Living Reviews in Relativity

"Interferometer Techniques for Gravitational-Wave Detection"
Andreas Freise and Kenneth Strain  

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1 Introduction
1.1 The scope and style of the review
1.2 Overview of the goals of interferometer design
1.3 Overview of the physics of the primary interferometer components
1.4 Plane-wave analysis
1.5 Frequency domain analysis
2 Optical Components: Coupling of Field Amplitudes
2.1 Mirrors and spaces: reflection, transmission and propagation
2.2 The two-mirror resonator
2.3 Coupling matrices
2.4 Phase relation at a mirror or beam splitter
2.5 Lengths and tunings: numerical accuracy of distances
2.6 Revised coupling matrices for space and mirrors
2.7 Finesse examples
3 Light with Multiple Frequency Components
3.1 Modulation of light fields
3.2 Phase modulation
3.3 Frequency modulation
3.4 Amplitude modulation
3.5 Sidebands as phasors in a rotating frame
3.6 Phase modulation through a moving mirror
3.7 Coupling matrices for beams with multiple frequency components
3.8 Finesse examples
4 Optical Readout
4.1 Detection of optical beats
4.2 Signal demodulation
4.3 Finesse examples
5 Basic Interferometers
5.1 The two-mirror cavity: a Fabry–Pérot interferometer
5.2 Michelson interferometer
5.3 Finesse examples
6 Interferometric Length Sensing and Control
6.1 Error signals and transfer functions
6.2 Fabry–Pérot length sensing
6.3 The Pound–Drever–Hall length sensing scheme
6.4 Michelson length sensing
6.5 The Schnupp modulation scheme
6.6 Finesse examples
7 Beam Shapes: Beyond the Plane Wave Approximation
7.1 The paraxial wave equation
7.2 Transverse electromagnetic modes
7.3 Properties of Gaussian beams
7.4 Astigmatic beams: the tangential and sagittal plane
7.5 Higher-order Hermite–Gauss modes
7.6 The Gaussian beam parameter
7.7 Properties of higher-order Hermite–Gauss modes
7.8 Gouy phase
7.9 Laguerre–Gauss modes
7.10 Tracing a Gaussian beam through an optical system
7.11 ABCD matrices
8 Interferometer Matrix with Hermite–Gauss Modes
8.1 Coupling of Hermite–Gauss modes
8.2 Coupling coefficients for Hermite–Gauss modes
8.3 Finesse examples
9 Acknowledgements
A The Interferometer Simulation Finesse
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