Bi-Zhen Dong

BEAM SHAPING IN THE FRACTIONAL FOURIER TRANSFORM DOMAIN

A new design approach for the diffractive phase elements (DPE’s) that implement beam shaping in the fractional Fourier transform (FRFT) domain is presented. The new algorithm can successfully achieve the design of DPE’s for beam shaping in both unitary and nonunitary transform systems. The unitarity transform condition of the FRFT domain is discussed. Modeling designs of the DPE’s are carried out for several fractional orders and different parameters of the beam for converting a Gaussian profile into a uniform beam. Our approach can realize beam shaping well for a nonunitary transform system in the FRFT domain.

Enhanced harmonic generation in aperiodic optical superlattices

We find that harmonic generation can be enhanced with aperiodic optical superlattice (AOS) structures realized by inverting poled ferroelectric domains in sample. The optimal 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. The simulations show that the constructed AOSs can enhance harmonic generation compared with the Fibonacci optical superlattice. The physical origin of this enhancement is ascribed to the constructive interference effect.

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.

Investigations of harmonic generations in aperiodic optical superlattices

We envisage the enhanced effect of harmonic generations from aperiodic optical superlattices (AOSs) achieved by inverting poled ferroelectric domains in samples. The search of optimal AOSs structures belongs to solving a difficult inverse source problem in nonlinear optics. We employ the simulated annealing method to successfully deal with this problem. We present the analyses of the design idea in the real-space representation and carry out several model designs. The constructed AOSs 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 versus the optical wave propagating distance from the impinging surface of incident light in the sample exhibit monotonically increasing behavior...

Numerical investigation of phase retrieval in a fractional Fourier transform

Recently the combination of the Gerchberg–Saxton (GS) algorithm and a fractional Fourier transform was proposed to implement beam shaping in the fractional Fourier domain [ Zalevsky , Opt. Lett.21, 842 (1996)]. We generalize this idea to deal with the problem of phase retrieval from two intensity measurements in a fractional Fourier transform system. The relevant equations for determining the unknown phases are derived, based on the general theory of amplitude–phase retrieval in an optical system. The unitarity condition of the fractional Fourier transform in a practical optical system with finite aperture is discussed. For different fractional orders P, the phase retrieval of several typical model images is studied in detail. A comparison of the GS and our algorithms is given, based on numerical simulations. It follows that our algorithm can offer the desired phase in all cases considered. However, the GS algorithm may fail when the transform system is nonunitary.

General theory for performing an optical transform

A general theory for making an optical transform is presented using amplitude-phase holographic lenses (masks). It can be shown that an optical system composed of many amplitude-phase masks can do any given linear transform. A set of equations for determining the amplitude-phase distributions of masks is given. A feedback iterative approach to deal with these equations is also suggested. We show that any given optical transform can be achieved even with a single mask by increasing the number of sampling points in the mask. The relevant equations and the necessary conditions satisfied by the mask are also given. To free the fabrication of the mask from difficulty in technique, sometimes the information quantity carried by the single mask must be relaxed. The dual-mask system is discussed in detail. The general theory is demonstrated by examples for performing the four- and eight-sequence Walsh transforms in three different orders. The results agree well with the theory. Some experimental results and relevant applications are also reviewed briefly.

Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory

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.

GENERATION OF PSEUDO-NONDIFFRACTING BEAMS WITH USE OF DIFFRACTIVE PHASE ELEMENTS DESIGNED BY THE CONJUGATE-GRADIENT METHOD

The design of diffractive phase elements (DPE’s) for generating pseudo-nondiffracting beams (PNDB’s) is carried out by employing the conjugate-gradient method. By selecting a trapezoid profile as the preset axial intensity distribution to guide the design and by using an error function with a weighting factor to evaluate the performance of the DPE, we develop a model design and obtain a satisfactory diffractive pattern of a single-segment PNDB. We demonstrate the effectiveness of the conjugate-gradient method in the design of DPE’s that produce multiple-segment PNDB’s in which two consecutive segments are separated by a dark region along the optical axis. We also evaluate the degree of nonuniformity of the axial intensity over a given axial region. The design results match the requirements quite well.

Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution

We first present nonparaxial designs for a microcylindrical axilens with different long focal depths and rigorously analyze electromagnetic field distributions of the axilens using integral equations and the boundary-element method. Numerical results show that the designed axilenses indeed have the special feature of attaining a long focal depth while keeping high transverse resolution for numerical apertures of 2.4, 2.0, and 1.0. The ratio between the extended focal depth of the designed axilens and the focal depth of the conventional focal lens is 1.41, the corresponding maximal extended focal depth of the axilens can reach 28 microm, and the spot size of the focal beam is approximately 10 microm over the focal range.

A new method for generating axially-symmetric and radially-polarized beams

A scheme for generating axially-symmetric and radially-polarized beams is proposed by using two diffractive phase elements (DPEs) made of birefringent materials. The design of these two DPEs is based on the general theory of phase-retrieval of optical system in combination with an iterative algorithm. The first DPE is used for demultiplexing two orthogonally linearly-polarized light beams to produce diffractive patterns, and the second DPE is used for compensating the phase difference to obtain the desired radially-polarized beam.