Pump depleted gain prediction by taking account of the linear and nonlinear

jp jp

L τ j s i

=δ = (16) where τ is the pump pulse duration, δ_jp =1v_gj−1v_gp is the group velocity mismatch between signal/idler pulses and pump pulse. In this work, the wavelength of optical pump pulse is at 800 nm. The corresponding GVM are δip=528.6 fs/mm for idler wavelength (THz) is at 300 μm; δsp=－9.5 fs/mm for signal wavelength is at 802 nm. Accordingly, the selected GaSe crystal length is about 3 mm for optical pump pulse duration 1.5 ps.

6.3.3 Pump depleted gain prediction by taking account of the linear and nonlinear absorption

The output of the terahertz signal after the THz-OPA system can be explained by the parametric amplification process under a depleted pump beam condition [19]:

_i( ) [( ⁱ ) (1_p ²[( ₀) / , ])] exp( )

p

I r ω I sn r r l r αr

= ω − − × − (17)

where 1/ ( ) 1 ^{s p}

p s

l I

I λ ω

= Γ + ω (18)

and ₀ 1

/ ln(16[1 ])

2

p s

s p

r l I

I ω

= + ω (19) In Eqs. (17)-(19), Ip is the pump intensity; Is is the seeding THz intensity; Γ(λ) is the parametric gain coefficient; α is the absorption coefficient, which includes the linear and nonlinear absorption; ωj, j=p, s, or i is the angular frequency of the pump, the signal and the idler pulses (THz wave), respectively; r is length of the GaSe crystal. We note that sn in Eq.

(17) is the Jacobian elliptic function resulting from an inversion operation of the elliptic integral [19]. From the calculating results, the net gain could be expected. For instance, the pump/seeding THz intensity are set as 2×10⁹ W/cm² and 3.5×10³ W/cm², respectively, in the calculations. Consequently, the power amplification gain magnitude could reach as high as approximately 4.5 for the central frequency located at 1 THz. The prediction gain profile is shown in Fig. 6-9.

0.0 0.5 1.0 1.5 2.0

0 2 4 6 8 10 12 14

Pump : 2*10⁹ W/cm² Seed : 3.5*10³ W/cm²

Gain

Frequency (THz) Theoretical gain prediction

Fig. 6-9 Theoretical gain prediction in this THz-OPA system.

6.3.4 THz amplification experimental achievement

The GaSe external phase matching angles is set 3°~5°, which corresponds to the phase matching wavelength 300~1000 μm (0.3 THz ~ 1 THz). For THz-OPA system, the seeding THz time domain profile is shown as the black-line in the Fig. 6-10(a). Then the THz output signal after amplification is depicted as the red-line. Figure 6-10(b) presents the seeded and amplified THz spectrum profile. The weak THz signal can be power amplified as 2.7 times respect to the input THz signal. The experimental achievement of the power amplification gain is a little lower than that calculated from the theoretical prediction. It is likely attributed to the imperfect phase matching and the beams overlap between the optical pump and the THz seed. Besides, the gain calculation method mentioned in Section 6.3.3 is under the plane wave assumption of the THz radiation. Therefore, the predictional gain factors for every frequency components satisfy the perfect phase-matching condition. The magnitude of the gain factor might be over-estimated. Therefore, the theoretical predition of the gain factor is even up to 4.5 at central frequency 1 THz, the lower magnitude of the gain factor, 2.7 times in this study, could be achieved for practical experiment.

0 5 10 15 20

-800 -600 -400 -200 0 200 400 600 800 1000

(a)

THz amplification

THz field (V/cm)

Time delay (ps)

0.5 1.0 1.5 2.0 2.5 3.0 0.0

0.5 1.0 1.5

2.0

(b)

Power spectrum (a.u)

Frequency (THz)

THz seeder THz amplification

Fig. 6-10 THz amplification by OPA process (a) THz time domain waveform (b) THz spectrum.

6.4 Summary

Femtosecond laser induced plasma in ambient air based on the third order nonlinearity is employed to construct a THz-TDS system in this study. The properties of the THz radiation from this configuration is characterized by altering the phase shift, the angle between polarizations of the fundamental (800 nm) and second harmonic beams (400 nm).

The dependence of the THz signal as a function of the fundamental pulse energy before the BBO crystal is also examined. Furthermore, GaSe crystal is a promising nonlinear optical medium to perform the generation of intense THz radiation. Herein, we report the experimental demonstration of terahertz wave amplification in GaSe crystal. Terahertz power amplification factor of about 2.7 times is preliminarily performed under the phase matching condition around 1 THz. The demonstration provides a potential way to further increase the terahertz electric field for nonlinear spectroscopic applications with a desktop femtosecond laser system.

References

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Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, “Observation of terahertz emission from a laser-plasma accelerated electron bunch crossing a plasma-vacuum boundary,” Phys. Rev. Lett. 91, 074802-1-4 (2003).

[5] E. Budiarto, J. Margolies, S. Jeong, J. Son, and J. Bokor, “High-intensity terahertz pulses at 1-kHz repetition rate,” IEEE J. Quantum Electron. 32, 1839-1846 (1996).

[6] G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken,

“Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter,” Rev. Sci. Instrum. 73, 1715-1719 (2002).

[7] K. Reimann, R. P. Smith, A. M. Weiner, T. Elsaesser, and M. Woerner, “Direct field-resolved detection of terahertz transients with amplitudes of megavolts per centimeter,” Opt. Lett. 28, 471-473 (2003).

[8] J. Hebling, G. Almasi, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for largearea THz-pulse generation,” Opt. Express 10, 1161-1166 (2002).

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[10] J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts Appl. Phys. B: Lasers Opt. 78, 593-599 (2004).

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[12] K. -L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121-1-3 (2007).

[13] T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805-2807 (2005).

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Instrum. 74, 1-18 (2003).

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Chapter 7

Conclusions and future works

The optical constants of a GaSe crystal are measured by the terahertz time-domain spectroscopy at terahertz frequencies. Based on experimental data, a modified complex ordinary and extraordinary dielectric function of GaSe is presented. A low-frequency rigid-layer phonon mode at 0.586 THz confirms the pure GaSe crystal to be in the ε-phase.

The transverse and longitudinal optical phonons in the reststrahlen band for the ordinary refraction index are experimentally determined to be 6.39 and 7.62 THz, respectively.

The infrared-active modes of ε-GaSe crystal at 237.0 cm^-1 and 213.5 cm^-1 were found to be responsible for the observed optical dispersion and infrared absorption edge. Based upon phase matching characteristics of GaSe for difference-frequency generation (DFG), new Sellmeier equations of GaSe were proposed. The output power variation with wavelength can be properly explained with the shape of parametric gain and the spectral profile of absorption coefficient of GaSe. The adverse effect of infrared absorption on (DFG) process can partially be compensated by doping GaSe crystal with erbium ions.

We propose and experimentally demonstrate the generation of single-cycle terahertz radiation with two-stage optical rectification in GaSe crystals. By adjusting the time delay between the pump pulses employed to excite the two stages, the terahertz radiation from the second GaSe crystal can constructively superpose with the seeding terahertz field from the first stage. The high mutual coherence between the two terahertz radiation fields is ensured with the coherent optical rectification process and can be further used to synthesize a desired spectral profile of output coherent THz radiation.

A THz-TDS system based on laser induced plasma in ambient air is also constructed in this study. A THz amplification process could be achieved by optical parametric amplification technique. High gain can be performed under the theoretical calculation.

Herein, we report the experimental demonstration of terahertz wave amplification in GaSe crystal. Terahertz power amplification factor of about 2.7 times is preliminarily performed under the phase matching condition around 1 THz. The demonstration provides a potential way to further increase the terahertz electric field for nonlinear spectroscopic applications with a desktop femtosecond laser system.

The recommendation in future work is represented as follows:

In this dissertation, the generation of mid- to far-infrared radiation has been perfomed by use of the GaSe crystal. Especially, the severe effect of the free carriers has been identified to reduce the output and performance of the THz emission systems, including the multiple-stage optical rectification and terahertz parametric amplifier. Therefore, in fundametnal, the elimination of the intrinsic nonlinear abosorption of the free carrier is the important issue to study. If the concentration of free carriers could be reduced, the performance of the high-power terahertz producer must be improved. The intense terahertz light source can be expected.

In practice, it could be devoted to perform the terahertz phase modulator. The external angles of the optical axis of the GaSe crystal between the direction of incident terahertz light are as a function of the phase shift. This relationship could be further determined for the convenient application to the scientists.

A simple calculation and design has been done for the prediction of the maximum energy output of the terahertz radiation from the multiple stage optical rectification system.

In photon factory (NCTU), the Spitfire could be operated under 10 Hz repetition rate, 800 nm central wavelength, 50 fs. The laser pulse energy could be as high as 15 mJ. After the theoretical calculation, a design case is preliminately proposed to achieve the maximum terahertz output from this technique:

The total laser pulse energy is devided to three parts for the three-stage optical rectifications. The pulse duration is stretched to 280 fs, focusing spot size is about 7mm, and the GaSe crystal length is 570 μm for each stage. The conversion efficiency for each stage is about ~2×10^-5. After the coherent superposition of terhertz electric fields in the time domain, the intense single-cycle terahertz pulse could be yielded. Therefore, in our prediction, the maximum pulse energy of terahertz radiation output by means of the multiple stage optical rectification is as high as 300 nJ.