Huygens' principle in inhomogeneous,isotropic media and a general integral equation applicable to optical resonators

Huygens' principle is derived for short wavelengths in inhomogeneous, isotropic media from considerations of Green's second theorem and the solution to the time-independent wave-equation for a point-source in an inhomogeneous, isotropic medium. This principle leads to an integral equation for the field distribution on optical resonator mirrors, whose parameters depend only upon the geometrical-optics ABCD-matrices. The resonator parametersF, G ₁,G ₂, the resonance and stability conditions as well as the spot size of the fundamental mode at the mirrors are given as functions of A, B, C, D, for the special case of a rotationally symmetric optical system between square mirrors. The resonator parameters,F, G ₁,G ₂, are calculated by this new method for a case familiar from the literature.This work forms part of a dissertation approved by the Faculty of Electrical Engineering of the University (T.H.) of Karlsruhe.     

RADIATION PATTERN MEASUREMENTS ON A MILLIMETER-WAVE OPEN RESONATOR

Far-field radiation patterns can be used for identifying different kinds of resonant modes in a gyrotron cylindrical open resonator. The operating TE₀₂₁ mode is identified among its closest competitors TE₂₂₁ and TE₆₁₁ by measuring radiation patterns obtained experimentally based on millimeter wave source for exciting the open resonator. A good agreement between experimental and, theoretically predicted values was found.     

Open Resonator System for Automatic and Precise Dielectric Measurement at Millimeter Wavelengths

As low loss dielectric materials, ZnS, MgF₂, MgAl₂O₄ and quartz ceramic have a very important application at millimeter frequencies. However, there is little information about their dielectric properties in the millimeter wavelength band. To obtain their dielectric properties, an automatic open resonator measurement system at Ka-band is designed and constructed. The importance on the precision determination of cavity length over a broad band and the checking of a measurement system are emphasized and their solutions are put forward in this paper for the first time so far as we know. The solutions of above problems ensure the credibility and high accuracy of our measurement system. The certified measurement system after a series of checking is used to measure the above materials. Lots of measurement results show that the standard deviation of measurement error is less than 0.154% in permittivity and 20.42% in loss tangent. Meanwhile, some experimental summaries on the open resonator technique are provided. Software that controls the measurement system is developed and it improves the testing efficiency greatly.     

Open Resonators with Conducting Cylindrical Inserts. 2. Resonators with Finite-Length Mirrors

We present the results of experimental studies of controlling the spectrum and Q-factors of modes in an open resonator with a conducting cylindrical insert. The phenomenon of an increase in the diffraction Q-factor is experimentally observed for the fundamental TEM_00q mode for two resonant diameters of the conducting cylindrical insert located inside the open resonator. The features of excitation of modes in an open resonator with smooth cylindrical finite-length mirrors and in an open resonator with cutoff bevels at the mirror edges are studied. Prospects for using open resonators with conducting inserts in quasi-optical devices in the millimeter-wave range are discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 684–691, August 2005.     

Thermal lens determination of LD end-pumped solid-state laser with stable resonator by slit scanning method

A simple method to determine the thermal focal length of LD end-pumped solid-state laser with stable resonator is presented. The M² factor describing the quality of the beam can be obtained by scanning a slit through the multi-mode Gaussian beam field. The waist width of the beam and the corresponding TEM₀₀ under the same parameters of laser are then deduced through the law of multi-mode Gaussian beam propagation. Based on the standard matrix theory of stable resonator, the thermal focal length of the gain medium can be easily achieved. To show the application of this approach, the thermal focal length of an LD pumped Nd:YVO₄ laser is measured and the experimental results are in agreement with the theoretical prediction.     

光学微盘腔与三能级量子点系统中的模耦合研究

用一种全量子理论方法研究了波导、光学微盘腔与三能级量子点耦合系统的动力学过程,求出其耦合后的透射模和反射模的解析解. 由于微腔表面粗糙引起反向散射,在微腔内形成两简并回音壁耦合共振模,其耦合率为β;量子点的两激发态分别以耦合率g₁,g₂与回音壁耦合共振模产生耦合. 在实数空间里,得出透射光谱和反射光谱的数值解,这些三能级模型结果比二能级模型结果更接近真实光学微盘腔系统,能更好地显示耦合系统的动力学特性. 关键词： 模耦合 光学微盘腔 三能级量子点 全量子理论     

Measuring entanglement-induced quantum correlations in the oscillatory motion of a trapped ion

The preparation of a wide class of entangled vibrational states involving two or three phononic modes of a three-dimensional trapped ion has been reported in the literature from both theoretical and experimental points of view. Here, the time evolution of such a system from an initial condition wherein two oscillatory modes (M _x, M _y) are reciprocally entangled and both are disentangled to the third mode (M _z) is studied. By coupling one of the entangled oscillators (M _x) with the third oscillator (M _z), a correlation between the two uncoupled modes (M _y, M _z) is induced, well visible when the mean value of a suitable operator is considered. A method of measuring the expectation value of a vibrational observable is briefly sketched and then exploited in order to reveal such nonclassical behavior.     

Variational study of the ground state energy of theE−b 1,b 2 Jahn-Teller system

In this paper a variational method for the ground state energy approximation of theE−b ₁,b ₂ Jahn-Teller system is presented. This method is based on the choice of a suitable variational ground state wave function. This trial wave function — a correlated squeezed state — is used to account for the correlation and anharmonicity of the interaction between the two vibrational modes; the anharmonicity of both modes is taken into account by the squeeze effects of these modes. The ground state of mode 1 in this trial wave function is considered as a linear combination of the two displaced harmonic oscillators. The ground state energies for the linearE - e Jahn-Teller system calculated by this method are not only in good agreement with the exact diagonalization results, but they are also better than those from the previous analytical studies. Another conclusion which results from the presented model is the following one: the squeezing effect of mode 1 for the linearE - e Jahn-Teller system is substantially smaller, in contrast with the results which are presented in the previous analytical studies.     

Lattice dynamics of Al‐containing MAX‐phase carbides: a first‐principle study

A systematic study on lattice dynamics of M_{n + 1}AlC_n (n = 1–3) phases using first‐principle calculations is reported, where the Raman‐active and infrared‐active (IR) modes are emphasized. The highest phonon wavenumber is related to the vibration of C atoms. The ‘imaginary wavenumber’ in the phonon spectrum of Nb₃AlC₂ contributes to the composition gap in Nb‐Al‐C system (Nb₂AlC and Nb₄AlC₃ do appear in experiments, but there are no experimental reports on Nb₃AlC₂). The full set of Raman‐active and IR‐active modes in the 211, 312, and 413 M_{n + 1}AX_n phases is identified, with the corresponding Raman and IR wavenumbers. The 211, 312, and 413 M_{n + 1}AX_n phases have 4, 6, and 8 IR‐active modes, respectively. There is no distinct difference among the wavenumber ranges of IR‐active modes for 211, 312, and 413 phases, with the highest wavenumber of 780 cm⁻¹ in Ta₄AlC₃. The Raman wavenumbers of M₂AlC phases all decrease with increasing the d‐electron shell number of transition metal M. However, this case is valid only for the Raman‐active modes with low wavenumbers of M₃AlC₂ and M₄AlC₃. Copyright © 2015 John Wiley & Sons, Ltd.     

On surface phonons and reconstruction: Comparison of the W and the Fe (001) surface

A phenomenological surface phonon model of the (001) surface of W and Fe is used to clarify some questions related to the problem of which high-symmetry surface phonon mode is the most perspective candidate for the tungsten (001) surface reconstruction observed experimentally. Conditions are derived for the appearance and softening of the relevant modes. The ¯M ₁,¯M ₅ and ¯X ₃ modes seem to be the most promising. A few points from the current literature on the reconstruction problem are discussed. The results seem to support the idea about the general instability of the tungsten (001) surface.     

On the theory of second harmonic generation

It is shown how the theory of non-linear interaction between the modes of the open resonator, developed previously [1] and used to study resonant second harmonic generation [2], can be applied to second harmonic generation in the absence of a resonator. The conditions under which the second harmonic output, in the small conversion approximation, can be approximated by a Gaussian beam are derived.The optimum value of the focusing parameter I/z₀ (hereI is the length of the crystal, andz ₀ is one-half the confocal parameter of the fundamental beam) for the total output is shown to be 5.68 agreeing precisely with the value given by Boyd and Kleinman [3].     

Pulsed wideband orotrons of millimeter and submillimeter waves

We have developed a series of low-voltage orotrons operated in the short-wave part of the millimeter and long-wave section of the submillimeter wavelength range. The use of an open resonator as the electrodynamic system of the orotron ensures high stability of the radiation frequency and a wide band of frequency tuning. The output orotron power achieved experimentally amounts to hundreds of milliwatts, which is sufficient for many promising spectroscopy methods. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 958–963, November 2006.     

AN OPEN RESONATOR FOR PHYSICAL STUDIES

The excitation efficency of the TEM_01q oscillation of an two-mirror hemispherical open resonator (OR) is studied. The resonator is excited by the TE₀₁ wave of a circular waveguide joined in the middle of the OR plane mirror. Given the waveguide optimum size, the TEM_01q mode excitation efficiency reaches 78%. Analysis of the resonant system spectrum in the 4-mm wave region shows that this waveguide-OR system offers a single mode resonance curve across almost a 10-GHz tuning range. The TEM₀₁₁₀ mode field distribution with and without the circular waveguide in the middle of the OR plane mirror is available due to the small scatterer method. It is shown that the considered open system is suitable for measuring electromagnetic characteristics of high-loss substances and metamaterials in the short-wave end of the millimeter (mm) region as well as in the submillimeter (submm) wave region.     

Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_s, N_t and M_s, M_t, respectively, are given. The torques N_s, N_t (the angular momentums M_s, M_t), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.     

Two-mirror resonator for studying high-pressure electrodeless microwave discharge

An electromagnetic centimeter-wave quasi-optical two-mirror open resonator is studied. The eigen-frequency spectrum of the resonator is determined and the Q factor is measured. The structure of a standing wave in the resonator is visualized by an electrodeless microwave discharge. The experimental results are compared with theoretical values.     

Analysis of a right-angle conical reflector resonator by the transfer matrix method

A resonator with a right-angle conical reflector has been proposed to produce high-power CO₂ laser beams. To analyze eigenfields of the right-angle conical reflector resonator, this paper adopts and demonstrates the transfer matrix method. In this paper, the mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. The calculation results reveal that the right-angle conical reflector resonator could be used for a high-power CO₂ laser to achieve low-order modes. However, the beam quality is reduced due to the residual blind-hole, which is in accord with the experimental result.     

Formation of a Fundamental Transverse Mode in Lasers with Prismatic Reflectors

We describe the developed optical schemes of lasers with prismatic reflectors that made it possible to increase the energy yield of a TEM₀₀ mode due to change in the resonator geometry, increase in the number of passes of radiation over the active element, and more efficient use of the active medium volume. We carried out an experimental investigation of the parameters of radiation of this type of ruby lasers in the modes of free generation and switched Q for passive, active, and combined preventions of resonator losses with the use of an electrooptic shutter and a bleaching filter.     

Infrared absorptions and band widths of dilute solutions of CF3H in liquid Ar,N2, and Xe

The spectra of fluoroform (CF₃H) in the solvents Ar, N₂, and Xe have been obtained in the fundamental region (400–4000cm^?1) using a low temperature cryostat and a Fourier transform infrared spectrophotometer. Ab initio calculations at the HF/6-31G? level have been performed to obtain the calculated vibrational frequencies of the isolated CF₃H molecule and CF₃H in the presence of the solvents (Ar, N₂, and Xe). Comparison of the frequency shifts of CF₂H in solution with respect to the gas phase frequencies is made for the experimental and theoretical results. Lorentzian functions were used to fit the bands and obtain the wavenumber at the peak absorbance and the vibrational band widths. An analysis of the dynamics of relaxation has been made based on the infrared time correlation functions for three of the fundamental modes (ν₁, ν₃, and ν₄). Bandwidths, band moments, and relaxation times were obtained by appropriate fitting of the experimental correlation functions to theoretical models. In liquid argon, the temperature dependence of the second moment (M ₂) indicates that rotational relaxation explains the bandwidth of the ν₃ mode. For the ν₄ mode, the temperature dependence of M ₂ can be attributed to rotational relaxation if it is corrected with a Coriolis coupling term. The bandwidths of the ν₁ mode do not follow the rotational relaxation model, and probably vibrational relaxation is the dominant mechanism.     

Vibrational spectra of nickel metalloporphyrins: An algebraic approach

One of the most interesting areas of current research in molecular physics is the study of the vibrationally excitated states of medium and large molecules. In view of the considerable amount of experimental activity in this area, one needs theoretical models within which to interpret experimental data. Using Lie algebraic method, the vibrational energy levels of nickel metalloporphyrins like Ni(OEP), Ni porphyrin and Ni(TPP) are calculated for 16 vibrational modes. The algebraic Hamiltonian

Effect of intermode coupling on the compression of radio pulses in an oversize cavity with an interference switch

The results of an experimental investigation of the effect of intermode coupling at the exit window of a cavity on the compression of radio pulses in an oversize cylindrical cavity with an interference switch, operating on H _01(n) modes, are reported. The effect of the intermode coupling at the exit window of a cavity on the energy extraction process is analyzed in a simple model in which the interacting modes are represented in the form of a system of two coupled cavities. The results of the analysis are compared with the experimental data. Zh. Tekh. Fiz. 69, 84–86 (February 1999)