Detection of electron paramagnetic resonance absorption using frequency modulation

A frequency modulation (FM) method was developed to measure electron paramagnetic resonance (EPR) absorption. The first-derivative spectrum of 1,1-diphenyl-2-picrylhydrazyl (DPPH) powder was measured with this FM method. Frequency modulation of up to 1.6 MHz (peak-to-peak) was achieved at a microwave carrier frequency of 1.1 GHz. This corresponds to a magnetic field modulation of 57microT (peak-to-peak) at 40.3 mT. By using a tunable microwave resonator and automatic control systems, we achieved a practical continuous-wave (CW) EPR spectrometer that incorporates the FM method. In the present experiments, the EPR signal intensity was proportional to the magnitude of frequency modulation. The background signal at the modulation frequency (1 kHz) for EPR detection was also proportional to the magnitude of frequency modulation. An automatic matching control (AMC) system reduced the amplitude of noise in microwave detection and improved the baseline stability. Distortion of the spectral lineshape was seen when the spectrometer settings were not appropriate, e.g., with a lack of the open-loop gain in automatic tuning control (ATC). FM is an alternative to field modulation when the side-effect of field modulation is detrimental for EPR detection. The present spectroscopic technique based on the FM scheme is useful for measuring the first derivative with respect to the microwave frequency in investigations of electron-spin-related phenomena.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

1.1-GHz continuous-wave EPR spectroscopy with a frequency modulation method

Continuous-wave EPR spectroscopy using a frequency modulation (FM) scheme was developed. An electronically tunable resonator and an automatic tuning control (ATC) system were used. Using the FM scheme instead of magnetic field modulation, we detected EPR absorption at the first derivative mode. We used a microwave frequency of 1.1 GHz in the present experiment. Similar signal-to-noise ratios were obtained with conventional field modulation and the FM method, and a low-quality factor EPR resonator was not necessary to suppress the significant microwave reflection from the resonator. The FM method with a tunable resonator may be an alternative solution to achieving phase-sensitive detection, when the side-effects of magnetic field modulation, such as microphonic noise and mechanical vibration, are detrimental for EPR detection.     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

EPR在体测量专用调制磁场驱动装置

利用电子顺磁共振（electron paramagnetic resonance,EPR）在体测量人牙齿可以实现无损伤地快速评估人体辐射剂量,具有实际应用价值.本文针对EPR在体测量牙齿剂量的应用特点,研制了专用调制磁场驱动装置,包括功率放大器、调制磁场激励线圈、调制频率设定模块、感应型调制幅度显示模块等.功率放大器采用脉冲功率放大方式取代传统的线性放大方式,用多N-MOSFET管H桥电路,功率容量大、效率高、结构简单,且调制频率设定自如.实验结果表明：（1）此装置可在大于9 cm磁极间距的中心样品位置产生调制幅度为0~0.9 mT的调制磁场,调制频率为10~100 kHz;（2）用该装置与EPR在体测量谱仪配合使用,可以明显观测到1,1-二苯基-2-三硝基苯肼（1,1-diphenyl-2-picrylhydrazyl,DPPH）样品谱线调制增宽过程以及辐射诱发的整体牙齿中的自由基信号,验证了该装置的高调制效率和实用性.     

基于波长调制技术的激光器调制特性研究

在流场诊断技术中,可调谐半导体吸收光谱技术（TDLAS）成为主要的诊断技术之一,其可实现非接触、原位检测。波长调制（WMS）和直接吸收(DA)是两种最常用的TDLAS气体传感方法,在目标含量很低或者极端流场环境下,波长调制技术呈现出更多的优势,检测灵敏度与直接吸收相比可以提高1～2个数量级。在近红外波长调制技术应用领域,分布反馈式（DFB）半导体激光器成为流场诊断技术的光源选择之一,无论利用谐波信号（或者归一化谐波信号）的线型拟合,还是选择谐波信号的峰值来反演流场参数,吸收模型的准确建立均十分重要。在模型建立时,激光器频率-时间响应以及光强-时间响应的准确表示尤为重要。为解决吸收模型准确建立问题,提出了一种准确测量激光器调制参数的完整方法,通过实验测量了用于探测水汽吸收的1 392和1 469 nm激光器的调制特性,研究了分布反馈式激光器的调制参数随调制幅度,调制频率以及工作温度的变化。根据该方法得到的调制参数,建立吸收模型,测得常温下空气中水汽浓度为1.97%,直接吸收方法测得浓度为1.99%,验证了该测量方法的准确性。研究表明,调制深度随调制幅度的增加线性增加,随调制频率的增加非线性单调减小,随工作温度的升高线性增加;激光器的出光强度和频率同时被调制,强度变化超前频率变化的相位,随调制幅度的变化不明显,随调制频率的增加单调增加,随工作温度的升高单调减小;归一化一次谐波振幅和二次振幅均随调制幅度的增加而增加,随调制频率的增加而减小,随工作温度的变化不明显。在吸收光谱应用领域,波长调制技术发挥的作用愈加重要,调制系数与谐波信号的峰值息息相关,在波长调制技术应用时,选取适当的调制参数,有利于得到合适的谐波信号,可通过改变调制幅度、调制频率、工作温度得到最优调制系数。研究了近红外分布反馈式半导体激光器的调制特性,该方法同样适用于不同封装和不同波段激光器调制特性的研究,利于推广吸收光谱技术在各领域的应用。     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.     

Absorption line CW EPR using an amplitude modulated longitudinal field

In standard continuous wave electron paramagnetic resonance (CW-EPR) experiments, the first derivative of absorption lines is detected. This type of a line shape is caused by the magnetic field modulation and is usually an undesired feature, since the sensitivity of CW-EPR drastically decreases with increasing linewidth. A new approach is introduced, which allows for the measurement of absorption line EPR spectra in systems with broad inhomogeneous lines. The method makes use of multiple-photon transitions that are induced in spin systems when a transverse microwave and a longitudinal radio frequency field are simultaneously applied. The absorption lines are obtained by using amplitude modulation of the radio frequency field and slight saturation of the spectral lines. The basics of the new approach are discussed and experimental examples are given.     

A low-cost implementation of EPR detection in a dissolution DNP setup

The implementation of electron paramagnetic resonance (EPR) detection in a low-temperature dissolution dynamic nuclear polarization (DNP) setup is presented. Using a coil oriented parallel to the static magnetic field, the change of the longitudinal magnetization of free radicals is measured upon resonant irradiation of an amplitude or frequency modulated microwave (mw) field. The absorption EPR spectrum is measured if the amplitude of the mw field is modulated, whilst the first derivative of the spectrum is obtained with frequency modulation. Using a burst of pulses, it is also possible to perform pump-probe experiments such as saturation-recovery or electron-electron double resonance experiments. Furthermore, the magnetization could be monitored in a time-resolved manner during amplitude modulation, thus making it possible to record its transient as it is approaching an equilibrium value. Experimental examples are shown with frozen solutions of trityl radical and TEMPO, two commonly used radicals for dissolution DNP experiments.     

Collective modes and the far-infrared absorption of the two-dimensional electron gas in a periodic quantizing magnetic field

We investigate the far-infrared (FIR) absorption of a two-dimensional electron gas in a periodically modulated quantizing magnetic field. The magnetic field varies along only one spatial direction and the external time-dependent electric field is linearly polarized along that axis. The mutual Coulomb interaction of the electrons is treated self-consistently in the ground state and in the absorption calculation within the Hartree approximation. The effects of the magnetic material on top of the heterostructure as a grating coupler is included in the time-dependent incident FIR electric field. We show that, similar to an electric modulation, the absorption can be directly correlated to the underlying electronic energy bands. In addition, the magnetic modulation leads to absorption spectra with a richer structure due to the quite different static response of the electron density to the modulation.     

Application of magnetic field over-modulation for improved EPR linewidth measurements using probes with Lorentzian lineshape

Magnetic field modulation in CW electron paramagnetic resonance (EPR) is used for signal detection. However, it can also distort signal lineshape. In experiments where the linewidth information is of particular importance, small modulation amplitude is usually used to limit the lineshape distortion. The use of small modulation amplitude, however, results in low signal-to-noise ratio and therefore affects the precision of linewidth measurements. Recently, a new spectral simulation model has been developed enabling accurate fitting of modulation-broadened EPR spectra in liquids. Since the use of large modulation amplitude (over-modulation) can significantly enhance the EPR signal, the precision of linewidth measurements is therefore greatly improved. We investigated the over-modulation technique in EPR oximetry experiments using the oxygen-sensing probe lithium octa-n-butoxy-substitued naphthalocyanine (LiNc-BuO). Modulation amplitudes 2-18 times the intrinsic linewidth of the probe were applied to increase the spectral signal-to-noise ratio. The intrinsic linewidth of the probe at different oxygen concentrations was accurately extracted through curve fitting from the enhanced spectra. Thus, we demonstrated that the over-modulation model is also applicable to particulate oxygen-sensing probes such as LiNc-BuO and that the lineshape broadening induced by oxygen is separable from that induced by over-modulation. Therefore, the over-modulation technique can be used to enhance sensitivity and improve linewidth measurements for EPR oximetry with particulate oxygen-sensing probes with Lorentzian lineshape. It should be particularly useful for in vivo oxygen measurements, in which direct linewidth measurements may not be feasible due to inadequate signal-to-noise ratio.     

准连续激光调制吸收谱的多谐波分析

使用准连续二极管激光器进行多重调制光谱检测时,发现吸收光谱信号中存在着丰富的倍频、和频以及差频成分;从激光与气体吸收谱线的非线性作用角度研究了倍频、和频及差频等信号存在的必然性;从实验角度对信号特征进行研究,发现其中有些和频、差频成分的幅度比传统调谐二极管激光吸收光谱技术中的二次谐波信号的幅度更大,有望在准连续调制谱技术中提高检测的灵敏度。     

应用频率调制激光制备二离子暗EPR态

提出了制备势阱中的两离子EPR态的一种方法. 这种方法是基于频率调制的行波光场与囚禁离子的相互作用.这种方法的一个突出优点是所制备的量子态为“暗态”,即自发辐射相消的量子态。另外,讨论了二模压缩运动态（两离子质心模式和呼吸模式）的制备.     

Probe Response of an Optomechanical System with Optomechanical Coupling Modulated Periodically

In this study, the probe response of a cavity optomechanical system with periodic modulation of the optomechanical coupling is investigated. The modulation arises from the beat effect between two external coherent driving lights, with the beat frequency matching the modulation frequency. The transmission coefficient is derived for the probe field and significant amplification, rather than absorption in the conventional optomechanically induced transparency schemes, is observed near the transparent point when the modulation is introduced. In addition, the coupling modulation can also enhance the slow light effect.     

Anisotropic motion effects in CW non-linear EPR spectra: relaxation enhancement of lipid spin labels

Continuous-wave (CW) EPR measurements of enhancements in spin-lattice (T(1)-) relaxation rate find wide application for determining spin-label locations in biological systems. Often, especially in membranes, the spin-label rotational motion is anisotropic and subject to an orientational potential. We investigate here the effects of anisotropic diffusion and ordering on non-linear CW-EPR methods for determining T(1) of nitroxyl spin labels. Spectral simulations are performed for progressive saturation of the conventional in-phase, first-harmonic EPR signal, and for the first-harmonic absorption EPR signals detected 90 degrees -out-of-phase with respect to the Zeeman field modulation. Motional models used are either rapid rotational diffusion, or strong-jump diffusion of unrestricted frequency, within a cone of fixed maximum amplitude. Calculations of the T(1)-sensitive parameters are made for both classes of CW-experiment by using motional parameters (i.e., order parameters and correlation times), intrinsic homogeneous and inhomogeneous linewidth parameters, and spin-Hamiltonian hyperfine- and g-tensors, that are established from simulation of the linear CW-EPR spectra. Experimental examples are given for spin-labelled lipids in membranes.     

On reasons for the hysteresis of melting and crystallization of nanoparticles

The specific features of the EPR spectra of Tm³⁺ impurity ions in synthetic forsterite have been studied by continuous-wave EPR spectroscopy in the frequency range of 270–310 GHz at a temperature of 4.2 K in weak magnetic fields. Narrow resonance signals unrelated to the modulation of the resonance conditions of EPR under the modulation of the external magnetic field have been discovered in measurements at frequencies corresponding to the zero field splitting between the ground and first excited singlet electron states of Tm³⁺ ions in zero magnetic field. The origin of these narrow lines is discussed.     

Spin dynamics of magnetic resonance with parametric modulation in a potassium vapor cell

A typical magnetic-resonance scheme employs a static bias magnetic field and an orthogonal driving magnetic field oscillating at the Larmor frequency, at which the atomic polarization precesses around the static magnetic field. Here we demonstrate both theoretically and experimentally the variations of the resonance condition and the spin precession dynamics resulting from the parametric modulation of the bias field. We show that the driving magnetic field with the frequency detuned by different harmonics of the parametric modulation frequency can lead to resonance as well. Also, a series of frequency sidebands centered at the driving frequency and spaced by the parametric modulation frequency can be observed in the precession of the atomic polarization. We further show that the resonant amplitudes of the sidebands can be controlled by varying the ratio between the amplitude and the frequency of the parametric modulation. These effects could be used in different atomic magnetometry applications.     

Detection of undistorted continuous wave (CW) electron paramagnetic resonance (EPR) spectra with non-adiabatic rapid sweep (NARS) of the magnetic field

A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented.     

The continuous wave electron paramagnetic resonance experiment revisited

When the modulation frequency used in continuous wave electron paramagnetic resonance (cw EPR) spectroscopy exceeds the linewidth, modulation sidebands appear in the spectrum. It is shown theoretically and experimentally that these sidebands are actually multiple photon transitions, sigma(+)+kxpi, where one microwave (mw) sigma(+) photon is absorbed from the mw radiation field and an arbitrary number k of radio frequency (rf) pi photons are absorbed from or emitted to the modulation rf field. Furthermore, it is demonstrated that both the derivative shape of the lines in standard cw EPR spectra and the distortions due to overmodulation are caused by the unresolved sideband pattern of these lines. The single-photon transition does not even give a contribution to the first-harmonic cw EPR signal. Multiple photon transitions are described semiclassically in a toggling frame and their existence is proven using second quantization. With the toggling frame approach and perturbation theory an effective Hamiltonian for an arbitrary sideband transition is derived. Based on the effective Hamiltonians an expression for the steady-state density operator in the singly rotating frame is derived, completely describing all sidebands in all modulation frequency harmonics of the cw EPR signal. The relative intensities of the sidebands are found to depend in a very sensitive way on the actual rf amplitude and the saturation of single sidebands is shown to depend strongly on the effective field amplitude of the multiple photon transitions. By comparison with the analogous solutions for frequency-modulation EPR it is shown that the field-modulation and the frequency-modulation technique are not equivalent. The experimental data fully verify the theoretical predictions with respect to intensities and lineshapes.