Ben-Yuan Gu

Generation of nondiffracting beams by diffractive phase elements

We present a design of the diffractive phase elements (DPE’s) that produce nondiffracting beams according to the beam-shaping scheme, in which the incident Gaussian-profile beam is converted into a Bessel-function J0 beam. An optimization method is applied to solving this special beam-shaping problem. Numerical investigation of the generating J0 Bessel beam shows that the designed DPE can satisfactorily produce the J0 Bessel beam.

Recursive algorithm for phase retrieval in the fractional Fourier transform domain

We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.

Phase retrieval in the Fresnel transform system: a recursive algorithm

We first discuss the discrete Fresnel transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the Fresnel transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase value compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.

Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit

The process of the light passing through a single subwavelength metal slit is analyzed by the finite-difference time-domain method. The simulation results show that the slit can be considered as an effective dielectric region sandwiched by two scattering regions at the two slit ends. Thus, the slit is analogous to a Fabry-Perot (FP) etalon consisting of a dielectric slab with high-reflection coatings on its two surfaces. A formula is presented to evaluate the phase shift caused by the amplitude transmissivity of the coatings.

Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers.

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.

Rigorous electromagnetic analysis of the common focusing characteristics of a cylindrical microlens with long focal depth and under multiwavelength illumination

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.

Enhanced effect of local fields in subwavelength metallic series nanocavities from surface plasmon polaritons

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.

A New Method for Phase Retrieval in the Optical System

In this letter, a new recursive algorithm to implement phase retrieval from two intensities in the two-dimensional Fourier transform domain is presented. In terms of the cascading property and additivity of the order of the fractional Fourier transform, a set of convolution equations is exactly derived. Applying recursive algorithm, these equations can be easily solved. This approach simplifies significantly computational manipulations comparing with conventional iterative algorithms and does not need initial phase distribution.

Beam shaping and its solution with the use of an optimization method.

We present an exact mathematical description of beam shaping and indicate that a rigorous solution does not exist: only an optimal solution can be found. An optimization method is proposed to search for the solution. The simulation results for an example are given in detail.

Analysis of microlens array with long focal depth and small f -number by improved first Rayleigh-Sommerfeld method

The improved first Rayleigh?Sommerfeld method (IRSM1) is applied to analyse the focusing performance of dual-?and tri-cylindrical microlens arrays with long focal depth and small f-number for the TE polarization. The real extended focal depth, the diffraction efficiency, the spot size, and the real position of the focal plane of the microlens array with different f-numbers and the preset extended focal depths are calculated by the IRSM1, rigorous boundary element method (BEM), and original Rayleigh?Sommerfeld method (ORSM1), respectively. The accuracies of the IRSM1 and the ORSM1 are evaluated along the longitudinal direction. The results indicate that the IRSM1 can be used for analysing the cylindrical microlens array with long focal depth and small f-number, but the ORSM1 completely fails for those microlens arrays with small f-number. It is expected that this investigation will provide useful information in the design of the micro-optical elements for realizing longitudinal optical field modulation.