Here, we present a continuous-wave optical parametric terahertz light source that does not require cooling. It coherently emits a diffraction-limited terahertz beam that is tunable from 1.3 to 1.7 THz with power levels exceeding 1 µW. Simultaneous phase matching of two nonlinear processes within one periodically-poled lithium niobate crystal, situated in an optical resonator, is employed: The signal wave of a primary parametric process is enhanced in this resonator. Therefore, its power is sufficient for starting a second process, generating a backwards traveling terahertz wave. Such a scheme of cascaded processes increases the output power of a terahertz system by more than one order of magnitude compared with non-resonant difference frequency generation due to high intracavity powers. The existence of linearly polarized terahertz radiation at 1.35 THz is confirmed by analyzing the terahertz light with metal grid polarizers and a Fabry-Pérot interferometer.
©2009 Optical Society of America
Applications of terahertz radiation in spectroscopy [1, 2], astronomy  and communications [1, 4] plus improved ways to transmit  and manipulate terahertz waves  – including microscopy with nanoscopic resolution  – have raised much interest in terahertz photonics. The optimum light source is still the largest challenge, with continuous-wave (cw) operation being most desired for many applications because of its small linewidth. Established techniques to generate narrow-band terahertz radiation rely on electronic and opto-electronic systems, which are limited in output power and maximum achievable frequency .
Several attempts have been made to overcome this hurdle. There are two approaches that deserve special attention since they have the potential to outdate the traditional devices: Firstly, there are quantum cascade lasers [9, 10] with remarkable recent improvements, regarding operation parameters and beam profile characteristics [11, 12]. However, they still need cryogenic temperatures and they can hardly produce radiation with frequencies below 1 THz. Secondly, nonlinear-crystal-based light sources fill the gaps in the electromagnetic spectrum where lasers struggle to emit light, and this also applies to the terahertz range. But so far these systems could not achieve more than some nanowatts .
Looking onto nonlinear-optical methods: to create monochromatic terahertz radiation so far only difference frequency generation has been employed [14, 13]. Optical parametric oscillators (OPOs), however, are more versatile because of their tuning properties. Unfortunately, the power threshold for the onset of such an oscillation generating terahertz waves is in the order of several hundreds of watts because of the high absorption of terahertz radiation by vibrational excitations . Here, we report on an approach that utilizes intensity enhancement within an optical cavity to overcome this threshold. For that we exploit a cascaded nonlinear process, where in a first step a near-infrared pump wave generates a signal and an idler wave, the signal field being trapped within the cavity. This signal wave can reach kilowatt power levels inside the resonator  and acts, in a second step, as a pump wave for another simultaneously phase-matched process, generating the desired terahertz wave .
2. Concept of cascaded nonlinear processes
For optical parametric oscillation, two requirements have to be fulfilled: the resonance condition, ω p=ω s+ω i, and the phase-matching condition
Here, ω p,ω s and ω i are the angular frequencies while k⃗p,k⃗s and k⃗i are the wavevectors of pump, signal and idler waves, respectively, and K⃗ is the grating vector of an alternating second-order nonlinearity induced by periodic poling of crystals. By selecting K⃗ properly, so-called quasi-phase- matching can be achieved, i.e. the energy transfer from the pump wave to signal and idler waves is optimized.
These requirements apply to difference frequency generation as well. In optical parametric oscillators, however, the signal light is resonantly enhanced by the cavity. Such oscillation starts once the pump threshold is overcome. For periodically-poled lithium niobate crystals, the possibility of a cascaded, phase-matched process has been discovered . Combined with the high intra-cavity power, this should produce terahertz radiation, as depicted in Fig. 1. at the beginning, the pump wave (p) is converted into a signal (s1) and an idler wave (i1) of the primary process (Fig. 1(a)). In a second parametric process, this first signal wave (s1) serves as a pump wave for the second, cascaded process, in which it is converted into a second signal (s2) and a second idler wave k⃗i2=k⃗THz, being the desired terahertz radiation (Fig. 1(b)).
The cavity is resonant at the same time for both signal waves, since their frequencies are very similar. All wavevectors are collinear to ensure a long interaction length. The terahertz wave travels backwards (see Fig. 1(b)) because of the condition
The big advantage of our system is, that the high-power signal wave (s1), used for driving the cascaded process, is generated within the cavity itself. This first nonlinear process automatically selects an existing mode and is hence self-adaptive. In contrast, any effort to feed high-power light directly into the cavity would require an active stabilization of the resonator plus careful impedance matching of the mirror reflectivities.
3. Experimental methods
3.1. Optical parametric oscillator
Our experimental setup comprises a singly-resonant optical parametric oscillator with a bow-tie cavity pumped by a cw Yb:YAG laser at 1030 nm. The linewidths of pump and signal waves are about 1 MHz. The OPO cavity consists of two concave mirrors (curvature radius 100 mm) and two plane ones (see Fig. 2). All mirrors are highly reflecting (>99.9 %). As the nonlinear medium we use a periodically-poled, MgO-doped lithium niobate crystal with a thickness of 0.5 mm. The measurements presented in Figs. 3–5 were performed with a 2.5-cm-long crystal with the period length 30.0 µm which is kept at 125 °C. We achieve tuning of the infrared and the terahertz waves by using crystal sections with different phase-matching periods from 24.4 to 31.0 µm .
3.2. Terahertz wave detection
To extract the terahertz wave from the OPO cavity, an off-axis parabolic aluminium mirror is placed into the cavity directly after the first concave mirror (see Fig. 2). A hole of 1 mm diameter is drilled into this parabolic mirror to let the infrared waves pass through. The backwards propagating terahertz wave is much more divergent than the pump and signal waves is therefore reflected almost entirely. This terahertz wave is then sent onto a second off-axis parabolic mirror which focusses the beam onto a calibrated Golay cell, chopped with 10 Hz. Calibration is specified by the manufacturer Tydex Corp. to be 80 kV/W, while the noise-equivalent-power-level of this Golay cell is 100 pW/. To keep away visible and infrared light, the diamond incidence window of the Golay cell is covered by a blackened high-density polyethylene foil (provided by GSE Lining Technology Inc.). We measured the transmittance of this filter at 1.35 THz to be 25 %. The output power values were corrected by this amount.
3.3. Terahertz wave analysis
All interacting waves are extraordinarily polarized. Therefore, the terahertz wave should have linear polarization as well. To test this, a metal grid polarizer, consisting of tungsten wires (width 15 µm, spacing 60 µm), is inserted between the off-axis parabolic mirrors. For residual infrared waves the polarizer just acts as a shadow mask. To determine the wavelength of the terahertz radiation, a Fabry-Pérot interferometer (FPI) was assembled with crossbred meshes of gold-plated tungsten wire (thickness 30 µm, spacing 100 µm) acting as mirrors with a size of 4×4 cm2. This FPI for terahertz waves has got a free spectral range of 10 GHz and a finesse of approximately 4. For the FPI measurement the setup was slightly modified to get a parallel beam passing through the interferometer: the second parabolic mirror was replaced by a plane mirror, followed by the FPI, and afterwards the second parabolic mirror once more focussed the beam onto the Golay cell.
We have built and tested the described terahertz source. Figure 3 shows the power of the signal waves and that of the THz wave versus the power of the external pump wave (p). Three regions can be distinguished: below 2.8Wof pump power no oscillations occur at all. Then, the primary process sets in (p, s1 and i1). Starting at 4.7W, the secondary process (s1, s2 and i2) is observed directly by detecting the emitted terahertz radiation. At a pump power (p) of 12 W, we reach remarkable 2.2 µW of terahertz power.
The spectra of the signal waves, presented in Fig. 4, underline the onset of the second parametric process. The frequency of the terahertz wave is given by the frequency difference between the two signal waves: 1.35 THz as shown in Fig. 4. Thus, the signal-wave linewidths Δν s1,s2 also determine the linewidth Δν THz of the terahertz wave. With a scanning Fabry-Pérot interferometer for near-infrared radiation we measured Δν s1,s2≈1 MHz, which implies that Δν THz is of the same order of magnitude as well. The absolute terahertz frequency has been confirmed by analyzing the terahertz beam in a THz Fabry-Pérot interferometer (see section 3.3). As a further validation of the existence of terahertz radiation, we place the metal grid polarizer in front of the detector and rotate it. Figure 5 shows that the detected terahertz power drops drastically for the grid wires being parallel to the light polarization.
By varying the period length of the poling structure and by changing the crystal temperature, we are able to tune the terahertz frequency from 1.3 to 1.7 THz. This tuning range can be widened easily with crystals having different poling periods. It should be noted, that, in addition to the terahertz radiation, tunable near and mid infrared waves from 1.2 to 1.8 µm and 2.3 to 5.3 µm are generated. Optical parametric oscillators are the only light sources providing such a broad wavelength variety in the near, mid and far infrared within one device.
At first glance, one would expect a disappointing terahertz output power, since the absorption is 40 cm-1 at 1.3 THz , giving a Lambert-Beer penetration depth of 0.25 mm only. However, evaluating the coupled wave equations including losses [18, 19] shows that a build-up of the terahertz wave over millimeters is possible . With reasonable parameters (effective nonlinear coefficient 107 pm/V ; first signal wave at 1.56 µm with a power of around 300 W; power of the second signal wave one tenth of that of the first (see Fig. 4); diameters of all waves 200 µm), we expect a second idler wave with a frequency of 1.35 THz and the remarkable power of 10 µW. This is higher than our measured powers, however some additional losses have to be considered: The major loss occurs because of reflection at the crystal surface just before the terahertz wave leaves the crystal. Furthermore, part of the terahertz wave is absorbed on its way through air to the detector. The distance between the OPO crystal and the Golay cell is around 30 cm. No flooding with nitrogen was performed, i.e. the terahertz radiation has to travel through normal laboratory air.
There are several opportunities to extend the concept presented here. With regard to the power: one can change the nonlinear-optical material used since the process presented here works in principle for any second-order nonlinear medium that can be periodically oriented. Candidates are, for example, lithium tantalate, potassium titanyl phosphate, and gallium arsenide. One can also optimize the optical parameters, i.e. the diameter and the power of the first pump wave (p). For the latter an upper limit is present because too high pump powers cause multi-mode operation of the optical parametric oscillator . With regard to the foot-print of the setup: monolithic optical parametric oscillators have been reported , but the large absorption of the terahertz waves makes their operation challenging.
We have presented a continuous-wave optical parametric terahertz source based on a cascaded nonlinear process. The generated terahertz radiation is tunable and reaches output powers exceeding 1 µW at a frequency of 1.35 THz. This source is therefore ideally suited for applications such as, e.g., spectroscopy. Based on these insights, we foresee a complementary use of quantum cascade lasers  and cascaded nonlinearities, as they are presented here. For those applications where high terahertz powers are important, quantum cascade lasers will be used.
If tunability, diffraction limited beam profiles and room-temperature operation matter, the cascaded nonlinear processes are the method of choice.
Financial support by the Deutsche Forschungsgemeinschaft DFG (FOR 557 and BU 913/18) and the Deutsche Telekom AG is gratefully acknowledged.
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