Noncollinear second-harmonic generation in sub-micrometer-poled RbTiOPO<sub>4</sub>

S. Moscovich; A. Arie; R. Urneski; A. Agronin; G. Rosenman; Y. Rosenwaks

doi:10.1364/OPEX.12.002236

Optics Express
Vol. 12,
Issue 10,
pp. 2236-2242
(2004)
•https://doi.org/10.1364/OPEX.12.002236

Noncollinear second-harmonic generation in sub-micrometer-poled RbTiOPO₄

S. Moscovich, A. Arie, R. Urneski, A. Agronin, G. Rosenman, and Y. Rosenwaks

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S. Moscovich, A. Arie, R. Urneski, A. Agronin, G. Rosenman, and Y. Rosenwaks, "Noncollinear second-harmonic generation in sub-micrometer-poled RbTiOPO₄," Opt. Express 12, 2236-2242 (2004)

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About this Article
History
- Original Manuscript: April 20, 2004
- Revised Manuscript: May 5, 2004
- Manuscript Accepted: May 5, 2004
- Published: May 17, 2004

Abstract

We have generated noncollinear quasi-phase-matched second harmonic wave in an RbTiOPO₄ crystal that was poled using the high-voltage atomic force microscope (HV-AFM). To the best of our knowledge, this is the first systematic nonlinear frequency conversion study of samples produced by the HV-AFM method. The short poling period of 1.18 μm enabled us to observe second harmonic generation at very large angles with respect to the fundamental wave. The setup was used to optically explore the homogeneity of the poled area. The measurements are in a reasonable agreement with an analytic calculations.

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Fig. 1. Experimental setup for noncollinear second harmonic generation. Inset: K vector diagram for noncollinear second harmonic generation.

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Fig. 2. Variation of the second harmonic power in 1^st order QPM as the beam travels along the x-axis (length dimension) of the crystal.

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Fig. 3. Variation of the second harmonic power in 1^st order QPM as the beam travels along the z-axis (thickness dimension) of the crystal.

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Fig. 4. K Vector diagram for positive and negative angles in noncollinear SHG: Phase matching is achieved for one direction of propagation (a), but not for the opposite direction (b).

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Tables (2)

Table 1. Calculated and measured fundamental input angle and second harmonic output angle (both of them in air) for different QPM orders of noncollinear second harmonic generation. The angles are given in degrees.

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Table 2. Calculated and measured frequency doubling efficiency, effective interaction length and measured peak second harmonic power for different QPM orders of noncollinear second harmonic generation.

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Equations (6)

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\frac{λ_{2 ω}}{n_{2 ω}} = \frac{2 π}{∣ G ∣} \sqrt{{(1 - \frac{n_{ω}}{n_{2 ω}})}^{2} + 4 \frac{n_{ω}}{n_{2 ω}} \sin^{2} θ},

P_{2 ω} = \frac{2 ω_{1}^{2} d_{eff}^{2} k_{ω}}{π n_{ω}^{2} n_{2 ω} ε_{0} c^{3}} Lh P_{ω}^{2},

d_{eff} = \frac{2 d_{33}}{πm},

h (B, ξ) \approx ξG (2 B \sqrt{2 ξ}),

G (t) = \sqrt{\frac{2 π}{t^{2}}} \erf (\frac{t}{\sqrt{2}}) - \frac{2}{t^{2}} (1 - e^{\frac{- t^{2}}{2}}),

P_{2 ω} ≅ \frac{1.7 Lh P_{ω}^{2}}{m^{2}} .

Order	Calculated		Measured
m	θ_ω	θ _2ω	θ_ω	${θ_{2 ω}}^{+}$	${θ_{2 ω}}^{-}$
1	3.09	29.85	3	30	32
2	17.8	35.57	18	35	34
3	35.02	49.26	35	48	-
8	39.68	39.68	40	39	-

m	η _experiment	η _theory	L [μm]	P_2w [mW]
1	4.94e-4	3e-3	150	518
2	1.44e-4	6.8e-4	152	145
3	6.37e-5	2.3e-4	158	54.8
8	4.3e-5	8.35e-5	329	38.2

Order	Calculated		Measured
m	θ_ω	θ _2ω	θ_ω	${θ_{2 ω}}^{+}$	${θ_{2 ω}}^{-}$
1	3.09	29.85	3	30	32
2	17.8	35.57	18	35	34
3	35.02	49.26	35	48	-
8	39.68	39.68	40	39	-

m	η _experiment	η _theory	L [μm]	P_2w [mW]
1	4.94e-4	3e-3	150	518
2	1.44e-4	6.8e-4	152	145
3	6.37e-5	2.3e-4	158	54.8
8	4.3e-5	8.35e-5	329	38.2

Abstract

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Tables (2)

Equations (6)

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