1. Introduction

Narrowband terahertz radiation can be obtained by mixing a pair pulses of slightly different wavelengths in a nonlinear crystal (Difference Frequency Generation, or DFG). The required pulses can be obtained from synchronized Q-switched lasers [1–5] or optical parametric oscillators [6,7]. THz generation by DFG using an organic crystal as the nonlinear mixing medium - for example, DAST - has been reported by several groups [8–12], where the pair of signals were generated with OPO's based on periodically poled lithium niobate (PPLN). In [10], both signals were generated from a single 40 mm long PPLN sample that has two consecutive periodically-poled sections, each with the required poling periodicity to generate one of the signals. In [12], narrowband THz was achieved by mixing in a DAST crystal two signals derived from injection-seeded optical parametric generation in two separate PPLN crystals. Other experiments have been carried out with different organic nonlinear crystals to obtain THz, such as DSTMS [13], OH1 [2] and, more relevant to this work, HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2,4,6-trimethyl-benzenesulfonate] [14].

In [15] we reported two different sources of pairs of signals based on aperiodically poled lithium niobate (APLN) that could be used to generate THz radiation; one is an OPO that is pumped by a 12 ns long Q-switched laser and the other is an OPG source pumped by a 1.6 ns Q-switched laser. The aperiodic crystal is designed such that a pair of signal and idler waves is generated throughout the entire crystal; the difference in frequency of the pair of signal waves equals the THz frequency that is to be achieved through DFG in another nonlinear medium. The advantages of APLN over PPLN are that the emission bandwidth is narrower and the effective nonlinearity is larger; both of these advantages increase the brightness of the THz radiation obtained by DFG and reduce the requirements of the pump source.

Here we present the generation of THz radiation using our previously reported APLN-based optical parametric generation source [15] using the organic crystal HMQ-TMS as the mixing medium; it has a high second-order nonlinearity and a refractive index dispersion suitable for obtaining ∼1-10 THz radiation by DFG using signal wavelengths close to 1.45 µm [16]. Using this simple, compact source, we obtained sub-nanosecond pulses between ∼1.4 and 10 THz.

2. Experiment

The experimental system consists of three parts, the source of pairs of signal waves, the nonlinear crystal that produces the THz radiation through DFG, and the detection system. The entire experimental set-up is shown in Fig. 1. A homemade diode-pumped, passively Q-switched Nd:YLF laser that emits short pulses at 1047 nm [17] pumps an APLN crystal to obtain OPG. A spherical lens ($f = 75\textrm{ mm}$) focuses the pulses of this laser onto the APLN sample. The focused beam waist inside the crystal is ∼ 120 µm diameter (FWHM), and its diameter is ∼190 µm at the entrance and exit planes of the crystal. The APLN crystal is 50 mm long and has several aperiodic structures to generate different pairs of signal and idler waves. The wavelengths of all of the signal waves generated with this crystal are close to 1.45 µm and were designed to produce signal pairs with a difference in frequency between ∼1.4 to 10 THz. The reason why we chose 1.45 µm is because at this wavelength the refractive indexes of the signals and of the THz radiation are very close, which is required to get efficient conversion through phase-matching [18]. The pump laser and APLN crystal are the ones described in [15]; the theory used to design the APLN crystal as well as the advantages that aperiodically-poled crystals have over sequentially-poled crystals - higher effective nonlinearity and half the bandwidth for a given crystal length - is given in [19] and extended in the Appendix. The APLN crystal was made using standard electric field poling techniques, similar to the one explained in [20]; the specific details of how we made it are given in [21]. Since the laser emits pulses with a 1.6 ns (FWHM) pulsewidth, a cavity to convert the OPG into OPO is pointless since the length of the pump pulse is comparable to the minimum round-trip length the OPO could possibly have. All of the experiments were performed at repetition rate of 27 Hz.

 

Fig. 1. Experimental set-up.

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A dichroic beamsplitter that reflects wavelengths below ∼1300 nm separates the pump from the signal waves generated in the crystal. It also reflects the “red beams,” produced by the non-phase-matched sum-frequency generation between the pump and signal beams as well as the second harmonics of the signals and their sum. The transmitted signal waves go through a high-pass filter (Thorlabs FEL1300) - which rejects any remnant of the pump pulse (extinction ratio at 1.047 µm ∼ 2 × 10⁻⁴) - and then are incident on the HMQ-TMS crystal. It is a 0.46 mm thick trapezoidally-shaped plate, prepared by a cleaving method [14]; it has an area of ∼ 16 mm², with its polar axis parallel to the plate’s surfaces. The diameter of the incident signal beams was ∼ 1 mm, the FWHM duration of the pair of signal pulses was 0.85 ns, and their combined energy was 20-38 µJ, depending on which pair of signals was used, so the instantaneous irradiance was between ∼ 0.75 and 1.4 MW/cm². The crystal was mounted on a rotation stage to observe the dependence of the energy of the THz signal on its orientation with respect to the polarization of the signal beams.

A ∼ 1 mm thick piece of black HDPE blocks the signals that emerge from the HMQ-TMS crystal, transmitting only the THz signal, which is sensed by a calibrated pyroelectric detector (Sciencetech SCI420BJ-0) and sent to an oscilloscope. According to its specifications, the peak voltage response of this detector is 1mV per 1 nJ of incident energy, calibrated from $\lambda = 100\textrm{ nm} - 1\textrm{ mm}$. We verified this calibration at 1.047 µm with our laser using another calibrated detector. The detection of the THz signal was triggered by the 1.047 µm pulse reflected by the dichroic beamsplitter. A second beamsplitter reflects the “red beams,” the second harmonics of the signal beams and their sum into a fiber-coupled visible spectrometer (Ocean Optics HR4000), which has a resolution of ∼ 200 GHz. By measuring the wavelength ${\lambda _R}$ of the “red beams,” the wavelength of the signals could be determined by ${\lambda _s} = {\lambda _p}{\lambda _R}/({\lambda _p} - {\lambda _R})$ [15]. The wavelengths were also detected directly with an infrared spectrometer (not shown in Fig. 1), but since its accuracy was not as good, it was only used once to corroborate the measurements obtained with the visible spectrometer.

3. Results

We obtained THz radiation from the OPG signals created with four different aperiodic gratings, corresponding to 1.43, 2.39, 6.61 and 10.05 THz with a conversion efficiency of ∼ 0.1%. The results obtained for one specific frequency, 2.39 THz, are shown in Fig. 2. The spectra of the signals obtained around 1.45 µm are shown in Fig. 2(a). The main peaks are saturated on purpose to reveal two other smaller, satellite peaks on each side of the main ones. These satellite peaks are predicted by theory, which is given in the Appendix. The wavelengths and bandwidths were estimated from the “red beams” shown in Fig. 2(b): 1.4380 µm and 1.4547 µm; the separation between them is 2.39 THz and the bandwidth of each signal is ∼ 200 GHz, which is more or less the resolution of the spectrometer. The combined FWHM pulsewidth of the pair of pulses is 0.85 ns. Notice that the satellite signals also appear, separated by 2.39 THz from the main peaks. Figure 2(c) shows the second harmonics of the signals as well as their sum. Again, the second harmonics and the sum-frequency peaks are separated by 2.40 THz, which - within experimental error - coincides with the 2.39 THz separation of the red beams, as expected. The presence of the sum-frequency indicates that the signals overlap in space and time, which is a requirement to obtain THz by DFG. Finally, Fig. 2(d) shows the response of the pyroelectric detector seen on the oscilloscope. Care was taken to ensure that the signal being detected was actually THz radiation produced by the organic crystal. In order to reduce background noise, a few baffles were placed in the set-up (not shown in Fig. 1) to block spurious reflections of the signals and pump beams; these baffles also blocked air currents that created noise in the pyroelectric detector. Since we simultaneously recorded the spectra of the sum-frequency generation of the signals, we could determine if the signal beams were synchronized or not. Whenever they were not, we did not get a signal from the pyroelectric detector, even though both signal beams were present. This is a clear indication that what we measured was THz radiation produced by DFG and not leakage of the signal or pump beams through the HDPE filter. As further proof, we rotated the organic crystal to change the direction of polarization of the signal beams with respect to the crystal's polar axis: the maximum occurred when the beams were polarized parallel to the polar axis and was zero when rotated by 90°, as expected [14].

 

Fig. 2. THz generation and detection. a) Signal wavelengths and satellites detected directly with an infrared spectrometer; b) “Red beams” detected with a visible spectrometer; the satellites also appear; c) second harmonics and sum-frequency of the signals; here the satellites barely appear; d) response of the pyroelectric detector to the THz signal. The polarizations of the signal beams are aligned with the polar axis of the HMQ-TMS sample.

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We also measured the pulse-to-pulse stability of the THz signal. The main source of instability is the pulse-to-pulse variation of energy the 1.047 µm laser pump pulses, which is low (<1%), which creates a variation of the signal pulses. Figure 3(a) shows a histogram of the combined energy of the signal pulses obtained using the same grating used in Fig. 2, $\Delta v = 2.39\textrm{ THz}$; the peak is at 22.2 µJ, with a spread of about ${\pm} 0.2\textrm{ }\mathrm{\mu} \textrm{J}$. Figure 3(b) shows ten traces of the 2.39 THz signal and their average. Here the average energy is 38.6 nJ per pulse, with a variation of ${\sim}{\pm} 2\textrm{ nJ}$, which corresponds to a pulse-to-pulse fluctuation of ∼5%.

 

Fig. 3. Pulse-to-pulse fluctuations. a) Histogram of the combined energies of 200 signal pulses; b) oscilloscope traces of the THz signal; the thin lines correspond to ten individual traces and the thick blue line corresponds to their average.

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Similar results were obtained with the other three gratings and are summarized in Table 1; the energies and the conversion efficiencies are plotted in Fig. 4. Notice that in all four cases the energy conversion efficiency (THz energy/combined signal pair energy) is around 0.1%. According to the data given in [19], at ${\lambda _p} = 1.45\textrm{ }{\mathrm{\mu} }\textrm{m}$ the coherence length for all of these frequencies is larger than the length of the crystal, so phase-matching is ensured. The absorption of the pump is negligible; however, for all the THz frequencies the absorption coefficient is ∼ 10 mm^-1, which reduces the THz output. Finally, the maximum energy conversion efficiency that can possibly be attained is when every photon of one of signal beams produces a THz photon; in other words, the maximum energy conversion efficiency is limited by the ratio of the photon energies ${{{\nu _{THz}}} / {{\nu _{signal}}}}$, where ${\nu _{THz}}$ and ${\nu _{signal}}$ are the THz and signal frequencies, respectively. Table 1 also includes the quantum efficiency obtained for each one of the four cases.

 

Fig. 4. Energy and conversion efficiency obtained at different frequencies.

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Table 1. THz radiation generated by DFG between different pairs of signals.

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4. Concluding remarks

We presented a compact pulsed source of THz radiation based on DFG in an HMQ-TMS crystal where the OPG pump beams are produced by an APLN sample designed specifically for this use. The use of short 1.047 nm pulses (1.6 ns) as well as a long (5 cm) APLN crystal allowed producing a pair of short (0.85 ns) narrowband (< 200 GHz) signals by OPG. The measured signal bandwidth was limited by the resolution of the spectrometer; however, considering 200 GHz to be the actual bandwidth of the signals, we expect the THz signal to also have a bandwidth < 200 GHz. The high instantaneous irradiance, ∼ 1 MW/cm², was enough to produce THz radiation with a conversion efficiency of the order of 0.1%.

Although the main advantage of this source is its simplicity and low cost, the energy per pulse is comparable to other systems that are far more complex and bulky. For comparison, the system described in [13] that is based on DSTMS produces close to 100 nJ per pulse, which is more than twice what is presented here, but the signal pulses required to obtain the THz pulses are far more energetic, over 2.5 mJ, whereas our system only requires around 40 µJ. The bandwidth of the THz pulses emitted by our system is limited by the bandwidth of the signal beams. This can be reduced by different means, such as using a longer APLN crystal or by injection-seeding with an external CW laser. If this seeding laser were tunable, then we could also achieve tunable narrowband THz radiation. The lowest bandwidth that could be obtained is limited by the pulsewidth, which is close to 0.5 ns (considering that the signal pulses have a pulsewidth of ∼ 0.8 ns), so the lowest achievable bandwidth with this system is of the order of 2 GHz.

Appendix: Variation of the effective nonlinearity with wavenumber mismatch

For an aperiodically-poled crystal, the effective second-order nonlinearity as a function of the wavevector mismatch parameter $\Delta k$ for three extraordinary polarized waves in general is given by [18]

(1)$$\chi _{eff}^{(2)}({\Delta k} )= \frac{{{\chi _{33}}}}{L}\int\limits_0^L {g(x)\exp [{i\Delta kx} ]} dx,$$

where $g(x)$ describes the spatial variation of the sign of the nonlinearity ($g(x) ={\pm} 1$) and L is the length of the aperiodic structure. We want to obtain two signal frequencies ${\omega _{s,1}}$ and ${\omega _{s,2}}$ that are separated by the desired THz frequency $\delta \omega$. Let ${k_1} = 2\pi /{\Lambda _1}$ and ${k_2} = 2\pi /{\Lambda _2}$, where ${\Lambda _1}$ and ${\Lambda _2}$ are the poling periods needed to get ${\omega _{s,1}}$ and ${\omega _{s,2}}$ by quasi-phase-matching. The aperiodic structure we use is given by

(2)$$g(x) = sign[{\cos ({{k_1}x} )- \cos ({{k_2}x} )} ]= sign\left[ {\sin ({\bar{k}x} )\sin \left( {\frac{{\delta k}}{2}x} \right)} \right].$$

Here $\bar{k}$ is the average of ${k_1}$ and ${k_2}$, that is $\bar{k} = ({k_1} + {k_2})/2$, and $\delta k = {k_2} - {k_1}$. The structure is essentially a periodic structure with a period $\Lambda = 2\pi /\bar{k}$ that has 180° phase shifts every distance D, given by $D = 2\pi /\delta k$, as shown in Fig. 5. If for simplicity we restrict the lengths such that D is an integer multiple of the period $\Lambda $ and in turn the length L of the crystal is an integer multiple of D, then it can be shown that

(3)$$|{\chi_{eff}^{(2)}({\Delta k} )} |= {\chi _{33}}\left|{\frac{2}{{\Delta kL}}\tan \left( {\frac{{\Delta k\Lambda }}{4}} \right)\tan \left( {\frac{{\Delta kD}}{2}} \right)\cos \left( {\frac{{\Delta kL}}{2}} \right)} \right|.$$

The position of the peaks is governed mainly by the values of $\Delta k$ where $\tan ({{{\Delta k} / 2}} )$ is large, that is, when its argument is close to an odd multiple of $\pi /2$, so the peaks occur when

(4)$$\Delta k \approx \frac{\pi }{D}(2q + 1).$$

where q is an integer. The separation between peaks is therefore $2\pi /D$.

 

Fig. 5. Aperiodic structure.

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The magnitude of the effective nonlinearity given in Eq. (3), normalized to ${\chi _{33}}$, is plotted in Fig. 6. As can be seen, there are two sets of peaks that are essentially mirror images of each other, where the mirror plane is at $\Delta k = 2\pi /\Lambda $, that is, when $q = D/\Lambda $. Each peak is described approximately by the magnitude of a sinc function, centered around the values of $\Delta k$ given by Eq. (4). On the right hand side of the mirror plane, the first and largest peak occurs at $\Delta k = \pi (2/\Lambda + 1/D)$, with a maximum value of ${(2/\pi )^2}$; the next peaks decrease to 1/3, 1/5… of this value. The widths are governed by the $\cos ({\Delta kL/2} )$ factor of Eq. (3), and are equal to $2\pi /L$ for all of the peaks. For comparison, Fig. 6(b) shows the effective nonlinearity for the case of two consecutive periodically-poled regions, each with a different poling period and length $L/2$, such as what was used in [10]. Two peaks appear, but they are shorter ($1/\pi$) and twice as wide ($4\pi /L$), since only half of the crystal contributes appreciably to each peak.

 

Fig. 6. Effective nonlinearities of aperiodic and sequentially periodic structures. a) large scale that shows the secondary peaks of the aperiodic structure; b) close-up of one of the two main peaks. Values used in the simulation: $\Lambda = 28\mathrm{\mu} m$, $D = 150\mathrm{\mu} m$, $L = 35mm$.

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Funding

Consejo Nacional de Ciencia y Tecnología (FOINS CONACYT 2016-01-1904); National Research Foundation of Korea (2014R1A5A1009799).

Acknowledgments

We thank S. Stepanov for the loan of the oscilloscope for the acquisition of the temporal profiles of the pulses, L. Ríos for technical assistance and C. E. Minor for assistance with the design and construction of the Nd:YLF laser. We also thank M. Jazbinsek for many fruitful discussions.

Disclosures

The authors declare no conflict of interests.

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