Statistical properties of single-mode fiber coupling of satellite-to-ground laser links partially corrected by adaptive optics

Lucien Canuet; Nicolas Védrenne; Jean-Marc Conan; Cyril Petit; Geraldine Artaud; Angelique Rissons; Jerome Lacan

doi:10.1364/JOSAA.35.000148

Journal of the Optical Society of America A
Vol. 35,
Issue 1,
pp. 148-162
(2018)
•https://doi.org/10.1364/JOSAA.35.000148

Statistical properties of single-mode fiber coupling of satellite-to-ground laser links partially corrected by adaptive optics

Lucien Canuet, Nicolas Védrenne, Jean-Marc Conan, Cyril Petit, Geraldine Artaud, Angelique Rissons, and Jerome Lacan

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Lucien Canuet, Nicolas Védrenne, Jean-Marc Conan, Cyril Petit, Geraldine Artaud, Angelique Rissons, and Jerome Lacan, "Statistical properties of single-mode fiber coupling of satellite-to-ground laser links partially corrected by adaptive optics," J. Opt. Soc. Am. A 35, 148-162 (2018)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: September 4, 2017
- Revised Manuscript: November 18, 2017
- Manuscript Accepted: November 22, 2017
- Published: December 18, 2017

Abstract

In the framework of satellite-to-ground laser downlinks, an analytical model describing the variations of the instantaneous coupled flux into a single-mode fiber after correction of the incoming wavefront by partial adaptive optics (AO) is presented. Expressions for the probability density function and the cumulative distribution function as well as for the average fading duration and fading duration distribution of the corrected coupled flux are given. These results are of prime interest for the computation of metrics related to coded transmissions over correlated channels, and they are confronted by end-to-end wave-optics simulations in the case of a geosynchronous satellite (GEO)-to-ground and a low earth orbit satellite (LEO)-to-ground scenario. Eventually, the impact of different AO performances on the aforementioned fading duration distribution is analytically investigated for both scenarios.

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Downlink Scenario	GEO	LEO
Elevation	30 deg	20 deg
Range	38,000 km	1584 km
Orbital velocity	$3.0 km \cdot s^{- 1}$	$7.5 km \cdot s^{- 1}$
Rx aperture diameter	50 cm	25 cm
Fried parameter $r_{0}$	0.069 m	0.056 m
Log-amplitude variance $σ_{χ}^{2}$	0.067	0.135
AO parameters ${\begin{matrix} N_{r} & 9 & 6 \\ f_{s} & 1 kHz & 2 kHz \\ σ_{res}^{2} & 0.4 & 0.5 \\ μ_{f_{SMF}} & - 2.7 dB & - 3.2 dB \end{matrix}$

	$N_{r}$	$f_{s}$	$σ_{res}^{2}$	$μ_{f_{SMF}}$
GEO ${\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	9	1.0 kHz	$0.4 {rad}^{2}$	−2.7 dB
	5	0.4 kHz	$1.3 {rad}^{2}$	−5.2 dB
	4	0.3 kHz	$1.9 {rad}^{2}$	−6.7 dB
LEO ${\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	6	2.0 kHz	$0.5 {rad}^{2}$	−3.2 dB
	3	0.8 kHz	$1.3 {rad}^{2}$	−5.2 dB
	2	0.5 kHz	$2.0 {rad}^{2}$	−6.7 dB

	Fading Duration [ms]	Interfading Duration [ms]
$\Pr (τ_{fade} > τ_{fade}^{0}) = . 99 {\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	0.032	10
	0.065	0.4
	0.098	0.3
$\Pr (τ_{fade} > τ_{fade}^{0}) = . 01 {\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	15	4500
	30	190
	45	140

	Fading Duration [ms]	Inter-Fading Duration [ms]
$\Pr (τ_{fade} > τ_{fade}^{0}) = . 99 {\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	0.003	1.3
	0.008	0.2
	0.014	0.1
$\Pr (τ_{fade} > τ_{fade}^{0}) = . 01 {\begin{cases} HP . \\ MP . \\ LP . \end{cases}$	1.4	611
	3.7	90
	6.4	45

Downlink Scenario	GEO	LEO
Elevation	30 deg	20 deg
Range	38,000 km	1584 km
Orbital velocity	$3.0 km \cdot s^{- 1}$	$7.5 km \cdot s^{- 1}$
Rx aperture diameter	50 cm	25 cm
Fried parameter $r_{0}$	0.069 m	0.056 m
Log-amplitude variance $σ_{χ}^{2}$	0.067	0.135
AO parameters ${\begin{matrix} N_{r} & 9 & 6 \\ f_{s} & 1 kHz & 2 kHz \\ σ_{res}^{2} & 0.4 & 0.5 \\ μ_{f_{SMF}} & - 2.7 dB & - 3.2 dB \end{matrix}$

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Journal of the Optical Society of America A