1. Introduction

Time-domain terahertz (TD-THz) methods using single- or few-cycle THz pulses have found promising applications in spectroscopy, imaging, and sensing[1–3]. The use of broadband THz pulse trains in a TD-THz system enables time-gated coherent detection, which offers sensitivity orders of magnitude higher than the incoherent detection of narrowband THz signal using liquid-helium cooled bolometers. However, the lack of high power broadband THz sources has hampered the development of convenient and versatile TD-THz systems for many applications. A high power THz source will improve both the signal-to-noise ratio (SNR) and the dynamic range of imaging and sensing systems by providing the capability to penetrate deeper into dense and/or strongly scattering and absorbing materials. Furthermore, high-power THz sources promise to reduce drastically the data acquisition time at current SNR levels, which opens up the possibility for real-time imaging of objects.

Present TD-THz emitters exploit either a current surge in a photoconductive antenna or optical rectification in a nonlinear optical crystal. Currently, photoconductive THz generators can only achieve an average power on the order of 1 µW at best [4]. Further average power scaling is significantly impeded by thermal effects due to the absorbed pump power. In contrast, optical rectification of a femtosecond pulse train in a nonlinear crystal offers much better THz power scalability [5–8].

Both of the aforementioned THz generation methods are based on the conversion of an ultrafast optical pulse into a THz pulse. For the past ten years, this has been accomplished most readily using solid-state Ti:sapphire laser systems and tailoring THz generation devices to the characteristics of these lasers [5–7]. In recent years, the rapid advancement of ultrafast fiber lasers has motivated efforts to incorporate them into TD-THz systems [8–13]. Due to their advantages over solid-state lasers, such as high wall-plug efficiency, diffraction-limited beam quality, compactness, robustness, and superior heat dissipation due to the large surface-to-volume ratio of a fiber, ultrafast fiber amplifiers operate at much higher average power level than can be implemented in the Ti:sapphire system [14]. Recently we have employed an ultrafast Yb-doped fiber amplifier to drive optical rectification in nonlinear crystals and have generated both linearly and radially polarized broadband THz pulses [8, 13]. Using a simple collinear geometry, we were able to generate linearly polarized THz pulses with an average power of 6.5 µW by pumping a 1-mm thick, 〈110〉-cut GaP crystal with an average pump power of 10 W [8].

 

Fig. 1. Diagram of the terahertz generation inside a thick, bulk GaP crystal. Generation near the entrance face (first ellipse) quickly diffracts and is a negligible contribution to the final emitted beam.

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Since optical rectification is a second order nonlinear optical process, it is expected that further THz power scaling can be achieved by increasing the crystal length. However, previous studies have shown that the optimal optical spot size should be roughly equal to the peak generated THz wavelength inside the crystal [16]. In this regime, the THz only remains collimated for a few wavelengths within the bulk crystal. As shown in Fig. 1, any THz pulse generated near the entrance face of the crystal quickly diffracts and only maintains a small spatial overlap with the THz generated near the exit surface of the crystal. Furthermore, diffraction not only reduces the power scaling benefits of using a longer crystal by preventing the coherent buildup of THz radiation, it also degrades the quality of the THz beam at the exit face of the crystal by spatially chirping it. In order to mitigate the detrimental effects of diffraction, in this work we reduce the crystal cross-section and thus confine the radiated THz in a waveguide as shown in Fig. 2; it is important to note that only the THz radiation is confined by the waveguide, and not the optical pump. We investigate the emitter design by considering both dispersion and material loss. Furthermore, we demonstrate broadband THz generation experimentally from two GaP waveguides with different cross-sections (shown in Fig. 2). Lastly, we demonstrate the generation of THz pulses with an average power of 120 µW at 25 MHz repetition rate, which represents the highest average power achieved for a broadband THz source pumped by fiber laser systems. GaP waveguides can also be used to generate narrow band THz based on difference-frequency mixing of two optical beams at different wavelengths, which has been demonstrated in Ref [17].

 

Fig. 2. The GaP waveguide emitters for broadband THz generation used in this study. The waveguide dimensions and crystal orientations of two GaP waveguides are shown in the figure.

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2. Design of GaP waveguide THz emitter

THz generation via optical rectification requires the group velocity of the optical pulse to match the phase velocity of the THz pulse. To quantify this velocity matching, a coherent length is introduced as

where λ_THz, n_THz, and n_g denote the free space THz wavelength, the refractive index for the THz wave, and the group index for the optical pump pulse, respectively. The requirement of velocity matching can be satisfied for specific combinations of nonlinear crystals and laser systems. For example, ZnTe has become the most popular optical rectification crystal for Ti:Sapphire lasers due to a much longer coherent length at 0.8 µm as compared to other crystals with similar nonlinearity. For THz systems based on 1.0 µm lasers, GaP becomes the optimal crystal for broadband optical rectification. Fig. 3 shows the frequency dependent refractive index of bulk GaP (the solid black curve) with the Sellmeier coefficients taken from Ref. [18]. Owing to the higher optical phonon resonance (11 THz for GaP versus 5.3 THz for ZnTe [19]), GaP has a much flatter index curve, which indicates a broad velocity-matching bandwidth with less dispersion. The broader velocity-matching bandwidth allows efficient generation of broadband THz pulses; in the meanwhile, the smaller dispersion allows those pulses to propagate through a longer GaP crystal with less distortion. It is these two distinct properties that make it possible to implement broadband THz emitters using GaP waveguides.

 

Fig. 3. The dependence of THz indices on frequency. The solid black curve denotes the refractive index of bulk GaP. Four curves represent the calculated effective indices of the fundamental mode for GaP waveguides with different cross-sections. The dashed curve represents the group index of GaP at 1.064 µm.

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We have numerically modeled such a dielectric waveguide by solving the eigenvalue problem based on a finite difference frequency domain (FDFD) method [20]. This method calculates the effective indices of the propagating modes at a certain THz frequency supported by a GaP waveguide given the cross-section. Figure 3 illustrates the effective index of the fundamental modes versus THz frequency for GaP waveguides with different cross-sections.

For comparison, the optical group index at 1.064 µm is also shown in the same figure. In addition to confining the THz, the waveguide also modifies the effective dispersion. As we shrink the waveguide cross-section, the effective index curve tends to bend and intersect with the optical group index curve at a higher THz frequency. For example, the intersection frequency shifts from 0.25 THz to 1.5 THz as the waveguide width changes from 2 mm down to 0.25 mm. Since perfect velocity matching is achieved at the intersection point, the generated THz spectrum will be peaked around this point, as suggested by Equation (1).

One might speculate that the THz power would continue to scale with the waveguide length. Unfortunately as the GaP reaches a certain length, the material loss overtakes the generation of the THz pulses, preventing further power scaling. Another drawback of using long waveguides is that dispersion narrows the generated THz spectrum and thus stretches the time-domain THz pulse. An optimal length for a waveguide emitter should be chosen in order to achieve the best overall performance in terms of power scaling, THz pulse duration, and THz spectrum width. With regards to a GaP waveguide, it can be shown that this optimal length falls between 5 mm to 1 cm depending on its cross-section. In this paper, our THz emitters are constructed from GaP waveguides of 6 mm length.

3. Setup and experimental results

Figure 4 illustrates the schematic setup. The fiber laser system used to drive optical rectification is based on parabolic pulse amplification [21]. In this configuration, the pulse train from a fs-oscillator is amplified by a Yb-doped fiber amplifier and then the linear chirp developed during amplification is removed by a compressor. In our setup, the seed to the fiber amplifier is a passively mode-locked Nd:glass oscillator (High-Q UC-100fs) with an average power of 120 mW and a repetition rate of 72 MHz. The optical pulse has duration 110 fs and its spectrum is centered at 1.064 µm. The fiber amplifier consists of a 6.5-m polarization-maintaining fiber with a 30-µm Yb-doped core and a 400-µm hexagonal-shaped inner cladding. A 1.2-m photonic bandgap fiber (PBGF) is employed to recompress the stretched, amplified pulse. The details for a similar parabolic fiber amplifier can be found in Ref [8].

 

Fig. 4. Experimental setup for THz wave generation and detection. HWP: half-wave plate, HDPE: high density polyethylene

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During the parabolic pulse amplification, the pulse spectrum broadens and the amplified pulse may be compressed even shorter than the initial duration given a complete compensation of the pulse chirp. However due to the dispersion mismatch between the fiber amplifier and the PBGF compressor, the pulses in our current setup are only compressed to ~200 fs with an average power of 6 W. We prepared two 6-mm long GaP rectangular waveguides with cross-sections of 1 mm×0.7 mm and 0.6 mm×0.4 mm, and their 6-mm-long sides along the <110> orientation as shown in Fig. 2. The waveguide emitters were mounted onto a gold mirror with their shorter edges touching the gold surface. In the experiments, the 6 W, ~200 fs compressed pulses were focused into the waveguide with ~200 µm beam diameter. At the exit face of the crystal, the diffracting THz and collimated optical were collected by a 3” paraboloid, and a high density polyethylene slab was used to separate the collinear beams. Coherent detection of the THz pulses was achieved using a photoconductive based receiver fabricated by Picometrix, which is optically gated with a small portion of the fiber amplifier output with variable delay.

 

Fig. 5. Measured THz temporal waveforms from two GaP waveguide emitters.

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Figure 5 shows the measured THz waveforms from the GaP waveguide emitters. Both waveforms exhibit multi-cycle oscillations due to dispersion. Furthermore, as can be seen from Fig. 3, the waveguide with a smaller cross-section has a sharper index curve compared to a larger one, which implies that the smaller emitter is more dispersive than the larger one. This explains qualitatively why the THz pulse generated from 0.6 mm x 0.4 mm emitter has more oscillating cycles.

 

Fig. 6. Measured THz spectra from two emitters. Insets are the computed coherent length for two GaP waveguide emitters used in the experiments.

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The spectra of the THz pulses, which are obtained by taking the Fourier transform of the temporal waveforms, are plotted in Fig. 6. Both spectra extend beyond 1.5 THz. As previously discussed, the emitter with the smaller cross section favors higher THz frequency emission. Coherent length calculations based our asymmetric waveguides are shown in the inset. Clearly the peaks of the two spectra coincide with the perfect velocity-matching frequencies where the corresponding coherence lengths are maximized, respectively.

It is worth noting that the coherent length of a bulk GaP is enhanced as the pump wavelength shifts towards 1.000 µm [18]. Thus it is more convincing to compare the power scaling potential of a GaP waveguide emitter and its bulk counterpart at pump wavelength less than 1.064 µm, the operating wavelength of current parabolic fiber amplifier. For this purpose, we employed a commercially available Yb-doped fiber amplifier system (Clark-MXR Impulse) to pump the 1 mm x 0.7 mm waveguide. This laser system was able to deliver up to 14 W, ~230 fs pulses centered at 1.035 µm with a repetition rate of 25 MHz. The THz power was measured using a liquid-helium-cooled silicon bolometer together with a lock-in amplifier. Under the same conditions, we also measured the power scaling of a 1-mm thick, 〈110〉 GaP bulk crystal. Both power measurements are presented in Fig. 7. A comparison of these two power scaling curves indicates that using 6 mm long waveguide emitter improves the THz power yield by almost an order of magnitude. At an optical power of ~14 W, we were able to generate broad broadband THz pulses with an average power of 120 µW.

 

Fig. 7. Comparison of THz power scaling between a 1 mm bulk GaP and the 6 mm long GaP waveguide emitter with 1 mm×0.7 mm cross-section. In the experiment, a commercially available Yb-doped fiber laser system (Clark-MXR Impulse) was used to pump these two samples.

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4. Discussion and conclusion

In principle, the strong index contrast between the crystal and surrounding air combined with the relatively wide core creates a highly multimode waveguide. Fortunately by manipulating the spot size of the optical beam in the waveguide, one can optimize the THz excitation crosssection to match the fundamental mode profile. It can be shown theoretically that the fundamental mode can carry more than 95% of total emitted THz power. Unfortunately, single mode excitation is unadvisable for waveguides wider than 600 um, since the optical beam diameter must scale with the increasing waveguide width. Unless the pulse energy can be increased to maintain peak intensity, the THz power will drop precipitously with larger waveguides.

For a rectangular waveguide, the fundamental mode has two different spatial profiles corresponding to horizontal and vertical polarizations respectively. These two orthogonal modes propagate at slightly different speeds leading to modal dispersion. Although this detrimental effect is minimal for 6 mm long waveguides, a GaP emitter with square or circular cross-section is preferred in order to achieve a degeneracy of these two orthogonal modes.

In conclusion, we have demonstrated that GaP waveguides are capable of emitting broadband THz pulses, and have investigated their power scalability. With a 6-mm emitter, a record average power of 120 µW is obtained by pumping it with a high power Yb-doped fiber laser system. We also demonstrated that the dispersion can be tailored by changing the waveguide cross-section, which opens the possibility of building compact broadband THz sources centered at a select frequency by engineering the dispersion of waveguide emitters. In fact, additional design flexibility can be achieved by encapsulating a GaP waveguide with other materials (dielectric or metal).