Active phase control of terahertz pulses using a dynamic waveguide

Control over the spectral phase of a light pulse is a fundamental step toward arbitrary signal generation in a spectral band. For the terahertz spectral regime, pulse shaping holds the key for applications ranging from ultra-high speed wireless data transmission to quantum control with shaped fields. In this work, we demonstrate a technique for all-optical and reconfigurable control of the spectral phase of a light pulse in the important terahertz (THz) band. The technique is based on interaction of a guided THz pulse with patterned photoexcited regions within a uniform silicon-filled parallel-plate waveguide. We use this platform to demonstrate broadband and tunable positive and negative chirp of a THz pulse, as well as control of the pulse carrier envelope phase. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (230.1150) All-optical devices; (320.5540) Pulse shaping; (300.6495) Spectroscopy, Terahertz. References and links 1. 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Introduction
Terahertz (THz) light is an important spectroscopic tool for probing low energy excitations in condensed matter [1][2][3], molecular [4,5] and biological systems [6,7]. Recently nonlinear spectroscopy in this spectral region has become possible [8], due to efficient generation of intense THz pulses [9][10][11]. States-of-matter can now be prepared and manipulated using engineered THz fields in the time domain [12,13]. A key aspect of any such optical coherent control experiment is a means to tune the pulse spectral phase, ideally in a fast and reconfigurable manner. Such phase control can be used to change the evolution of these states in a prescribed manner, enhancing desired interactions and suppressing background signals [14]. Many highly nonlinear interactions are also crucially sensitive to the absolute, or carrier-envelope phase (CEP), of the pulse. THz-scanning tunnelling microscopy, for example, using the THz pulse field as a temporal gate, is intrinsically sensitive to the CEP of the pulse [15][16][17][18][19][20]. Field emission of electrons from a metal nanotip [21][22][23] also depends critically on the pulse polarity.
The phase of a THz pulse generated using short pulsed lasers is intrinsically locked at generation. Control over the chirp of the THz pulse has most commonly been accomplished post-generation, by introducing a dispersive medium with variable thickness in the beam path [24], or by using stacked prism wave plates [25]. There are far fewer methods for controlling the CEP of the pulse, for example by using the Guoy shift at the THz focus or by variable delay between two pulses undergoing difference frequency generation in a nonlinear crystal [26]. Though simple, these methods rely on mechanical actuation of the dispersive element or optical delay stage, which is slow. A handful of demonstrations have also been made for tunable narrowband THz generation [27][28][29][30][31], though again few solutions adjust the waveform chirp in an active fashion.
In this work, we demonstrate a technique for complete phase control of THz light pulses. Our technique shapes the phase of THz pulses by reflection from patterned photoexcited regions inside a silicon-filled parallel-plate waveguide (PPWG). These light-induced reflectors are spatially tailored in the propagating plane of the THz pulse using a two dimensional spatial light modulator (SLM). This makes them fully reconfigurable and capable of introducing both negative and positive chirp and gives control over the CEP. We believe the versatility that this platform offers will make it a useful tool for several THz applications.

Methods
The technique relies on a silicon-filled PPWG, depicted in Fig. 1(a) and detailed in previous work [32]. The THz pulse is coupled and guided in the dispersionless TM 00 mode. The silicon is made optically addressable by using a transparent conductive oxide coating as a top plate, thereby allowing photoexcitation of the silicon within and creating localized metallic domains experienced by the THz pulse propagating in the plane. This optically addressable THz waveguide is a versatile platform for a variety of THz pulse control experiments, having already demonstrated amplitude modulation [33], pulse delay and beam steering [34], guided mode coupling [35], frequency selection [36], tunable frequency comb generation and information encoding [32]. For these experiments, a solid-state Yb:KGW femtosecond laser amplifier providing 180 fs duration, 1 mJ pulses with a center wavelength of 1028 nm was used to generate, detect and modulate the THz pulse. THz pulses were efficiently generated by tilted pulse-front optical rectification in a LiNbO 3 prism. The platform's core consists of a tapered aluminium PPWG that provides coupling between free-space and a silicon-filled guided section [32]. A 150 nm gold layer is deposited on the bottom side of a double-side polished, 150 µm thick high resistivity float zone silicon slab (resistivity >10,000 Ω-cm). A thick (sheet resistance of 1 Ω/sq) indium tin oxide (ITO) coating was deposited on the top surface of the silicon to form the second conducting plate in the waveguide while allowing optical access for the pump light. The NIR pump beam is spatially patterned using a two dimensional SLM, and the intensity profile of the pump beam on the sample is measured in-situ by splitting a fraction of the beam before illumination and casting the image onto a CMOS array. The SLM used is a commercial product from Holoeye with a 1920 × 1080 pixel array (8 µm pixel pitch) each providing 256 phase levels and a 2π maximum phase shift. The SLM and imaging optics define structures with a spatial resolution of approximately 40 µm, much smaller than THz wavelengths inside silicon (100 µm). The 1028 nm pump pulse wavelength is chosen close to the indirect band gap of silicon such that the optical penetration depth (≈ 200 µm) is larger than the waveguide thickness, creating a uniform excitation through the thickness of the silicon slab. The resultant charge carrier density profile created by the patterned pump distribution locally modulates the complex-valued refractive index inside the waveguide (see Fig. 1(b)). The subsequent space-to-time mapping that occurs upon THz pulse reflection is the key to the functionality of the device. A silicon beamsplitter introduced before the waveguide at 45 • (not shown here) redirects the reflected THz pulse for electro-optic sampling detection inside a GaP crystal.

Results and discussions
The broadband phase φ of the THz pulse can be shifted easily by multiples of π by reflection off an even or odd number of conducting interfaces within the waveguide. We can demonstrate this phase flipping capability by retro-reflecting the THz pulse off a single or a pair of photoexcited lines in the silicon. Figure 2 shows the THz reflection from a structure which holds the possibility of either odd (Region I, red) or even (Region II, blue) reflective surfaces, combining a single line excitation and two interfaces at 45 • and −45 • . The interfaces of these pump-induced reflectors are patterned by a lithographically-defined gold shadow mask deposited atop the ITO layer, shaping the transmitted pump pulses and ensuring a sharp conductive interface and optimal reflection. The SLM is then used to direct light to the two reflectors, and can tune the individual line reflectance. The Drude optical conductivity of injected photocarriers in silicon is purely real and flat to a good approximation over the entire 0.2 -1 THz bandwidth of the pulse and so the dispersion of the carriers can be neglected. The excited regions are 20 µm in width, and their conductivity is adjustable via pump power tuning over each section. Figure 2(a) shows the reflected pulse when 40% of the 120 µJ NIR pulse is used to create Region I, a normal incident reflection off a single surface. With a single interface, we achieve a peak electric-field reflection coefficient of 43% and 19% is reached when both regions are photoexcited. Note, some light leakage in the dark areas defined by the SLM results in the small amount of reflection observed at 42 ps and 14 ps in the ∆φ = π and ∆φ = 2π data sets, respectively. When the pump is switched to illuminate only Region II, in Fig. 2(b), the pulse is time-shifted due to the extra path length travelled within the waveguide but now the phase is flipped by 2π. If, however, both regions are illuminated with Region I acting as a partial reflector, a phase flipped pair of pulses is received at the detector as shown in Fig. 2(c). Reflection from a distributed interface allows the possibility of broadband phase manipulation and can be used to control the CEP of a pulse [16]. Figures 3(a)-3(c) show THz pulses reflected off three different charge carrier distributions, each with a carrier-envelope phase shift ∆φ = −π/2, 0 and +π/2, respectively. The pump intensity profiles giving rise to these charge carrier distributions are defined by the SLM and the measured profiles are shown in the adjacent graphs. Taking the intensity profile of Fig. 3(a) as an example, one can think of this carrier distribution as two separate regions. The first, spanning from 0.1 to 0.3 mm, acts as a phase delay for the THz pulse as it passes through the region twice with minimal losses; the second, a peak at 0.37 mm, redirects the pulse as a mirror. An analytical estimate can capture the main contributions to the phase change in the dc limit of the Drude conductivity, where the angular frequency and the scattering time product ωτ 1, assuming a constant real conductivity σ 1 of length d. This is appropriate for silicon in the range of frequencies investigated as τ ∼ 50 fs at room temperature for carrier density on the order of 10 16 cm −3 [37]. In the first, low photoconductivity region, the change in CEP phase is approximately ∆φ CE P = d 2c 0 where σ 1 is the real part of the conductivity, 0 is the vacuum permittivity and c 0 is the speed of light in vacuum, respectively. The slowly-varying square root dependence on THz frequency serves to introduce a relatively flat phase shift accross the pulse; continuously tunable through the thickness of the medium traversed. Finite-difference time-domain (FDTD) simulations performed using a software developed by Larsen et al. [38] provided the intensity profiles required to achieve the desired phase modulation, however minor fine-tuning is performed in situ to achieve the desired pulse shape. We note that given the reconfigurable nature of this phase shaping method it could easily be implemented with a genetic algorithm for pulse shape optimization. The ability to arbitrarily control the chirp of a pulse is also valuable for control experiments such as vibrational ladder climbing in a molecular system [39]. For a first demonstration, we designed a shadow mask with 20 µm wide lines with a pitch of ∆z = 90 × 0.98 n µm, where n is an integer indexing lines in the array. By using a mask, we sacrifice the reconfigurability of the device for better contrast and smaller details in the photoinjected structure, thus reaching higher resonant frequencies. By illuminating the shadow mask with a Gaussian intensity profile, the reflected THz pulse becomes positively chirped as seen in Fig. 4(a). Due to the distributed nature of the reflector, the peak electric field reflectivity demonstrated here is kept at 2.3% per cycle. A short-time Fourier transform (STFT) of the waveform, presented in Fig. 4(b), shows the instantaneous frequency as a function of time increasing from 0.47 THz to 0.75 THz with an average chirp of 8 GHz/ps. The inset shows the pump intensity profile parallel to the THz propagation axis as recorded by the camera. The cyan line follows the position of the intensity maxima of the STFT data and shows excellent agreement with the predicted instantaneous frequency ν(t) (black dashed curve). From the mask design (∆z), we calculate ν(t) = c/2n Si ∆z where n Si = 3.42 is the refractive index of silicon.
Negative chirped THz pulses are as easily generated as positive. In this case, we present a maskless implementation using only the SLM to shape the carrier distribution within the waveguide. Operation in this manner is currently limited to chirped frequencies below 0.45 THz due to the pixel size of the SLM and imaging optics used, however the waveforms are completely reconfigurable. Presented in Fig. 4(c), the chirped waveform shows a clear increase in cycle period as a function of time. The STFT performed on this data is shown in Fig. 4(d), explicitly showing a negative chirp of -11 GHz/ps on average between 10 and 30 ps over a 220 GHz bandwidth. The inset shows the pump intensity profile achieved using the SLM overlaid with the image recorded by the camera. The STFT maxima (solid cyan curve) shows excellent agreement with the expected instantaneous frequency (dashed black curve), calculated directly from the recorded the pump intensity profile. From the pump intensity profile design, the chirp can be reversed from negative to positive within the same pulse as it does here at 30 ps. This feature is intentionally created by a region near 2 mm (see inset of Fig. 4(d)) where the pump induced features are slightly closer together, and this reversal is very well reproduced by the experimentally observed waveform.

Conclusion
We have demonstrated CEP control over broadband THz pulses using spatially engineered photoinjected reflectors inside a silicon-filled PPWG. Odd or even integer multiples of π phase flips are demonstrated using a single or a pair of pump-induced reflective interfaces, respectively. Broadband tuning of THz pulse phase over ±π/2 increments was also demonstrated by photoinjection of low-conductivity phase delay volumes adjacent to the photoinduced reflectors. In addition, arbitrarily chirped THz waveforms were demonstrated in the same platform, both positive and negative, showing 8 and -11 GHz/ps chirp between 0.25 and 0.75 THz. We believe this device will be a great asset for THz dispersion control, wireless communication, and spectroscopy of molecular and solid state systems.

Funding
Natural Sciences and Engineering Research Council of Canada (NSERC) and Fonds de Recherche du Québec-Nature et Technologies (FRQNT).

Disclosures
The authors declare that there are no conflicts of interest related to this article.