Generation of high-order optical vortices using directly machined spiral phase mirrors

We report on the generation of high-order optical vortices by spiral phase mirrors (SPMs). The mirrors are produced by direct machining with a diamond tool and are shown to produce high-quality optical vortices with topological charges ranging from 1 to upwards of 100 at a wavelength of 532 nm. The direct machining technique is flexible and offers the promise of high-precision, large-diameter SPMs that are compatible with high optical powers.     

Propagation of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system

Based on the generalized Huygens–Fresnel integral, analytical expressions for the mutual coherence function, the spatial complex degree of coherence, and the effective size of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system have been derived. As a numerical example, the propagation of a partially coherent higher-order cosh-Gaussian beam through an optical Fourier-transforming system with a limiting aperture is illustrated. The normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size for the partially coherent higher-order cosh-Gaussian beam are numerically demonstrated in the observation plane. The influences of the spatial coherence length and the limiting aperture on the normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size are also examined in detail.     

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems is investigated based on the generalized Collins formula for treating the propagation of a partially coherent beam through such optical systems. Analytical formulas for the cross-spectral density of a partially coherent Hermite-Gaussian beam propagating through such optical systems are derived. As an application example, we derive the propagation formulas for a partially coherent flattened Gaussian beam by expressing it as a superposition of a series of partially coherent Hermite-Gaussian beams by using polynomial expansion. The focusing properties of a partially coherent Hermite-Gaussian beam focused by a thin lens are studied as a numerical example.     

Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics

We report the experimental observation of the fractional Fourier transform (FRT) for a partially coherent optical beam with Gaussian statistics [i.e., partially coherent Gaussian Schell-model (GSM) beam]. The intensity distribution (or beam width) and the modulus of the square of the spectral degree of coherence (or coherence width) of a partially coherent GSM beam in the FRT plane are measured, and the experimental results are analyzed and agree well with the theoretical results. The FRT optical system provides a convenient way to control the properties, e.g., the intensity distribution, beam width, spectral degree of coherence, and coherence width, of a partially coherent beam.     

Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication

A partially coherent quasi-monochromatic Gaussian laser beam propagating in atmospheric turbulence is examined by using a derived analytic expression for the cross-spectral density function. Expressions for average intensity, beam size, phase front radius of curvature, and wave-front coherence length are obtained from the cross-spectral density function. These results provide a model for a free-space laser transmitter with a phase diffuser used to reduce pointing errors.     

Scattering coherent and partially coherent space-time pulses through few-mode optical systems

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.     

Generation of partially coherent diffraction-free fields with tunable geometry

The synthesis of diffraction-free fields with different profiles is described. The synthesis is done by illuminating a screen containing a circular slit with a cosine beam. The treatment is equivalent to the modulation of the slit transfer characteristics and makes possible a tunable interference interaction of Bessel beams with noncommon axes. These results are generalized, and it is shown that coherent diffraction-free fields with arbitrary profiles can be expressed as the superposition of shifted zero-order Bessel beams and temporary parametric representations of the shifted functions. Diffraction-free fields with partially coherent features can be obtained. Experimental results are shown for each case.     

Propagation-induced polarization changes in partially coherent optical beams

Propagation of a partially coherent optical beam inside a linear, nondispersive, dielectric medium is studied, taking into account the vector nature of the electromagnetic field. Propagation-induced polarization changes are studied by using the Gaussian-Schell model for the cross-spectral-density tensor. The degree of polarization changes with propagation and also becomes nonuniform across the beam cross section. The extent of these changes depends on the coherence radius associated with the cross-correlation function. For optical beams with symmetric spectra, the bandwidth of the source spectra is found to play a relatively minor role.     

Propagation of a partially coherent beam from an unstable resonator through turbulent atmosphere

The influence of atmospheric turbulence on the propagation of a partially coherent beam from an unstable resonator was studied numerically. The resonant mode of the unstable resonator is obtained by iterative calculation using the Huygens–Fresnel formula. Also, using the extended Huygens–Fresnel integral, the intensity distribution of a propagating laser beam is calculated for different conditions. The influence of turbulence on the profile of partially coherent beams of an unstable resonator is studied. The effects of geometrical parameters of the resonator on the far-field beam profile are investigated. The results show that an unstable resonator with higher magnification has a superior far-field beam profile under partial coherency and turbulence conditions.     

Rotational frequency shifts in partially coherent optical fields

We study the frequency shifts taking place when a random, stationary optical field rotates with respect to an observer. The field is expanded in terms of fully coherent Laguerre-Gaussian basis modes, for which the rotational frequency shifts have been studied previously. We demonstrate the formalism by considering the spectrum of a Gaussian Schell-model field, and show that for a spatially highly incoherent field, significant spectral changes can be expected.     

部分相干平顶光束的实验研究

本文利用对入射光进行相干度调制的方法,在实验上研究了聚焦光场中的部分相干平顶光束,用CCD记录了光束的产生和演变过程,验证了聚焦光场中部分相干平顶光束的存在.此外,还研究了对于不同的聚焦透镜焦距和环形光阑中心拦截比,不同空间相干度对平顶光束的影响.研究表明,两处平顶光束的大小及两处平顶光束之间的距离随着空间相干长度和环形光阑拦截比的增大而减小,随聚焦透镜焦距的增大而增大.     

A class of partially coherent beams carrying optical vortices

A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.     

Optical superresolution of focused partially spatially coherent laser beams

We report design theories of a diffractive superresolution element (DSE) to implement optical superresolution of focused partially spatially coherent laser beams. The design problem of the DSE can be transformed into a problem of linear programming to obtain a globally optimal solution. By using the design theories, some fundamental limits of optical superresolution of focused partially spatially coherent laser beams are proposed, and several design examples are provided. As expected, both the fundamental limits and the design examples show that worse spatial coherence will cause worse superresolution performance. The design theories provide a design approach with partially coherent beams and may be useful for other design problems under partially coherent illumination.     

Target-based coherent beam combining of an optical phased array fed by a broadband laser source

The target-based phasing of an optical phased array (OPA) fed by a broadband master oscillator laser source is investigated. The specific scenario examined here considers an OPA phasing through atmospheric turbulence on a rough curved object. An analytical expression for the detected or received intensity is derived. Gleaned from this expression are the conditions under which target-based phasing is possible. A detailed OPA wave optics simulation is performed to validate the theoretical findings. Key aspects of the simulation set-up as well as the results are thoroughly discussed.     

Topology optimization for optical microlithography with partially coherent illumination

This article revisits a topology optimization design approach for micro‐manufacturing and extends it to optical microlithography with partially coherent illumination. The solution is based on a combination of two technologies, the topology optimization and the proximity error correction in microlithography/nanolithography. The key steps include (i) modeling the physical inputs of the fabrication process, including the ultraviolet light illumination source and the mask, as the design variables in optimization and (ii) applying physical filtering and heaviside projection for topology optimization, which corresponds to the aerial image formulation and the pattern development processes, respectively. The proposed approach results in an effective source and a binary design mask, which can be sent directly to fabrication without additional post‐processing steps for proximity error correction. Meanwhile, the performance of the device is optimized and robust with respect to process variations, such as dose/photo‐resist variations and lens defocus. A compliant micro‐gripper design example is considered to demonstrate the applicability of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam

The fractional Fourier transform (FRT) is applied to a partially coherent off-axis Gaussian Schell-model (GSM) beam, and an analytical formula is derived for the FRT of a partially coherent off-axis GSM beam. The corresponding tensor ABCD law for performing the FRT of a partially coherent off-axis GSM beam is also obtained. As an application example, the FRT of a partially coherent linear laser array that is expanded as a sum of off-axis GSM beams is studied. The derived formulas are used to provide numerical examples. The formulas provide a convenient way to analyze and calculate the FRT of a partially coherent off-axis GSM beam.     

Propagation properties of a partially coherent anomalous hollow vortex beam in uniaxial crystal orthogonal to the optical axis

The concept of a partially coherent anomalous hollow vortex beam generated by a Schell-model source was introduced in this paper. Next, the analytical expressions of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal orthogonal to the optical axis were derived, and the evolution properties of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal were illustrated using numerical examples. Finally, the influences of the uniaxial crystal and the beam parameters on the spreading properties of partially coherent anomalous hollow vortex beam were analysed in detail.     

Performance of diffractive optical elements for homogenizing partially coherent light

The effectiveness of different types of diffractive optical element (DOE) for homogenizing partially coherent beams is analyzed, both analytically and numerically. The effectiveness is described by the homogenizing parameter, defined as the inverse of the normalized variance of the dose distribution. For an important class of DOEs designed with common discrete-Fourier-transform methods, it is found that the homogenizing parameter is only of the order of the number of coherence cells in the illuminating beam. However, for a different type of DOE that produces distinct beams under coherent illumination, the homogenizing parameter can be an order of magnitude higher. The inherent dehomogenizing effect caused by the limited temporal duration of the beam, a phenomenon sometimes referred to as dynamic speckle, is also considered.     

Polarization changes of partially coherent pulses propagating in optical fibers

We consider polarization changes of partially coherent pulses propagating through birefringent dispersive fibers in the linear regime. We show that the evolution of the degree of polarization across such pulses is determined not only by the coherence properties of the pulse in the source plane, but also by the spatial walk-off introduced by the group-velocity mismatch between the two polarization components. The interplay between these two factors determines the asymptotic value of the degree of polarization of an initially unpolarized statistical pulse. We compare our results with previously discussed coherence-induced polarization changes of partially coherent beams propagating in free space.