Study on the sensitivity of optical cavity length to light power fluctuation

Wen Qi; Yanyi Jiang; Xueyan Li; Li Jin; Zhiyi Bi; Longsheng Ma

doi:doi:10.3788/COL201614.101401

Chinese Optics Letters, 2016, 14 (10): 101401, Published Online: Aug. 2, 2018

Study on the sensitivity of optical cavity length to light power fluctuation Download： 933次

Wen Qi Yanyi Jiang ^*Xueyan Li Li Jin Zhiyi Bi Longsheng Ma

Author Affiliations

State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China

Figures & Tables

Fig. 1. (a) Diagram of a high-reflective mirror. It is coated at the center with a diameter of 10 mm. The red spot at the coating center represents a light spot to which an absorbed light power is applied. Schematic diagram of (b) a football cavity and (c) a cylinder cavity.

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Fig. 2. Experimental setup for the measurement of the cavity sensitivity S. EOM, electro-optic modulator; PBS, polarization beam splitter; λ∕4, quarter-wave plate; PD, photo detector; RF, radio frequency; DBM, double balance mixer.

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Fig. 3. (a) The thermally induced deformations of the cavity. (b) The temperature change of the probe points inside ω0 (blue open squares) and those on the mirror contacting surface (pink dots) over time.

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Fig. 4. Simulation results of S/S0 (a) when the parameters of the cavity and coating are doubled and (b) when the CTE (blue open squares, upper axis) or the thermal conductivity (black filled triangles, lower axis) of the cavity and mirror substrate changes.

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Table1. Main Parameters Used in the Numerical Calculations

Material	ULE^a	FS^a^[13]	Silicon^b^[7,14–16]	Sapphire^c^[14,17,18]	${SiO}_{2} / {Ta}_{2} O_{5}$ ^a^[13,14,19]	${SiO}_{2} / {Ta}_{2} O_{5}$ ^d^[14,20]	$GaAs / {Al}_{0.92} {Ga}_{0.08} As$ ^a^[21,22]
E (GPa)	67.6	72	187.5	464	72/140	60/140	100
$σ$	0.17	0.17	0.28	0.23	0.17/0.23	0.159/0.21	0.32
$ρ$ ( $kg / m^{3}$ )	2210	2200	2330	3997	2200/6850	2200/6850	4551
$α$ (/K)	$2 \times 10^{- 10}$ ^†	$5.5 \times 10^{- 7}$	$1.7 \times 10^{- 9} / 4.6 \times 10^{- 13}$ ^#	$8.8 \times 10^{- 11}$	$5.1 \times 10^{- 7} / - 4.4 \times 10^{- 5}$	$- 2.5 \times 10^{- 7} / 5.8 \times 10^{- 7}$	$5.7 \times 10^{- 6} / 5.2 \times 10^{- 6}$
$κ$ (W/m/K)	1.31	1.38	500/10^#	110	1.38/33	0.13/0.07	62.9^§
$C$ (J/kg/K)	767	670	0.22	0.09	746/306	1/3.17	360^§
$ε$	0.85	0.85	0.55	0.47	N.A	N.A	N.A

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Table2. Calculated Effective CTEs for Coatings

Substrate	Coating	$α_{c}^{eff}$ (/K)	$β_{c}^{eff}$ (/K)
ULE	${SiO}_{2} / {Ta}_{2} O_{5}$	$- 6.5 \times 10^{- 5}$	$- 1.4 \times 10^{- 5}$
FS	${SiO}_{2} / {Ta}_{2} O_{5}$	$- 6.3 \times 10^{- 5}$	$- 1.4 \times 10^{- 5}$
Silicon^*	${SiO}_{2} / {Ta}_{2} O_{5}$	$2.6 \times 10^{- 7}$	$2.7 \times 10^{- 6}$
Sapphire^†	${SiO}_{2} / {Ta}_{2} O_{5}$	$2.1 \times 10^{- 7}$	$2.7 \times 10^{- 6}$
FS	$GaAs / {Al}_{0.92} {Ga}_{0.08} As$	$1.9 \times 10^{- 5}$	$7.9 \times 10^{- 5}$

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Table3. Simulated Sensitivity S when the Cavity Material Variesa

Spacer	Mirror	Coating	$Δ L_{TE}$ (m)	$Δ L_{TR}$ (m)	$S$ (/μW)	$Δ L / L$ ( $10^{- 18}$ )
FS	FS	${SiO}_{2} / {Ta}_{2} O_{5}$	$5.7 \times 10^{- 15}$	$7 \times 10^{- 17}$	$5.8 \times 10^{- 14}$	58
ULE	ULE	${SiO}_{2} / {Ta}_{2} O_{5}$	$3.1 \times 10^{- 15}$	$7 \times 10^{- 17}$	$3.2 \times 10^{- 14}$	32
ULE	FS	${SiO}_{2} / {Ta}_{2} O_{5}$	$3.4 \times 10^{- 15}$	$7 \times 10^{- 17}$	$3.5 \times 10^{- 14}$	35
ULE	FS	$GaAs / {Al}_{0.92} {Ga}_{0.08} As$	$4.0 \times 10^{- 16}$	$2 \times 10^{- 16}$	$6 \times 10^{- 15}$	6
Silicon	Silicon	${SiO}_{2} / {Ta}_{2} O_{5}$	$6 \times 10^{- 18}$ ^*/ $8 \times 10^{- 18}$ ^#	$2 \times 10^{- 18}$	$8 \times 10^{- 18}$ ^*/ $1 \times 10^{- 17}$ ^#	0.008^*/0.01^#
Sapphire	Sapphire	${SiO}_{2} / {Ta}_{2} O_{5}$	$3 \times 10^{- 18}$ ^†	$2 \times 10^{- 18}$ ^†	$5 \times 10^{- 18}$ ^†	0.005^†

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Wen Qi, Yanyi Jiang, Xueyan Li, Li Jin, Zhiyi Bi, Longsheng Ma. Study on the sensitivity of optical cavity length to light power fluctuation[J]. Chinese Optics Letters, 2016, 14(10): 101401.

Study on the sensitivity of optical cavity length to light power fluctuation Download： 933次

Fig. 1. (a) Diagram of a high-reflective mirror. It is coated at the center with a diameter of 10 mm. The red spot at the coating center represents a light spot to which an absorbed light power is applied. Schematic diagram of (b) a football cavity and (c) a cylinder cavity.

Fig. 2. Experimental setup for the measurement of the cavity sensitivity S. EOM, electro-optic modulator; PBS, polarization beam splitter; λ∕4, quarter-wave plate; PD, photo detector; RF, radio frequency; DBM, double balance mixer.

Fig. 3. (a) The thermally induced deformations of the cavity. (b) The temperature change of the probe points inside ω0 (blue open squares) and those on the mirror contacting surface (pink dots) over time.

Fig. 4. Simulation results of S/S0 (a) when the parameters of the cavity and coating are doubled and (b) when the CTE (blue open squares, upper axis) or the thermal conductivity (black filled triangles, lower axis) of the cavity and mirror substrate changes.

Table1. Main Parameters Used in the Numerical Calculations

Table2. Calculated Effective CTEs for Coatings

Table3. Simulated Sensitivity S when the Cavity Material Variesa

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Study on the sensitivity of optical cavity length to light power fluctuation Download： 933次

Fig. 1. (a) Diagram of a high-reflective mirror. It is coated at the center with a diameter of 10 mm. The red spot at the coating center represents a light spot to which an absorbed light power is applied. Schematic diagram of (b) a football cavity and (c) a cylinder cavity.

Fig. 2. Experimental setup for the measurement of the cavity sensitivity S. EOM, electro-optic modulator; PBS, polarization beam splitter; λ∕4, quarter-wave plate; PD, photo detector; RF, radio frequency; DBM, double balance mixer.

Fig. 3. (a) The thermally induced deformations of the cavity. (b) The temperature change of the probe points inside ω0 (blue open squares) and those on the mirror contacting surface (pink dots) over time.

Fig. 4. Simulation results of S/S0 (a) when the parameters of the cavity and coating are doubled and (b) when the CTE (blue open squares, upper axis) or the thermal conductivity (black filled triangles, lower axis) of the cavity and mirror substrate changes.

Table1. Main Parameters Used in the Numerical Calculations

Table2. Calculated Effective CTEs for Coatings

Table3. Simulated Sensitivity S when the Cavity Material Variesa

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