Generation of on-demand quasi-Mathieu beams with a controlled generation of spatial spectrum of angular Mathieu-Gauss functions with a digital laser.

This study provided an intra-cavity method for the selective generation of all kinds of quasi-Mathieu beams. The method employed L-type digital lasers to selectively generate the Fourier spectrum of the gaussian-modulated angular Mathieu function. The lasing field then underwent a Fourier-transform with an extra-cavity lens, and was converted into quasi-Mathieu beams after passing through an axicon. The selection of the lasing quasi-Mathieu beams was controlled by the projection phase of the intra-cavity spatial light modulator (SLM) of digital lasers, which provided flexibility in dynamically generating on-demand quasi-Mathieu beams. The formalism of the resulting quasi-Mathieu beams is detailed in this paper. The nondiffracting characteristics of the resulting quasi-Mathieu beams were verified both numerically and experimentally. The capability of dynamically controlled generation and manipulation of lasing quasi-Mathieu beams by the proposed method is beneficial to practical applications of Mathieu beams.

Generating a geometric structure light field from a digital laser by specifying a laser cavity phase boundary with a Gaussian-convoluted target field.

This research proposed a simple method to design the projected phase boundary of the SLM (spatial light modulator) of the digital laser for the generation of a structure light field of geometric shape. In the proposed method, the phase boundary of the digital laser was designed to match the convolution field of the specified geometric structure field and Gaussian field instead of matching the specified geometric structure field. The phase boundary design suppressed the light reflected from the SLM of a high-inclination angle that is difficult to achieve stable oscillation in the laser resonator. Using the proposed phase boundary design, the laser output with energy distribution closed to geometric structures such as a quadrangular pyramid, triangular pyramid, cone, and multi-ring was produced through experiments. The geometric structure light field generated in this research will be beneficial to the related applications of photolithography and photopolymerization for making micro-elements.

Design of a high-efficiency LED low-beam headlamp using Oliker's compound ellipsoidal reflector.

This paper presents a design for a high-efficiency, low-beam headlamp with Oliker's ellipses technology [Computing Lett.2, 29 (2006)1574-040410.1163/157404006777491981]. In addition to the one-time intrinsic light absorption of reflection, the designed low-beam lampshade can reflect all the light from the LED in the on-demand illumination range. This study proposes and adopts a matrix calculation method to accelerate the calculation speed of constructing an Oliker's composite ellipsoidal reflector, which in turn increases the ellipsoidal facet number of the compound ellipsoidal reflector. In the design of the low-beam headlamp, the illumination weight on the target plane is defined by the method of curve fitting, which ensures that the light-field pattern of the low-beam headlamp changes smoothly rather than in a patchy distribution. The content of this study itself also provides a design method and example for applying Oliker's ellipses technology to on-demand spatial lighting.

Experimental Investigation of Generating Laser Beams of on-Demand Lateral Field Distribution from Digital Lasers.

A new type of laser system, known as a digital laser, was proposed in 2013. Many well-known laser beams with known analytical forms have been successfully generated in digital lasers. However, for a light field that does not have an analytical form, such as a multi-point light field or a light field with an arbitrary lateral distribution, how to generate such a light field from a digital laser has not been explored. The goal of this study was to experimentally explore how to generate an on-demand lateral laser field in a digital laser. In this study, a multi-point Gaussian laser beam was successfully generated in a digital laser by both controlling the range of the laser gain and the modulation of the phase boundary of the end of the cavity. This study then generated laser beams with an on-demand lateral field distribution by generating a superimposed multi-point laser field in a digital laser. Examples of triangles, rectangles, and letter T-shaped light fields produced by digital lasers were experimentally demonstrated. In summary, this study experimentally showed that a laser beam with an on-demand lateral field distribution could be generated in a digital laser by generating a superimposed multi-point laser field in a digital laser, in which a laser gain region covering the entire intra-cavity multi-point light field and the projected SLM (spatial light modulator) modulation function adopting a mimic amplitude mask are both used.

Dynamic control of the interference pattern of surface plasmon polaritons and its application to particle manipulation.

This study proposes a method of dynamically controlling the interference pattern of surface plasmon polaritons (SPPs) within a four-slit structure by changing the phase difference between multiple-incident Gaussian beams. The theoretical analysis of the controlling mechanism of the SPP interference field and the numerical simulation of the generation and movement of both one-dimensional and two-dimensional SPP interference fields are provided. In addition, through simulation, this study demonstrates using the controllable two-dimensional SPP interference bright spots field for manipulating particles in static liquids.

Launching of surface plasmon polaritons with tunable directions and intensity ratios by phase control of dual fundamental Gaussian beams.

This study proposes a method to achieve excitation of surface plasmon polaritons (SPPs) with tunable directions and intensity ratios on a designed two thin slit structure by the phase control of dual fundamental Gaussian beams. Simply modulating the phase difference between two incident fundamental Gaussian beams (i.e. TEM0,0 mode laser beam) controls the propagating direction of the resulting SPP wave between two opposite linear directions and also the value of the intensity ratio between propagating SPP waves in two opposite directions. The proposed method achieves a wide dynamic SPP intensity ratio adjusting range from -20 dB to 20 dB. This easy method of changing the direction of SPPs makes the dynamic control of the direction of SPP waves practicable, which shows great potential in plasmonic applications.

Characteristic matrix operation for finding global solution of one-time ray-tracing optimization method.

The one-time ray-tracing optimization method is a fast way to design LED illumination systems [Opt. Express22, 5357 (2014)10.1364/OE.22.005357]. The method optimizes the performance of LED illumination systems by modifying the LEDs' luminous intensity distribution curve (LIDC) with a freeform lens, instead of modifying the illumination system structure. In finding the LEDs' LIDC for optimizing the illumination system's performance, the LEDs' LIDC found by means of a general gradient descent method can be trapped in a local solution. This study develops a matrix operation method to directly find the global solution of the LEDs' LIDC for the optimization of the illumination system's performance for any initial design of an illumination system structure. As compared with the gradient descent method, using the proposed characteristic matrix operation method to find the best LEDs' LIDC reduces the cost in time by several orders of magnitude. The proposed characteristic matrix operation method ensures that the one-time ray-tracing optimization method is an efficient and reliable method for designing LED illumination systems.

One-time ray-tracing optimization method and its application to the design of an illuminator for a tube photo-bioreactor.

This study details a one-time ray-tracing optimization method for the optimization of LED illumination systems [S.-C. Chu and H.-L. Yang, "One-time ray-tracing method for the optimization of illumination system," in Proceedings of International Conference on Optics in Precision Engineering and Nanotechnology (icOPEN, 2013), 87692M]. This method optimizes the performance of illumination systems by modifying the light source's radiant intensity distribution with a freeform lens, instead of modifying the illumination system structure. Because illumination system structures are unchanged in the design process, a designer can avoid the common problems faced when designing illumination systems, i.e., the repeated and time-consuming ray-tracing process when optimizing the illumination system parameters. The easy approaches of the proposed optimization method to sample the target illumination areas and to divide the light source radiant intensity distribution make the proposed method can be applied to both direct-lit and non-direct-lit illumination systems. To demonstrate the proposed method, this study designs an illuminator for a tube photo-bioreactor using the proposed one-time ray-tracing method. A comparison shows that in the designing of the photo-bioreactor, tracing all rays one time requires about 13 hours, while optimizing the light source's radiant intensity distribution requires only about twenty minutes. The considerable reduction in the ray-tracing time shows that the proposed method is a fast and effective way to design illumination systems.

Numerical study of the properties of optical vortex array laser tweezers.

Chu et al. constructed a kind of Ince-Gaussian modes (IGM)-based vortex array laser beams consisting of p x p embedded optical vortexes from Ince-Gaussian modes, IG(e)(p,p) modes [Opt. Express 16, 19934 (2008)]. Such an IGM-based vortex array laser beams maintains its vortex array profile during both propagation and focusing, and is applicable to optical tweezers. This study uses the discrete dipole approximation (DDA) method to study the properties of the IGM-based vortex array laser tweezers while it traps dielectric particles. This study calculates the resultant force exerted on the spherical dielectric particles of different sizes situated at the IGM-based vortex array laser beam waist. Numerical results show that the number of trapping spots of a structure light (i.e. IGM-based vortex laser beam), is depended on the relation between the trapped particle size and the structure light beam size. While the trapped particle is small comparing to the beam size of the IGM-based vortex array laser beams, the IGM-based vortex array laser beams tweezers are suitable for multiple traps. Conversely, the tweezers is suitable for single traps. The results of this study is useful to the future development of the vortex array laser tweezers applications.

Ray-leakage-free sawtooth-shaped planar lightguide solar concentrators.

This paper details the design of a ray-leakage-free sawtooth-shaped planar lightguide solar concentrator. The concentrator combines Unger's dimpled planar lightguide solar concentrators [1] with a prism array dimpled planar lightguide solar concentrator. The use of a sawtooth-shaped boundary on the planar lightguide prevents leakages of the guiding ray after multiple reflections in the lightguide. That is, the proposed solar concentrator can achieve a higher geometrical concentration ratio, while maintaining a high optical efficiency at the same time. Numerical results show that the proposed sawtooth-shaped planar lightguide solar concentrator achieves 2300x geometrical concentration ratio without any guiding ray-leakages from the planar lightguide.

Modulation of shape and polarization of beam using a liquid crystal q-plate that is fabricated via photo-alignment.

A liquid crystal (LC) device, called a "q-plate" (QP), which is based on axially symmetric photo-alignment was investigated. The electrically tunable LC QP device could be modulated to control the shape and polarization of a linearly polarized Gaussian laser beam that propagated through it. The intensity profile and polarization distribution were simulated by MATLAB and 1D-DIMOS. The results of the simulation were consistent with experimental findings. In the fabricated electrically tunable LC QP device, switching between different beam-profile configurations can be realized by applying a voltage. Moreover, the fabrication of an LC QP is relatively simple, and the device has potential for such practical applications as beam shape modulators and spatial polarization converters use in diffractive optics and imaging systems.

Microchip solid-state cylindrical vector lasers with orthogonally polarized dual laser-diode end pumping.

We report a simple method for generating cylindrical vector beams directly from laser-diode (LD)-pumped microchip solid-state lasers by using dual end-pumping beams. Radially as well as azimuthally polarized vector field emissions have been generated from the common c-cut Nd:GdVO4 laser cavity merely by controlling the focus positions of orthogonally polarized LD off-axis pump beams. Hyperbolically polarized vector fields have also been observed, in which the cylindrical symmetry of vector fields is broken. Experimental results have been well reproduced by numerical simulations.

High-efficiency Fresnel lens fabricated by axially symmetric photoalignment method.

In this study, a Fresnel lens with radial and azimuthal liquid crystal (LC) alignments in the odd and even zones was fabricated using the photoalignment technique based on an azo dye doped in LC cells. The lens has approximately 35% focusing efficiency as determined using a linearly polarized probe beam. In addition, the lens converts the input linear polarization into axially symmetrical polarization at the focal plane. The fabricated Fresnel lens is polarization-independent and has electrically controllable focusing efficiency. Moreover, the far-field pattern of a probe beam through the device placed between the polarizers agrees with the pattern obtained from the simulation.

Electrical control of shape of laser beam using axially symmetric liquid crystal cells.

This work demonstrates the electrical tuning of laser beam shape using an axially symmetric dye-dope liquid crystal (ASDDLC) device that is fabricated using a photo-alignment method. Various beam shapes can be obtained by linearly polarized Gaussian laser beams through an ASDDLC device under various applied voltages. The far-field intensity patterns generated by laser beams of selected shapes under various applied voltages are simulated, and the results are consistent with experiment. A rotatable petal-shaped beam is obtained by controlling the polarization of the output donut-shaped beam. The tenability of beam shape of light with a wavelength of 1064 nm, which is commonly used in biomedical applications, is also demonstrated.

Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation.

This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.

Numerical study for selective excitation of Mathieu-Gauss modes in end-pumped solid-state laser systems.

This study reports a possible first systematic approach to the selective excitations of all Mathieu-Gauss modes (MGMs) in end-pumped solid-state lasers with a new kind of axicon-based stable laser resonator. The study classifies MGMs into two categories, and explores and verifies the approach to excite each MGM category using numerical simulations. Controlling both the "cavity mode gain" and the "cavity conical asymmetry" of the axicon-based stable laser resonator achieves the proposed selective MGM-excitation approach.

Chaotic oscillations associated with the breakup of polarization entangled coherent states in a microchip solid-state laser.

We demonstrate the breakup of spatial-polarization entangled lasing patterns, which possess vector phase singularities, and the resultant dynamic instabilities featuring chaotic oscillations. The frequency splitting between a pair of Ince-Gauss (IG) lasing modes, originally forming a coherent entanglement state, and a self-excited additional nonorthogonal IG mode through a new class of transverse effect of self-injection pattern seeding, is shown to result in modal-interference-induced modulation at the beat frequency, leading to chaotic oscillations.

Generation of vortex array beams from a thin-slice solid-state laser with shaped wide-aperture laser-diode pumping.

We demonstrate vortex array-beam generations from a thin-slice, wide-aperture, solid-state laser with laser-diode end-pumping. Radial and rectangular vortex arrays were found to be formed in a controlled fashion with symmetric and asymmetric pump-beam profiles, respectively. Most of these vortices exhibited single-frequency oscillations arising from a spontaneous process of transverse mode locking of degenerate or nearly degenerate modes assisted by the laser nonlinearity. Single-frequency rectangular array beams consisting of a large number of vortices, e.g., closely packed 25, 36, or 46 vortex pixels, were generated, originating from Ince-Gaussian modes excited by the asymmetric pumping.

Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer.

This paper proposes a new scheme for generating vortex laser beams from a laser. The proposed system consists of a Dove prism embedded in an unbalanced Mach-Zehnder interferometer configuration. This configuration allows controlled construction of p x p vortex array beams from Ince-Gaussian modes, IG(e) (p,p) modes. An incident IG(e)(p,p) laser beam of variety order p can easily be generated from an end-pumped solid-state laser system with an off-axis pumping mechanism. This study simulates this type of vortex array laser beam generation, analytically derives the vortex positions of the resulting vortex array laser beams, and discusses beam propagation effects. The resulting vortex array laser beam can be applied to optical tweezers and atom traps in the form of two-dimensional arrays, or used to study the transfer of angular momentum to micro particles or atoms (Bose-Einstein condensate).