ABSTRACT
The enhancement and confinement characteristics of the local field in the two-dimensional (2D) subwavelength-size series cavities structure are investigated numerically by using the boundary integral method. The series cavities are built of two pieces of finite silver thin slabs with subwavelength corrugations on their inner boundaries, set in a face-to-face arrangement with a separating space, and the central part is a narrow channel (NC). We calculate the average amplitude of the local field in the NC as a function of the wavelength for exploring the influence of the structural parameters and demonstrate the amplitude distribution of the magnetic field in the structure and the cross-section distributions of the local field in the NC region along both the longitudinal axis direction and the transverse directions. The simulations show that the local field in the NC has significant enhancement, up to 2 orders of magnitude, of the incident light field, and the local light field is confined to a small region less than one fifth of the resonant wavelength in the longitudinal direction and one twentieth of the resonant wavelength in the lateral direction. Replacing the metallic material of the cavity walls with the semiconductor germanium leads to the complete disappearance of the enhancement of the local field. It is clearly shown that surface plasmon polaritons on the metal play a critical role for this enhancement phenomenon. The influences of various geometric parameters on the resonant wavelength and the peak value of the average amplitude of the local field are extensively investigated.
Subject(s)
Models, Theoretical , Nanostructures , Radiometry/methods , Surface Plasmon Resonance/methods , Computer Simulation , Light , Scattering, RadiationABSTRACT
The common focusing characteristics of a cylindrical microlens with a long focal depth and under a given multiple-wavelength illumination are analyzed based on the boundary element method (BEM). The surface-relief profile of a finite-substrate-thickness microlens with a long focal depth is presented. Its focusing performances, such as the common extended focal depth (CEFD), the spot size, and the diffraction efficiency, are numerically studied in the case of TE polarization. The results show that the CEFD of the microlens increases initially, reaches a peak value, and then decreases with increasing preset focal depth. Two modified profiles of a finite-substrate-thickness cylindrical microlens are proposed for enlarging the CEFD. The rigorous numerical results indicate that the modified surface-relief structures of a cylindrical microlens can successfully modulate the optical field distribution to achieve longer CEFD, higher transverse resolution, and higher diffraction efficiency simultaneously, compared with the prototypical microlens. These investigations may provide useful information for the design and application of micro-optical elements in various multiwavelength optical systems.
ABSTRACT
We present a fast and general iterative design method for both diffractive and nondiffractive two-dimensional optical elements. The method is based on a finite-thickness model in combination with the Yang-Gu phase-retrieval algorithm. A rigorous electromagnetic analysis (boundary element method) is used to appraise the designed results. We calculate the transverse-intensity distributions, diffraction efficiency, and spot size of the designed microlenses at the focusing plane for microlenses designed using the presented method and the conventional zero-thickness model. The main findings show the superiority of the presented method over the conventional method, especially for nondiffractive optical elements.
ABSTRACT
We calculate the lifetime distribution function of an assembly of polarized atoms in two-dimensional (2D) photonic crystals (PCs) at different polarization orientations of atomic dipole moments. We reveal a switching effect of atomic spontaneous emission (SE) and find a significant change of atomic lifetime, up to a factor of 33, by tuning the polarized orientation of the atoms. These observations suggest that the tuning of the polarized orientation of atoms provides a new way for the effective control of atomic SE processes in 2D PCs.
ABSTRACT
We present an effective design of aperiodically stacked layers of nonlinear material and air, sandwiched by two truncated photonic crystals, in terms of the simulation annealing method. The constructed structure can achieve multiple-wavelength second-harmonic generation (SHG) at the preassigned wavelengths. We derive a general solution of SHG in 1D inhomogeneous systems and apply it to evaluate the SHG conversion efficiency. Numerical simulations show that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequencies are assigned to the designed defect states.
ABSTRACT
Green's tensors for photonic crystal (PC) slabs are numerically solved by the coupled-dipole approximation (CDA) technique. The obtained components of Green's tensors satisfy discontinuous or continuous conditions at interfaces of scatterers. This shows that the CDA technique is very applicable to studying the properties of PC slabs. Green's tensors exhibit obviously periodic oscillation with the increase of the number of scatterers; furthermore, the effect of each scatterer on Green's tensors displays a localization feature in the sample containing one row of scatterers; on the contrary, this localized effect disappears in the sample consisting of multiple rows of scatterers.
ABSTRACT
The lifetime distribution functions of the spontaneous emission (SE) of the excited atoms embedded in two-dimensional (2D) photonic crystals (PCs) with square lattice, consisting of square air rods in dielectric medium with different filling factors, are calculated by using the plane wave expansion method. The numerical results show that the SE in the 2D PCs cannot be prohibited completely but it can be inhibited intensively by the pseudo-PBG of the PCs. In the pseudoband edges, the SE is accelerated obviously. The reduced average lifetime of the excited atoms and the extension of the reduced lifetime distribution in the 2D PCs both are the same as those in the 3D PCs in the order of magnitude. Our results provide an available way to control the behavior of the SE by changing the structures of the 2D PCs.
ABSTRACT
Based on the previous Letter [Opt. Lett. 29, 2345 (2004)], we significantly extend the applications of the improved first Rayleigh-Sommerfeld method (IRSM1) to analyze the focusing performance of cylindrical micro-lenses for different types of profile (continuous or stepwise), different f-numbers (from f/1.5 to f/0.75), and different polarizations (the TE or TM). A number of performance measures of the cylindrical microlenses, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized sidelobe power, are studied in detail. We compare numerical results obtained by the IRSM1, by the original first Rayleigh-Sommerfeld method (ORSM1), and by the rigorous boundary element method (BEM). For continuously refractive lenses, the results calculated by the IRSM1 are quite close to those obtained by the BEM; in contrast, the results calculated by the ORSM1 significantly deviate from those obtained from the rigorous BEM. For multilevel diffractive lenses, the IRSM1 also provides much more accurate results than the ORSM1. In addition, compared with the BEM, a notable advantage of the IRSM1 is much lower computer memory and time consumption in computations.
ABSTRACT
An improved first Rayleigh-Sommerfeld method (IRSM1) is proposed and applied to the analysis of cylindrical microlenses with small f-numbers. Numerical results obtained by both the IRSM1 and the original Rayleigh-Sommerfeld method (ORSM1) are compared with those obtained by the rigorous boundary element method (BEM). For both refractive and diffractive lenses, the results obtained by the IRSM1 are close to those obtained by the BEM even for small f-numbers; by contrast, the results by the ORSM1 differ significantly from those obtained by the BEM. Moreover, the IRSM1 uses much less time and computer memory in the computations than the BEM.
ABSTRACT
We investigated the focal characteristics of open-regional cylindrical microlens arrays with long focal depth by using a rigorous boundary-element method (BEM) and three scalar methods, i.e., a Kirchhoff and two Rayleigh-Sommerfeld diffraction integral forms. Numerical analysis clearly shows that the model cylindrical microlens arrays with different f-numbers can generate focusing beams with both long focal depth and high transverse resolution. The performance of the cylindrical microlens arrays, such as extended focal depth, relative extended focal depth, diffraction efficiency, and focal spot size, is appraised and analyzed. From a comparison of the results obtained by the rigorous BEM and by scalar approximations, we found that the results are quite similar when the f-number equals f/1.6; however, they are quite different for f/0.8. We conclude that the BEM should be adopted to analyze the performance of a microlens array system whose f-number is less than f/1.0.
ABSTRACT
We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.
ABSTRACT
Designs of aperiodic photonic quantum-well (APQW) structures to achieve multiple channeled filtering at arbitrary preassigned frequencies are done by using the simulated annealing algorithm with a special merit function. The APQW structure consists of aperiodically stacked dielectric-layers sandwiched by two finite-length prototype photonic crystals (PCs). The insert of the APQWs can generate the specified defect states with predetermined frequencies. Numerical simulations show that the designed APQWs can achieve the desired specification.
ABSTRACT
Order-of-magnitude enhancement of light absorption can take place near the photonic band gaps in three-dimensional layer-by-layer metallic photonic crystals in the mid-infrared wavelength regime where a conventional bulk metallic material shows weak absorption. In this paper we investigate the dependence of this enhanced absorption on several structural parameters of the crystal by means of a plane-wave-based transfer-matrix method in combination with an analytic model expansion approach. We find that when the metallic layers are brought out of touch, the magnitude of the absorption peaks grows rather than decays, in contrast with the conventional wisdom that the connectivity of metallic structure can enhance the absorption. Besides, the increase in the metallic layer separation distance will result in redshifts of absorption peak. The position of the absorption peak can also be engineered conveniently by simply changing the refractive index of the dielectric material filling the open domain between metal walls. Due to the approximate scalability of Maxwell's equations, the absorption peak shows a nearly linear dependence in position on this refractive index.
ABSTRACT
Decay kinetic properties of a two-level atom near the band edges of photonic crystals (PCs) with absolute gaps are studied based on the Green's function expression for the evolution operator. The local coupling strength between the photons and an atom is evaluated by an exact numerical method. It is found that the decay behavior of an excited atom can be fundamentally changed by the variation of the atomic position: Weisskopf-Wigner and non-Weisskopf-Wigner decay phenomena occur at different atomic positions in the PCs as a result of a significant difference in the local coupling strength. Our finding implies that it is possible to engineer the luminescence spectrum by controlling the atomic position.
ABSTRACT
We find that a microcylindrical axilens with a closed boundary and with an f-number less than 1 still can achieve the properties of long focal depth and high transverse resolution, unlike a microcylindrical axilens with an open boundary, which fails to maintain those properties for low f-numbers. The focusing characteristics of the closed-boundary axilens and the open-boundary axilens are numerically investigated based on the boundary integral method. The numerical results show that the ratio of the extended focal depth of the closed-boundary axilens to the focal depth of the conventional microlens can reach up to 1.26 and 2.12 for the preset focal depths 3 and 5 microm, respectively, even though the f-number is reduced to 1/3.
ABSTRACT
Spontaneous decay behaviors from an assembly of atoms (or molecules) in 3D photonic crystals (PC's) with pseudogaps are investigated. Theoretically, a lifetime distribution function for these atoms or molecules is defined to reveal decay kinetics. Our calculations show that quite wide or narrow lifetime distributions can occur for different spread configurations of the atoms (or molecules). The pure PC effect may lead to coexistence of both accelerated and inhibited decay processes. These results provide theoretical clarification for substantial discrepancies in the recent reported experiments.
