Transfer matrix method for optimizing quasioptical EPR cavities

We present a convenient method for characterizing and optimizing the performance of quasioptical electron paramagnetic resonance (EPR) sample cavities. The formalism is based on the transfer matrix method used in transmission line analysis. Transfer matrix representations are defined for each of the essential components of an open resonator, and the method is demonstrated by application to selected practical examples. Emphasis is given to optimization of quasioptical EPR for aqueous biological samples.     

Use of Dirac matrices in polarization optics

Several matrix methods have been developed for studying polarization properties of light. Jones was the first to apply the matrix method to the study of polarization optics. In Jones matrix formalism the polarized wave field is represented by 2-element column matrix known as Jones Vector and the polarization device encountered by light is represented by a 2×2 matrix, known as the characteristic Jones matrix of the device. Mueller introduced a new matrix method where the wave field is represented by a 4-dimensional vector. The elements of the vector are the Stokes parameters of the beam. In Mueller matrix formalism the optical device is represented by a 4×4 real matrix known as ‘Mueller Matrix’ of the device. The use of coherency matrix also proves to the useful in the study of partially polarized light. Pauli spin matrices have been used to unify the different matrix treatments of polarization optical phenomena. The present article is an attempt to unify the analysis of polarization phenomena using Dirac matrices used by Dirac in quantum mechanics. We have however redefined the set of Dirac matrices in terms of the Kronecher product of Pauli spin matrices.     

High-field/high-frequency EPR spectrometer operating in pulsed and continuous-wave mode at 180 GHz

A novel electron paramagnetic resonance (EPR) spectrometer is reported, which has been developed to allow pulsed EPR experiments with high sensitivity and time resolution at a microwave (MW) frequency of 180 GHz (G-band) and wavelengths of approximately 1.6 mm. This corresponds to a magnetic field of about 6.4 T forg ≈ 2 signals. The “hybrid” system architecture combines components of quasioptical as well as conventional MW techniques, making it possible to achieve excellent spectrometer performance with respect to sensitivity and time resolution. Quasioptical MW components have been used to design an MW circulator allowing high sensitivity and low bias operation in the reflection mode. A miniaturized, closed-type cylindrical cavity provides a high sample filling factor and an adequate MW field strength (B₁) enhancement and thus permits reasonably short MW pulses (60 ns for a π/2 pulse) even with a moderate MW input power (15 mW at the cavity). Commercial quartz capillaries (up to 0.5 mm internal diameter) can be used as sample holders for a broad range of applications.     

X波段脉冲电子顺磁共振谱仪的矩形腔与微型平面腔的设计

为了满足脉冲式电子顺磁共振谱仪的需要,设计并制作了连续波谐振腔和脉冲谐振腔. 连续波谐振腔采用矩形谐振腔的设计,而脉冲谐振腔采用了微型平面腔的设计. 在设计阶段,使用Ansoft-HFSS三维电磁仿真软件对2种谐振腔进行模拟计算. 微型平面腔的加工采用了微纳加工技术. 制作完成的谐振腔的参数指标由网络分析仪测定. 实验测得2种谐振腔的参数指标符合理论模拟值,并满足脉冲式电子顺磁共振谱仪的要求.     

Modern description of polarized light: matrix methods

Problems involving the calculation of the passage of a polarized light beam through a succession of polarizing devices are often difficult and tedious. These may be simplified if modern methods of describing polarized light are used, namely the Stokes and Jones vectors, the Mueller and Jones calculi and the coherency matrix formalism. In this paper these concepts are presented and the vectors for various states of polarized light and the matrices of polarizers and retardation plates are given, together with examples of their method of use.     

Elastic resonances of a periodic array of fluid-filled cylindrical cavities embedded in an elastic matrix

The resonant scattering by a periodic infinite array of fluid-filled cylindrical cavities in an elastic matrix is studied. The exact reflection and transmission coefficients of the array are calculated by means of a multiple scattering formalism taking into account all the interactions between the cavities. Numerical results are next given for low frequencies for which only the longitudinal and transverse zero modes propagate. A first study based on the analysis of the transmission coefficients clearly shows that the resonances of the array can be classified into two sets: those close to the resonances of a single cavity and those due to a resonant coupling between a cavity and its nearer neighbors. The resonant coupling is due to the interaction between the whispering-gallery surface waves propagating around each cavity. In the case of cavities with very close spacing, it is observed that the dispersion curves of the waves propagating along the array can also be classified into two sets: those with a positive group velocity have cut-off frequencies that correspond to the resonances of a single cavity, those with a negative group velocity have cut-off frequencies that correspond to the resonances resulting from the strong coupling. A new method for the analysis of the resonances is presented. It is based on the properties of the scattering matrix and consists in studying the resonant eigenvalues of the scattering matrix of the array once the background is removed. For the detection of very fine resonances, as well as in the separation of several resonances very close to each other, this method proves to be more efficient than one based on the analysis of the reflection and transmission coefficients.     

新型X波段多功能EPR谱仪的设计与性能

本文设计和研制了一款新型X波段多功能电子顺磁共振（electron paramagnetic resonance,EPR）谱仪,并为其开发一款新的控制和读出系统（control and readout system,CRS）来操控微波脉冲的产生和信号的采集,提高了系统的集成度和可扩展性. 该谱仪可实现常规的连续波EPR（continuous-wave EPR,cw-EPR）、脉冲EPR（pulsed EPR）和瞬态EPR（transient EPR,trEPR）实验,并装配了6~300 K的无液氦变温装置,以及兼具平行模式与垂直模式的新型双模连续波谐振腔和用于脉冲EPR及trEPR的介质腔. 针对新型EPR谱仪和新谐振腔,本文利用双模连续波、脉冲和瞬态三个不同方式的EPR实验,对其功能进行了验证.     

Quasioptical design for an EPR spectrometer based on a horizontal-bore superconducting solenoid

We describe a novel high-frequency electron paramagnetic resonance (HF-EPR) spectrometer design based on a horizontal-bore superconducting solenoid. Designs for components of a quasioptical HF-EPR spectrometer operating with a horizontal-bore 7.85 T solenoid are discussed. A rigid concentric tube construction permits precise placement and control of the optical elements in the magnet bore. A mechanically coupled, sliding optical table bearing the quasioptical bridge is another essential feature of the design. The horizontal configuration greatly improves optical alignment as well as physical access to the sample area compared to existing vertical-bore instruments. As a result, the minimum spin concentration that is detectable with an inexpensive room-temperature diode is comparable to the lowest values reported for aqueous samples in vertical-bore magnets using high-sensitivity detectors.     

Analysis of the tuning and operation of reflection resonator EPR spectrometers

This paper investigates basic characteristics of the electron paramagnetic resonance (EPR) signal obtained from spectrometers employing reflection resonators. General equations are presented which reveal the phase and amplitude dependence on instrumental parameters of both components of the continuous wave (CW) EPR signal (absorption and dispersion). New phase vector diagrams derived from these general equations are presented for the analysis of the EPR response. The dependence of the phase and absolute value of the CW EPR signal on the local oscillator (LO) phase and on resonator offset and coupling is presented and analyzed. The EPR spectrometer tuning procedures for both balanced and unbalanced heterodyne receivers are analyzed in detail using the new phase diagrams. Extraneous signals at the RF input of the microwave receiver (resulting from circulator leakage and reflections in the resonator transmission line) have been taken into account and analyzed. It is shown that a final tuning condition that corresponds to an extremum of the receiver output as a function of the resonator frequency is necessary and sufficient for the acquisition of pure absorption signal. This condition is universal: it applies to all spectrometer configurations in all frequency ranges. High Frequency EPR spectrometer (130 GHz) data are used to generate experimental phase diagrams that illustrate the theoretical concepts presented in the paper. Conditions are presented under which the absorption signal can be measured with complete suppression of the dispersion, independent of the mutual frequency offset between the microwave source and the EPR sample resonator. Equations describing the approximate relationship between changes of the resonator properties (Q-factor and frequency) and paramagnetic susceptibility are derived and analyzed.     

On the effect of tilted roof reflectors in Martin-Puplett spectrometers

In this paper we analyze theoretically and experimentally the effect of tilt of the roof mirrors in a double pendulum Martin-Puplett Polarizing Interferometer (MPI), focusing on the polarization of the interfering beams. In principle, the tilt affects the efficiency and polarimetric properties of the interferometer. The case of a moderate resolution spectrometer is analysed in detail. Using the Stokes formalism we recover the analytical expressions for the orientation angle and the ellipticity of the beam reflected from a metallic surface, and we compute these quantities for the roof-mirror of a MPI. We find that the polarization rotation and depolarization are small. Using the Jones formalism we propagate their effect on the measured interferogram and spectrum, and demonstrate that the performance degradation is small compared to other systematic effects.     

Quasioptical hardware for a flexible FIR-EPR spectrometer

In this paper we present and summarize recent accomplishments of the Freed High Field Electron Paramagnetic Resonance group. In particular, we discuss the application of quasioptical design techniques to instrumentation problems in the far-infrared. We stress that there is no “universal spectrometer” or “universal resonator”. Rather, we demonstrate with a variety of examples from the liquid and solid state that the spectrometer configuration and the resonator used should be optimized for the experiment at hand in order to achieve the ultimate in sensitivity. Quasioptical techniques and methods of analysis offer a unified framework to analyze the expected performance of a proposed spectrometer design, as well as suggest the important control parameters for optimizing the sensitivity of a given experiment as we show in the text. The flexibility of quasioptical methods will also be demonstrated with a variety of resonator designs and sample configurations.     

单模光纤二阶偏振模色散的Jones矩阵

利用单模光纤PMD矢量与Jones矩阵之间的关系,推导了由该矢量表示的光纤二阶PMD的Jones矩阵解析表达式,利用该矩阵可以确定输出端时域脉冲在二阶PMD近似下的表达式,并由此仿真二阶PMD对信号传输质量的影响.通过比较输入与输出信号脉冲波形和眼图发现,随着传输速率和传输距离的增加输出信号劣化.最后结果表明,当主偏振态的旋转速率为零时,二阶PMD的影响可以忽略;但当其值增大时,输出信号劣化严重.在光纤通信系统设计时,需要考虑偏振模色散影响分析结果,可提供参考依据.     

Extension of the Jones matrix formalism to higher-order transverse modes

The well-known Jones matrix formalism, which can be directly applied to the propagation of the polarization of fundamental (TEM(00)) laser resonator modes, has to be modified for higher-order transverse modes. It is shown that this can be done in straightforward manner by using N x N matrices instead of the 2 x 2 Jones matrices, where N denotes the number of orthogonal polarization states of the transverse mode under consideration. The most common case of TEM(01) Hermite-Gaussian modes, where N is four, is discussed in detail.     

Simulation of a Homodyne Quadrature Displacement Measuring Interferometer

Optics and Spectroscopy - Based on the Jones matrix formalism, the paper describes the optical scheme of a single-pass homodyne displacement measuring interferometer with a quadrature principle of...     

Electronically tunable surface-coil-type resonator for L-band EPR spectroscopy

The automatic frequency control (AFC) circuit in conventional electron paramagnetic resonance (EPR) spectrometers automatically tunes the microwave source to the resonance frequency of the resonator. The circuit works satisfactorily for samples stable enough that the geometric relations in the resonance structure do not change in a significant way. When EPR signals are measured during in vivo experiments with small rodents, however, the distance between the signal source and the surface-coil detector can change rapidly. When a conventional AFC circuit keeps the oscillator tuned to the resonator under those conditions, the resultant frequency change may exceed +/-5 MHz and markedly shift the position of the EPR signal. Such a shift results in unacceptable effects on the spectra, especially when the experimenter is dealing with narrow EPR lines. The animal movement also causes a mismatching of the resonator and the 50-ohm transmission line. Direct results of this mismatching are increased noise; shifts in the position of the baseline; and a high probability of overdriving the signal preamplifier with consequent loss of the EPR signal. We therefore designed, built, and tested a new surface-coil resonator using varactor diodes for tuning the resonance frequency to the fixed frequency oscillator and for capacitive matching of the resonator to the 50-ohm transmission line. The performance of the automatic matching system was tested in vivo by measuring EPR spectra of lithium phthalocyanine implanted in rats. Stability and sensitivity of the spectrometer were evaluated by measuring EPR spectra with and without the use of the automatic matching system. The overall experimental performance of the spectrometer was found to significantly improve during in vivo experiments using the automatic matching system. Excellent matching between the 50-ohm transmission line and the resonator was maintained under all experimental circumstances that were tested. This should allow us now to carry out experiments that previously were not possible.     

光致各向异性记录介质偏振全息图的透射矩阵

在给定参、物光波的偏振态和位相差的关系以后,用光致各向异性介质记录偏振全息图的光学常数分布便被确定。这样,可以把偏振全息图看作是一种复杂的偏振元件,按照偏振元件的矩阵理论,可以求出偏振全息图的透射矩阵。透射矩阵与照明光的琼斯矢量相乘,便可以求出再现光波的琼斯矢量。 关键词：     

Generalized ellipsometry and the 4 × 4 matrix formalism

The 4 × 4 matrix formalism described by Berreman and others provides a method of determining the reflection and transmission properties of general stratified anisotropic materials. This formalism, when combined with the work of Azzam and Bashara and others on generalized ellipsometry, can be used to predict the extinction settings of a nulling ellipsometer for reflection of light from virtually any type of film covered surface provided that the surface is flat and that any films are uniform. In the present work the 4 × 4 matrix formalism is reviewed and combined with the equations necessary to predict the null settings of an ellipsometer. Examples of the application of these calculations to an optically active surface and a biaxial surface are also presented.     

Absolute EPR spin echo and noise intensities.

EPR signal and noise, calculated from first principles, are compared with measured values of signal and noise on an S-band (ca. 2.7 GHz) EPR spectrometer for which all relevant gains and losses have been measured. Agreement is within the uncertainty of the calculations and the measurements. The calculational model that provided the good agreement is used to suggest approaches to optimizing spectrometer design.     

Influence of the tilt of electro-optical crystal in an intracavity modulation laser on the light intensity

When an electro-optical (EO) crystal is used in an intracavity modulation laser, one can find that a slight tilt of the EO crystal could even result in a great influence on the output intensity of the laser. With the theories of light propagation in an EO crystal and the Jones matrix formalism, the above mentioned phenomenon is explained and an optimal configuration of the EO crystal for the intracavity modulation laser is suggested in this paper. To confirm the validity of the theoretical analysis, experiments are also performed. Their results are found to be in good agreement with those of the theoretical prediction.     

Xe-broadening coefficients of 12CH3D: a test of theoretical line shapes

We present the Xe-broadening coefficients for six lines belonging to the ν₃ band of ¹²CH₃D measured at room temperature with a diode-laser spectrometer. The collisional widths are obtained from least-squares fitting of each absorption line with theoretical line shapes. We used the well-known Voigt profile, the soft and hard collision models considering the collisional narrowing and also line shapes taking into account the speed dependence of the collisional cross-section. The results derived by these different models are compared with each other and with theoretical broadening coefficients. The calculations are based on a semiclassical impact formalism that includes the atom–atom Lennard–Jones potential for CH₃D–Xe interactions in which CH₃D is considered as a linear molecule.