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Information about photonics

Published on February 16, 2009

Author: gururajjoshi


Slide 1: PHOTONIC CRYSTALS Igor ZozoulenkoSolid State ElectronicsDepartment of Science and TechnologyLinköping UniversitySweden Brief outline: Motivation Basic concepts and photonic band structure Computational techniques Photonic crystal devices: lasers, cavities, waveguides, filters, ... Nonlinear effects in photonic crystals Surface modes of photonic crystals and their applications Slide 2: Current developments in optics and photonics: The number of bits per second doubles every nine month. Optics and photonics are at the stage that electronics expierenced 30 years ago – with the developments and integration of component parts into larger systems Slide 3: Technologies for All-Optical Networks Slide 4: Photonic crystals: structures with periodically varying refractive indexPhotonic band gaps were first predicted in 1987: Eli Yablonovitch (Bell Communications Research in New Jersey) Sajeev John (University of Toronto) Quantum-mechanical - electromagnetic similarity ³ ¡ r 2 + V ( r ) ´ ª ( r ) = E ª ( r ) Bloch theorem Slide 5: Fabrication of photonic crystal structuresTwo-dimensional photonic crystals in a slab geometry(a representative example Alvarado-Rodriguez &. Yablonovitch, J. Appl. Phys. 92, 6399 (2002)) Sample layout Scanning electron micrograph Cross section Notomi et al PRL 87, 253901 (2001) Slide 6: Photonic crystals in nature: Minerals feather of a bird Slide 7: COMPUTATIONA TECHNIQUES Finite difference time domain (FDTD) methods Greens function technique Scattering matrix technique ... Slide 8: Advantage: Speed, flexibility, ease of computational storage requirements Slide 9: Green’s function technique (Martin et al, PRL 74, 526 (1995)) photonic structure is described by a dielectric constant Slide 10: Calculation of the Green’s function G of the complete system Analytical expression for the Green’s function G0 of the homogeneous reference system Dyson equation: In order to calculate G we use the recursive technique based on the Dyson equation Slide 11: Suppose we want to calculate electromagnetic field in the system shown below Slide 12: Discretize the system Slide 13: Start with the reference system described by G0 Slide 14: Repeatedly use the Dyson equation to add one cell until the Green’s function of the complete system is calculated Slide 15: Scattering matrix technique: Calculation of the resonant states of a disc cavity of an arbitrary shape and arbitrary refraction index.A. I. Rahachou and I. V. Zozoulenko, Applied Optics 43, 1761 (2004);A. I. Rahachou and I. V. Zozoulenko, J. Appl. Phys. 94, 7929 (2003) This method is specially tailored for the case when geometry varies very smoothly on a very small scale. (Conventional FDTD methods would require very fine discretization) FDTD grid Slide 16: We start from 2D Helmholtz equation in polar coordinates ( for TM (TE) modes) Slide 17: GENERAL IDEA OF THE S-MATRIX TECHNIQUE: Slide 18: Details of the metod: Slide 19: Details of the metod: Slide 20: Details of the metod: finding coefficients {ai}m, {bi}m(continuity of the tangential component of E-field): Slide 21: Combining S-matrixes: Slide 22: Photonic crystal devices: waveguides Transmission through sharp bends in photonic crystals (Mekis et al., PRL 77, 3787 (1996) Elimination of crosstalk in waveguide crossing (Johnson et al., Opt. Lett. 23, 1855 (1998)) no transmission in the perpendicular direction Slide 23: Photonic crystal devices: cavities Applications: filters, add-drop multiplexer, lasing resonators, etc. Modal volume V Purcell effect: enhancement of the spontaneous emission ? ?3 Q/V One of the important characteristic of the cavity resonances is their quality factor (Q factor) k Intensity ?k Slide 24: Noda et al. Nature 425, 944 (2003): Q = 45 000, Q/V = 120 000/?3Noda et al. Nature Materials 4, 207 (2005): Q = 600 000 Slide 25: Photonic band-gap cavity lasers Painter et al, Science 284, 1820 (1999) Schematic diagram spectrum lasing action Slide 26: Cavity drop filters(Akahane et al., Appl. Phys. Lett. 83, 1512 (2003)) drop intensity Slide 27: Cavity add-drop filters Fun et. al., PRL 80, 960 (1998) Slide 28: frequency frequency frequency Slide 29: negative refractive index n < 1; ? < 1, ? < 1. Left handed materials (Veselago, Usp. Fiz. Nauk. 92, 517 (1964)). Poynting vector P forms a right-handed triad with E and H; k-vector forms a left-handed triad with E and H ? phase velocity has a direction opposite to P. lensing Luo et al., PRB 65, 201104(R) (2002) Martinez et al.,PRB 69,165119 (2004) Slide 30: photonic crystal fibers Slide 31: Nonlinear effects in photonic crystals For true all-optical signal processing, one needs a way of influencing light with light itself: one has to use optical nonlinearities. Kerr effect: the refractive index depend on E Slide 32: Optical isolation One of the biggest obstacles to achieving large-scale optics integration today is the lack of integrated optical isolators (active and nonlinear devices typically do not tolerate small reflections coming from other devices they are integrated with, so one has to have a way of discarding such reflections). cavity (resonator) Fan et al, PRL80, 960 (1998). Slide 33: hight incoming power Soljacic et al., Opt. Lett. 28, 637 (2003). Slide 34: Yanik et al. Opt. Lett 28, 2506 (2003) All-optical switch Slide 35: Surface states in photonic crystals Slide 36: Waveguide in a photonic crystal coupled to the open space Slide 37: Surface mode lasers (Rahachou & Zozoulenko, PRB 72, 155117 (2005)) surface mode residing on the surface of a semi-infinite photonic crystal. lifetime t = ??quality factor Q = ?? Slide 38: Q factors of surface mode resonators Slide 40: Resonant pattern of the surface mode lasers Slide 41: Resonant pattern of the surface mode lasers Slide 42: Waveguiding properties of surface states (Rahachou & Zozoulenko, J. Opt. Soc. Am. B, in press) Effect of imperfections Slide 43: Integration of surface-state waveguides with PC waveguides How to feed light in a photonic-crystal structure? Air Incident light Transmitted light Reflected light Surface-state waveguide PC waveguide Slide 44: feeding light into waveguides in photonic crystals Integration of surface-state waveguides with PC waveguides Slide 45: Schematic of a variety of photonic functions that could be realised in a photonic crystal based integrated circuit. The circles represent holes etched into a semiconducctor heterostructure. Outline for the future

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