The fluctuations of the probe light intensity seriously affect the performance of the sensitive atomic magnetometer. Here we propose a novel method for the intensity stabilization based on the second harmonic component of the photoelastic modulator (PEM) detection in the atomic magnetometer. The method not only could be used to eliminate the intensity fluctuations of the laser source, but also remove the fluctuations from the optical components caused by the environment. A relative fluctuation of the light intensity of 0.035% was achieved and the corresponding fluctuation of the output signal of the atomic magnetometer has decreased about two orders of magnitude from 4.06% to 0.041%. As the scheme proposed here only contains optical devices and does not require additional feedback controlled equipments, it is especially suitable for the integration of the atomic magnetometer.

Light intensity stabilization based on the second harmonic of the photoelastic modulator detection in the atomic magnetometer.

Optical-phase-retardation elements are widely used in many fields. Accurate measurement of their phase retardation is crucial to the practical effect of the element’s processing and application. The development and present situation of the methods for optical phase retardation measurement are reviewed, with the wave plate, the most typical phase-retardation element, as an example. The latest research progress in this field is introduced; the principles and characteristics of individual measurement method are summarized and discussed. Three new methods based on laser frequency splitting or laser feedback are presented in detail, in which the laser is not only regarded as a light source but also plays a role of sensor. Moreover, no standard wave plates are needed and arbitrary phase retardation can be measured. Traceability, high precision and high repeatability are achieved as well.

Methods for optical phase retardation measurement: A review

The fast and full range measurements of ellipsometric parameters ψ and Δ using a 45° dual-drive symmetric photoelastic modulator (PEM) are proposed. The PEM operates in a pure traveling modulation mode with a constant retardation magnitude and the modulation axis performing circular motion. A field programmable gate array is used to control the PEM and fulfill the data processing. The parameters sin 2ψ sinΔ, sin 2ψ cosΔ, and sin 2ψ can be measured simultaneously, providing accurate measurements of ψ and Δ over the full range. The experimental results show that the repeatability and sensitivity of this system are at 10-3°, and the data acquisition rate is 1 ms/point.

Fast and full range measurements of ellipsometric parameters using a 45° dual-drive symmetric photoelastic modulator.

Ultra-sensitive multi-channel optically pumped atomic magnetometers based on the spin-exchange relaxation-free (SERF) effect are powerful tools for applications in the field of magnetic imaging. To simultaneously achieve ultra-high spatial resolution and ultra-high magnetic field sensitivity, we proposed a high-resolution multi-channel SERF atomic magnetometer for two-dimensional magnetic field measurements based on a digital micro-mirror device (DMD) as the spatial light modulator for a single vapor cell. Under the optimal experimental conditions obtained via spatial and temporal modulation of the probe light, we first demonstrated that the average sensitivity of the proposed 25-channel magnetometer was approximately 25fT/Hz1/2 with a spatial resolution of 216µm. Then, we measured the magnetic field distribution generated by a gradient coil and compared the experimentally obtained distributions with those calculated via finite element simulation. The obtained g value of 99.2% indicated good agreement between our experimental results and the theoretical calculations, thereby confirming that our proposed multi-channel SERF magnetometer was effective at measuring magnetic field distributions with an ultra-high spatial resolution.

High spatial resolution multi-channel optically pumped atomic magnetometer based on a spatial light modulator

A high-speed Mueller matrix ellipsometer (MME) based on photoelastic modulator (PEM) polarization modulation and division-of-amplitude polarization demodulation has been developed, with which a temporal resolution of 11 µs has been achieved for a Mueller matrix measurement. To ensure the accuracy and stability, a novel approach combining a fast Fourier transform algorithm and Bessel function expansion is proposed for the in-situ calibration of PEM. With the proposed calibration method, the peak retardance and static retardance of the PEM can be calibrated with high accuracy and sensitivity over an ultra large retardance variation range. Both static and dynamic measurement experiments have been carried out to show the high accuracy and stability of the developed MME, which can be expected to pave the way for in-situ and real-time monitoring for rapid reaction processes.

High-speed Mueller matrix ellipsometer with microsecond temporal resolution.

A method for simultaneous measurement of the retardance and the fast axis angle of quarter-wave plate using one photoelastic modulator is presented. A laser beam passes through a polarizer, a photoelastic modulator, the quarter-wave plate to be measured, and an analyzer to be detected. Before and after the quarter-wave plate is rotated 45° at any initial fast axis direction, two detection signals are obtained to resolve simultaneously the retardance and the fast axis angle. In experiments, a quarter-wave plate was measured with fast axis angles from −89° to 90°. The average and the standard deviation of the retardances at different fast axis directions are respectively 89.50° and 0.17°. The maximum measurement deviation of the fast axis angle is 0.5°. The usefulness of the method is verified.

Simultaneous measurement of retardance and fast axis angle of a quarter-wave plate using one photoelastic modulator

Simultaneous measurement of small birefringence magnitude and direction in real time

Real-time measurement of retardation and fast axis azimuth of wave plates is proposed. The light emitted from the laser passes through a circular polarizer and the sample successively. Then the beam is diffracted to three sub-beams by a grating. One sub-beam passes through a standard quarter-wave plate and then is split and analyzed by a Wollaston prism. The other two sub-beams are all directly split and analyzed by Wollaston prisms. Six intensities are simultaneously detected to calculate the retardation and the fast axis azimuth. Experiments show that for the quarter-wave plate the average and standard deviation of the retardation are 89.78° and 0.14°, respectively, and the maximum deviation of the fast axis azimuth is 0.6°; for the eighth-wave plate, the average and standard deviation of the retardation are 45.15° and 0.15°, respectively, and the maximum deviation of the fast axis azimuth is 0.53.

Real-time measurement of retardation and fast axis azimuth for wave plates

A polarization lateral shear interferometer is composed of a polarization beam splitter, a birefringent crystal plate, a polarization direction rotation module, a zoom lens group, an image sensor and a computer. The polarization beam splitter, the birefringent crystal plate and the polarization direction rotation module are arranged on the incident beam advancing direction in turn and the zoom lens group and the image sensor are arranged in turn in the reflection optical path along the opposite direction of the incident beam advancing direction and an output end of the image sensor is connected with the computer and the include angle between a main plane of the birefringent crystal plate and the polarization direction of the polarization beam from the polarization beam splitter is 45degree and the polarization direction rotation module is quarter wave plate with a back surface coated with a high reflection film and the include angle between the quick axle direction of the quarter wave plate and the main plane of the birefringent crystal plate is 45degree. The interferometer has features of equal optical path interference and adjustable shearing amount.

Polarization lateral shear interferometer

The invention provides a device and a method for measuring phase retardation and fast axis azimuth angle of a wave plate in real time. The device comprises a collimating laser, a circular polarizer, a one-dimensional grating, a standard quarter-wave plate, a first Wollaston prism, a second Wollaston prism, a third Wollaston prism, a first collimating lens, a second collimating lens, a third collimating lens, a first double-quadrant detector, a second double-quadrant detector, a third double-quadrant detector, an attenuator and a signal processing system, and can simultaneously measure the phase retardation and fast axis azimuth angle of the wave plate in real time; the measurement range is wide and the measurement result is free from the influence of initial light intensity fluctuation, diffraction efficiency difference and sub-beam circuit constant difference.

Fanyue Li

Papers

Simultaneous measurement of retardance and fast axis angle of a quarter-wave plate using one photoelastic modulator

Simultaneous measurement of small birefringence magnitude and direction in real time

Real-time measurement of retardation and fast axis azimuth for wave plates

Polarization lateral shear interferometer

Device and method for measuring phase retardation and fast axis azimuth angle of wave plate in real time