Electromagnetic coherence theory of laser resonator modes

A theory of open laser resonators is formulated within the framework of the electromagnetic coherence theory. It is shown that if only one Fox-Li mode contributes to the field at a given frequency, then the field at that frequency is necessarily completely coherent in view of the space-frequency counterpart of the recently introduced degree of coherence of electromagnetic fields [Opt. Express 11, 1137 (2003)]. It is also shown that the relation between the number of Fox-Li modes and the new degree of coherence is analogous to the relation established in the scalar theory of laser resonator modes. Difficulties that arise with the formerly introduced visibility-based definition of the electromagnetic degree of coherence are briefly discussed.     

A diplexer based on an open resonator with corrugated mirrors

A diplexer with a resonance frequency of 34 GHz has been created based on a four-mirror ring resonator with two corrugated mirrors. When the incident wave frequency varies by more than 20 MHz, the output wave beam is completely switched from one direction to another. A diplexer of this type can be used for discrete frequency scanning of high-power wave beams in systems for the suppression of the hydrodynamic instabilities of plasma in magnetic traps. Such diplexers can also be combined so as to form a multiplexer, which can be used in long-range multichannel communication and radar systems with synthesized frequency bands.     

Improvement of open resonator technique for dielectric measurement at millimetre wavelengths

An open resonator system is designed and constructed for the accurate measurement of complex permittivity at Ka band. It is solved successfully for the first time in how to achieve the consistency of cavity lengths corresponding to different resonant frequencies over a broad band and how to determine the proper permittivity from multiple transcendental equation roots of one sample. Many kinds of samples such as fused quartz, Teflon, quartz ceramic, MgF₂ and MgAl₂O₄ are measured and the results are in good agreement with published data. The systematic error analysis shows that the relative standard deviation of the measurement system is less than 0.172% for permittivity and 18.35% for loss tangent. The software developed to control the system improves the measurement efficiency greatly.     

Use of confocal microscopes in conoscopy and ellipsometry. 1. Electromagnetic theory

An optical system consisting of two objective lenses in a confocal arrangement is examined. It is shown that a simple algebraic relation exists between the electric field in the back focal plane of the first objective lens, which focuses the incident light, and the Fourier transform of the electric field in the focal plane of the same lens. The relation holds for high angles. If a thin object is placed in the focal plane it is possible to write the electric field by use of a Fourier transform relation at the exit aperture of the second lens. The theory is generalized for objects that are positioned at oblique angles with respect to the optical axis of the system. This configuration is clearly identical to the setup of a spatially resolving ellipsometer.     

Simplified transformation circle theory in analyzing a laser resonator

Transformation circle theory is simpler than other methods for analyzing laser resonators. In our analysis only sigma circles and simple mathematical knowledge are used to analyze the stability and calculate the parameters of the laser resonator, which further simplifies the transformation theory. The results agree well with the well-known matrix theory. Two- and three-mirror (including a thermal lens) laser resonators are used as examples to present the stability formula and the Gaussian beam dimensions at the mirrors. Furthermore, we apply the commonly used example in which the laser medium is close to the cavity mirror.     

Two-dimensional simulation of an unstable resonator with a stable core.

An optical resonator simulation code based on the idea of a partially coherent optical field has been developed and used to optimize the design parameters of an unstable resonator with a stable core. The resonator was intended for use with low-gain, large-bore lasers, such as the chemical oxygen-iodine laser (COIL). First the design parameters of the resonator were optimized by the simulation code; then a set of mirrors was fabricated for a small-scale COIL. A 14-W output with M(2) = 29 was obtained. The experimentally obtained results were in good agreement with calculations.     

The open resonator with a longitudinally placed dielectric film in measurement technique

The case when a thin dielectric film is placed longitudinally in an open resonator is considered. When measuring the parameters of the film this arrangement enables one to increase the volume of material introduced into the field without any appreciable distortion of the field of the open resonator and also increases the deviations of the measured parameters.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 50–51, October, 1993.We wish to thank V. N. Apletalin for his help with the experiment.     

Characterization of scattering in an optical Fabry-Perot resonator

Roughness-induced scattering affects the performance of a resonator. We study the scattering of a single mirror first and compare the result with the losses of a two-mirror Fabry-Perot resonator. Besides some standard tools to characterize the losses, a new method based on the spectrally averaged transmission is introduced.     

Thermoelastic damping in a micro-beam resonator using modified couple stress theory

In this paper, analytical expressions for the quality factor (QF) of thermoelastic damping (TED) applying modified couple stress theory (MCST) are presented for plane stress and strain conditions. For gold and nickel micro-beam resonators, which have a considerable length-scale parameter as case studies, the effect of the length-scale parameter on the QF of TED has been discussed in details. Results for the QF of TED show that when the beam thickness is close to the length-scale parameter of the material, the MCST diverges from the classical theory; otherwise, the two theories converge to each other. Also critical thickness variation due to applying MCST is studied.     

Multilayered optical memory with bits stored as refractive index change. I. Electromagnetic theory

With the Lippman-Schwinger equation, dyadic Green's functions, and the vector coherent transfer function method, an electromagnetic theory of a waveguide multilayered optical memory is first developed for the static case, from which a theory describing a conventional multilayered optical memory with bits stored as a refractive index change is also derived. In addition, the formulas for readout signals and cross talk are given, and some problems of numerical calculations are discussed. The theories can be used effectively for optimum design of a multilayered optical memory with bits stored as a refractive index change.     

Electromagnetic properties of liquid nitrogen nanolayers on the surface of various substances measured in microwave resonator

Parameters of a microwave resonator containing various substances have been measured on cooling to low temperatures in the frequency range of 12–17 GHz. It is established that the resonance frequency and maximum transmitted microwave power of the resonator sharply change at a temperature of −196°C. The observed effect is explained by the appearance of highly conducting layers at the boundary between the adsorbed liquid nitrogen film and solid substrate.     

Eigenfields and output beams of an unstable Bessel-Gauss resonator

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreover, based on the eigenfields across two mirrors that resulted from the transfer-matrix method, we simulate the field distributions in the cavity and the propagation of output beams by means of the angular spectrum method. The computation results show that the UBGR easily produces a fundamental Bessel-Gauss mode of good quality, and the output beams retain the original Bessel-Gauss distribution during propagation.     

Investigation of thermoelastic damping in rectangular microplate resonator using modified couple stress theory

Thermoelastic damping is a significant energy lost mechanism at room temperature in micro-scale resonators. Prediction of thermoelastic damping (TED) is crucial in the design of high quality MEMS resonators. In this study the governing equations of motion and the thermal couple equation of a microplate with an arbitrary rectangular shape are derived using the modified version of the couple stress theory. Analytical expressions are presented for calculating the quality factor (QF) of TED in a rectangular microplate considering the plane stress and plane strain conditions. As a case study, a rectangular microplate resonator is considered with material property of gold that has a considerably high value of length-scale parameter in comparison with silicon and the effect of the length-scale parameter on the QF of TED is discussed in detail. The relation between QF and temperature increment for microplates with clamped boundary conditions based on plane stress and plane strain models are studied and results obtained by considering classical and modified couple stress theory (MCST) are compared. The effect of thickness of the plate on the rigidity ratio is studied and the critical thickness which is an important design parameter is obtained using the MCST for three boundary conditions. Variations of TED versus the plate thickness for various boundary conditions according to the classical and the modified couple stress theories are investigated.     

Study of deflection and damping in microbeam resonator based on microstretch thermoelastic theory

This article deals with the deflection and thermoelastic damping analysis in homogeneous, isotropic, micropolar microstretch generalized thermoelastic thin beam based on Euler–Bernoulli theory. Analytical expressions for deflection, thermoelastic damping, frequency shift, temperature distribution and microstretch functions have been obtained for various boundary conditions viz. clamped, simply supported and cantilever beam by using Laplace transform technique. The analytical results have been numerically analyzed with the help of MATLAB software in case of magnesium like materials. The computed results have been presented graphically in view of various boundary conditions.     

Generation of radially polarized beams with an image-rotating resonator

We show how a passive image-rotating optical resonator can be used to convert a linearly polarised, lowest-order Gaussian beam into a radially polarized beam. The image and polarization rotation of the cavity removes the frequency degeneracy of the modes, making it possible to select the radially polarized mode by cavity tuning. With the addition of gain, the same cavity should operate as a radially polarized laser when injection seeded at the proper wavelength.     

Capacitance theory of open quantum systems with classical contacts

We consider semiconductor devices composed of a small quantum structure as the active device region and two classical environments constituting the source- and the drain contact. The contacts are taken as free electron gases with infinite conductivity defining the chemical potentials in the contacts. The transport through the quantum structure is described in the Landauer–Büttiker formalism using electronic scattering wave functions which determine the electron density in the quantum system. In our Hartree approximation these charges and the induced charges in the contacts are the sources of the self-consistent Coulomb field. As a particular quantum structure we study a GaAs heterostructure device consisting of a two-dimensional electron gas sandwiched between a gate contact and an AlGaAs blocking barrier [see V.T. Dolgopolov et al., Phys. Low-Dim. Struct. 6 (1996) 1]. We demonstrate the quantitative agreement of our theory with the experimental results.