Efficient generation of ultrashort, wavelength-tunable infrared pulses

E. C. Cheung; J. M. Liu

doi:10.1364/JOSAB.8.001491

Journal of the Optical Society of America B
Vol. 8,
Issue 7,
pp. 1491-1506
(1991)
•https://doi.org/10.1364/JOSAB.8.001491

Efficient generation of ultrashort, wavelength-tunable infrared pulses

E. C. Cheung and J. M. Liu

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E. C. Cheung and J. M. Liu, "Efficient generation of ultrashort, wavelength-tunable infrared pulses," J. Opt. Soc. Am. B 8, 1491-1506 (1991)

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Abstract

A theory for a cw synchronously pumped, singly resonant optical parametric oscillator with Gaussian beams is presented. It accounts for most of the spatial and temporal effects of the interacting beams in the nonlinear crystal. The optimum design criteria for the focus tightness of the signal and the pump beams and the length of the crystal are given. We consider various nonlinear crystals with two differently mode-locked Nd:YLF sources used as pumps to generate wavelengths from 1 to 13 μm. Results from numerical simulations indicate that with the proper design of the optical parametric oscillator it is possible to obtain energy conversion efficiencies from the pump to the signal and the idler of ~70% while maintaining signal-pulse durations shorter than the pump-pulse duration.

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Type of Collinear Interaction^b	Optimum Beam-Waist Ratios	Other Ratios Used	Geometric Gain Coefficient g
o → e + e	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = \| \frac{α_{2} - α_{1}}{α_{3} - α_{2}} \|$	—	(\|α₂ − α₁\| + \|α₃ − α₁\| + \|α₃ − α₂\|)⁻²
e → e + e
e → e + o	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = \| \frac{α_{2} - α_{1}}{α_{3} - α_{1}} \|$
e → o + e
o → e + e	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = {(\frac{{w_{10}}^{2}}{{w_{10}}^{2} + {w_{30}}^{2}})}^{1 / 2}$	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = 4$	${[{α_{1}}^{2} (1 + \frac{{w_{30}}^{2}}{{w_{10}}^{2}} + \frac{{w_{30}}^{2}}{{w_{20}}^{2}}) (1 + \frac{w_{20}}{{w_{30}}^{2}})]}^{- 1}$
o → o + e	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = {(\frac{{w_{20}}^{2}}{{w_{20}}^{2} + {w_{30}}^{2}})}^{1 / 2}$	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = 4$	${[{α_{2}}^{2} (1 + \frac{{w_{30}}^{2}}{{w_{10}}^{2}} + \frac{{w_{30}}^{2}}{{w_{20}}^{2}}) (1 + \frac{{w_{10}}^{2}}{{w_{30}}^{2}})]}^{- 1}$
e → o + o	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = \frac{{w_{10}}^{2}}{{w_{30}}^{2}} {(1 + \frac{{w_{10}}^{2}}{{w_{30}}^{2}})}^{- 1 / 2}$	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = \frac{1}{4}$	${[{α_{3}}^{2} (1 + \frac{{w_{10}}^{2}}{{w_{20}}^{2}} + \frac{{w_{10}}^{2}}{{w_{30}}^{2}}) (1 + \frac{{w_{20}}^{2}}{{w_{10}}^{2}})]}^{- 1}$

Type	Process	Symbol	Formula
Temporal	Pulse walk-off	l_pulse	$\frac{c}{n_{1} - n_{3} + ω_{1} (d n_{1} / d ω_{1}) - ω_{3} (d n_{3} / d ω_{3})} Δ t_{3}$
Temporal	Crystal bandwidth	l_Δ_ω	$\frac{c}{n_{2} - n_{1} + ω_{2} (d n_{2} / d ω_{2}) - ω_{1} (d n_{1} / d ω_{1})} Δ t_{3}$
Temporal	Crystal dispersion	l_disp	$Δ {t_{3}}^{2} {(\frac{{λ_{1}}^{3}}{π c^{2}} \frac{d^{2} n_{1}}{d {λ_{1}}^{2}})}^{- 1}$
Spatial	Maximum interaction	l_max	$2^{1 / 2} l_{d 2} {- (\frac{{l_{d 1}}^{2}}{{l_{w}}^{2}} - 4) + {[{(\frac{{l_{d 1}}^{2}}{{l_{w}}^{2}} - 4)}^{2} + 16 \frac{{l_{d 1}}^{2}}{{l_{d 2}}^{2}}]}^{1 / 2}}^{1 / 2}$
Spatial	Crystal acceptance angle	l_accept	${[{tan}^{- 1} (\frac{λ_{3}}{π w_{30} n_{3}}) (\frac{1}{λ_{3}} \frac{d n_{3}}{d θ} - \frac{1}{λ_{1}} \frac{d n_{1}}{d θ} - \frac{1}{λ_{2}} \frac{d n_{2}}{d θ})]}^{- 1}$

Parameter	Value
a1	0.84810
a2	0.37104
a3	0.40125
a4	0.74010

Property	AgGaS₂^a	AgGaSe₂^b	β-BaB₂O₄^c	Ba₂NaNb₅O₁₅^d	KNbO₃^e	KTiOPO₄^f	LiB₃O₅^g	LiIO₃^h	LiNbO₃ⁱ
Point group	$\bar{4}$ 2m	$\bar{4}$ 2m	3m	mm2	mm2	mm2	mm2	6	3m
n_x(n₀)
A	2.958	4.7357	1.7052	1	2.5880	2.1146	1.0686	2.1664	2.4273
B	2.770	2.1187	1.0307	3.9495	1.8066	0.89188	1.3831	1.2476	2.4775
C (μm²)	0.08703	0.19264	0.018225	0.040389	0.057107	0.043518	0.00851	0.037106	0.047502
D (μ⁻²)	0.00210	0.0012838	0.01345	0	0.000256	0.01320	0.0096	0.0076032	0.027169
n_y(n₀)
A	2.958	4.7357	1.7052	1	2.0344	2.1518	5.5540	2.1664	2.4273
B	2.770	2.1187	1.0307	3.9495	2.7649	0.87862	−3.0262	1.2476	2.4775
C (μ²)	0.08703	0.19264	0.018225	0.040140	0.050051	0.047528	−0.005459	0.037106	0.047502
D (μ⁻²)	0.00210	0.0012838	0.01345	0	0.000048	0.01327	0.01137	0.0076032	0.027169
n_z(n_e)
A	3.947	5.2958	1.6411	1	2.7868	2.3136	1.3956	1.9367	2.3501
B	1.550	1.3955	0.7342	3.6008	2.1610	1.00012	1.1862	0.98612	2.2319
C (μm²)	0.1307	0.28365	0.016667	0.032199	0.070156	0.056792	0.01192	0.033335	0.044428
D (μm²)	0.00233	0.0013430	0.01516	0	0.000555	0.01679	0.01457	0.0042623	0.021950
d₃₁ (pm/V)^j	0	0	0.15	−12.8	−15.8	6.5	−1.09	−4.64	−4.72
d₃₂	0	0	= d₃₁	−12.8	−18.3	5.0	1.17	= d₃₁	= d₃₁
d₃₃	0	0	—	−17.6	−27.4	13.7	0.065	−4.84	−45.1
d₂₄	0	0	= d₃₁^k	−12.2	17.1	7.6^l	−1.10	—	= d₃₁^k
d₁₅	0	0	= d₂₄	−12.8	16.5	6.1^l	1.00	= d₂₄	= d₂₄
d₃₆	28.7	49.3	0	0	0	0	0	0	0
d₁₄	= d₃₆^k	= d₃₆^k	0	0	0	0	0	0.31	0
d₂₅	= d₁₄	= d₁₄	0	0	0	0	0	= −d₁₄	0
d₂₂ = −d₂₁ = −d₁₆	0	0	2.2	0	0	0	0	0	2.40
Transmission window (nm)	500–13000	780–18000	200–3500	370–5000	400–5000	350–4500	160–2600	300–5500	400–5000
Damage threshold^m (GW/cm²)	0.02	0.02	10	1	1	1	25	0.5	1
	>25 (20 ps)		>10⁵ (100 fs)			>10⁵ (100 fs)		>10⁵ (100 fs)
dn_x/dT (×10⁻⁵/°C)	5	4	1.59	−2.5	5.83	1.1		−8.9	2.0
dn_z/dT (×10⁻⁵/°C)	5	4	0.517	8	−3.73	1.6		−7.8	7.6
Most efficient Interaction(s)	A, e → o + o	e → o + oⁿ	B, e → o + o	C, e → e + o	E, e → o + o	F, o → o + e	H, o → o + e	J, e → o + o	K, e → o + o
				D, e → o + e		G, o → e + o	I, o → e + o

Type of Collinear Interaction^b	Optimum Beam-Waist Ratios	Other Ratios Used	Geometric Gain Coefficient g
o → e + e	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = \| \frac{α_{2} - α_{1}}{α_{3} - α_{2}} \|$	—	(\|α₂ − α₁\| + \|α₃ − α₁\| + \|α₃ − α₂\|)⁻²
e → e + e
e → e + o	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = \| \frac{α_{2} - α_{1}}{α_{3} - α_{1}} \|$
e → o + e
o → e + e	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = {(\frac{{w_{10}}^{2}}{{w_{10}}^{2} + {w_{30}}^{2}})}^{1 / 2}$	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = 4$	${[{α_{1}}^{2} (1 + \frac{{w_{30}}^{2}}{{w_{10}}^{2}} + \frac{{w_{30}}^{2}}{{w_{20}}^{2}}) (1 + \frac{w_{20}}{{w_{30}}^{2}})]}^{- 1}$
o → o + e	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = {(\frac{{w_{20}}^{2}}{{w_{20}}^{2} + {w_{30}}^{2}})}^{1 / 2}$	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = 4$	${[{α_{2}}^{2} (1 + \frac{{w_{30}}^{2}}{{w_{10}}^{2}} + \frac{{w_{30}}^{2}}{{w_{20}}^{2}}) (1 + \frac{{w_{10}}^{2}}{{w_{30}}^{2}})]}^{- 1}$
e → o + o	$\frac{{w_{20}}^{2}}{{w_{30}}^{2}} = \frac{{w_{10}}^{2}}{{w_{30}}^{2}} {(1 + \frac{{w_{10}}^{2}}{{w_{30}}^{2}})}^{- 1 / 2}$	$\frac{{w_{10}}^{2}}{{w_{30}}^{2}} = \frac{1}{4}$	${[{α_{3}}^{2} (1 + \frac{{w_{10}}^{2}}{{w_{20}}^{2}} + \frac{{w_{10}}^{2}}{{w_{30}}^{2}}) (1 + \frac{{w_{20}}^{2}}{{w_{10}}^{2}})]}^{- 1}$

Abstract

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Tables (4)

Equations (67)

Journal of the Optical Society of America B