We investigate the focusing action of refractive microlens based on the rigorous electromagnetic theory by boundary element method. We numerically simulate total electric-field patterns, the electric-field intensity distributions on the focal plane, and their diffractive efficiencies at the focal spots for describing the focusing behaviours of these microlenses with continuous and multilevel surface-envelopes. Focusing action of incident beam with a certain angle of inclination is indagated as well. The present numerical and graphical results may provide an useful information for the analysis and the design of refractive elements in micro-optics.
Motivated by the significant controversy between the two dispersion models and Weisskopf-Wigner approximation (WWA), for the first time to our knowledge, we introduce the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical treatment on spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formulism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formulism may be reduced to the famous Lorentzian spectrum. In this case, we introduced a lifetime distribution function for an assembly of atoms and found that the lifetime distribution strongly depend on the spread configuration of these atoms in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we found that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.
In this paper we investigated the focal performances of the refractive cylindrical micro-lenses made of anisotropic material(uniaxial crystal ) with the use of the rigorous diffraction theory and boundary element method (BEM). The expressions of conversion from the H-field into the E-field for the TM-polarization are given. The lateral and axial intensity distributions of the E- ( H-)field for the TM- polarization and E-field of the TE-polarization are calculated. The focusing features of the micro-lenses, including the focal spot size, the focal length, and the diffractive efficiency are appraised. The focusing characteristics of both isotropically and anisotropically refractive cylindrical micro-lenses with different f-numbers have been analyzed and compared. The numerical simulations show that in the case of isotropic dielectricity the E- and H- field distributions for the TE- and TM-polarizations exhibit almost the same focusing behavior for all different f-numbers (f/4, f/2, f/1.5). However, in the case of anisotropic dielectricity, we found that the focal spot size of the E-field for the TM-polarization is quite larger than that of the E-field for the TE- polarization, for instance, the focal spot sizes of the E-field for TM- and TE-polarizations are 2.35μm and 1.98μm in the case of f/2, respectively. It is noted that the positions of the focal plane of the E-field for the TE- and TM-polarizations are shifted remarkably away from each other. The focal length of the E-field of the TE-polarization is shorter than that of the E-field of the TM-polarization. For instance, the positions of the focal plane of the E-field for the TE- and TM-polarizations are 59.35μm and 70.79μm in the case of f/2, respectively. This result can be understood from the simple argument owing to the different refraction index for two polarizations in the uniaxial crystal. These interesting features are reported here for the first time. It is anticipated that this kind of elements may serve as the ideal light switching devices with high speed in the MEMS.
We propose a new kind of closed-boundary axilens (CBA) for achieving the property of the increasing focal depth even when the f-numbers of system <2/3, superior to an open boundary axilens (OBA). As the propagating beam in the CBA is experienced twice modulations by two boundaries ( closed-boundary) of the CBA, consequently, the focal depth of the CBA may be longer than that of the OBA in which the incident wave is modulated only once. In this presentation, we analyze the focusing characteristics of the CBA with the use of the boundary integral method. The numerical simulations show that the CBA can produce long focal depth for the preset focal depth of 3 and 5 μm in the small f / # of 2/3 , 1/2, and 1/3. For a comparison, we also carry out the calculation for the OBA in the same parameters as those of the CBA. We find that the ratio of the relatively extended focal depth for the CBA to that of the conventional micro-lens is 1.57 (or 2.17) for the preset focal depth of 3μm (or 5μm) at f / # set to 1/2. In contrast, this ratio for the OBA is only 0.75 (or 1.04) for the preset depth of 3μm (or 5μm), with fixed f / # of 1/2. The results sufficiently verify that the CBA has good superiority of long focal depth even for the lower f / # <2/3. In contrast, the OBA almost loses the property of long focal depth for the lower f / # <2/3. It is expected that the proposed CBA may be much useful for practical applications in MEMS.
We present the optimization design of aperiodic optical superlattices (AOSs) realized by inverting poled ferroelectric domains in sample. This design problem belongs to solving an inverse source problem in nonlinear optics. The optical design of the AOS can be achieved with use of the simulated annealing method. The constructed AOSs can implement multiple wavelength second-harmonic generation and the coupled third-harmonic generation with an identical effective nonlinear coefficient, at the preassigned wavelengths. The simulations show that the harmonic generations in the constructed AOSs can approach the prescribed goal better than those with the Fibonacci optical superlattice. The effective nonlinear coefficients vs the optical wave propagating distance from the impinging surface of incident light in samples exhibit monotonically increasing behavior. This clearly infers that the contribution form every block to the otpical parametric processes is with each other in the constructive interference state. It is expected that this new design method may provide an effective and useful technique for flexibly constructing nonlinear optical material to achieve the desired functions and match various practical applications.
We employ conjugate gradient algorithm for designing diffractive phase elements (DPEs) that implement the predefined axial-intensity modulations over a given region. We introduce an error function used for guiding the design of DPEs and appraising their performance. We derive the analytical expression for the gradient of the error function with respect to the phases of DPEs. To demonstrate effectiveness of the related algorithms, we carry out model designs of several DPEs that realize different axial- intensity modulations. For instance, we achieve the designs of the DPEs for focusing incident uniform wave into four foci with equal or unequal spacing between the consecutive foci along the optical axis, and the DPE for realizing sinusoid-like axial-intensity modulation over a given region. We also present the designs of the DPEs for generating pseudo-nondiffracting beams with multiple-segment character. The results show that the designed DPEs can satisfactorily fulfill the practical requirements.
Based on the general theory of the amplitude-phase retrieval problem, we present a new approach for the design of diffractive phase elements (DPEs) to implement beam shaping in the fractional Fourier transform (FRFT) domain. We derive the unitarity transform condition for a FRFT system and find that for the given structural parameters of optical system, the nonunitarity of the discrete FRFT depends on its fractional order. Numerical simulations are carried out in designing the DPEs to convert a Gaussian-profile beam into a uniform-profile beam in 1D optical system and the rotationally symmetric optical system both, for different fractional orders and different parameters of beam. In all the cases studied, our algorithm provide an effective method in designing the DPEs that can implement the beam shaping with a high quality.
Optical linear transform architectures bear good potential for future developments of very powerful hybrid vision systems and neural network classifiers. The optical modules of such systems could be used as pre-processors to solve complex linear operations at very high speed in order to simplify an electronic data post-processing. However, the applicability of linear optical architectures is strongly connected with the fundamental question of how to implement a specific linear transform by optical means and physical imitations. The large majority of publications on this topic focusses on the optical implementation of space-invariant transforms by the well-known 4f-setup. Only few papers deal with approaches to implement selected space-variant transforms. In this paper, we propose a simple algebraic method to design diffractive elements for an optical architecture in order to realize arbitrary space-variant transforms. The design procedure is based on a digital model of scalar, paraxial wave theory and leads to optimal element transmission functions within the model. Its computational and physical limitations are discussed in terms of complexity measures. Finally, the design procedure is demonstrated by some examples. Firstly, diffractive elements for the realization of different rotation operations are computed and, secondly, a Hough transform element is presented. The correct optical functions of the elements are proved in computer simulation experiments.
We present a design of diffractive phase elements (DPEs) that produce point/ring patterns based on the general theory of phase retrieval. The optical system is illuminated by monochromatic or dual-wavelength light. We carry out numerical simulations. The results show that the designed DPE's can satisfactorily generate monochromatic or color point/ring patterns with the given radii of rings in the above-mentioned illuminating systems. The color of the diffractive patterns can be arbitrarily altered. One of the designed DPE's was fabricated and its performance was measured. Experimental measurement is in good agreement with the numerical simulations. These DPE's suit for the applications in optical space communication.
KEYWORDS: Near field scanning optical microscopy, Semiconducting wafers, Near field, Magnetism, Near field optics, Electromagnetism, Diffraction, Dielectrics, Electromagnetic coupling, Wafer-level optics
The near-field scanning optical microscopy is widely applied in obtaining local optical information on the surface structures with subwavelength resolution. In the common illumination-transmission operation mode, the sample is illuminated by a near-field probe formed from an aluminum- coated, tapered optical fiber with subwavelength aperture and the transmitted light is collected by a conventional objective lens. Commonly the aperture tip is modeled according to Bethe's theory as the effective electric and magnetic dipoles whose magnitudes are only related to the incident electromagnetic fields. However, the coupling of the tip with the sample and the extended wafer can not be neglected as the tip is located in the proximity of the sample. In this work we treat the electromagnetic coupling of the tip with the sample and wafer in the real-space self- consistent approach and simplify the coupling of the wafer by the image method. The magnitudes of the effective dipoles are determined by the incident fields above the aperture as well as the perturbed fields reflected from below by the sample and wafer. When the coupling tip-sample-wafer system is solved in self-consistency, the transmitted optical signal collected by the lens can be derived straightforwardly, relating to the effective dipoles and the polarization of the sample. The simulation results show that the signal is sensitive to the polarization character of the incident fields.
An intersecting waveguide modulator which utilizes the carrier injection effects is presented and characterized. Using O+ implantation to render the implanted region electrically inactive, a well confined injection carrier channel is formed. This area can be driven to function as waveguide or as antiwaveguide. A transversal electrode switches the modulator from the On-state to the Off-state or vice versa. By the use of carrier induced refractive index modeling and the finite difference beam propagation method (FD-BPM) simulation, good performance and small injection current ofthis modulator are predicted.
This paper is a summary of the theory of the amplitude-phase retrieval problem in any linear transform system and its applications based on our previous works in the past decade. We describe the general statement on the amplitude-phase retrieval problem in an imaging system and derive a set of equations governing the amplitude-phase distribution in terms of the rigorous mathematical derivation. We then show that, by using these equations and an iterative algorithm, a variety of amplitude-phase problems can be successfully handled. We carry out the systematic investigations and comprehensive numerical calculations to demonstrate the utilization of this new algorithm in various transform systems. For instance, we have achieved the phase retrieval from two intensity measurements in an imaging system with diffraction loss (non-unitary transform), both theoretically and experimentally, and the recovery of model real image from its Hartley-transform modulus only in one and two dimensional cases. We discuss the achievement of the phase retrieval problem from a single intensity only based on the sampling theorem and our algorithm. We also apply this algorithm to provide an optimal design of the phase-adjusted plate for a phase-adjustment focusing laser accelerator and a design approach of single phase-only element for implementing optical interconnect. In order to closely simulate the really measured data, we examine the reconstruction of image from its spectral modulus corrupted by a random noise in detail. The results show that the convergent solution can always be obtained and the quality of the recovered image is satisfactory. We also indicated the relationship and distinction between our algorithm and the original Gerchberg- Saxton algorithm. From these studies, we conclude that our algorithm shows great capability to deal with the comprehensive phase-retrieval problems in the imaging system and the inverse problem in solid state physics. It may open a new way to solve important inverse source problems extensively appearing in physics.
The effect of different tunneling modulations on the quantized conductance in a coupled double electron waveguide is theoretically investigated with the use of a model of two coupled chains. The calculated results show that both the accuracy of the quantization in the conductance and the resonance pattern strongly depend on the tunneling modulation between two channels. The resonance structures in the conductance plateaus are smeared when the corresponding tunneling modulation alters smoothly over the obstacle region. We also study the variation of the quantized conductance with the Fermi energy for various doubly-connected structures. A series of new novel features in the conductance curve emerge. We find that this two coupled chain model is shown to describe the essence of quantum ballistic transport of electrons in the two coupled electron waveguide in a simple and transparent way.
Propagation of guided electron waves in two coupled quantum wells is studied and analyzed by decomposing 1-D coupled eigenstates in terms of multiple eigenstates of individual wells. The energy transfer from one mode to the other modes in either channel is characterized. The dominant transfer is to the matched mode in the other channel. But tunneling to other modes nearest in energy to the incident mode is found to be quite large, particularly under high mode injection.
A new algorithm for the reconstruction of a real image from its Hartley transform modulus only is presented based on the general theory of the amplitude-phase retrieval problem. From our simulating calculation, it is shown that the image reconstruction can be successfully achieved from its Hartley transform modulus only by using the Y/G algorithm. The influence of noise contained in Hartley transform intensity on the convergent solution is also examined in detail.
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