Thermal Noise Analysis Based on Higher-Order Mode Laser Frequency Stabilization

Lianlian Du; Jingfang Liu; Jiamin Liu; Rongguo Yang; Hengxin Sun; Jiangrui Gao

doi:10.3788/AOS240547

Acta Optica Sinica, Volume. 44, Issue 13, 1314001(2024)

Thermal Noise Analysis Based on Higher-Order Mode Laser Frequency Stabilization

Lianlian Du¹, Jingfang Liu¹, Jiamin Liu¹, Rongguo Yang^2,3, Hengxin Sun^1,2、*, and Jiangrui Gao^1,2

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, Shanxi , China

²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, Shanxi , China

³College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, Shanxi , China

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Figures & Tables(14)

Fig. 1. Noise model for laser frequency stabilization. (a) Feedback control block diagram; (b) relationship diagram between noise source and total frequency noise

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Fig. 2. Higher-order mode frequency stabilization scheme. (a) Experimental implementation scheme; (b) control block diagram of noise transfer

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Fig. 3. Pressure distribution maps. (a) Hermite-Gauss mode; (b) Laguerre-Gaussian mode

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Fig. 4. Mirror thermal noise

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Fig. 5. Thermal noise of reference cavity. (a) Frequency noise of the fundamental mode when substrate is ULE material; (b) total frequency noise of LG_p_,0 mode at 1 Hz when substrate is fused silica and ULE material

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Fig. 6. Schematic diagram of mode mismatch. (a) Change waist position; (b) change waist size

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Fig. 7. Mode mismatch coupling efficiency. (a) Change waist position; (b) change waist size

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Fig. 8. Maximum coupling efficiency of each order of Laguerre-Gaussian mode LG_p_,0

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Fig. 9. Noise curves when P_in=10 μW. (a) LG_0,0; (b) LG_10,0; (c) LG_20,0

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Fig. 10. Total noise of LG_0,0, LG_10,0, LG_20,0 mode

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Fig. 11. LG_p_,0 mode noise. (a) P_in=10 μW, f =10 Hz; (b) P_in=100 μW, f =1 Hz

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Table 1. Reference cavity parameters
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Table 1. Reference cavity parameters
Material Poisson ratio Loss angle Young’s modulus /Pa Thickness /mm
ULE 0.18 $1 / 6 \times 10^{- 4}$ $6.8 \times 10^{10}$ 6.35
Fused silica 0.17 $1 \times 10^{- 6}$ $7.3 \times 10^{10}$ 6.35
SiO₂/Ta₂O₅ 0.17 $0.5 \times 10^{- 4}$ $7.2 \times 10^{10}$ $2 \times 10^{- 3}$

Table 2. Reference cavity overall frequency thermal noise $\sqrt[]{S_{ν, t h} (f)}$ generated by mode LG_p_,_l

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Table 2. Reference cavity overall frequency thermal noise $\sqrt[]{S_{ν, t h} (f)}$ generated by mode LG_p_,_l

p	l
p	0	1	2	3	4	5
0	0.0961	0.0943	0.0925	0.0909	0.0893	0.0877
1	0.0926	0.0909	0.0894	0.0879	0.0864	0.0850
2	0.0894	0.0879	0.0865	0.0851	0.0838	0.0826
3	0.0865	0.0852	0.0839	0.0827	0.0815	0.0804
4	0.0839	0.0827	0.0816	0.0805	0.0794	0.0784
5	0.0816	0.0805	0.0795	0.0785	0.0776	0.0766

Table 3. Different modes of noise and reduction rate

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Table 3. Different modes of noise and reduction rate

P_in /μW	f /Hz	Minimum total noise corresponds to mode	S_ν /（Hz/Hz^1/2）	Reduction rate /%
1	0.5	LG_17，0	0.0343	15.98
	1.0	LG_13，0	0.0254	12.17
	10.0	LG_0，0	0.0092	0
10	0.5	LG_25，0	0.0316	22.55
	1.0	LG_25，0	0.0227	21.53
	10.0	LG_13，0	0.0080	12.17
100	0.5	LG_25，0	0.0312	23.49
	1.0	LG_25，0	0.0221	23.38
	10.0	LG_25，0	0.0072	21.53

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Lianlian Du, Jingfang Liu, Jiamin Liu, Rongguo Yang, Hengxin Sun, Jiangrui Gao. Thermal Noise Analysis Based on Higher-Order Mode Laser Frequency Stabilization[J]. Acta Optica Sinica, 2024, 44(13): 1314001

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Paper Information

Category: Lasers and Laser Optics

Received: Jan. 22, 2024

Accepted: Mar. 7, 2024

Published Online: Jul. 4, 2024

The Author Email: Sun Hengxin (hxsun@sxu.edu.cn)

DOI:10.3788/AOS240547

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Reference cavity parameters

Table 1. Reference cavity parameters

Table 2. Reference cavity overall frequency thermal noise Sν,th(f) generated by mode LGp, l

Table 2. Reference cavity overall frequency thermal noise Sν,th(f) generated by mode LGp, l

Table 3. Different modes of noise and reduction rate

Table 3. Different modes of noise and reduction rate

Table 2. Reference cavity overall frequency thermal noise $\sqrt[]{S_{ν, t h} (f)}$ generated by mode LG_p_,_l

Table 2. Reference cavity overall frequency thermal noise $\sqrt[]{S_{ν, t h} (f)}$ generated by mode LG_p_,_l