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.
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 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.
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.
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.
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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