Gaussian Beam Divergence Research Articles

Experimental scheme and noise analysis of weak-light phase locked loop for large-scale intersatellite laser interferometer.

In the current space gravitational wave (GW) detection, satellites are separated by millions of kilometers. As a result, watts of laser from one satellite is attenuated to the picowatt level at the other end due to the Gaussian beam divergence and the finite aperture of the telescope. Establishing an effective interferometry with such weak-light is a major challenge. The key is to enhance the weak-light while preserving its phase information, which carries the actual GW signal. This can be accomplished by employing an optical phase-locked loop (PLL) to lock the phase of a local oscillator (LO) laser to the weak-light and then sending the power-amplified LO back to the interferometer on the other satellite. Although shot-noise-limited performance of the picowatt level weak-light PLL has been achieved for high frequencies, it remains elusive for frequencies below 0.1Hz. Here, we propose a three-step experimental scheme to identify the main noise sources of the weak-light PLL, which turn out to be the low-frequency phase measurement noise, the weak-light shot noise, and the laser phase noise. In this paper, the first step experiment result shows that the out-loop phase noise can be suppressed to a level less than 6 × 10-6 rad/√Hz from 6 mHz to 1Hz by first using the special pilot-tone technique in the PLL to directly reduce the sampling time jitter noise in the digital phasemeter. The out-loop phase noise is mainly limited by the signal amplitude variation and differential time jitter noise of the reference clock.

Use of Gaussian beam divergence to compensate for misalignment of underwater wireless optical communication links

The vast majority of underwater wireless optical communication systems use collimated blue/green laser beams to deliver high-speed data over a transmission range of a few metres to tens of metres. However, such systems are extremely susceptible to misalignment of the transmitter and the receiver. The mitigation techniques for misalignment reported in the literature are complex and costly at times. In this study, the authors consider the simple approach of increasing the divergence angle of the transmitted Gaussian beam to mitigate misalignment. Both plane and spherical beams are considered as the limitation cases. Using Monte Carlo simulations, the authors show that an optimum divergence angle for the maximum acceptable lateral offset exists with respect to the receiver sensitivity in clear waters while this is not an efficient method in harbour waters. Results demonstrate that there is a design trade-off between acceptable lateral offset, power loss and channel bandwidth. Furthermore, the authors show how the proposed scheme of beam divergence affects the maximum allowed link span as well as the channel bandwidth for a given distance.

Cylindrically polarized Bessel–Gauss beams

We present a study of radially and azimuthally polarized Bessel–Gauss (BG) beams in both the paraxial and nonparaxial regime. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for BG beams. We show that independently on the ratio between the Bessel aperture cone angle and the Gaussian beam divergence , the nonparaxial corrections are alway very small and therefore negligible. The explicit expressions for the nonparaxial vector electric field components are also reported.

All-silicon Michelson instrument on chip: Distance and surface profile measurement and prospects for visible light spectrometry

A miniature Michelson interferometer is analyzed theoretically and experimentally. The fabricated micro-interferometer is incorporated at the tip of a monolithic silicon probe to achieve contactless distance measurements and surface profilometry. For infrared operation, two approaches are studied, based on the use of monochromatic light and wavelength sweep, respectively. A theoretical model is devised to depict the system characteristics taking into account Gaussian beam divergence and light spot size. Furthermore, preliminary results using visible light demonstrate operation of the probe as a visible light spectrometer, despite silicon absorbance, thanks to the micrometer thickness involved in the beam splitter.

Advances in Modeling, Design, and Fabrication of Deep-Etched Multilayer Resonators

We present recent advances in modeling, design, and fabrication of in-plane multilayer optical resonators fabricated by high aspect ratio etching of silicon. We first revisit the model of Gaussian beam divergence proposed by A. Lipson to correct a mistake that leads to an underestimation of the losses affecting this type of resonator. Secondly, we discuss the influence of surface roughness at the silicon-air interfaces of multilayered structures. Roughness profiles-measured by white light interferometry on the sidewalls of silicon trenches etched by deep reactive ion etching (DRIE)-are presented. The single absorbing layer model of Carniglia is used to predict the influence of the measured roughness ( nm RMS). This model is combined with the corrected model for Gaussian beam divergence and is compared with recent experimental results obtained for a new generation of deep-etched Fabry-Perot refractive index sensors. These sensors are fabricated using the contour lithography method, which is demonstrated to greatly improve the predictability of their optical characteristics. The combined model for roughness and divergence is found to correspond remarkably well with the experimental results, with predictions of loss and finesse of the resonances within an average error of 1.3 dB and 25%, respectively. We therefore expect the models and the simulations presented in this article to become a useful tool for the design of devices based on deep-etched multilayer resonators.

散斑相关在椭圆高斯光束发散角测量中的应用

散斑相关在椭圆高斯光束发散角测量中的应用

Physical-parameter design in 2-D MEMS optical switches

Free-space micromachined optical switching technology has emerged as a promising candidate for the transparent optical cross connects that are needed in next-generation optical transport networks. This paper deals with the system design of two-dimensional (2-D) microelectromechanical system (MEMS)-based cross connects. In particular, we propose a method, applicable to any kind of 2-D MEMS switching architectures, which finds the best choices of the basic geometrical parameters of the device (such as mirror radius and beam-waist size) allowing the achievement of given insertion-loss and differential-loss target values for the overall switching matrix. Our proposal is based on a widely used model of the loss mechanisms in a 2-D MEMS switch, keeping Gaussian-beam divergence and free-space/fiber mode mismatching into account. By adopting the proposed design technique, we compare various 2-D MEMS architectures recently proposed in the technical literature in terms of cost and feasibility of large port count optical switches.

Comparative analysis of optical-transition-radiation-based electron-beam emittance measurements for the Los Alamos free-electron laser

A series of measurements have been performed to determine the emittance of the electron beam of the LANL FEL. These measurements were made both before and after installation of a photoelectric injector on the LANL linac. An optical-transition-radiation (OTR) interferometer was used to determine the beam divergence while simultaneously using the beam spot imaged in OTR to determine the spatial profile at a beam waist. We have developed two methods to analyze the OTR interference patterns in order to determine the beam divergence from the observed interference-fringe visibility. The first method relies on a simple analytical model in which a Gaussian beam divergence is convolved with the OTR interference pattern for a single particle. The second method uses a numerical convolution of the phase-space distribution in beam angle and energy with the single-particle OTR interference pattern. The six-dimensional phase space used to simulate the experimental OTR patterns was produced by the particle code PARMELA which was run for the beam parameters appropriate for the two sets of experiments. We present a comparison of these two methods with each other and with the experimental observations. The effects of both the beam divergence and the beam energy spread on the emittance measurement is illustrated.