The research in the field of gradient-index optics provided at the Institute of Applied Optics is reviewed. In particular, achievements in Luneburgs lens theory, measurements of refractive index profiling of gradient index elements and technology of GRIN optics making using ion- exchange in glass during the thermodiffusion process are presented. The bibliography of this work was done.

A general set of formulae for calculating the optical paraxial parameters of spherically surfaced GRIN lens with arbitrary index profile has been derived and some special cases are discussed, which show that the GRIN lens with unique properties has its superiority in some cases in addition to its more freedoms to correct the aberrations.

Weak nonlinear process of propagation of short optical pulses in graded-index light guides with the quadratic dependence of the refractive index on the transverse coordinate and a slight dependence on the longitudinal coordinate is modelled with the nonlinear wave equation. Transverse distribution of the wave field is shown to be characterized with the parabolic cylinder functions, and the nonlinear Schroedinger equation with variable coefficients is obtained for the pulse envelope. A solution of this equation describing a soliton pulse is found for a class of longitudinal inhomogeneities and formulae are presented for variations of amplitude, shape and velocity of the pulse during its propagation.

One of the most powerful features of the computer is the ability to deal with symbolic formulae. Three of the most widely distributed computer algebra systems: Derive XM, Mathematic and Reduce have been tested for evaluation of exact formulae of fifth-order aberrations of GRIN media of cylindrical symmetry.

We study propagation of gaussian beam through an inhomogeneous planar optical waveguide whose refractive index profile is characterize by the hyperbolic secant function n²(x) equals n₀²sech²((alpha) x). It is shown that this profile can contract, expand or maintain the width of a beam incident with the beam waist at the input end of the waveguide. We also obtain an analytical expression for the mode width of the fundamental mode of the hyperbolic secant media.

Several designs to obtain quasi-free spherical aberration rods are shown in this work, using GRIN elements with curved faces. We develop appropriated merit functions to minimize and show results to apply in general optical systems.

An optical isolator with GRIN lenses has been developed. The device operates in 1.55 micrometers wavelength range. Its isolation appears to be better than 40 dB with an insertion loss of 0.5-0.6 dB and polarization sensitivity lesser than 0.1 dB.

This paper is devoted to the theoretical analysis of the modal properties of planar antiresonant reflecting optical waveguides (ARROWs) with graded-index core layers. It is shown, that the presence of antiresonant cladding layers beneath the core results in reduction of the number of guided modes, which enables the single-mode operation of the waveguides with thicker cores. Spatial properties of the modes are also investigated with emphasis on the variation of field profiles with the parameters of the cladding layers. The analysis is restricted to the lossless planar ARROW configuration and bound ARROW modes.

Loci of the optical admittance of GRIN thin films are studied. We have investigated by means of the computer modeling, how the trajectory of the loci will change if the layer will have a different inhomogeneity coefficient. During the modeling we have employed a method of discretization of the GRIN layer by dividing the layer to sublayers which have equal thickness and constant refractive index. We have also examined how these loci will be affected by absorption in the layer, determined by different values of the extinction coefficient. Layers are assumed to be deposited on the bare glass substrate or substrate with a quarter- or eight-wave optical thickness layer. Results may be applied to the interpretation of the monitoring signals of the thin-film optical monitors.

Manufacturing problems concerning glasses used for making of GRIN type lenses have been presented. The most important requirements to glass quality is its high chemical and physical homogeneity. The results in obtaining of GRIN structure made of glasses melted on a laboratory scale in electrical resistance furnace as well in induction furnace have been presented. The quality of the glasses obtained has been compared with the glass melted in Optical Glass Works in Jelenia Gora. It has been determined the direction of the glass homogeneity optimization by the use of the single-step method of glass rods manufacturing by pulling them from the induction heated crucible.

Gradient-index lenses have been made form phosphate glass containing silver by exchange of Ag⁺ ions from glass for Na⁺ ions from salt. The refraction index profiles of these lenses have been measured and the parabolic profile has been produced by the method of diffusion and annealing glass after diffusion. Maximum (Delta) n is equal approximately -0.067 for axial diffusion and for the parabolic profile maximum (Delta) n approximately equals -0.032. Diameters of obtained lenses range from 4.6 to 7.8 mm.

Various gradient optical waveguides (OWs) made in glasses and crystals made by diffusion method are studied. In particular, OWs with step, exponential, parabolic, and secant hyperbolic refractive index profiles were investigated. To achieve minimum optical losses while hybridization of the circuit with storage of the desired mode structure, radiation power, wavelength and so on, the optimization was carried out. Design possibilities of integrated optic circuits on the basis of gradient OWs are shown.

New possibilities of photochromic glasses ceramics for integrated and gradient optics have been shown. The ion- exchanged technique for waveguide fabrication was developed. T he waveguides with gradients of refractive index, absorption, and photosensitivity were made. Photoinduced light absorption effects and photosensitive properties of these structures have been studied. Spacing and polarizing selectors of waveguide modes were made.

Manufacture of continuous-phase diffractive free-space elements by thermal ion exchange in glass has been proposed and demonstrated. In contrast to aiming at binary phase modulation by trying to minimize the inevitable lateral diffusion, side diffusion to obtain a smoothly carrying continuous phase profile was deliberately employed. This can be done if the mask aperture configuration and ion exchange time are numerically optimized to result in the desired optical function.

Preparation of radial gradient refractive index glass rods has been undertaken using alcoholate sol-gel method. The investigation were carried out on two oxide systems SiO₂-TiO₂ and SiO₂-Bi₂O₃. To obtain the gradient of the chemical composition determining the refraction gradient the controlled leaching of gels in HCl was carried out. Materials after leaching were heated up to 950 degrees C at controlled rate. As a result of thermal treatment of leached gels there were obtained bulk glasses in the form of rods with dimensions: length approximately equals 20 mm; diameter approximately equals 2-3 mm. The radial distribution of refractive index in the obtained glass rods was examined in the transmission interference microscope. Applying the X-ray microfluoresence analysis, using capillary optics the profiles of bismuth and titanium concentration were determined for the rods cross-section. On this basis the diffusion parameters D for titantium and bismuth have been calculated.

The growing number of instruments measuring the characteristics of components of fiber-optical data transmission (FODT) systems increases the importance of instrument verification and calibration. To solve these problems it is necessary to have a metrological protection system in this field. This report gives consideration of the problems of metrological protection and possible ways of their solution. The major methods and hardware designed until now in Russia for metrological protection of the given application area are described. More attention is paid to parameters of passive components of FODT systems.

Wavefront shear microinterferometric techniques are discussed as far as they apply to the determination of refractive index profiles of optical GRIN fibers. Special emphasis, however, is placed on a double-refracting microinterferometer with variable wavefront shear developed by the author of this paper more than 30 years ago and then used by a number of researchers for profile refractometer of both fiber and planar lightguides. The microinterferometer incorporates birefringent prisms of Wollaston's type which are capable of giving both fringe-field and uniform-field interference patterns with various wavefront shear. The basic feature of this systems is a combination of two simultaneously acting birefringent prisms localized in the image space of the microscope objective. Recently this instrument was used to phase-stepping transverse interferometry of GRIN fibers and planar waveguides and professionally computerized in its commercial version.

Fabrication of the single modal channel waveguides in lithium niobate with a large waveguide-substrate index difference meets technological and material difficulties. It has been proved during our experimental work that because of the photolithography limitations low index increase in the channel region resulting in monomodal waveguiding needs more sophisticated technology. The waveguiding effect arises in the processed region in an annealing carefully performed after proton exchange. The precise control of redistribution of the dopant is realized by m-line spectroscopy of the processed area at the wavelength (lambda) ' < (lambda) _op-operation wavelength. The method of precise control of waveguiding properties at (lambda) ' is especially useful for manufacturing of the optical switches aimed at the wavelengths of the transmission bands of long-distance communication fibers.

The simple nondestructive method for reconstruction of the refractive index distribution in the waveguide cross section is presented. Waveguide surface immersing and the interferometric method of registration are utilized in this technique. The interference model is discussed.

The paper presents a modified method of attenuation measurement in planar optical waveguides using two prism couplers. In this method, the output prism has been replaced with the immersion coupler. The assumed solution ensures the maintenance of constant coupling conditions when leading out the wave from the tested planar waveguide, at the moments when the length of propagation distance in the waveguide undergoes changes. The method enables the attenuation measurement of a selected mode. Furthermore,t he assumed solution makes it possible to automation the measurement process.

In this paper are presented numerical optimizing investigations of planar polarimetric interferometer made by K⁺-Na⁺ ion exchange in glass for sensor applications. Two cases are considered: phase modulation of guided light waves caused by refractive index changes of the waveguide cover for applications of the polarimetric interferometer as refractometers or chemical sensors, and phase changes induced by nanometers of a dielectric layer separated from the waveguide by an air gap of the width below wavelength of light for using of the polarimetric interferometer as an acoustical transducer and pressure or displacement sensor.

A new interference method for measurement of the refractive index of glass has been developed. The method is based on the Mach-Zehnder interferometry and GRIN elements are used for a scale of refractive index. Cone, pyramid or wedge elements are privileged in this method. Both the object under study and GRIN elements are placed in an oil immersion container, then oil is heated until the specimen becomes invisible. For such a situation the interference fringes produced by the GRIN standard are analyzed. The accuracy of refractive index measurements is equal to +/- 0.00001.

The influence of thermally induced GRIN effects on the output characteristics of cw diode pumped lasers was investigated theoretically and experimentally. Several configurations of cavity and pump geometry were examined. The changes of the Rayleigh range, waist size and divergence were observed with the changes of pump power. A thermally aberrated Bessel-like beam was observed for high intensities of a pump. Satisfactory accordance between theoretical predictions and experimental results was demonstrated.

A symmetrization procedure for astigmatic laser-diode beams with different values of beam propagation factors M_x² and M_y² by means of a conversion into twisted beams of axisymmetrical X-shaped variance matrix is proposed. Properties of the symmetrization are analyzed and practically realizable optical systems consisting of twisted, cylindrical lenses or GRIN lenses rate presented. The modified 4 by 4 matrix notation which is closely connected with the common 2 by 2 matrix notation is proposed.

The investigation and utilization of noncritical phase matchings in optical devices is a new focus for bulk and integrated nonlinear optics research. The use of vectorial group and multiple noncritical phase matchings of the sum- and difference-frequency generation in nonlinear crystals permits both to extend essentially the tuning range of the wide-band conversion to cover practically the entire transparency region of a crystal and attain the bandwidth of conversion of the order of 10³ cm^-1 in the mid- IR and the near-IR spectral region. We discuss where possible applications of noncritical phase matchings.

The paper presents the design of nonpolarizing beam- splitters inside a glass cube, which bases on quarter-wave layers at (lambda) ₀ equals 632.8 nm and 45 degrees incidence angle. This example shows the design for achieving a 50 percent reflectance and 50 percent transmittance at (lambda) ₀ for both polarization states.

The paper presents transmission diffraction gratings as radiation splitters. The solution of the diffraction integral is obtained by expansion in Fourier transform. The resulting analytic expression facilitates consideration of phase gratings of any shallow profiles and is convenient for fast numerical computation. Such computation has been carried with splitting coefficient and its error taken into consideration. We obtain optical signals from triangularly, rectangularly and sinusoidally shaped grooves.