Stochastic electromagnetic beams focused by a bifocal lens

In this paper, we study the focusing of a stochastic electromagnetic beam by a bifocal lens. By taking the electromagnetic Gaussian Schell-model (EGSM) beam as an example, the changes in the spectral density, in the spectral degree of coherence, and in the spectral degree of polarization of the EGSM beam as the beam is focused by an unapertured bifocal lens are investigated. It is shown that the spectral density, the spectral degree of coherence, and the spectral degree of polarization of the focused electromagnetic EGSM beams depend upon the coherence lengths and focal lengths of the bifocal lens. The influence of the coherence lengths and the focal lengths on the focused spectral density, the spectral degree of coherence, and the spectral degree of polarization are investigated in great detail.     

Diffractive optical element used in an external feedback configuration to tune the wavelength of uncoated Fabry-Pérot diode lasers

Abstract

A diffractive optical element (DOE) has been designed, fabricated and used in an external feedback configuration to set the wavelength of operation of uncoated Fabry-Pérot diode lasers. The DOE was designed to replace the conventional elements of an external feedback system, which are a collimating lens and grating in the Littrow configuration. The goal was to simplify use of the external cavity laser by replacing the lens and grating with a single optical element while maintaining the performance that is achieved with a grating and lens. Four DOEs were fabricated with two different focal lengths and two different reflectivities. DOE external cavity lasers were tested for maximum tunable range and stability of the wavelength of operation and compared with an external cavity laser based on a lens and grating in the Littrow configuration. A 40 nm tuning range was achieved with the DOE external cavity laser and this is comparable with the tuning range of the external cavity lasers based on a grating and collimating lens in the Littrow configuration.     

Modeling, fabrication, and characterization of tungsten silicide wire-grid polarizer in infrared region

We designed and fabricated a tungsten silicide wire-grid polarizer. To examine its polarization characteristics, the transmission spectra of the polarizer were simulated using the effective medium theory. The polarizer was fabricated based on the simulation results. The transverse magnetic (TM) polarization transmittance of the fabricated polarizer was greater than 50% over the 5 mum wavelength, and the ratio of TM and transverse electric transmittance was greater than 100 (20 dB) in the infrared range. This fabricated polarizer has higher durability and better compatibility with microfabrication processes than conventional infrared polarizers.     

Tunable microfluidic microlenses

A novel type of liquid microlens, bounded by a microfabricated, distensible membrane and activated by a microfluidic liquid-handling system, is presented. By use of an elastomer membrane fabricated by spin coating onto a dry-etched silicon substrate, the liquid-filled cavity acts as a lens whereby applied pressure changes the membrane distension and thus the focal length. Both plano-convex and plano-concave lenses, individual elements as well as arrays, were fabricated and tested. The lens surface roughness was seen to be approximately 9 nm rms, and the focal length could be tuned from 1 to 18 mm. This lens represents a robust, self-contained tunable optical structure suitable for use in, for example, a medical environment.     

Achromatic hybrid refractive-diffractive lens with extended depth of focus

A method for designing achromatic hybrid refractive-diffractive elements that can produce beams with long focal depths while they preserve the entire aperture for capture of light and high transverse resolution is presented. Its working principle is based on the combination of a diffractive optical element that generates a long range of pseudonondiffractive rays and a refractive lens of opposite dispersion to form an achromatic hybrid lens. A hybrid lens with a fast f-number (f/1) that works in the entire visible wave band (400-700 nm) was designed and fabricated. Simulation results demonstrate a factor-of-10 improvement in depth of focus compared with that of a conventional f/1 lens, with matching 1-microm lateral resolution. Experimental results confirm the effectiveness of the proposed method through demonstration of an achromatic hybrid lens with better than a factor-of-7 improvement in depth of focus and 1-microm transverse resolution.     

Analysis of the focal characteristics of cylindrical lenses made of anisotropically dielectric material based on rigorous electromagnetic theory

Abstract

The focal characteristics of refractive cylindrical lenses made of anisotropically dielectric material (uniaxial crystal) are analysed based on rigorous electromagnetic theory and the boundary element method. The performances of the lenses with different f numbers are appraised for both incident waves of the TE (transverse electric) and TM (transverse magnetic) polarizations. Numerical results show that the focal performance of this kind of lens for the TE polarization and the TM polarization of incident light wave is a difference, in particular, different focal lengths, owing to the anisotropy of the material. However, for the conventional isotropic lens, the focal features for both the TE and TM polarizations are the same. It is anticipated that this new kind of lens proposed for the first time may serve as a light switching device with high speed used in the micro-optical communication.     

Controlling the three-dimensional shape of a focal spot with a three-annular-zones-polarizing filter

A linear polarization through a high numerical aperture yields an elliptical spot on the focal plane due to depolarization, which is explained by the vector diffraction theory. Depolarization results from orthogonal polarizations are generated after diffraction by a high numerical aperture lens. In this paper, it has been shown that the elliptical focal shape can be suppressed by adding perpendicular polarization to the incident beam. By a specially designed three-annular-zones-polarizing filter which modifies the linear polarization properly, the ellipticity and volume size of the focal spot are reduced from 0.395 to 0.10 and 0.405λ³ to 0.381λ³, respectively. Furthermore, the filter elongates the focal spot longitudinally by 50.9% and divides the focus into two spots longitudinally separated by 0.754λ.     

All-optical switchable holographic Fresnel lens based on azo-dye-doped polymer-dispersed liquid crystals

Fabrication of an all-optical switchable holographic liquid crystal (LC) Fresnel lens based on azo-dye-doped polymer-dispersed LCs is reported using a Michelson interferometer. It is found that, upon circularly polarized photoirradiation, the diffraction efficiency of the fabricated Fresnel lens was increased significantly in a reversible manner. We believe this is due to the anisotropy induced by reorientation of the LC molecules coupled with azo-dye molecule orientation due to trans-cis-trans photoisomerization, which modulates the refractive index of the LC-rich regions. We also studied the effect of azo dye on the polarization dependency of the fabricated lens.     

Phase function encoding of diffractive structures

We analyzed the direct sampling (DS) method for diffractive lens encoding, using exact electromagnetic diffraction theory. In addition to previously published research [Pure Appl. Opt. 7, 565 (1998)] we present what we believe to be new results for TM polarization. We found that the validity of the scalar-based DS method is even more extended for TM than for TE polarization. Additionally, we fabricated and characterized DS-encoded blazed gratings and found good agreement between the experimental and theoretical diffraction efficiencies. We analyzed quantitatively the influence of the encoding schemes DS and analytic quantization (AQ) on the quality of the focal spot. We also investigated the focal spot sizes (FWHM) and the Strehl ratios of the DS- and the AQ-encoded cylindrical lenses.     

用于OCT动态聚焦的液晶菲涅尔波带透镜研究

提出了利用液晶菲涅尔波带透镜实现光学相干层析成像(OCT)动态聚焦的方法.根据扭曲相液晶空间光调制器(TN-LCSLM)的光学特性,设计了适用于OCT动态聚焦的菲涅耳波带透镜.利用TN-LCSLM型菲涅耳波带透镜进行了变焦控制实验,焦距实测结果与设计值比较吻合.此外,本文讨论了采用TN-LCSLM型菲涅耳波带透镜实施动态聚焦涉及到的一些问题.     

Reconfigurable imaging systems using elliptical nanowires

Materials that have subwavelength structure can add degrees of freedom to optical system design that are not possible with bulk materials. We demonstrate two lenses that are composed out of lithographically patterned arrays of elliptical cross-section silicon nanowires, which can dynamically reconfigure their imaging properties in response to the polarization of the illumination. In each element, two different focusing functions are polarization encoded into a single lens. The first nanowire lens has a different focal length for each linear polarization state, thereby realizing the front end of a nonmechanical zoom imaging system. The second nanowire lens has a different optical axis for each linear polarization state, demonstrating stereoscopic image capture from a single physical aperture.     

Modeling microlenses by use of vectorial field rays and diffraction integrals

A nonparaxial vector-field method is used to describe the behavior of low-f-number microlenses by use of ray propagation, Fresnel coefficients and the solution of Maxwell equations to determine the field propagating through the lens boundaries, followed by use of the Rayleigh-Sommerfeld method to find the diffracted field behind the lenses. This approach enables the phase, the amplitude, and the polarization of the diffracted fields to be determined. Numerical simulations for a convex-plano lens illustrate the effects of the radii of curvature, the lens apertures, the index of refraction, and the wavelength on the variations of the focal length, the focal plane field distribution, and the cross polarization of the field in the focal plane.     

Drop‐on‐Demand Inkjet Printing of Thermally Tunable Liquid Crystal Microlenses

In this letter, the authors demonstrate Drop‐on‐Demand printing of variable focus, polarization‐independent, liquid crystal (LC) microlenses. By carefully selecting the surface treatment applied to a glass substrate, the authors are able to deposit droplets with a well‐defined curvature and contact angle, which result in micron‐sized lenses with focal lengths on the order of 300–900 µm. Observations with an optical polarizing microscope confirm the homeotopic alignment of the LC director in the droplets, which is in accordance with the polarization independent focal length. Results show that microlenses of different focal lengths can be fabricated by depositing successive droplets onto the same location on the substrate, which can then be used to build up programmable and arbitrary arrays of microlenses of various lens sizes and focal lengths. Finally, the authors utilize the thermal dependency of the order parameter of the LC to demonstrate facile tuning of the focal length. This technique has the potential to offer a low‐cost solution to the production of variable focus, arbitrary, microlens arrays.

     

Focal shifts in focused nonuniformly polarized beams.

We present a simple formula to evaluate the relative focal shift in a circular-aperture lens system illuminated by a nonuniformly polarized (NUP) light wave. Specifically, it is shown that the relative focal shift is determined by the effective Fresnel number. The effective Fresnel number is equal to the product of the Fresnel number of the lens aperture and the parameter sigma, which describes the uniformity of the polarization distribution of the NUP beam across the lens aperture. Some examples are given to illustrate the use of this approach. The influence of the polarization distribution of the incident NUP light wave on the polarization distribution in the axial points of the focused field is also presented.     

Possibility of an optical focal shift with polarization masks

The polarization phase shift (PPS) has emerged as an important analytical tool in optical metrology. The present study utilizes the concept of controlling the polarization phase in applications such as focal shift and automatic focusing. When elliptically polarized light, in general, is incident upon a circularly symmetric polarization mask consisting of circular and annular zones with each zone having a unique linear polarizability, the polarization-phase difference introduced between the polarization-masked zones is also circularly symmetric. With the mask at the lens aperture, the polarization phase introduced is multiplicative with the lens function and is shown to result in a shift of the Gaussian focus plane. Because the polarization phase can be controlled by variation of the polarization parameters, the effective focal length of the imaging system can be varied within a small range. A study of the point-spread functions at the shifted focal planes has shown that the quality of the focal patch in these planes is comparable with that produced by a diffraction-limited imaging system at Gaussian focus. The shift of focus can be achieved by control of the polarization of the input beam. It is anticipated that this technique may find application in areas for which dynamic focusing within a small range is required.     

Aberrations introduced by a lens made from a birefringent material

We incorporate an algorithm for ray tracing in birefringent media into a full ray-tracing package based on the Mathematica software application. To validate the package, we compare the calculated and observed wave-front aberration introduced by an optical system that comprises lenses fabricated from birefringent material. Using the package, we calculate the influence of the lens shape factor on the aberrations associated with the e-ray polarization and show that it differs significantly from that of the o-ray polarization.     

Transient thermal effects in end-pumped cryogenic Yb:YAG regenerative amplifier

The three-dimensional heat deposition of the cryogenic Yb:YAG regenerative amplifier, which is yielded by pulsed pumped laser, is derived in details based on the theory of quasi-three-level rate equations. Furthermore, the transient temperature field, stress, and strain induced by the thermal gradients in the laser crystal are analyzed by use of the finite element method. Then the thermally induced lens and depolarization in the cryogenic regenerative amplifier are theoretically studied. We find that for the pump and cooling structure which has been designed, the focal length of the thermally induced lens is about 15?m and the depolarization rate could be ignored. The maximum output energy 10.2?mJ at a repetition rate of 10?Hz with nearly TEM₀₀ mode profile is obtained using the designed pump and cooling structure.     

Imaging multispectral polarimetric sensor: single-pixel design,fabrication, and characterization

A discrete-component approach was taken to establish the operational feasibility of a novel, imaging, midinfrared, multispectral, polarimetric sensor for remote-sensing application. The sensor is designed to exploit the spectral and polarimetric characteristics of the scene as discriminants. Pixelated multispectral filters and polarization filters were designed and fabricated on sapphire and Si substrates, respectively, and both were characterized. A single-pixel spectropolarimetric composite filter was characterized by use of a Fourier transform infrared spectrometer and a Pt-Si thermal-imaging camera. The experimental results show excellent agreement with theoretical predictions.     

Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debye's approximation, we demonstrate benefits of using asymmetric to polar angle ? binary phase distributions (such as arg[cos ?] or arg[sin 2?]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.     

The novel pyridine based symmetrical Schiff base ligand and its transition metal complexes: synthesis,spectral definitions and application in dye sensitized solar cells (DSSCs)

The pyridine based azo-linked symmetrical Schiff base ligand, (E)-2,2′-((1E,1′E)-(pyridine-2,6-diylbis(azanylylidene))bis(methanylylidene))bis(4-((E)-phenyldiazenyl)phenol) (H₂L), and its Co(II), Ni(II) and Pd(II) transition metal complexes were prepared, and defined by using elemental analysis, Fourier transform infrared, UV–visible, mass, nuclear magnetic resonance spectra, molar conductance, magnetic susceptibility and thermal analysis techniques. The conductivity results pointed out the non-electrolytic nature of all metal complexes. Elemental composition, ultraviolet spectra and magnetic susceptibility data showed that the synthesized complexes are in the binuclear structure and square plane geometry. When compared to the characteristic infrared bands for the functional groups of the ligand structure with complex molecules are reached, the ligand binds to the metal atom via phenolic OH and azomethine-nitrogen. Furthermore, the dye-sensitized solar cells (DSSCs) based on H₂L and its metal complexes were fabricated, and photovoltaic properties of these devices were also investigated. The power conversion efficiency of fabricated devices based on ligand H₂L can be improved with the incorporation of the transition metal complex.