Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal

Remarkable advances in terahertz (THz) technologies have been made over recent decades. THz waves, which lie between microwave and infrared (IR) waves in the electromagnetic spectrum, have unique features. Novel THz technologies are eagerly anticipated in many fields. These include security, medicine, communication, and spectroscopy.^1,2 To further develop THz applications, we must improve sources of THz radiation so that we can obtain waves with a higher power and bandwidth. Many methods have been used to generate THz waves, for example, using plasma,³ optical rectification using a tilted optical pulse front,^4–6 and photoconductive antenna (PCA).^7,8

A typical application of THz waves is THz time domain spectroscopy (THz-TDS),⁹ which is a spectroscopic method that employs femtosecond laser pulse excitations. Two methods based on femtosecond pulse laser pumps are widely used to generate THz waves. One is the PCA,^7,8 and the other is based on non-linear optical (NLO) crystals, which allows for the optical rectification of femtosecond laser pulses.^10–16 Although PCAs are well known to emit THz waves, there are problems with using this type of source, as this type of source has a low laser induced damage threshold. This makes it difficult to generate high power THz waves. In contrast, NLO crystal-based sources have a higher damage threshold, so we expect them to be better at generating high power THz waves. The power of THz waves generated by NLO crystals is proportional to the square of the pump laser power. Therefore, NLO crystals are suitable for high power THz generation. In this study, we used ridged lithium niobate (LiNbO₃) waveguide excited by high power fs laser for the emission of high power, single-cycle THz pulse.

When we use a femtosecond pulse laser with an appropriate wavelength and a crystal that has an appropriate thickness, as determined by the coherence length, we are able to generate coherent, broadband THz waves. In collinear phase matching scheme, the propagation of these waves is parallel to the pump laser. However, there are issues with this method of generating THz waves, as the NLO crystal absorbs a lot of the THz radiation. Further, the coherence length of the crystal is also an issue. Therefore, we used Cherenkov phase matching to generate the THz waves.^17–21 Cherenkov phase matching condition is satisfied when the velocity of the light inside the NLO crystal is faster than that of the generated THz waves. The Cherenkov angle $θcrystal$ is calculated using the following equation:

where $λTHz$ is the wavelength of THz waves, the group refractive index of the pumping laser in the crystal is n_g—and that of the THz waves in the crystal is n_THz—and Lc is the coherence length of the pumping laser. This method makes it possible to suppress absorption by the NLO crystal and generate coherent THz waves along the Cherenkov angle. Furthermore, the prism-coupled Cherenkov phase matching method (PCC-PM) is an elegant way to generate THz waves using NLO crystals.²² By making a prism from cladding material with a suitable refractive index, we can extract THz waves from the NLO crystals without total internal reflection occurring inside the crystal. The angle of the cladding–nonlinear-crystal interface, $θclad$⁠, is determined using Snell’s law:

where n_opt is the refractive index of the crystal at the pump wavelength, and n_clad is the refractive index of the cladding layer in the THz-frequency range.²² Equation (2) indicates that the refractive index of NLO crystals is not an issue when following the PCC-PM method; hence, many crystals can be used as THz wave emitters without the phase matching condition being satisfied inside the crystal along a direction of the pump beam.

However, the PCC-PM method has several disadvantages, including absorption and phase mismatching caused by the thickness of the crystal. Due to its thinness, the waveguide structure of the NLO crystal solves these issues.¹⁵ Further, the ridges of the waveguide are able to concentrate the pump beams on a narrower area; hence, it is possible to increase the power density of the pump beams.

In this work, we report successful THz wave generation from a ridged LiNbO₃ waveguide. Moreover, we also report on the design of a Si lens with a diagonal cut in order to efficiently collect the THz wave emitted from the waveguide. We evaluated the resulting radiation using PCA, a THz camera, a silicon (Si) bolometer, and a deuterated-triglycine sulfate (DTGS) detector. The generated THz wave has a broadband spectrum extending from 0.1 THz to 7 THz with a maximum dynamic range (DR) of 80 dB.

The waveguide crystal, which was made from magnesium-oxide-doped lithium niobate (MgO:LiNbO₃), had dimensions $3μm×7μm$ × 10 mm (see Ref. 20 for further details).²⁰ We used an aspherical lens to focus the pump laser pulses onto the waveguide crystal. The operation of the pump and the passage of laser pulses through the waveguide were verified by measuring the shape of the beam of the resulting laser as it passes through the crystal. We made these measurements using an IR viewer. To extract the THz waves, we coupled the waveguide crystal to a Si lens. This extraction technique is based on the theory of PCC-PM. The Si lens was designed to satisfy the PCC-PM conditions which enable us to produce a collimated beam of THz waves.²⁰ Figure 1(a) shows the schematic design of the Si lens.

We used several methods to monitor the THz waves, including Si bolometer (Infrared, Arizona, USA), DTGS, and a THz camera. These methods are based on thermal detection and were used to measure the power of the generated THz waves. We also used a method based on PCA detection, which we discuss in Sec. II C. Figure 1(b) is a schematic diagram showing the measurement of the THz emission power. We used a femtosecond fiber laser producing two wavelengths which are used to pump waveguide crystal and photoconductive antenna with 1560 nm and 780 nm, respectively.

To quantitatively evaluate the power output from the waveguide crystal, we measured both the waveguide crystal output, and for comparison, the output of a PCA (dipole type based on LT-GaAs, Hamamatsu Photonics, Shizuoka, Japan). We made the measurements using a Si bolometer. The results are shown in Figure 2. In these measurements, the maximum power of the pump laser in the case of the PCA was 15 mW and for the waveguide was 35 mW. In the case of the PCA, the input power is limited by the low damage threshold. In Figure 2, it can be seen that the THz output from the waveguide is greater than that from the PCA. When the pump power was the same for both methods of generation, the THz output from the waveguide was 100 times greater than that from the PCA. When the pump laser power was 35 mW, the output power from the waveguide was 1000 times greater than that of the PCA. The limitations incurred by the low damage threshold of the PCA limit the output power. NLO crystals have a higher damage threshold²³ so are expected to emit powerful THz radiation. The nonlinear optical constants of LiNbO₃ are 34 pm/V at 458 nm²⁴ and 152.4 pm/V at THz region.²⁵ Some crystals, such as DAST, have a higher NLO constant. No damage to the NLO crystals occurred during the experiments; hence, we were able to use a stronger pump laser to increase the output power.

We now consider the spatial distribution of the waveguide-generated THz waves. In terms of the intensity of the THz waves, we expected two cases. In one case, mainly towards the end of the waveguide, stronger THz waves were generated due to nonlinear optical interaction along the direction of the pump light propagation. In the other case, intense THz waves were generated at the front of the waveguide, and the output power decreased as the crystal absorbed the pumped laser light. Therefore, the output power of the THz waves from the further end of the waveguide was weak. We measured the intensity distribution of the THz waves using the knife edge method and a DTGS detector. The DTGS detector was placed immediately behind the Si lens. The distance between the Si lens and the detector was 1 mm. The measurement results are shown in Figure 3. We observed significant generation of THz waves at the front of the waveguide. This shows that the THz waves were concentrated over a few millimeters. Hence, the THz waves propagate in a narrow beam.

We monitored the spatial distribution of the THz radiation using a THz camera (NEC, Tokyo, Japan). The camera was located immediately behind the Si lens and was moved vertically along the edge of the Si lens. Although THz cameras are not generally able to detect THz waves reliably, we succeeded in observing the generated THz waves. The spatial distribution of THz waves was arc shaped, as shown in Figure 4(a). The waves had dimensions 30.6 mm × 21.5 mm. The observed form of the waves was consistent with the results of our other measurements, which, together with the fact that the shape of the Si lens was a half cone, suggests that they were generated towards the end of the crystal.

We also observed the output pattern from both the PCA and the waveguide to verify the usability of the waveguide emitter, as shown in Figures 4(b) and 4(c). The THz waves were guided and focused on a point using parabolic mirrors. Although in the case of the waveguide-generated waves, a clear image was observed, no sign of the THz waves was observed in the case of the PCA, even at the focal point. These observations suggest that the THz waves from the waveguide were significantly more intense than those from the PCA. The THz waves from the waveguide were visible to the THz camera both at the focal point and at other locations. This means that we can trace the spatial pattern of the propagation of the THz waves, which may help us to construct an optical system.

The DR is a common measure of the performance of a spectroscopic system. The DR is defined as the ratio of the maximum magnitude of the signal amplitude and the root mean square of the noise floor.²⁶ A system which has high DR is able to accurately detect even weak signals in noise. Moreover, high DR systems produce more information at each frequency, making them suited to applications in sensing technologies. THz-TDS systems generally have a relatively high DR. Even THz-TDSs based on PCA emitters with weak THz pulses are known to have a DR of 6 orders of magnitude. In this work, where the THz waves generated were over 1000 times stronger than those generated by PCA, we anticipate that the system will have a high DR.

We measured the THz time domain spectrum, shown in Figure 5, and the frequency spectrum of the ridged LiNbO₃ waveguide, shown in Figure 6, using a conventional TDS system. The TDS system employed a femtosecond laser (IMRA femtolite HFX-400) with pulse width 48 fs and a maximum laser power of 270 mW. This laser is able to emit dual wavelengths (1560 and 780 nm) simultaneously. Hence, we used this laser as both a THz emitter and a THz detector. The laser beam was divided by a dichroic mirror into a pump pulse of 1560 nm light, which was directed to the waveguide, and a probe pulse of 780 nm light directed to the PCA. We used a bowtie PCA, which was fabricated at a low temperature and grown on GaAs (Hamamatsu Photonics). Although we observed outputs from 0.1 to 7 THz and a DR of over 50 dB, the output became saturated in the low frequency region around 2 THz.²⁰ The improvement in the DR over the PCA-generated waves was not as pronounced as the improvement in output power. To address this issue, we modified our procedure. We used a bowtie PCA detector that was more sensitive to low frequency signals to suppress the saturation, and a high precision feedback delay stage (FS-1050UPX; Sigmatech, Inc., Huntsville, AL, USA) with a 2 nm repeat positioning accuracy to lower the noise floor. The observed frequency spectra are shown in Figure 6.

In Figure 6, the red line shows the output from the waveguide, and the black line shows the THz frequency spectrum from a PCA for comparison. In comparison to the output from the PCA, the output from the LiNbO₃ is 2 THz broader and 20 dB higher. For clarity, we used the same noise floor for both curves in Figure 6. The high output power from the LiNbO₃ crystal enables us to detect thick or dense objects. The high DR allows us to measure samples more precisely. These results should support new developments in THz technology.

Furthermore, we can see in Figure 5 that the shape of the time domain pulse is a clear single pulse. This makes THz tomography easier than it is with standard THz emitters such as PCA or NLO crystals. PCA-generated waves cannot be used to measure thin samples due to the narrow bandwidth of the emitted THz radiation. NLO crystals have strong THz absorption characteristics, making the temporal profile of the time domain pulse complex in the usual THz wave generation.²⁷ Therefore, these emitters are not appropriate in time-of-flight tomography to distinguish multiple layers. Due to the broadband output of the LiNbO₃ waveguide, the pulse width is small. This means that the waveguide generated radiation can be used to analyze thinner samples without the multiple reflections observed when complex time domain pulses are used. If we used crystals other than LiNbO₃, with higher optical non-linearity, we could generate more powerful THz radiation. This work explores the possibility of creating THz-TDS using nonlinear optical crystals and the Cherenkov phase matching method.

We demonstrated highly effective THz wave generation using the Cherenkov phase matching method and a ridged LiNbO₃ waveguide coupled with a Si lens. The power of the THz wave output was approximately 1000 times greater than that of PCA. The THz wave emitted by our waveguide can be detected by room temperature detector such as THz camera and DTGS. We also observed the path of the THz waves using a THz camera and found that it was possible to trace the propagation of the waves. This will facilitate the design of optical systems. We measured the time domain waveform and frequency spectrum which extends from 0.1 THz to 7 THz with a maximum dynamic range of 80 dB. Further, a regular single-cycle THz pulse emitted from the waveguide could be used for high resolution THz tomography measurements.

The authors thank Professor M. Tani of Fukui University, Dr. T. Ikari of Spectra Design, J. Seto, K. Oota, and S. Ishida of Nagoya University for their experimental support and helpful discussion. This work was supported by the Japan Science and Technology Agency (JST) and JSPS KAKENHI (Grant No. 25220606).