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Velocity matching by pulse front tilting for large-area THz-pulse generation

János Hebling, Gábor Almási, Ida Z. Kozma, and Jürgen Kuhl

Open Access Open Access

Abstract

We propose a generally applicable velocity matching method for THz-pulse generation by optical rectification in the range below the phonon frequency of the nonlinear material. Velocity matching is based on pulse front tilting of the ultrashort excitation pulse and is able to produce a large-area THz beam. Tuning of the THz radiation by changing the tilt angle is experimentally demonstrated for a narrow line in the range between 0.8-0.97 times the phonon frequency. According to model calculations broadband THz radiation can be generated at lower frequencies. Advantages of the new velocity matching technique in comparison to the electro-optic Cherenkov effect and non-collinear beam mixing are discussed.

©2002 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Two different schemes of THz excitation. For the usual Cherenkov geometry (a), the THz radiation is emitted as a cone characterized by the angle ΘC. Velocity matching (see Eq. 4) is satisfied, but the exciting beam has to be very narrow (see Eq. 3). Velocity matching by pulse front tilting (b) creates a plane THz wave without any upper limit for the exciting beam cross-section.

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Fig. 2.
Fig. 2. Measured differential transmission versus probe delay for γ = 39.3° tilt angle. The inset shows the corresponding spectrum of the radiation. Its peak at 10.16 THz is in good agreement with the 10.12 THz calculated from Eq. 4. Changing γ, we were able to tune the spectrum from 9.0-10.7 THz.

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Fig. 3.
Fig. 3. Calculated dependence of the THz field amplitude spectrum on the GaP crystal length for velocities adjusted to generate a narrow spectrum at 9 THz (a), and 6 THz (b), respectively. During the calculations the excitation pulse duration and the polariton linewidth were supposed to be 30 fs and 1.1 cm-1, respectively.

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Fig. 4.
Fig. 4. Illustration of phase-matching (wave-vector conservation) for THz generation (a). Application of two ultrashort pulses without pulse front tilt for mixing achieves only partial overlap of the beam cross-sections, (b). For a beam with tilted pulse front (see Fig. 1b), the spectral components overlap across the whole cross-section of the beam, resulting in efficient THz generation.

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Equations (6)

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v vis gr = v THz ph
w ≪ v vis gr ∙ τ ,
Θ C = cos − 1 ( v THz ph v vis gr ) .
v vis gr ∙ cos γ = v THz ph .
Δ k = k vis + THz − k vis − k THz = 0 ,
tan γ = − n n g r ∙ ω ∙ d Θ d ω , where n g r = n − ω ∙ d n d ω = c v vis g r
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