Theoretical analysis of the influence of crystalline orientation on Brillouin gain of whispering gallery mode resonators

Jingyi Tian; Jingyi Tian; Guoping Lin; Guoping Lin

doi:10.1364/JOSAB.509176

Journal of the Optical Society of America B
Vol. 41,
Issue 3,
pp. 712-719
(2024)
•https://doi.org/10.1364/JOSAB.509176

Theoretical analysis of the influence of crystalline orientation on Brillouin gain of whispering gallery mode resonators

Jingyi Tian and Guoping Lin

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Jingyi Tian and Guoping Lin, "Theoretical analysis of the influence of crystalline orientation on Brillouin gain of whispering gallery mode resonators," J. Opt. Soc. Am. B 41, 712-719 (2024)

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- Nonlinear or High Field Optics
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About this Article
History
- Original Manuscript: October 11, 2023
- Revised Manuscript: December 4, 2023
- Manuscript Accepted: January 31, 2024
- Published: February 26, 2024

Abstract

Brillouin scattering, arising from the interaction between photons and acoustic phonons, is well-known for its narrow gain profile, imposing stringent requirements for Brillouin lasers. However, in crystalline whispering gallery mode (WGM) optical resonators, the circular phonon path leads to intriguing gain profiles for Brillouin scattering due to the strong dependence of the phase velocity of acoustic waves on the crystalline axes’ orientation. Here, we present a theoretical investigation of Brillouin gain profiles in crystalline WGMRs considering different tangential directions and angles. Various host crystals ranging from tetragonal, cubic, and trigonal crystal groups, including magnesium fluoride, calcium fluoride, barium fluoride, lithium fluoride, strontium fluoride, sapphire, and lithium niobate, are studied. Our findings reveal significant variations in Brillouin shift depending on the crystal and its orientation, with the frequency shift broadening ranging from MHz to GHz.

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Configuration	Acoustic Velocity (km/s)	Brillouin Shift (GHz)	$Δ Ω (G H z) / 2 π$	Brillouin Gain Range (GHz)	Experimental Results (GHz)
$x, y - c u t M g F_{2}$	[6.6404–8.0222]	[11.7427–14.1863]	2.4436	[11.7250–14.2080]	[11.729–14.466] [26]
$z - c u t M g F_{2}$	[6.6404–8.1372]	[11.7427–14.3897]	2.6470	[11.7300–14.4120]
$[111] - c u t M g F_{2}$	[7.3812–8.1372]	[13.0528–14.3897]	1.3369	[[13.0350–14.4030]
$x, y, z - c u t C a F_{2}$	[6.5325–7.2142]	[12.0197–13.2740]	1.2543	[12.0080–13.2890]	12.0 derived from 17.5 at 1064 nm [35]
$[111] - c u t C a F_{2}$	[6.5325–6.5883]	[12.0197–12.1225]	0.1028	[12.0160–12.1280]
$x, y, z - c u t B a F_{2}$	[4.3094–4.3331]	[8.2240–8.2692]	0.0452	[8.2240–8.2700]	8.223 [23]
$[111] - c u t B a F_{2}$	[4.3094–4.3095]	[8.2240–8.2241]	0.000155	[8.2180–8.2300]
$x, y, z - c u t L i F$	[6.5767–7.4043]	[11.7336–13.2102]	1.4766	[11.7220–13.2340]
$[111] - c u t L i F$	[7.4043–7.4554]	[13.2102–13.3015]	0.0913	[13.2070–13.3050]
$x, y, z - c u t S r F_{2}$	[5.2417–5.4212]	[9.6764–10.0078]	0.3314	[9.6690–10.0150]	9.80 [25]
$[111] - c u t S r F_{2}$	[5.2417–5.2458]	[9.6764–9.6841]	0.0077	[9.6720–9.6880]
$x - c u t A l_{2} O_{3}$	[10.3956–11.2962]	[23.4229–25.4522]	2.0293	[23.4100–25.4800]
$y - c u t A l_{2} O_{3}$	[10.7185–11.2453]	[24.1504–25.3375]	1.1871	[24.1300–25.3500]
$z - c u t A l_{2} O_{3}$	[11.1803–11.1965]	[25.1911–25.2275]	0.0364	[25.2000–25.2200]
$[111] - c u t A l_{2} O_{3}$	[10.5949–11.2892]	[23.8721–25.4363]	1.5642	[23.8600–25.4500]
$x - c u t L i N b O_{3}$	[6.3686–7.2013]	[18.1716–20.5473]	2.3757	[18.1580–20.5620]
$y - c u t L i N b O_{3}$	[6.5440–7.2013]	[18.6720–20.5473]	1.8753	[18.6290–20.5640]
$z - c u t L i N b O_{3}$	[6.5600–6.5680]	[18.7177–18.7405]	0.0228	[18.7220–18.7350]
$[111] - c u t L i N b O_{3}$	[6.5191–6.8098]	[18.6010–19.4302]	0.8292	[18.5920–19.4410]

Abstract

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Equations (11)

Journal of the Optical Society of America B