Analysis of electro-optic crystal-based Fabry-Perot etalons for high-speed spatial light modulators

Kuniharu Takizawa

doi:10.1364/AO.42.001052

Applied Optics
Vol. 42,
Issue 6,
pp. 1052-1067
(2003)
•https://doi.org/10.1364/AO.42.001052

Analysis of electro-optic crystal-based Fabry-Perot etalons for high-speed spatial light modulators

Kuniharu Takizawa

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Kuniharu Takizawa, "Analysis of electro-optic crystal-based Fabry-Perot etalons for high-speed spatial light modulators," Appl. Opt. 42, 1052-1067 (2003)

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Abstract

The use of electro-optic (EO) crystal-based Fabry-Perot modulators (FPMs) as high-speed spatial light modulators is proposed. The FPMs operate with an extremely low drive voltage and a high extinction ratio. It is revealed by analysis of both the linear EO effect and the inverse piezoelectric effect of various EO crystals that three kinds of crystal configuration are suitable as FPMs. One of these is applicable to isotropic crystals, point groups 23 and 4̅3m, and the others are better suited for uniaxial EO crystals, point groups 4̅2m and 3m. Typical EO crystals suitable as FPMs are ferroelectric crystals such as LiNbO₃, LiTaO₃, and LiIO₃ and sillenite compounds such as Bi₁₂SiO₂₀ and Bi₁₂GeO₂₀ as well as compound semiconductors such as GaAs and GaP.

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Material	Point Group	EO Coefficient r ₄₁ (pm/V)	n ₀ ³ r ₄₁ (pm/V)	Refractive Index	Wavelength (nm)	Piezoelectric Strain Coefficient d ₁₄ (pC/N)	Relative Dielectric Constant
Bi₁₂SiO₂₀	23	5.0	81.98	2.5504	633	40	56
Bi₁₂GeO₂₀	23	3.40	52.8	2.5405	633	31	40
Bi₁₂TiO₂₀	23	5.17	85.77	2.5504	633		47
GaAs	4̅3m	-1.44	53.63	3.455	1150	-2.7	12.5
GaP	4̅3m	-0.97	35.17	3.3098	633		11.1

Material	Point Group	EO Coefficient (pm/V)	Refractive Index	Wavelength (nm)	Piezoelectric Strain Coefficient (pC/N)	Relative Dielectric Constant
LiIO₃	6	r ₁₃ = +6.4			d ₁₄ = 7.3
		r ₃₃ = +4.2			d ₁₅ = 49.3
		r ₄₁ = +3.1	n _o = 1.8830		d ₃₁ = 7.3	k ₁ = 7.9
		r ₅₁ = +7.9	n _e = 1.7367	633	d ₃₃ = +92.7	k ₃ = 6.4
LiNbO₃	3m	r ₁₃ = +9.6			d ₁₅ = +74.0
		r ₂₂ = +6.8			d ₂₂ = +20.7
		r ₃₃ = +30.9	n _o = 2.2868		d ₃₁ = -0.86	k ₁ = 84.6
		r ₅₁ = +32.6	n _e = 2.2030	633	d ₃₃ = +16.2	k ₃ = 28.6
LiTaO₃	3m	r ₁₃ = +8.49			d ₁₅ = +26
		r ₂₂ = -0.2			d ₂₂ = +8.5
		r ₃₃ = +30.5	n _o = 2.1774		d ₃₁ = -3.0	k ₁ = 53.6
		r ₅₁ = +20	n _e = 2.1818	633	d ₃₃ = +9.2	k ₃ = 43.4
Pb₅Ge₃O₁₁	3	r ₁₁ = 0.276			d ₁₁ = 0.1
		r ₁₃ = 10.9			d ₁₄ = 0.2
		r ₂₂ = 2.35			d ₁₅ = 3
		r ₃₃ = 15.2			d ₂₂ = 2
		r ₄₁ = 0.62	n _o = 2.116		d ₃₁ = 5.2	k ₁ = 22
		r ₅₁ = 6.1	n _e = 2.151	633	d ₃₃ = 6.2	k ₃ = 36
KH₂PO₄	4̅2m	r ₄₁ = 8.6	n _o = 1.5100		d ₁₄ = 1.28	k ₁ = 43.2
		r ₆₃ = -10.5	n _e = 1.4684	556	d ₃₆ = -20.9	k ₃ = 20.8
KD₂PO₄	4̅2m	r ₄₁ = 8.8	n _o = 1.5079			k ₁ = 58
		r ₆₃ = -26.4	n _e = 1.4683	546	d ₃₆ = +58	k ₃ = 48
(NH₄)H₂PO₄	4̅2m	r ₄₁ = 23.76	n _o = 1.52662		d ₁₄ = 1.76	k ₁ = 55.8
		r ₆₃ = -8.51	n _e = 1.48079	546	d ₃₆ = -48.3	k ₃ = 15.3
BaTiO₃	4mm	r ₁₃ = 24			d ₁₅ = 587
		r ₃₃ = 80	n _o = 2.4037	633	d ₃₁ = -34.7	k ₁ = 2920
		r ₅₁ = +1640a	n _e = 2.3607		d ₃₃ = 85.7	k ₃ = 168

Material	EO Coefficient (pm/V)	Refractive Index	Piezoelectric Strain Coefficient (pC/N)	Relative Dielectric Constant
KNbO₃	r ₁₃ = +28
	r ₂₃ = +1.3
	r ₃₃ = +64	n ₁ = 2.280		k ₁ = 160
	r ₄₂ = 380	n ₂ = 2.329		k ₂ = 1000
	r ₅₁ = 105	n ₃ = 2.169		k ₃ = 55
Ba₂NaNb₅O₁₅	r ₁₃ = 15		d ₁₅ = 32
	r ₂₃ = 13		d ₂₄ = 45
	r ₃₃ = 48	n ₁ = 2.326	d ₃₁ = -6.8	k ₁ = 238
	r ₄₂ = 92	n ₂ = 2.324	d ₃₂ = -6.9	k ₂ = 228
	r ₅₁ = 90	n ₃ = 2.221	d ₃₃ = 34	k ₃ = 43
Li(COOH)H₂O	r ₁₃ = -1.0		d ₁₅ = -15.0
	r ₂₃ = +3.2		d ₂₄ = +1.2
	r ₃₃ = -2.6	n ₁ = 1.3645	d ₃₁ = -2.1	k ₁ = 4.5
	r ₄₂ = +1.0	n ₂ = 1.4784	d ₃₂ = -6.7	k ₂ = 5.0
	r ₅₁ = +2.4	n ₃ = 1.5163	d ₃₃ = +9.2	k ₃ = 6.0

Material	Point Group	Half-Wave Voltage (V)	\|2n ³ r _ij\| (pm/V)	\|2n _o ³ r ₁₃ - 4n _o d ₃₃\| (pm/V)	\|δn\|	ξ₀ (deg)	Wavelength (nm)	Configuration
Bi₁₂SiO₂₀	23	3820	166	–	–	–	633	Fig. 8
Bi₁₂GeO₂₀	23	5860	111	–	–	–	633	Fig. 8
Bi₁₂TiO₂₀	23	3690	172	–	–	–	633	Fig. 8
GaAs	43m	9680	119	–	–	–	1150	Fig. 8
GaP	43m	9000	70.3	–	–	–	633	Fig. 8
KH₂PO₄	42m	7670	72	–	–	–	556	Fig. 8
KD₂PO₄	42m	3020	181	–	–	–	546	Fig. 8
(NH₄)H₂PO₄	42m	9020	60.6	–	–	–	586	Fig. 8
Pb₅Ge₃O₁₁	3	4160	152	–	–	–	633	Fig. 8
LiIO₃	6	1040 (810)	–	610 (780)	–	–	633	Fig. 11
LiTaO₃	3m	6650 (2480)	–	95.2 (255)	–	–	633	Fig. 11
		7780 (1670)	–	81.4 (378)	–	–		Fig. 11
LiNbO₃	3m	1510 (1670)	–		418 (378)	101 (0)	633	Fig. 15
BaTiO₃	4mm	4020 (425)	–	160 (1490)	–	–	633	Fig. 11
Li(COOH)H₂O	mm2	54,600 (145,000)	–	–	11.6 (4.36)	44.2 (46.3)	633	Fig. 15

Material	Point Group	EO Coefficient r ₄₁ (pm/V)	n ₀ ³ r ₄₁ (pm/V)	Refractive Index	Wavelength (nm)	Piezoelectric Strain Coefficient d ₁₄ (pC/N)	Relative Dielectric Constant
Bi₁₂SiO₂₀	23	5.0	81.98	2.5504	633	40	56
Bi₁₂GeO₂₀	23	3.40	52.8	2.5405	633	31	40
Bi₁₂TiO₂₀	23	5.17	85.77	2.5504	633		47
GaAs	4̅3m	-1.44	53.63	3.455	1150	-2.7	12.5
GaP	4̅3m	-0.97	35.17	3.3098	633		11.1

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Applied Optics