2. [CrossRef]
  11. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transform,” Appl. Opt. 17, 3039–3050 (1978). [CrossRef] [PubMed]
  12. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988). [CrossRef] [PubMed]
  13. B. G. Bovard, “Fourier transform technique applied to quarter-wave optical coatings,” Appl. Opt. 27, 3062–3063 (1988). [CrossRef] [PubMed]
  14. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990). [CrossRef] [PubMed]
  15. P. G. Verly, “Fourier transform technique with frequency filtering for optical thin-film design,” Appl. Opt. 34, 688–694 (1995). [CrossRef] [PubMed]
  16. M. C. Parker, R. J. Mears, S. D. Walker, “A Fourier transform theory for photon localization and evanescence in photonic bandgap structures,” J. Opt. A Pure Appl. Opt. 3, 171–183 (2001). [CrossRef]
  17. P. Baumeister, “Simulation of a rugate filter via a stepped-index dielectric multilayer,” Appl. Opt. 25, 2644–2645 (1986). [CrossRef] [PubMed]
  18. M. M. Sánchez-López, J. A. Davis, K. Crabtree, “Coaxial cable analogs of multilayer dielectric optical coatings,” Am. J. Phys. 71, 1314–1319 (2003). [CrossRef]
  19. G. J. Schneider, S. Hanna, J. L. Davis, G. H. Watson, “Defect modes in coaxial photonic crystals,” J. Appl. Phys. 90, 2642–2649 (2001). [CrossRef]
  20. J. N. Munday, W. M. Robertson, “Negative group velocity pulse tunneling through a coaxial photonic crystal,” Appl. Phys. Lett. 81, 2127–2129 (2002). [CrossRef]
  21. A. Haché, A. Slimani, “A model coaxial photonic crystal for studying band structures, dispersion, field localization, and superluminal effects,” Am. J. Phys. 72, 916–921 (2004). [CrossRef]
  22. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  23. S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000). [CrossRef]
  24. L. Carretero, M. Ulibarrena, S. Blaya, A. Fimia, “One-dimensional photonic crystals with an amplitude-modulated dielectric constant in the unit cell,” Appl. Opt. 43, 2895–2899 (2004). [CrossRef] [PubMed]
  25. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 3.
  26. G. F. Miner, Lines and Electromagnetic Fields for Engineers (Oxford U. Press, 1996), Chap. 1.
  27. N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, “Temperature and wavelength tuning of second, third and fourth-harmonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B 19, 2263–2272 (2002). [CrossRef]
  28. J. Mes, E. J. Van Duijn, R. Zinkstok, S. Witte, W. Hogervorst, “Third-harmonic generation of a continuous-wave Ti: sapphire laser in external resonant cavities,” Appl. Phys. Lett. 82, 4423–4425 (2003). [CrossRef]

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