## Abstract

We investigated terahertz pulses from a rotating fan-out type poled lithium niobate (LiNbO_{3}) pumped by femtosecond laser pulses. In particular, the rotating fan-out type poled sample produces an uncertain phase-matching wave vector perpendicular to input laser pulses. Such a wave vector allowed us to observe terahertz pulses normally unobservable from bulk or periodically poled LiNbO_{3} at large rotation angles because of the terahertz wave critical angle of LiNbO_{3}. Further, we explained center frequency dependence on rotation angles by difference frequency generation process with the uncertain wave vector. We also discussed bandwidth dependence and terahertz pulse power regarding rotation angles.

©2010 Optical Society of America

## 1. Introduction

Terahertz (THz) pulses with narrow bands have been generated from periodically poled LiNbO_{3} pumped by femtosecond laser pulses [1–12]. A generation mechanism is based on an χ^{(2)} nonlinear process, difference frequency generation (DFG) [6–9]. Center frequency and bandwidth of THz pulses depend on poling periods and poled domain numbers, respectively.

Based on position-dependent periods of the fan-out structure, fan-out type poled LiNbO_{3} has been proposed for tuning THz pulse center frequency [10]. However, rotating the fan-out type poled structure on the poled direction axis, i.e., Z-axis, at the center of the structure input face does not provide well-defined periods of poled domains for input femtosecond laser pulses propagating on an XY-plane, unlike the periodic poled structure. The unwell-defined period of poled domains produces phase-matching wave vector uncertainty. Reports of wave vector uncertainty due to tight input laser pulse focusing have revealed unusual THz pulse generation in periodically poled LiNbO_{3}, such as the case of THz pulse generation perpendicular to input laser pulses [13]. Thus, phase-matching wave vector uncertainty in the rotating fan-out type poled structure gives rise to interesting THz generation not observable in a rotating periodically poled structure.

In this paper, we investigated the effects of an uncertain phase-matching wave vector of rotating fan-out type poled LiNbO_{3} on THz generation. We observed THz pulses at large rotation angles in which such pulses are normally unobservable in bulk or periodically poled LiNbO_{3} due to the THz wave critical angle in LiNbO_{3}. DFG process with the uncertain phase-matching wave vector perpendicular to input laser pulses explains well such THz pulse generation, as well as the dependence of THz pulse center frequency on rotation angles. We also discussed bandwidth dependence and THz pulse power on rotation angles.

## 2. Experiment

Figure 1
shows a schematic view of THz pulse generation from fan-out type poled LiNbO_{3} rotating at the center of the structure input face on the poled direction axis, i.e., Z-axis. Further, input laser and generated THz pulses were propagated on an XY-plane. The input laser incident angle corresponded to rotation angle *α*. It should be emphasized that the propagation direction of generated THz pulses varied from that of laser pulses, whereas the direction of laser and THz pulses were identical in a periodically poled structure, due to phase-matching wave vector uncertainty in a rotating fan-out poled structure, producing wave vectors perpendicular to laser pulse propagation. Finally, angle γ denoted the angle between laser direction and THz pulse propagation.

Fan-out type poled LiNbO_{3} was fabricated by conventional electric-polling. The period of poled domains varied from 60 (left) to 80 μm (right) along the sample (Fig. 1). Sample size was 5 mm (width) × 0.5 mm (thickness) × 20 mm (length). The axes of LiNbO_{3}, *x*, *y* and *z*, are parallel to X, Y and Z axes, respectively. A conventional photoconductive THz time-domain setup was used in experiments. A femtosecond laser with 76 MHz of repetition rate and 190 fs of pulse width was employed. The center wavelength of the laser pulse was 800 nm and average output power was 1.1 watts before a mechanical chopper. The beam size of the focused input pulse was about 0.5 mm at the input face. A generated THz pulse was collimated and guided by two 90° off-axis metal parabolic mirrors with 4-inch of focal length. A photoconductive dipole antenna with 5-μm of dipole gap, being fabricated with low-temperature grown GaAs and a hyper-hemi spherical silicon lens, was used to detect THz pulses. All measured data were acquired in an air tight box under 10% of humidity.

## 3. Result

Figure 2
shows time-domain waveforms of THz pulses during sample clockwise (a) and counter-clockwise rotation (c) with rotation angle α = 40°, as well as THz pulse spectra during sample clockwise (b) and counter-clockwise rotation (d) with rotation angle α = 0°, 10°, 20°, 30° and 40°. Decayed oscillating time-domain waveforms present conventional THz pulse characteristics from multiple poled LiNbO_{3} pumped by femtosecond laser pulses. In the clockwise direction, THz pulse center frequency increases as α increases, while decreasing in the counter-clockwise direction. Accordingly, THz pulses were observed at large rotation angles such as 30° and 40°. Of note, when periodic poled LiNbO_{3} is rotated at large angles, THz pulses are unobservable from periodic poled LiNbO_{3} in which laser propagation directions and THz pulses are identical.

To comprehend the results, we considered THz generation based on a DFG nonlinear process. Momentum and energy conservation laws provided the following relations [13]:

*k*_{1}and

*k*_{2}are light wave vectors, taking a part in the DFG process, and parallel

*k*_{Λ}is a phase-matching wave vector of the poled domains. We assumed that

*k*_{Λ}was not parallel to

*k*_{1}because of the uncertain phase-matching wave vector via rotation. Thus,

*k*_{Λ}is able to be split into two components:

*k*_{Λ||}parallel to

*k*_{1}and the uncertain component,

*k*_{Λ⊥}, perpendicular to

*k*_{1}.

*k**represents a THz pulse wave vector, not being parallel to*

_{THz}

*k*_{1}due to

*k*_{Λ⊥}.

*c*is light velocity in free space, and

*n*and

_{laser}*n*are the LiNbO

_{THz}_{3}refractive indices for the laser and THz pulse, respectively. Accordingly,

*k*

_{Λ||}and

*k*

_{Λ⊥}are able to be expressed by

*k*and γ as follows:

_{THz}Since *k*
_{Λ||} = 2π/*Λ*(α)* _{eff}* and

*k*= 2π

_{THz}*n*/

_{THz}f_{c}*c*, where

*Λ*(α)

*is the effective angle-dependent period of the fan-out structure along the direction of laser pulse propagation and*

_{eff}*f*represents the center frequency of the THz pulse,

_{c}^{−1}[sinα/

*n*] – sin

_{laser}^{−1}[sinα/

*n*]) under the assumption that the THz output angle and laser pulses were identical. When γ = 0, relations corresponds to those of a periodically poled structure.

_{THz}Figure 3
represents measured center frequency dependency of the THz pulse on the rotation angle, being well explained by Eq. (5) because *Λ*(α)* _{eff}* shortened (longer) during clockwise rotation (counter-clockwise rotation) as α increased. Accordingly, the effective slope of clockwise center frequency differs from that of counter clockwise center frequency. The slope is roughly expressed by the effective period, Δ

*f*

_{c}/Δα = (−1/Λ

^{2}

_{eff})ΔΛ

_{eff}/Δα. As a matter of convenience, superscripts, ‘cw’ and ‘c-cw’ denote clockwise and counter-clockwise rotation, respectively. For example,

*f*

_{c}

^{cw}and

*f*

_{c}

^{c-cw}denote clockwise and counterclockwise center frequencies, respectively. The slope of Δ

*f*

_{c}

^{cw}/Δα was about 1.25 × 10

^{−3}THz/1°, while the slope of Δ

*f*

_{c}

^{c-cw}/Δα was about −2.5 × 10

^{−3}THz/1°. ΔΛ

^{cw}

_{eff}/Δα (ΔΛ

^{c-cw}

_{eff}/Δα) is negative (positive) because ΔΛ

^{cw}

_{eff}(ΔΛ

^{c-cw}

_{eff}) decreases (increases) as α increases, Δ

*f*

_{c}

^{cw}/Δα (Δ

*f*

_{c}

^{c-cw}/Δα) thus having a positive (negative) sign. We roughly estimated the absolute values of ΔΛ

^{cw}

_{eff}/Δα and ΔΛ

^{c-cw}

_{eff}/Δα, finding the absolute value of ΔΛ

^{cw}

_{eff}/Δα to be much smaller than that of ΔΛ

^{c-cw}

_{eff}/Δα. Therefore, the absolute value of Δ

*f*

_{c}

^{cw}/Δα was smaller than that of Δ

*f*

_{c}

^{c-cw}/Δα, although 1/Λ

^{2}

_{eff}of the counter-clockwise is larger than that of the clockwise case. Λ

^{cw}

_{eff}and Λ

^{c-cw}

_{eff}, being calculated from measured center frequencies and Eq. (5) with

*n*= 2.3 and

_{laser}*n*= 5.2, are summarized in Table 1 .

_{THz}Due to poled domain chirping, THz pulse bandwidth broadens as α increases. Further, chirping increases as α increases irrespective of rotation direction. In particular, chirping strongly contributes to the emergence of wave vector components perpendicular to the direction of laser pulse propagation. (Fig. 1) Thus, *k*
_{Λ⊥} is expected to increase when α increases, irrespective of rotation direction.

In Table 2
, we summarized *k*
_{Λ}, *k*
_{Λ||}, *k*
_{Λ⊥} and *k*
_{THz}, as well as the internal incident angles of THz pulses, θ, for clockwise and counter-clockwise rotations. The internal incident angles of THz pulses were less than 11.1°, equating the THz wave critical angle in LiNbO_{3} for all rotation angles. Accordingly, *k*
^{cw}
_{Λ⊥} was larger than *k*
^{c-cw}
_{Λ⊥} because our clockwise rotating fan-out type poled sample provides more chirped poled domains for input laser pulses.

THz pulse intensity decreases as α increases due to input laser pulse reflection on the input surface, *R*(α)_{in-laser}, as well as THz pulse internal reflection on the output surface, *R*(α)_{int-THz}, increasing as α increases. We assumed that THz pulse intensity would be proportional to (1 - *R*(α)_{in-laser}) × (1 - *R*(α)_{int-THz}) = *I*(α)_{THz}. Hence, we calculated *I*(α)_{THz} by using the Fresnel equation on input and output surface reflections when α = 0°, 10°, 20°, 30° and 40°. Output laser directions and THz pulses were assumed to be identical, as shown in Fig. 1. Laser and THz pulse polarization was parallel to the poled direction (Z-axis). The spectral intensity integral of measured THz pulses was proportional to THz pulse intensity over all frequencies, *S*(α). Thus, calculated *I*(α)_{THz} is examinable by *S*(α). Figure 4
represents *I*(α)_{THz} (solid circles) and *S*(α) (open circles) for the clockwise case, clearly revealing good agreement.

## 4. Conclusion

In conclusion, we investigated THz pulse characteristics of LiNbO_{3} with a rotating fan-out type poled structure. Phase-matching wave vector uncertainty of poled domains allowed us to observe THz pulses from the fan-out type sample at large rotation angles. We explained center frequency dependence on the rotation angle by considering the uncertain phase-matching wave vector perpendicular to the laser pulse wave vector in difference frequency generation process. Moreover, we explained the dependence of bandwidth and THz pulse power on the rotation angle by poled domain chirping as well as reflection of THz and laser pulses on the sample surfaces.

## Acknowledgement

This work was supported by the Ministry of Education, Science, and Technology through the National Research Foundation (2010-0001858), the Ministry of Knowledge and Economy of Korea through the Ultrashort Quantum Beam Facility Program and the Photonics 2020 research project through a grant provided by GIST in 2010.

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