Sellmeier equations and phase-matching characteristics of the nonlinear optical crystal RbBe2BO3F2

HuaXing Wu; GuiLing Wang; Xiao Yang Wang; Xin Zhang; Yong Zhu; Chuang Tian Chen

doi:10.1364/AO.48.004118

Applied Optics
Vol. 48,
Issue 21,
pp. 4118-4123
(2009)
•https://doi.org/10.1364/AO.48.004118

Sellmeier equations and phase-matching characteristics of the nonlinear optical crystal $Rb {Be}_{2} {BO}_{3} F_{2}$

HuaXing Wu, GuiLing Wang, Xiao Yang Wang, Xin Zhang, Yong Zhu, and Chuang Tian Chen

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HuaXing Wu, GuiLing Wang, Xiao Yang Wang, Xin Zhang, Yong Zhu, and Chuang Tian Chen, "Sellmeier equations and phase-matching characteristics of the nonlinear optical crystal RbBe₂BO₃F₂," Appl. Opt. 48, 4118-4123 (2009)

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Abstract

We have successfully grown a new nonlinear optical crystal, $Rb {Be}_{2} {BO}_{3} F_{2}$ (RBBF), which belongs to the group of borate-based nonlinear optical crystals. Its refractive indices in the visible spectral region and type I phase-matching angles from the deep ultraviolet to the near infrared have been determined. Based on the measured refractive indices and phase-matching angles, the Sellmeier equations of RBBF have also been derived.

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Wavelength (nm)	$n_{e}$			$n_{o}$
Wavelength (nm)	Calc.	Exp.	Δ^a	Calc.	Exp.	Δ^a
404.7	1.41998	1.41956	0.00042	1.49740	1.49761	$- 0.00021$
435.8	1.41789	1.41748	0.00041	1.49459	1.49469	$- 0.00010$
486.1	1.41535	1.41511	0.00024	1.49114	1.49128	$- 0.00014$
491.6	1.41511	1.41493	0.00018	1.49083	1.49092	$- 0.00009$
546.1	1.41319	1.41314	0.00005	1.48817	1.48827	$- 0.00010$
577	1.41234	1.41238	$- 0.00004$	1.48697	1.48706	$- 0.00009$
5893	1.41203	1.41178	0.00025	1.48653	1.48636	0.00017
656.3	1.41066	1.41071	$- 0.00005$	1.48454	1.48468	$- 0.00014$
694.3	1.41005	1.41011	$- 0.00006$	1.48362	1.48384	$- 0.00022$

Fundamental Wavelength (nm)	SHG Wavelength (nm)	Phase-Matching Angle (deg)
Fundamental Wavelength (nm)	SHG Wavelength (nm)	Exp.	Calc.	Δ
${354.7}^{IV}$	177.3	73.38	73.07	0.31
$360^{III}$	180	70.31	70.50	$- 0.19$
$365^{III}$	182.5	68.64	68.40	0.24
$370^{III}$	185	66.92	66.54	0.38
$375^{III}$	187.5	65.04	64.85	0.19
$380^{III}$	190	63.51	63.30	0.21
$385^{III}$	192.5	61.85	61.87	$- 0.02$
$390^{III}$	195	60.60	60.53	0.07
$395^{III}$	197.5	59.49	59.28	0.21
$400^{III}$	200	58.04	58.11	$- 0.07$
$405^{III}$	202.5	56.94	57.00	$- 0.06$
$410^{III}$	205	55.83	55.95	$- 0.12$
$415^{III}$	207.5	54.88	54.96	$- 0.08$
$420^{III}$	210	54.14	54.01	0.13
$425^{III}$	212.5	53.39	53.10	0.29
$430^{III}$	215	52.37	52.24	0.13
$435^{III}$	217.5	51.58	51.41	0.17
$440^{III}$	220	50.81	50.61	0.20
$515^{I}$	257.5	41.17	41.52	$- 0.35$
${529.6}^{I}$	264.8	39.86	40.18	$- 0.32$
$532^{I}$	266	39.97	39.97	0
${549.7}^{I}$	274.9	38.24	38.51	$- 0.27$
${570.2}^{I}$	285.1	36.74	36.96	$- 0.22$
${589.7}^{I}$	294.9	35.38	35.62	$- 0.24$
$610^{I}$	305	34.00	34.35	$- 0.35$
${629.7}^{I}$	314.9	32.89	33.22	$- 0.33$
${664.5}^{I}$	332.3	31.38	31.44	$- 0.06$
$730^{II}$	365	28.55	28.68	$- 0.13$
$740^{II}$	370	28.20	28.32	$- 0.12$
$750^{II}$	375	27.82	27.97	$- 0.15$
${750.1}^{I}$	375.1	27.83	27.97	$- 0.14$
$760^{II}$	380	27.55	27.63	$- 0.08$
${760.8}^{I}$	380.4	27.56	27.60	$- 0.04$
$770^{II}$	385	27.16	27.30	$- 0.14$
$780^{II}$	390	26.93	26.99	$- 0.06$
$790^{II}$	395	26.55	26.69	$- 0.14$
${799.7}^{I}$	399.9	26.30	26.40	$- 0.10$
$800^{II}$	400	26.26	26.39	$- 0.13$
$810^{II}$	405	26.04	26.11	$- 0.07$
${812.2}^{I}$	406.1	26.12	26.05	0.07
$820^{II}$	410	25.81	25.84	$- 0.03$
$830^{II}$	415	25.52	25.58	$- 0.06$
$840^{II}$	420	25.28	25.32	$- 0.04$
${849.4}^{I}$	424.7	25.05	25.09	$- 0.04$
$850^{II}$	425	25.05	25.08	$- 0.03$
$860^{II}$	430	24.80	24.84	$- 0.04$
$870^{II}$	435	24.66	24.62	0.04
$880^{II}$	440	24.36	24.40	$- 0.04$
${897.7}^{I}$	448.9	23.93	24.03	$- 0.10$
${949.8}^{I}$	474.9	23.22	23.07	0.15
${997.7}^{I}$	498.9	22.53	22.34	0.19
$1064^{I}$	532	21.62	21.53	0.09
${1109.0}^{I}$	554.5	21.42	21.10	0.32
${1203.1}^{I}$	601.6	20.90	20.46	0.44
${1299.2}^{I}$	649.6	20.44	20.12	0.32
${1399.5}^{I}$	699.8	20.34	20.02	0.32

Signal Output Wavelength (nm)	Idler Output Wavelength (nm)	Sum-Frequency Angle (deg)
Signal Output Wavelength (nm)	Idler Output Wavelength (nm)	Exp.	Calc.	Δ
664.5	760.8	29.37	29.41	$- 0.04$
629.7	812.2	29.02	29.25	$- 0.23$
610.0	847.5	28.88	29.11	$- 0.23$
589.7	890.1	28.73	28.90	$- 0.17$
570.2	938.5	28.48	28.64	$- 0.16$
549.7	999.9	28.23	28.29	$- 0.06$
529.6	1074.0	28.06	27.86	0.20
515.0	1139.6	27.51	27.47	0.04

Wavelength (nm)	$n_{e}$			$n_{o}$
Wavelength (nm)	Calc.	Exp.	Δ^a	Calc.	Exp.	Δ^a
404.7	1.41998	1.41956	0.00042	1.49740	1.49761	$- 0.00021$
435.8	1.41789	1.41748	0.00041	1.49459	1.49469	$- 0.00010$
486.1	1.41535	1.41511	0.00024	1.49114	1.49128	$- 0.00014$
491.6	1.41511	1.41493	0.00018	1.49083	1.49092	$- 0.00009$
546.1	1.41319	1.41314	0.00005	1.48817	1.48827	$- 0.00010$
577	1.41234	1.41238	$- 0.00004$	1.48697	1.48706	$- 0.00009$
5893	1.41203	1.41178	0.00025	1.48653	1.48636	0.00017
656.3	1.41066	1.41071	$- 0.00005$	1.48454	1.48468	$- 0.00014$
694.3	1.41005	1.41011	$- 0.00006$	1.48362	1.48384	$- 0.00022$

Fundamental Wavelength (nm)	SHG Wavelength (nm)	Phase-Matching Angle (deg)
Fundamental Wavelength (nm)	SHG Wavelength (nm)	Exp.	Calc.	Δ
${354.7}^{IV}$	177.3	73.38	73.07	0.31
$360^{III}$	180	70.31	70.50	$- 0.19$
$365^{III}$	182.5	68.64	68.40	0.24
$370^{III}$	185	66.92	66.54	0.38
$375^{III}$	187.5	65.04	64.85	0.19
$380^{III}$	190	63.51	63.30	0.21
$385^{III}$	192.5	61.85	61.87	$- 0.02$
$390^{III}$	195	60.60	60.53	0.07
$395^{III}$	197.5	59.49	59.28	0.21
$400^{III}$	200	58.04	58.11	$- 0.07$
$405^{III}$	202.5	56.94	57.00	$- 0.06$
$410^{III}$	205	55.83	55.95	$- 0.12$
$415^{III}$	207.5	54.88	54.96	$- 0.08$
$420^{III}$	210	54.14	54.01	0.13
$425^{III}$	212.5	53.39	53.10	0.29
$430^{III}$	215	52.37	52.24	0.13
$435^{III}$	217.5	51.58	51.41	0.17
$440^{III}$	220	50.81	50.61	0.20
$515^{I}$	257.5	41.17	41.52	$- 0.35$
${529.6}^{I}$	264.8	39.86	40.18	$- 0.32$
$532^{I}$	266	39.97	39.97	0
${549.7}^{I}$	274.9	38.24	38.51	$- 0.27$
${570.2}^{I}$	285.1	36.74	36.96	$- 0.22$
${589.7}^{I}$	294.9	35.38	35.62	$- 0.24$
$610^{I}$	305	34.00	34.35	$- 0.35$
${629.7}^{I}$	314.9	32.89	33.22	$- 0.33$
${664.5}^{I}$	332.3	31.38	31.44	$- 0.06$
$730^{II}$	365	28.55	28.68	$- 0.13$
$740^{II}$	370	28.20	28.32	$- 0.12$
$750^{II}$	375	27.82	27.97	$- 0.15$
${750.1}^{I}$	375.1	27.83	27.97	$- 0.14$
$760^{II}$	380	27.55	27.63	$- 0.08$
${760.8}^{I}$	380.4	27.56	27.60	$- 0.04$
$770^{II}$	385	27.16	27.30	$- 0.14$
$780^{II}$	390	26.93	26.99	$- 0.06$
$790^{II}$	395	26.55	26.69	$- 0.14$
${799.7}^{I}$	399.9	26.30	26.40	$- 0.10$
$800^{II}$	400	26.26	26.39	$- 0.13$
$810^{II}$	405	26.04	26.11	$- 0.07$
${812.2}^{I}$	406.1	26.12	26.05	0.07
$820^{II}$	410	25.81	25.84	$- 0.03$
$830^{II}$	415	25.52	25.58	$- 0.06$
$840^{II}$	420	25.28	25.32	$- 0.04$
${849.4}^{I}$	424.7	25.05	25.09	$- 0.04$
$850^{II}$	425	25.05	25.08	$- 0.03$
$860^{II}$	430	24.80	24.84	$- 0.04$
$870^{II}$	435	24.66	24.62	0.04
$880^{II}$	440	24.36	24.40	$- 0.04$
${897.7}^{I}$	448.9	23.93	24.03	$- 0.10$
${949.8}^{I}$	474.9	23.22	23.07	0.15
${997.7}^{I}$	498.9	22.53	22.34	0.19
$1064^{I}$	532	21.62	21.53	0.09
${1109.0}^{I}$	554.5	21.42	21.10	0.32
${1203.1}^{I}$	601.6	20.90	20.46	0.44
${1299.2}^{I}$	649.6	20.44	20.12	0.32
${1399.5}^{I}$	699.8	20.34	20.02	0.32

Abstract

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Tables (3)

Equations (1)

Applied Optics