Synthesis of optical systems that reduce the divergence of a laser beam with complete minimization of aberrations

Techniques and algorithms for the design of an optical system intended for decreasing the angular divergence of laser emission created by a flat optical resonator are proposed. __________ Translated from Izmeritel’naya Tekhnika, No. 4, pp. 26–29, April, 2008.     

Mathematical simulation of the transformation of radiation formed by a plane resonator and an optical system in a paraxial approximation

A mathematical model of the transformation of radiation produced by a flat optical resonator, single lens, and a two-lens optical system with the use of the Kirchhoff scalar theory of diffraction is constructed and investigated. __________ Translated from Izmeritel’naya Tekhnika, No. 11, pp. 20–23, November, 2007.     

Description of the propagation of a radially polarized beam with the scalar Kirchhoff diffraction

Since radially polarized beams have only one magnetic field component, the azimuthal component, a scalar Kirchhoff diffraction integral can be used to describe the propagation of the magnetic field. In the far-field zone, this diffraction formula gives an analytic expression for the magnetic field from which the electric field component expressions are derived by the Faraday relation. Numerical results from these expressions correctly reflect the properties of a radially polarized beam.     

Gaussian laser beam transformation into an optical vortex beam by helical lens

In this article, we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance ζ from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of pth order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles, and radii, at any z distance behind the HL plane, as well as in the near and far field.     

光学参数对非相干光纤激光组束效果的影响

提高非相干光纤激光组束功率,需要尽可能大的光栅衍射效率。通过理论分析和数值仿真,结果表明PTR布拉格光栅存在最佳厚度,并且光栅衍射效率随着光栅频率和组束波长带宽的减小而增大。在光纤阵列宽度一定的条件下,存在最佳光栅频率值使得总体衍射效率取极大值。实际应用中应选取光栅频率200～700mm^-1,组束波长带宽0-20nm,在此基础上进一步设计组束光学系统的其他参数。     

Technique of calculating the divergence at the exit of afocal optical systems, taking aberrations into account

A flexible system of approximations by means of which it is possible to precisely compute the Kirchhoff diffraction integral is analyzed. A beam of the null component mode (TEM₀₀) at the exit from a flat hollow resonator transformed by an afocal optical system that reduces aberration is considered. The possibility of reducing aberrations by a computation of the structural parameters of the lens using a newly developed procedure is investigated. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 45–48, October, 2006.     

Influence of laser array performance on spectrally combined beam

Abstract

Incoherent spectral beam combining (SBC) of multiple laser beams is accomplished along the emitters’ arraying direction. Considering that the output beams from a laser array (LA) usually have deflection angles, positional displacements and divergence angles even after being collimated, a propagation model of SBC systems based on multilayer dielectric gratings has been built up. On the basis, properties of the spectrally combined beam affected by parameters of the LA have been discussed in detail. Simulation results show that with the increase in the deflection angle, both the power and the beam quality of the combined beam degrade dramatically. The positional displacement has little impact on the intensity distribution and the beam quality of combined beam but change the wavelength composition of the combined beam. The divergence angle strongly affects the intensity distribution and the beam quality of the combined beam. Additionally, the effect of the deflection angle on the output beam quality is more obvious and may shift the beam spot when comparing with that of the divergence angle.     

Light intensity distributions of the Gaussian laser beam through an aperture team

Based on the propagating theory of the laser beam, the propagating characteristics of the Gaussian beam through an aperture team that comprises two apertures and a convergent lens, are studied. The approximate expressions for the field distribution are derived by the diffracted integral equation in detail under the condition of approximations. In comparison with the approximate expression and the precise expression, we know that there are the approximate same results for the two expressions if the radius of the second aperture is not too large. The numerical examples are given to confirm the correctness of our calculated results.     

Noise reduction by diaphragming laser beam in the optical detection system of an atomic force microscope

We propose to use a diaphragm in order to decrease the contribution of the transverse wandering of a laser beam to the total noise level in a system of the cantilever bending measurement using laser beam deviation in an atomic force microscope (AFM). The efficacy of this method has been experimentally verified, and it was found that, using a diaphragmed laser beam, the noise level can be reduced to 0.01 nm.     

Modeling the process of propagation of a laser beam using the Kirchhoff method

Simultaneous measurement of the distribution of intensity and phase of a laser beam in an arbitrary cross-section and modeling of the behavior of the beam along the axis of propagation by means of the Kirchhoff method are proposed. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 36–39, June, 2006.     

Influence of shadowing on ellipsometric quantities of randomly rough surfaces and thin films

In this paper the formulae enabling us to calculate the values of the ellipsometric parameters of randomly rough surfaces and very thin films with randomly rough boundaries with respect to the influence of the shadowing between the irregularities of roughness are presented. These formulae are derived within the scalar diffraction theory of light. The first formula allows the calculation of the ellipsometric parameters using a numerical method, while the second formula is the approximative one but it expresses the ellipsometric parameters in a closed form. The numerical analysis of both formulae is performed for several examples of randomly rough surfaces and thin films. Moreover, the comparison of the results achieved using both formulae respecting the shadowing and an earlier formula not including this effect is performed. The experimental data of two samples of the randomly rough silicon surfaces covered with very thin surface layers are interpreted using all the formulae mentioned. Using this experimental study, the correctness of both formulae taking into account the shadowing, is confirmed.     

On the construction of a geometric constraint frame by integral manifold theory for constrained manipulators

Abstract

For industrial constrained manipulators, the interactive motion and force dynamics between the end effector and the constrained environment occur at both the normal space and the tangent space to the constraint manifold. In order to characterize such interactive behaviors, it is advantageous to develop a specific coordinate frame to facilitate the formulation of such constrained dynamics. Most previous approaches solved the problem from the algebraic viewpoint. This paper, on the other hand, develops a systematic method to construct a geometric constraint frame from the perspective of integral manifold theory. A constraint frame, distinct from previous orthogonal moving frames, behaves as a partially orthogonal coordinate system and is endowed with intrinsic geometric implications which are beneficial to the dynamic analysis and the controller design. The algebraic and geometric points of view concerning the constrained systems are compared and discussed. An illustrative example for constrained manipulators will be demonstrated.     

Observation of the geometric amplitude factor in an optical system

Abstract

By manipulating the discrete optical levels inside an optical resonator, we obtain a classical realization of a twisted Landau-Zener model. We experimentally demonstrate the geometric amplitude factor in the transition amplitude that arises for this model. We consider in particular the region of parameter space addressed in the original study of the geometric amplitude factor by M. V. Berry [7].     

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.     

Influence of spatiotemporal coupling induced by an ultrashort laser pulse shaper on a focused beam profile

4f pulse shapers have been widely used to temporally manipulate femtosecond optical pulses by spectral filtering. When the temporal waveform is manipulated with a spatial light modulator consisting of segmented pixels, the spatial profile of the output beam also varies because of diffraction at the pixel array, which is known as a spatiotemporal coupling effect. This effect produces a complicated spatio-temporal profile near the focus of the ultrashort pulses, which may affect the interpretation of experimental results obtained with shaped ultrashort pulses. We investigate the spatial intensity distribution at the focus of temporally shaped pulses through ablation experiments. The three-dimensional space-time beam profile is also numerically calculated.     

Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system

On the basis of the generalized diffraction integral formula for an ABCD optical system in the spatial domain, a propagation law for the generalized Stokes parameters of a stochastic electromagnetic beam passing through an ABCD optical system is obtained. We describe the Stokes parameters of the source as linear combinations of the elements of the cross-spectral density matrix, and study the changes in the spectral degree of polarization and in the state of the polarization ellipse of a stochastic electromagnetic Gaussian Schell-model beam propagating through a gradient-index fiber with the help of generalized Stokes parameters and the cross-spectral density matrix. The medium has significant effect on the change of the spectral degree of polarization. However, when the correlation coefficients of the source satisfy the relation delta(xx)=delta(yy)=delta(xy)=delta(yx), the medium does not influence the spectral degree of polarization.     

Analysis of the characteristics of a system for digital recording of optical signals based on an array photodetector

An experimental investigation of the characteristics of an optoelectronic digital image recording system based on a charge-coupled photosensitive device is performed. The influence of the operating modes of the system on the statistical characteristics of its two-dimensional output signals is evaluated. A technique for estimating the resolution of the recording system and the measurement error of the displacement of an element of the image by means of optical target rods is developed. Translated from Izmeritel’naya Tekhnika, No. 4, pp. 29–33, April, 2009.     

Controlled modulation of laser beam and dynamic patterning of colloidal particles using optical tweezers

We present controlled generation of complex-structured beam profiles using diffractive optical element and demonstrate multiple dynamic trapping of colloidal particles. The phase element is programmed to generate various tailored optical fields having structures, similar to that of number three, spiral, and circle but in a tractable manner. Thus, the generated spatially tailored optical fields are confined to focal volume in optical tweezers. This enabled real-time trapping of multiple microscopic objects whereby its transverse organization was controlled in a dynamic manner from one structure to another with the help of spatial light modulator. Such a controlled beam shaping finds potential applications in biophotonics, super resolution imaging, and measurement of biophysical parameters, cell sorting, and micro-manipulation of colloidal particles.     

Influence of incident beam divergence on the intensity of diffuse streaks

The influence of incident beam divergence on the length of the streak intercepted by the Ewald sphere is considered, as a relpHK·L of a faulted hexagonal crystal, mounted about itsc-axis on the goniometer head attached to the ø-circle, is brought into diffracting condition for the bisecting setting of a 4-circle diffractometer. For the special crystal mounting correction factors required to convert the measured intensities corresponding to a fixed length of the streak are derived. A procedure for experimentally verifying the mathematical approach employed in these derivations is also presented.     

Some characteristics of an extremely-short-external-cavity laser diode realized by butt coupling a Fabry-Perot laser diode to a single-mode optical fiber

When butt coupling a Fabry-Perot laser diode to an extremely closely spaced waveguide (separation less than or equal to a few times the Rayleigh range of the laser beam), there is a trade-off between the optimal power coupling and the variation of the coupled laser diode's operational characteristics. Changes in the butt-coupling configuration parameters influence the coupling efficiency, as well as the strength of the feedback into the laser diode. Using a previously reported phenomenological model that treats the butt-coupled laser diode as an extremely short external-cavity (ESEC) device, we quantitatively describe how the butt-coupling parameters can be used to control the output power, threshold current, wavelength, and relative intensity noise of the ESEC laser diode. Our analyses are supported by experimental results. The importance of choosing the correct coordinate plane for evaluation of the overlap integrals that are used in the model is also discussed.