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11 - Photonic crystals, resonators, and cavity optomechanics

Published online by Cambridge University Press:  05 November 2012

Lukas Novotny  and
Bert Hecht
Lukas Novotny
Affiliation:
University of Rochester, New York and ETH Zürich, Switzerland
Bert Hecht
Affiliation:
Julius-Maximilians-Universität Würzburg, Germany
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Summary

Artificial optical materials and structures have enabled the observation of various new optical effects. For example, photonic crystals are able to inhibit the propagation of certain light frequencies and provide the unique ability to guide light around very tight bends and along narrow channels. With metamaterials, on the other hand, one can achieve negative refraction. The high field strengths in optical microresonators lead to nonlinear optical effects that are important for future integrated optical networks, and the coupling between optical and mechanical degrees of freedom opens up the possibility of cooling macroscopic systems down to the quantum ground state. This chapter explains the basic underlying principles of these novel optical structures.

Photonic crystals

Photonic crystals are materials with a spatial periodicity in their dielectric constant, a system that was first analyzed by Lord Rayleigh in 1887 [1]. Under certain conditions, photonic crystals can create a photonic bandgap, i.e. a frequency window within which propagation of light through the crystal is inhibited. Light propagation in a photonic crystal is similar to the propagation of electrons and holes in a semiconductor. An electron passing through a semiconductor experiences a periodic potential due to the ordered atomic lattice. The interaction between the electron and the periodic potential results in the formation of energy bandgaps. It is not possible for the electron to pass through the crystal if its energy falls within the range of the bandgap.

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Chapter
Information
Principles of Nano-Optics , pp. 338 - 368
Publisher: Cambridge University Press
Print publication year: 2012

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References

[1] Lord, Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure” Phil. Mag. (Series 5) 24, 145–159 (1887).Google Scholar
[2] Y. A., Vlasov, X. Z., Bo, J. C., Sturm, and D. J., Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).Google Scholar
[3] J. D., Joannopoulos, R. D., Meade, and J. N., Winn, Photonic Crystals. Princeton, MA: Princeton University Press (1995).Google Scholar
[4] J. D., Joannopoulos, P. R., Villeneuve, and S., Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).Google Scholar
[5] G., Floquet, “Sur les équations differentielles linéares à coefficients périodiques,” Ann. Ecole Norm. Supér. 12, 47–88 (1883).Google Scholar
[6] F., Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555–600 (1929).Google Scholar
[7] E., Moreno, D., Erni, and Ch., Hafner, “Modeling of discontinuities in photonic crystal waveguides with the multiple multipole method,” Phys. Rev.E 66, 036618 (2002).Google Scholar
[8] O. J., Painter, A., Husain, A., Scherer, et al., “Two-dimensional photonic crystal defect laser,” J. Lightwave Technol. 17, 2082–2089 (1999).Google Scholar
[9] R. P., Feynman, R. B., Leighton, and M., Sands, The Feynman Lectures on Physics, vol. 1. Reading, MA: Addison-Wesley (1977).Google Scholar
[10] V., Veselago, L., Braginsky, V., Shklover, and Ch., Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1–30 (2006).Google Scholar
[11] V. G., Veselago, “The electrodynamics of substances with simultaneously negative values of and μ,” Sov. Phys. Usp. 10, 509–514 (1968).Google Scholar
[12] J., Kästel and M., Fleischhauer, “Quantum electrodynamics in media with negative refraction,” Laser Phys. 15, 135–145 (2005).Google Scholar
[13] D. R., Smith, W. J., Padilla, D. C., Vier, S. C., Nemat-Nasser, and S., Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).Google Scholar
[14] J. P., Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).Google Scholar
[15] R. A., Shelby, D. R., Smith, and S., Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). Reprinted with permission from AAAS.Google Scholar
[16] C. M., Soukoulis and M., Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nature Photonics 5, 523–530 (2011).Google Scholar
[17] J., Valentine, S., Zhang, T., Zentgraf, et al., “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).Google Scholar
[18] R. E., Collin, “Frequency dispersion limits resolution in Veselago lens,” Prog. Electromagn. Res.B 19, 233–261 (2010).Google Scholar
[19] C., Hafner, C., Xudong, and R., Vahldieck, “Resolution of negative index slabs,” J. Opt. Soc. Am.A 23, 1768–1778 (2006).Google Scholar
[20] R., Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290–1292 (2004).Google Scholar
[21] T., Taubner, D., Korobkin, Y., Urzhumov, G., Shvets, and R., Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).Google Scholar
[22] Z., Jacob, L. V., Alekseyev, and E., Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).Google Scholar
[23] Z., Liu, H., Lee, Y., Xiong, C., Sun, and X., Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).Google Scholar
[24] J. B., Pendry, D., Schurig, and D. R., Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).Google Scholar
[25] S., Arnold, S., Holler, and S. D., Druger, “The role of MDRs in chemical physics: intermolecular energy transfer in microdroplets,” in Optical Processes in Microcavities, ed. R. K., Chang and A. J., Campillo. Singapore: World Scientific pp. 285–312 (1996).Google Scholar
[26] C. G., Bohren and D. R., Huffman, Absorption and Scattering of Light by Small Particles. New York: John Wiley (1983).Google Scholar
[27] H. M., Nussenzveig, Diffraction Effects in Semiclassical Scattering. Cambridge: Cambridge University Press (1992).Google Scholar
[28] B. R., Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am.A 10, 343–352 (1993).Google Scholar
[29] S. M., Spillane, T. J., Kippenberg, K. J., Vahala, et al., “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev.A 71, 013817 (2005).Google Scholar
[30] F., Vollmer and S., Arnold, “Whispering-gallery-mode biosensing: labelfree detection down to single molecules,” Nature Methods 5, 591–596 (2008).Google Scholar
[31] J., Schwinger, The Theory of Obstacles in Resonant Cavities and Waveguides, MIT Radiation Laboratory Report no. 43-34 (1943).Google Scholar
[32] W., Hauser, Introduction to the Principles of Electromagnetism. Reading, MA: Addison-Wesley (1971).Google Scholar
[33] T. J., Kippenberg and K. J., Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).Google Scholar
[34] V. B., Braginsky, Measurement of Weak Forces in Physics Experiments. Chicago, IL: University of Chicago Press (1977).Google Scholar
[35] P. F., Cohadon, A., Heidmann, and M., Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett. 83, 3174–3177 (1999).Google Scholar
[36] C. Höhberger, Metzger and K., Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).Google Scholar
[37] O., Arcizet, P. F., Cohadon, T., Briant, M., Pinard, and A., Heidmann, “Radiationpressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).Google Scholar
[38] S., Gigan, H. R., Bohm, M., Paternostro, et al., “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).Google Scholar
[39] A., Schliesser, P., Del'Haye, N., Nooshi, K. J., Vahala, and T. J., Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97, 243905 (2006).Google Scholar
[40] J., Van Bladel and D., De Zutter, “Reflections from linearly vibrating objects: plane mirror at normal incidence,” IEEE Trans. Antennas Propag. 29, 629–636 (1981).Google Scholar
[41] S., Arnold, M., Khoshsima, I., Teraoka, S., Holler and F., Vollmer, “Shift of whispering gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).Google Scholar

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