Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session L16: Photonic Crystals I |
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Sponsoring Units: DCMP Chair: Guy Ramon, Naval Research Laboratory Room: LACC 404A |
Tuesday, March 22, 2005 2:30PM - 2:42PM |
L16.00001: Optimization of two-dimensional photonic bandstructure systems using steepest-descent algorithm Feng Zhang, Kito Holliday, Paul Lammert, Vincent Crespi Conventionally, perturbation theory is used for the analytical study of small changes in a system. However, it can also be considered as an exact expression in differential form for the gradient of an objective function describing a system. Based on this idea, we have developed an efficient steepest-descent algorithm to optimize particular features of a photonic bandstructure system. We have applied the algorithm to optimize the size of the photonic bandgap at minimal dielectric contrast in two-dimensional photonic crystals on square and hexagonal lattices, obtaining non-zero complete gaps at very low dielectric contrast. [Preview Abstract] |
Tuesday, March 22, 2005 2:42PM - 2:54PM |
L16.00002: Efficient finite-element Green's function approach for CD metrology of 3D gratings on multilayer films. Yia-Chung Chang, Guangwei Li, Hanyou Chu, Jon Opsal We present an efficient method for calculating the reflectivity of 3D gratings on multilayer films based on a finite-element Green's function approach. Our method scales like $N^2$ (k-space version) or $N \log N$ (real-space version), where $N$ is the number of plane waves used in the expansion. Therefore, it is much more efficient than the commonly adopted rigorous coupled wave analysis (RCWA) method, which scales like $N^3$. We demonstrate the effectiveness of this method by applying it to a 2D periodic array of contact holes on a multilayer film. We find that our Green's function approach is at least one order of magnitude faster than the RCWA approach when applied to typical contact holes considered in industry. For most cases, this method is efficient enough for application as a real-time critical dimension (CD) metrology tool. [Preview Abstract] |
Tuesday, March 22, 2005 2:54PM - 3:06PM |
L16.00003: Photonic Crystal Defect Mode Analysis Using Discretized Vector Wannier Functions J.D. Albrecht, P. Sotirelis We present a theoretical approach for calculating the photonic structure of defects in 2D photonic crystals. The central feature of our approach is the basis construction of local vector Wannier functions from the perfect crystal eigenstates. It has been proposed$^a$ that this basis be used to expand photonic crystal defect states analogous to the expansion in linear combinations of atomic orbitals of electronic structure of the ideal silicon vacancy.$^b$ These approaches rely on a small number of basis states local to the defect region. In this work, we replace the fourier expansion of the perfect crystal by a real-space description in vector finite-elements. This method allows the computation of the basis on the same grid as the perfect structure and a simpler defect eigenvalue problem. We present results that verify the eigenmodes of the crystal and examine defect modes. \newline $^a$K.M. Leung, J. Opt. Soc. Am. B \bf{10}, 303 (1993). \newline $^b$G.A. Baraff and M. Schluter, PRL \bf{41}, 892 (1978); J. Bernholc, N.O. Lipari, and S.T. Pantelides, PRL \bf{41}, 895 (1978). [Preview Abstract] |
Tuesday, March 22, 2005 3:06PM - 3:18PM |
L16.00004: Tunable band gaps in two-dimensional semiconductor-dielectric photonic crystals Gerardo Martinez, Manvir Kushwaha This paper reports the multiple band gaps in the two-dimensional semiconductor-dielectric photonic crystals of several compositions: semiconductor (dielectric) thin cylinders in the dielectric (semiconductor) background. We consider both square lattice and hexagonal lattice arrangements and compute extensive band structures using a plane-wave method within the framework of an efficient standard eigenvalue problem for both E- and H-polarizations. The whole range of filling fractions has been explored to claim the existence of the lowest (the so-called acoustic band gap) and multiple higher-frequency band gaps within the first thirty to forty bands for various compositions. The completeness of the existing band gaps is substantiated by computing the band structures via detailed scanning of the principal symmetry directions covering periphery as well as the interior of the irreducible part of the first Brillouin zone and through the computation of the density of states. In general, the composition made up of doped semiconducting cylinders in the insulating background is found to be the optimum case for both geometries. Such semiconductor-dielectric photonic crystals which are shown to possess huge lowest band gaps below a threshold frequency (the plasma frequency) have an advantage over the dielectric photonic crystals in the emerging technology based on the photonic crystals. [Preview Abstract] |
Tuesday, March 22, 2005 3:18PM - 3:30PM |
L16.00005: Theory of Light Refraction at a Surface of a Photonic Crystal Wei Jiang, Ray T. Chen In past studies on photonic crystal refraction, how the surface orientation affects refraction was largely unexplored. In this work, a general, analytic theory of light refraction is developed for a photonic crystal (PC) that has an arbitrary lattice type and surface orientation. A simple topological argument is presented to prove the equal partition of forward and backward propagating modes by an arbitrary plane in any periodic optical media. Furthermore, we have discovered the surface-dependent degeneracy of crystal modes. The current theory addresses light refraction by a {\it natural} quasi- periodic surface, in addition to an ordinary periodic surface. Particularly interesting is the transition from a periodic surface to a quasi-periodic surface, which could happen upon a slight change of surface orientation. Such a transition could lift the surface-dependent mode degeneracy, which can be observed as a small number of refracted beams split into an essentially infinite number of beams. Harnessing such an extremely sensitive phenomenon could lead to interesting applications in optoelectronics. [Preview Abstract] |
Tuesday, March 22, 2005 3:30PM - 3:42PM |
L16.00006: Effective Index Model and Guided Modes in a Photonic Crystal Fiber Jesus Arriaga In the last few years, there has been intense work in photonic crystal fibers (PCF's). These systems can be obtained by surrounding the core of a normal fiber with a two-dimensional photonic crystal made of silica, with air holes running along the length of the fiber. To study the waveguiding properties of these fibers, the cladding surrounding the solid core is replaced by an effective homogeneous medium described by an effective refractive index. This effective index model has been used to explain some of the peculiar properties of these systems. However, using the effective index medium to calculate the number of guided modes in PCF's, it is necessary to know the radius of the core precisely. Because in PCF's there is no clear boundary between the cladding and the core, different values of the fiber's core have been used in the literature. In this work we calculate the waveguiding properties of PCF's solving the Maxwell equations by using the plane wave expansion and the supercell method. We calculate the propagation constant both, for the propagating modes in the PCF's and for the fundamental space-filling mode (FSM). The FSM is the fundamental mode of the infinite photonic crystal cladding when the core is absent. Our results predict single-mode behavior at higher values of the air holes radius when compared with those reported previously. [Preview Abstract] |
Tuesday, March 22, 2005 3:42PM - 3:54PM |
L16.00007: Flat lens without optical axis: Imaging theory W. T. Lu, S. Sridhar We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relation with negative group refraction. The medium can be viewed as having an effective anisotropic refractive index. Imaging can be achieved with both positive and negative refractive indices, although the image quality can vary greatly and multiple images may be present. The Veselago-Pendry lens is a special case of the theory with isotropic negative refractive index of -1. Snell's law for group refraction is valid and leads to ray diagrams. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and consequences for sub-wavelength imaging are also presented. Work supported by NSF and AFRL. [Preview Abstract] |
Tuesday, March 22, 2005 3:54PM - 4:06PM |
L16.00008: Focusing by plano-concave lens using negative refraction Plarenta Vodo, Patanjali Parimi, Wentao Lu, Srinivas Sridhar We demonstrate experimentally focusing of plane waves at microwave frequencies by a plano-concave lens using negative refraction. The lens was fabricated from a microwave dielectric photonic crystal acting as a left-handed metamaterial. The inverse experiment where the source is placed at the observed focal point was also performed and shows clearly an emerging plane wave. The focal point is observed to move with the radius of curvature of the lens. Different radii of curvature have different frequency ranges of focusing all of which lie in the second band frequencies along $\Gamma $-X propagation direction of the photonic crystal. The measured values of refractive index are in complete agreement with those determined from band structure calculations. Work supported by AFOSR and NSF-PHY-0098801. [Preview Abstract] |
Tuesday, March 22, 2005 4:06PM - 4:18PM |
L16.00009: Negative Refraction and Subwavelength Lensing in a Polaritonic Crystal Xiwen Wang, Krzysztof Kempa We show that a two-dimensional polaritonic crystal, which is made of metallic rods which support plasmon oscillations, can act in a narrow frequency range act as a medium in which a negative refraction, and subwavelength lensing occurs. The lensing effect in our crystal obeys the image-distance relationship characteristic of an n = -1 material. We show, that surface polaritonic modes are excited on the surface of the lens, and that they facilitate restoration of the evanescent waves, which carry the subwavelength image information. We also demonstrate, that this can occur in the visible frequency range for a wide range of materials, including silver and aluminum rods, as well as carbon nanotubes. This flexibility should allow for an experimental demonstration of this phenomenon in the visible frequency range. [Preview Abstract] |
Tuesday, March 22, 2005 4:18PM - 4:30PM |
L16.00010: Electron beam lithography based fabrication of omnidirectional photonic crystal structures for visible and near-infrared wavelengths Ganapathi Subramania We describe the fabrication of a three dimensionally periodic photonic crystal structure with omnidirectional band gap for the near-IR and visible wavelength region using a technique of direct electron beam write coupled with multi-level alignment. Using this method we have successfully fabricated silicon as well as gold based Iowa State ``woodpile'' structure with lattice spacings as small as 550 nm. We tested the devices for their optical properties and we find that the data reveals features consistent with the photonic band gap. [Preview Abstract] |
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L16.00011: The Extended Plane Wave Expansion Method for 3D Anisotropic Photonic Crystals\footnote{Supported by NSF(through the Northwestern MRC)} Y.C. Hsue, A.J. Freeman, B.Y. Gu Conventional plane-wave expansion (PWE) methods, good for calculating such properties as photonic band gaps for materials with periodic structure, are very difficult for calculating a crystal with an interface. While the dispersion relation used by PWE does not restrict the wave vectors, {\bf k}, to be real, the complex {\bf k} are the important for interface calculations. Therefore, we modified the PWE to make it possible to easily calculate the complex {\bf k} (EPWE) both in the 2D isotropic and the general 3D anisotropic cases. Advantages gained include: (i) the frequency is initially given and regarded as a known variable, rather than as an argument, and can always be set to be a positive real number even for complex systems with real, imaginary, or complex frequency-dependent permittivity or permeability; (ii) from the complex {\bf k} results, the resonant feature of the transmittivity can be easily analyzed; (iii) since EPWE is extended from the PWE, it obeys the same dispersion relation, and their results will also be the same, when providing PWE the {\bf k} derived from EPWE; (iv) because the imaginary part of {\bf k} is associated with the reciprocal of the penetration depth, the shortest width of the crystal when it is treated as a single crystal is well-defined. As an example, we present 3D isotropic GaAs crossed square prisms and find a good correspondence between results of both methods. [Preview Abstract] |
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L16.00012: Negative Refractive Index Materials Ahmad Alsaad, Heinz Schweizer The realization of dielectric and metallic periodical matrices in a bottom up fabrication procedure is proposed for realization of materials with negative refractive index (NIM) or pseudo NIM (PsNIM). The single elements of the periodical matrices (2D photonic crystal, 2D PC)) will be realized by high-resolution e-beam lithography and dry etching technique. Dielectric materials will be used for PsNIM approaches. Special importance in the case of metallic matrices (for NIM approaches) will be put on structures in the nanometre region to control the surface plasmon modes. By stacking of the 2D PC structures we will realize the 3D PC in a bottom up procedure with special consideration of adjustment of matrix modes (PC gap frequencies) and surface plasmon modes to control and enhance the NIM-effect. Furthermore a stacking of many as possible layers in the bottom up procedure is important for the reduction of the surface leakage rate of the electromagnetic field out of the NIM structure. Optical measurements with high resolution and time resolved measurements will be carried out with partners in narrow co-operation. [Preview Abstract] |
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