1. Introduction

Recently the generation of high-field THz pulses by optical rectification in nonlinear optical crystals has caused much scientific and technological interest due in part to their ability to drive strongly nonlinear responses in a variety of materials [1]. Strong sub-picosecond THz electromagnetic fields with multi octave-spanning bandwidths are often required in nonlinear spectroscopic applications for studying resonant effects in materials such as nonlinear gas phase molecular rotation dynamics [2, 3], anharmonic lattice vibrations in ferroelectrics [4, 5], and magnetization dynamics in ferro- and antiferro-magnets [6]. To obtain the desired high THz electromagnetic field strengths, generation crystals with: 1) small absorption at optical pump and generated THz wavelengths; 2) large second order nonlinear optical coefficients; and 3) good phase matching properties are needed for high optical to THz conversion efficiencies. Benchmark inorganic crystals such as ZnTe and GaP exhibit good properties for collinear type-0 phase matching at pump wavelengths between 800 nm and 1500 nm [7–9]. Yet energy conversion efficiencies on the order of 10⁻⁵ are typically measured in experiments due to their modest nonlinear optical coefficients [10, 11]. THz generation in inorganic ferroelectric crystals such as LiNbO₃ with larger nonlinear optical coefficients and higher damage thresholds has been demonstrated to have more than two orders of magnitude higher conversion efficiency [12], reaching up to 3.8% under cryogenic cooling conditions [13]. Such high conversion efficiencies require high pump fluence with optimized pump pulse duration and bandwidth and a more complicated noncollinear phase matching scheme with tilted-pulse-front excitation to compensate the huge index mismatch between optical pump and generated THz pulses. In comparison, recent developments in THz generation with organic crystals have shown comparable conversion efficiencies with simpler collinear phase matching conditions (as with ZnTe and GaP) and lower pump energies [14, 15]. One such organic crystal, HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2, 4, 6-trimethylbenzenesulfonate], has been shown to generate intense broadband THz pulses with an order of magnitude higher conversion efficiency than ZnTe and GaP [16, 17].

In many THz spectroscopy experiments, high peak fields often lead to unwanted electronic responses which show up as a peak at the arrival time of THz pump pulses at the sample and may sometimes drive longer-time nonlinear electronic responses; however, they usually reveal no information about resonant THz-frequency degrees of freedom that may be of interest. Multi-cycle narrowband THz pulses with lower peak amplitude but higher spectral brightness may serve as a way to circumvent such electronic responses and still maintain high excitation strength for resonant driving of specific electronic, lattice or magnetic nonlinear responses. Frequency tunability would further facilitate resonant excitation of specific resonant degrees of freedom. A Michelson interferometer-based temporal pump pulse shaping method yielding a sinusoidally modulated envelope has been implemented for multi-cycle THz generation by the chirp and delay method [18]. The Michelson interferometer in the chirp and delay scheme tends to be unstable in phase without active stabilization, and a long-time drift in phase stability makes measurements difficult to implement. More recently, a phase-stable pulse shaping method replacing the Michelson interferometer with an etalon has been utilized in THz generation by optical rectification in LiNbO₃ with tilted-pulse-front pumping [19]. Though etalon-based chirp and delay THz generation is simpler to implement than a Michaelson-based setup, unwanted harmonic frequency components resulting from interference of the multiple reflections of the etalon are preserved in the generated THz pulses and may hinder conducting experiments at a single narrow bandwidth of THz pumping frequencies.

In this paper, we report on multi-cycle narrowband THz generation continuously tunable between 0.3 and 0.8 THz with an etalon-based temporal pulse shaper and type-0 collinearly phase matched optical rectification in HMQ-TMS. By varying the crystal thickness, we enhance THz generation at selected frequencies while using the phase mismatch at higher THz frequencies to suppress the harmonic components. The energy conversion efficiencies at some frequencies are measured to be an order of magnitude higher than ZnTe under similar experimental conditions.

2. Parameterization of multi-cycle THz generation in HMQ-TMS

In the plane-wave and non-depleted pump approximation and ignoring cascaded nonlinear effects, the generated THz electric field for crystal length l, at a frequency $\omega$ is given by [20]

The optimum crystal length is defined as the shortest crystal length that gives the most efficient THz generation. The maximum effective generation length is a bound function of the optimum crystal length in the presence of phase mismatch. It can be seen from Fig. 1 that at the pump wavelength of 800 nm, the optimum crystal length has a large contrast below and above 0.8 THz. Hence by choosing crystal thicknesses between the optimum length of frequencies below and above 0.8 THz, we can obtain efficient THz generation below 0.8 THz and inefficient THz generation above 0.8 THz. We use this contrast in the optimum crystal length to suppress THz generation at the harmonic frequency components originating from the etalon multiple reflections.

 

Fig. 1 Calculated optimum crystal length (a) and maximum effective generation length (b) for HMQ-TMS with a pump wavelength of 800 nm.

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3. Experimental method

The experimental setup is shown in Fig. 2. Fourier transform-limited pulses with a duration of 100 fs at 800 nm from a Ti:sapphire amplifier were linearly chirped to 9 ps with the compressor at the output of the amplifier. 95% of the output was sent into an etalon consisting of a high reflector and a partial reflector (38% reflectivity) with a variable separation between them to yield a time delay $\tau$ between successive reflections. The resulting superposed chirped and delayed reflections produced a pulse with a quasi-sinusoidally modulated intensity profile. This output was directed into an HMQ-TMS crystal for optical rectification in a collinear phase matching geometry. The generated THz pulses were focused into a 1 mm electro-optic GaP crystal by three parabolic mirrors. The remaining 5% of the chirped amplifier output was compressed to the Fourier transform limit in a separate external compressor and then delayed in time and focused onto the GaP for electro-optic sampling. The number of cycles$N$and center frequency$\omega$of the generated multi-cycle THz pulses are given by [19]

 

Fig. 2 Experimental setup for multi-cycle THz generation in HMQ-TMS. HR: high reflector; PR: partial reflector; λ/2: half waveplate; P: polarizer; λ/4: quarter waveplate; PM: parabolic mirror; G: grating; DL: delay line; WP: Wollaston prism; PD: photodiode; LIA: lock-in amplifier.

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4. Results

The multi-cycle THz pulses were generated from two HMQ-TMS crystals grown by the slow cooling method [16] with thicknesses of 2.45 mm (sample 1) and 0.85 mm (sample 2). Sample 1 is optimum for THz generation below 0.6 THz and sample 2 optimum for below 0.8 THz, both at the pump wavelength of 800 nm. THz waveforms in the time domain and their spectra in the frequency domain generated from the two crystals using 310 μJ pump energy with various etalon spacings are shown in Fig. 3.

 

Fig. 3 THz waveforms in time domain and their spectra in frequency domain of sample 1 (a) and sample 2 (b).

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The center frequencies were tuned from 0.3 to 0.8 THz with a 50 GHz stepsize. For sample 1, the spectrum at 0.3 THz shows a small second harmonic component at 0.6 THz. The second harmonic components for frequencies between 0.35 and 0.6 THz are suppressed to be near the noise floor of the system. Above 0.6 THz, poor phase matching results in inefficient THz generation with distorted Gaussian envelopes and unwanted frequency bands below the center frequencies. THz spectra from sample 2 with center frequencies between 0.3 and 0.4 THz show some second harmonic frequency components since the harmonics at those frequencies are phase-matched well. Between 0.4 and 0.8 THz, the second harmonic components are suppressed. The suppression of harmonic components by varying crystal thicknesses is in good agreement with the above analysis.

We measured the generated THz pulse energy from the two HMQ-TMS crystals with a Microtech pyro-electric detector at the focus of the last parabolic mirror at different center frequencies as a function of pump pulse energy. As a control experiment, we also measured the THz energy of a 1 mm thick ZnTe crystal under the same experimental condition. The results of HMQ-TMS crystals are shown in Fig. 4. With a pump energy of 400 μJ and beam area of 0.38 cm², the optical to THz energy conversion efficiencies were measured to be ${\eta }_{1,0.46\text{THz}}=1.89\times {10}^{-5}$ for sample 1 at 0.46 THz and ${\eta }_{2,0.48\text{THz}}=0.91\times {10}^{-5}$ for sample 2 at 0.48 THz, which were respectively 25.6 and 12.4 times better than that of the 1 mm ZnTe for which ${\eta }_{\text{ZnTe,0}\text{.48THz}}=7.38\times {10}^{-7}$. The THz energy as a function of pump pulse energy follows a quadratic dependence as expected for optical rectification before saturation begins. Correspondingly, the energy conversion efficiency increases linearly as a function of pump energy before saturation. While sample 1 begins to saturate at around 300 μJ pump energy (Fig. 4a), saturation does not begin in sample 2 until the pump energy exceeds 2 mJ, as shown in Fig. 5. The energy conversion efficiency was measured to be ${\eta }_{2,0.54\text{THz}}=3.48\times {10}^{-5}$ at a center frequency of 0.54 THz for sample 2 with pump pulse energy of 2.4 mJ. We also measured and compared the spectra of the pump pulse at various energies. There was no sign of redshift in the pump pulse spectrum after optical rectification in HMQ-TMS, suggesting that cascaded nonlinear effects are insignificant (as expected for photon conversion efficiencies of less than 1%) and that the conversion efficiency can be further improved by increasing the pumping fluence.

 

Fig. 4 Output THz energy as a function of input pump pulse energy for sample 1 (a) and sample 2 (b) at different center frequencies. The dashed lines are quadratic fits to the data points with one fitting parameter.

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Fig. 5 Output THz energy as a function of input pump pulse energy for sample 2 at different center frequencies. The dashed lines are quadratic fits to the data points with one fitting parameter.

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5. Conclusions

We have generated multi-cycle THz pulses with frequencies continuously tunable from 0.3 to 0.8 THz in the organic nonlinear crystal HMQ-TMS with type-0 collinearly phase matched optical rectification pumped at 800 nm laser wavelength. Selective suppression of the unwanted harmonic frequency components inherent in the etalon-based pump pulse temporal shaping method is realized by simply varying the generation crystal thickness. The optical to THz energy conversion efficiencies are measured to be an order of magnitude higher than the benchmark inorganic THz generator ZnTe under the same experimental conditions.