Overview of Advanced LIGO adaptive optics.

This is an overview of the adaptive optics used in Advanced LIGO (aLIGO), known as the thermal compensation system (TCS). The TCS was designed to minimize thermally induced spatial distortions in the interferometer optical modes and to provide some correction for static curvature errors in the core optics of aLIGO. The TCS is comprised of ring heater actuators, spatially tunable CO2 laser projectors, and Hartmann wavefront sensors. The system meets the requirements of correcting for nominal distortion in aLIGO to a maximum residual error of 5.4 nm rms, weighted across the laser beam, for up to 125 W of laser input power into the interferometer.

The advanced LIGO input optics.

The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

Feedback control of optical beam spatial profiles using thermal lensing.

A method for active control of the spatial profile of a laser beam using adaptive thermal lensing is described. A segmented electrical heater was used to generate thermal gradients across a transmissive optical element, resulting in a controllable thermal lens. The segmented heater also allows the generation of cylindrical lenses, and provides the capability to steer the beam in both horizontal and vertical planes. Using this device as an actuator, a feedback control loop was developed to stabilize the beam size and position.

Thermal effects in the Input Optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers.

We present the design and performance of the LIGO Input Optics subsystem as implemented for the sixth science run of the LIGO interferometers. The Initial LIGO Input Optics experienced thermal side effects when operating with 7 W input power. We designed, built, and implemented improved versions of the Input Optics for Enhanced LIGO, an incremental upgrade to the Initial LIGO interferometers, designed to run with 30 W input power. At four times the power of Initial LIGO, the Enhanced LIGO Input Optics demonstrated improved performance including better optical isolation, less thermal drift, minimal thermal lensing, and higher optical efficiency. The success of the Input Optics design fosters confidence for its ability to perform well in Advanced LIGO.

Adaptive control of modal properties of optical beams using photothermal effects.

We present an experimental demonstration of adaptive control of modal properties of optical beams. The control is achieved via heat-induced photothermal actuation of transmissive optical elements. We apply the heat using four electrical heaters in thermal contact with the element. The system is capable of controlling both symmetrical and astigmatic aberrations providing a powerful means for in situ correction and control of thermal aberrations in high power laser systems. We demonstrate a tunable lens with a focusing power varying from minus infinity to -10 m along two axes using SF57 optical glass. Applications of the proposed system include laser material processing, thermal compensation of high laser power radiation, and optical beam steering.

Optical design of the proposed Australian International Gravitational Observatory.

Marginally stable power recycling cavities are being used by nearly all interferometric gravitational wave detectors.With stability factors very close to unity the frequency separation of the higher order optical modes is smaller than the cavity bandwidth. As a consequence these higher order modes will resonate inside the cavity distorting the spatial mode of the interferometer control sidebands. Without losing generality we study and compare two designs of stable power recycling cavities for the proposed 5 kilometer long Australian International Gravitational Observatory (AIGO), a high power advanced interferometric gravitational wave detector. The length of various optical cavities that form the interferometer and the modulation frequencies that generate the control sidebands are also selected.

On the interference of two Gaussian beams and their ABCD matrix representation.

Gaussian beam propagation is well described by the q-parameter and the ABCD matrices. A variety of ABCD matrices are available that represent commonly occurring scenarios/components in optics. One important phenomenon that has not been studied in detail is the interference of two optical beams with different q-parameters undergoing interference. In this paper, we describe the effect of interference of two Gaussian beams. We derive an ABCD matrix for the addition of two beams that takes into account both the amplitude and phase difference between two beams. This ABCD matrix will help greatly in determining the propagation of beams inside complex interferometers and finding the solutions for the coupled cavity Eigenmodes.

Design of the Advanced LIGO recycling cavities.

The current LIGO detectors will undergo an upgrade which is expected to improve their sensitivity and bandwidth significantly. These advanced gravitational-wave detectors will employ stable recycling cavities to better confine their spatial eigenmodes instead of the currently installed marginally stable power recycling cavity. In this letter we describe the general layout of the recycling cavities and give specific values for a first possible design. We also address the issue of mode mismatch due to manufacturing tolerance of optical elements and present a passive compensation scheme based upon optimizing the distances between optical elements.

Adaptive beam shaping by controlled thermal lensing in optical elements.

We describe an adaptive optical system for use as a tunable focusing element. The system provides adaptive beam shaping via controlled thermal lensing in the optical elements. The system is agile, remotely controllable, touch free, and vacuum compatible; it offers a wide dynamic range, aberration-free focal length tuning, and can provide both positive and negative lensing effects. Focusing is obtained through dynamic heating of an optical element by an external pump beam. The system is especially suitable for use in interferometric gravitational wave interferometers employing high laser power, allowing for in situ control of the laser modal properties and compensation for thermal lensing of the primary laser. Using CO(2) laser heating of fused-silica substrates, we demonstrate a focal length variable from infinity to 4.0 m, with a slope of 0.082 diopter/W of absorbed heat. For on-axis operation, no higher-order modes are introduced by the adaptive optical element. Theoretical modeling of the induced optical path change and predicted thermal lens agrees well with measurement.

Optoelectronic approach to adaptive radio-frequency transversal filter implementation with negative coefficients by using optical spectrum shaping.

A multitap negative and positive coefficient radio-frequency transversal filter is implemented by using a digital-micromirror-device spatial light modulator for weighting-factor control and a chirped fiber Bragg grating for time-delay control. The demonstrated architecture is reconfigurable, has high speed and low loss, and is robust through digital programmability for a wide variety of filtering algorithms. A design using an interleaver for differential detection realizes an ultrahigh bandwidth with a maximum processable frequency of 33.7 GHz. A multitap low-pass filter, a negative tap notch filter with 40 dB attenuation, and a multitap negative coefficient bandpass filter are experimentally demonstrated. The results are in agreement with theory.

Programmable broadband radio-frequency transversal filter with compact fiber-optics and digital microelectromechanical system-based optical spectral control.

To the best of our knowledge, for the first time a programmable broadband rf transversal filter is proposed that operates on the principle of broadband optical spectral control implemented with a spatial light modulator input rf signal time delay and weight selection over a near-continuous signal space. Specifically, the filter uses a chirped fiber Bragg grating in combination with a two-dimensional digital micromirror device to enable a programmable rf filter. As a first step, a two-tap rf notch filter is demonstrated with a tuning range of 0.563-6.032 GHz with a 25-dB notch depth at test notch frequencies of 845 and 905 MHz. The proposed filter can find applications in diverse fields such as radar, communications, medicine, and test and measurement.

Superwide-angle coverage code-multiplexed optical scanner.

A superwide-angle coverage code-multiplexed optical scanner is presented that has the potential to provide 4 pi-sr coverage. As a proof-of-concept experiment, an angular scan range of 288 degrees for six randomly distributed beams is demonstrated. The proposed scanner achieves its superwide coverage by exploiting a combination of phase-encoded transmission and reflection holography within an in-line hologram recording-retrieval geometry. The basic scanner unit consists of one phase-only digital mode spatial light modulator for code entry (i.e., beam scan control) and a holographic material from which we obtained what we believe is the first-of-a-kind extremely wide coverage, low component count, high speed (e.g., microsecond domain), and large aperture (e.g., > 1-cm diameter) scanner.

High-speed two-dimensional laser scanner based on Bragg gratings stored in photothermorefractive glass.

A high-speed free-space wavelength-multiplexed optical scanner with high-speed wavelength selection coupled with narrowband volume Bragg gratings stored in photothermorefractive (PTR) glass is reported. The proposed scanner with no moving parts has a modular design with a wide angular scan range, accurate beam pointing, low scanner insertion loss, and two-dimensional beam scan capabilities. We present a complete analysis and design procedure for storing multiple tilted Bragg-grating structures in a single PTR glass volume (for normal incidence) in an optimal fashion. Because the scanner design is modular, many PTR glass volumes (each having multiple tilted Bragg-grating structures) can be stacked together, providing an efficient throughput with operations in both the visible and the infrared (IR) regions. A proof-of-concept experimental study is conducted with four Bragg gratings in independent PTR glass plates, and both visible and IR region scanner operations are demonstrated.

Angstrom-range optical path-length measurement with a high-speed scanning heterodyne optical interferometer.

A highly accurate method of optical path-length measurement is introduced by use of a scanning heterodyne optical interferometer with no moving parts. The instrument has demonstrated the potential to measure optical path length at angstrom resolution over continuous thickness in the micrometer range. This optical path length can be used to calculate the thickness of any material if the refractive index is known or to measure the refractive index of the material if the thickness is known. The instrument uses a single acousto-optic device in an in-line ultra-stable reflective geometry to implement rapid scanning in the microsecond domain for thickness measurements of the test medium.

Code-multiplexed optical scanner.

A three-dimensional (3-D) optical-scanning technique is proposed based on spatial optical phase code activation on an input beam. This code-multiplexed optical scanner (C-MOS) relies on holographically stored 3-D beam-forming information. Proof-of-concept C-MOS experimental results by use of a photorefractive crystal as a holographic medium generates eight beams representing a basic 3-D voxel element generated via a binary-code matrix of the Hadamard type. The experiment demonstrates the C-MOS features of no moving parts, beam-forming flexibility, and large centimeter-size apertures. A novel application of the C-MOS as an optical security lock is highlighted.