Unstable resonator misalignment in ring and linear toroidal resonators

Optical axis motion in a ring resonator is investigated as a function of resonator mirror misalignment by constructing an equivalent paraxial model and applying the ray matrix formalism. Analytical expressions are derived for the optical axis motion. The paraxial model of the ring is shown to imply a linear resonator as a specific case, and the ring resonator expressions collapse to the familiar Krupke-Sooy results for that case. Using this method, new misalignment expressions are determined for more complex linear resonators. Uncorrectable misalignment conditions caused by toroidal mirror parameter errors are studied analytically and with a geometric optics code, and resulting phase front errors are given for a special case. These results are also examined as a basis for toroidal mirror quality specifications.     

Mirror tilt immunity interferometry with a cat's eye retroreflector

This paper describes the behavior of a cat's eye retroreflector, which is incorporated in a novel way in a double-pass homodyne polarization interferometer. The amount of mirror tilt immunity a cat's eye provides is calculated within the paraxial approximation using 4×4 ABCD matrices. It is found that there is a position of the target mirror in which the tilt immunity is at a maximum. A real cat's eye, which is affected by aberrations, is optimized and examined using Zemax software for optical design. The maximum amount of mirror tilt immunity is numerically calculated and written in terms of defocus and spherical aberration. Finally, for the purposes of comparison, the amplitude of the Lissajous pattern as the target mirror tilts is calculated for both an interferometer with an integrated cat's eye and an interferometer with a cube corner.     

Analytical study of the optical parameters for a multiple-path telescope

A reflecting telescope arrangement is proposed in which the focal distance of the objective system is greatly enhanced without increasing the overall length of the structure. The underlying idea is to use a multiply folded optical path. This setup may be viewed as a partially periodic optical system. For small departures of the mirror confocality, analytic results in the paraxial approximation are obtained.     

大尺寸反射镜高精度光学镜面Ni-P过渡层的制备方法

为了解决高精度光学系统中铝合金、铍反射镜易钝化、难加工的问题,采用自催化镍-磷合金作为过渡层后进行抛光的方法得到了高精度光学镜面．采用该方法所得到的镍-磷合金过渡层厚度为85gm,磷质量分数为11．88％,镀层显微硬度为730MPa镍-磷合金过渡层与反射镜结合牢固、耐蚀性较好,可通过±200℃热震试验及96h中性盐雾试验检测,适用于进行古典法抛光．经抛光后反射镜面形精度均方根值（RMS）为0．049λ（面形检测波长λ为0．6328μm）,表面疵病等级为Ⅳ级,能够满足光学系统的要求．     

Propagation properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator

Based on the scalar diffraction theory, the propagation and focusing properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator were investigated. Explicit expressions for the field distribution of the truncated beam that propagates through a paraxial optical ABCD system were derived in detail. Numerical examples are given to illustrate our analytical results.     

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.     

Measurement based on fringe reflection for testing aspheric optical axis precisely and flexibly

A method based on fringe reflection is proposed to measure the optical axis of an aspheric mirror precisely and flexibly. In the measurement, a screen displaying a fringe pattern is moved along its normal direction, and a camera is located beside and observes the fringe pattern reflected via a tested surface. This method can test the optical axis of an aspheric mirror quantitatively before measuring the absolute height of the tested surface. And it can be combined with some presented methods that need to fit the aspheric mirror according to the optical axis to measure the surface. To validate the ability of this method, it is combined with one of the presented methods to measure absolute height of an aspheric mirror precisely and flexibly. Computer simulations and preliminary experiment validate the feasibility of this method.     

Polarization aberrations. 1. Rotationally symmetric optical systems

The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed.     

神光Ⅲ原型装置中鬼像的近轴计算与分析

针对神光Ⅲ原型装置,提出了一种在复杂的光学系统中进行鬼像分析的有效方法。该方法的特点在于结合了近轴光线追迹法和二叉树的数据存储结构,能对整个神光Ⅲ原型装置中可能产生的1至多阶(最高6阶)鬼像进行全面的分析,且耗费时间较短。通过分析找出了神光Ⅲ原型装置中鬼像能量较集中的几个光学表面,它们分别是:泡克尔斯盒中一个开关的前后表面,经过主放大级后的垂直反射镜面和折返系统末端的一块透镜的后表面等,这些结果都将为设计阶段排除高能量鬼像对系统元件可能造成的损伤提供有力的参考。     

Development of a pumping laser system for x-ray laser research

A two-beam chirped-pulse-amplification Nd:glass laser system dedicated to x-ray laser research is described. Each beam provides an output energy of 20 J with a typical pulse duration of 1.3 ps. A prepulse of variable duration is generated by use of a novel, to our knowledge, optical system. A reflection optical system, comprised of an off-axis parabolic mirror and a spherical mirror, produces a line focus with 6-mm length and 165-microm width without chromatic aberration. By use of this pumping laser system, the nickel-like silver x-ray laser at a wavelength of 13.9 nm has been demonstrated.     

Propagation of a decentered elliptical Gaussian beam through apertured aligned and misaligned paraxial optical systems

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical formulas for a decentered Gaussian beam (DEGB) passing through apertured aligned and misaligned paraxial apertured paraxial optical systems are derived in terms of a tensor method. The results obtained by using the approximate analytical expression are in good agreement with those obtained by using the numerical integral calculation. Furthermore, approximate analytical formulas for a decentered elliptical Hermite-Gaussian beam (DEHGB) through apertured paraxial optical systems are derived. As an application example, approximate analytical formulas for a decentered elliptical flattened Gaussian beam through apertured paraxial optical systems are derived. Our results provide a convenient way for studying the propagation and transformation of a DEGB and a DEHGB through apertured paraxial optical systems.     

Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces. A piezoelectric transducer attached on the reference mirror can move precisely along the optical axis of the objective and permits implementation of four-step phase-shifting interferometry without changing the relative position between the CCD sensor and the test surface. Therefore, an absolutely constant optical magnification can be accurately kept to capture the interference fringe patterns resulting from a combination of light reflected from both the reference flat mirror and the test surface. The experimental result shows that surface profile on a fiber-end with surface features such as a small fiber diameter of 125 microm and a low reflection ratio of less than 4% are measurable. Measurements on a standard calibration ball show that the accuracy of the proposed setup is comparable with that of existing white-light interferometers and stylus profilometers.     

Propagation of hollow Gaussian beams through apertured paraxial optical systems

On the basis of the generalized Collins formula and the expansion of the hard-aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula for a hollow Gaussian beam propagating through an apertured paraxial stigmatic (ST) ABCD optical system is derived. Some numerical examples are given. Furthermore, by using a tensor method, we derive approximate analytical formulas for a hollow elliptical Gaussian beam propagating through an apertured paraxial general astigmatic ABCD optical system and an apertured paraxial misaligned ST ABCD optical system. Our results provide a convenient way for studying the propagation and transformation of a hollow Gaussian beam and a hollow elliptical Gaussian beam through an apertured general optical system.     

ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surfaces of the hyperboloid of revolution that separate media of different refractive indices. The analysis includes an arbitrary angle of incidence and is based on matching the optical phase at the interface. Finally, we deduce expressions for spot sizes and wave-front radii and use them to obtain the ABCD matrix. Based on the formulated ABCD matrix for refraction under paraxial approximation, we also report a simple theoretical investigation of the coupling efficiency of a laser diode to a single-mode fiber with a hyperbolic lens formed on its tip.     

Interferometer for optical coupling and mode selection in a multichannel laser array

A theoretical consideration is presented of the optical coupling and selection of laser array modes by the use of a developed Lummer-Gehrcke interferometer as a resonator reflector. Control of the mirror reflection of the proposed interferometer permits laser power to be redistributed through channels on the outlet resonator mirror; in particular, it makes it possible to lead power out of the resonator by a single beam. In this way it is possible to diminish the sidelobes in the far-field radiation profile of multichannel lasers and to raise the efficiency of the optical coupling of the laser array with waveguides and fibers. This method may be used for the redistribution of laser power on the outlet mirror in striped lasers as well.     

Propagation of anomalous hollow beams through a circular-apertured optical system

In this paper, we consider the propagation of anomalous hollow beams through a circular-apertured paraxial ABCD optical system. Based on the Huygens–Fresnel integral and the expansion of the circular aperture function into a finite sum of Gaussian functions, the approximation analytical expression of an anomalous hollow beam passing through a circular-apertured paraxial ABCD optical system is derived. Based on the approximation analytical expression, the propagation properties in free space are numerically illustrated. This method provides a convenient tool for studying the propagation and transformation properties of anomalous hollow beams passing through a circular-apertured paraxial ABCD optical system.     

Statistical ray method for deriving reflection models of rough surfaces

A statistical ray method is developed for deriving reflection models of rough surfaces. Using this method, we derive generic equations of reflection due to single scattering. We have studied an isotropic surface with Gaussian statistics, and the derived bidirectional reflectance distribution function is found with four distinct regimes, namely, mirror reflection, grazing reflection, retroreflection, and normal reflection. An explicit form of self-shadowing for a surface with Gaussian statistics is also derived, and the result agrees well with computer simulation. Our solution is useful to describe the entire reflection of a highly or moderately smooth surface and offers a basis for studying multiple scattering. While focusing on optical reflection, the approach also applies to other waves if the assumptions are satisfied.     

Grazing reflection of Gaussian beams

The reflectivities of most surfaces are higher for grazing or near-90-deg angles of incidence than for more perpendicular or near-zero-deg angles. Grazing-incidence configurations are especially important in the development of lasers and optical systems that operate in the far-ultraviolet and soft-x-ray regions of the spectrum, where transparent or highly reflecting media are almost unknown. Analytical solutions of the paraxial wave equation are obtained for the grazing reflection and complex interference effects that take place when a Gaussian beam interacts at shallow angles with a reflecting surface.     

The Membrane Light Modulator and Its Application in Optical Computers

An optical spatial phase modulator consisting of a thin polymer membrane mirror applied over a compartmented sub-structure has been devised for use as an input transducer for coherent optical computers. This device is called the ‘membrane light modulator’ or MLM. Membrane elements are 10 to 50 microns in diameter, have a sub-microsecond response time, and require only 10 picojoules per element to produce a full 360° phase reversal in reflection. An array of approximately 2000 elements is described having an active area of 4 by 4 mm. This MLM has been used as an input transducer for a coherent optical computer which takes one-dimensional Fourier transforms.     

Optical properties of pulse laser deposited AlN thin films on silicon

Aluminium-nitride thin films were deposited on silicon Si(111) substrate with pulsed laser deposition in a Riber LDM-32 system. The optical properties of the films were studied by means of optical spectroscopy with an incoherent light source mainly covering the visible range. It is demonstrated that, in comparison with an aluminium mirror, under certain deposition conditions, the film may behave as a metallic thin film as far as the optical reflection is concerned. In this case, there is an enhanced plasmonic reflection peak in the optical spectrum and the peak may be modified according to the degree of the phase transition. The microscopic structures as well as the surface topographies of the films were also studied with X-ray photoelectron spectroscopy and scanning electron microscopy. It turns out that the density and the size of the microscopic domains in the film determine whether the film remains dielectric or becomes metallic. The diamagnetic effect in the enhanced plasma increases in the process when the sample is smoothed out with the optimized nitrogen gas pressure. The nitrogen pressure is thus identified as the most influential deposition condition to the phase transition.