Modeling circulating cavity fields using the discrete linear canonical transform

A. A. Ciobanu; A. A. Ciobanu; D. D. Brown; D. D. Brown; P. J. Veitch; P. J. Veitch; D. J. Ottaway; D. J. Ottaway

doi:10.1364/JOSAA.433575

Journal of the Optical Society of America A
Vol. 38,
Issue 9,
pp. 1293-1303
(2021)
•https://doi.org/10.1364/JOSAA.433575

Modeling circulating cavity fields using the discrete linear canonical transform

A. A. Ciobanu, D. D. Brown, P. J. Veitch, and D. J. Ottaway

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A. A. Ciobanu, D. D. Brown, P. J. Veitch, and D. J. Ottaway, "Modeling circulating cavity fields using the discrete linear canonical transform," J. Opt. Soc. Am. A 38, 1293-1303 (2021)

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Abstract

Fabry–Perot cavities are central to many optical measurement systems. In high-precision experiments, such as aLIGO and AdVirgo, coupled cavities are often required, leading to complex optical behavior. We show, for the first time to our knowledge, that discrete linear canonical transforms (LCTs) can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare it with recently published results.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (47)

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Edge	Analytical	Discrete 1D	Discrete 2D
$T_{3 \leftarrow 1} [X]$	$i t_{1} L_{M_{T_{1}}} [X]$	$i t_{1} L_{M_{T_{1}}} X$	$i t_{1} L_{M_{T_{1 y}}} X (L_{M_{T_{1 x}}})^{T}$
$R_{3 \leftarrow 4} [X]$	$r_{1} L_{M_{R_{1}}} [X]$	$r_{1} L_{M_{R_{1}}} X$	$r_{1} L_{M_{R_{1 y}}} X (L_{M_{R_{1 x}}})^{T}$
$R_{6 \leftarrow 5} [X]$	$r_{2} L_{M_{R_{2}}} [X]$	$r_{2} L_{M_{R_{2}}} X$	$r_{2} L_{M_{R_{2 y}}} X (L_{M_{R_{2 x}}})^{T}$
$D_{4 \leftarrow 6} [X]$	$e^{i ϕ / 2} L_{M_{d}} [X]$	$e^{i ϕ / 2} L_{M_{d}} X$	$e^{i ϕ / 2} L_{M_{d}} X (L_{M_{d}})^{T}$
$D_{5 \leftarrow 3} [X]$	$e^{i ϕ / 2} L_{M_{d}} [X]$	$e^{i ϕ / 2} L_{M_{d}} X$	$e^{i ϕ / 2} L_{M_{d}} X (L_{M_{d}})^{T}$

Edge	Analytical	Discrete 1D	Discrete 2D
$T_{3 \leftarrow 1} [X]$	$i t_{1} L_{M_{T_{1}}} [X]$	$i t_{1} L_{M_{T_{1}}} X$	$i t_{1} L_{M_{T_{1 y}}} X (L_{M_{T_{1 x}}})^{T}$
$R_{3 \leftarrow 4} [X]$	$r_{1} L_{M_{R_{1}}} [X]$	$r_{1} L_{M_{R_{1}}} X$	$r_{1} L_{M_{R_{1 y}}} X (L_{M_{R_{1 x}}})^{T}$
$R_{6 \leftarrow 5} [X]$	$r_{2} L_{M_{R_{2}}} [X]$	$r_{2} L_{M_{R_{2}}} X$	$r_{2} L_{M_{R_{2 y}}} X (L_{M_{R_{2 x}}})^{T}$
$D_{4 \leftarrow 6} [X]$	$e^{i ϕ / 2} L_{M_{d}} [X]$	$e^{i ϕ / 2} L_{M_{d}} X$	$e^{i ϕ / 2} L_{M_{d}} X (L_{M_{d}})^{T}$
$D_{5 \leftarrow 3} [X]$	$e^{i ϕ / 2} L_{M_{d}} [X]$	$e^{i ϕ / 2} L_{M_{d}} X$	$e^{i ϕ / 2} L_{M_{d}} X (L_{M_{d}})^{T}$

Abstract

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Tables (2)

Equations (47)

Journal of the Optical Society of America A