Active terahertz (THz) waveform synthesis is desirable for a broad range of applications including high speed wireless communications at Tb/s speeds and coherent manipulation of quantum systems driven by engineered light fields. In this work, we demonstrate an all-optical, fully reconfigurable platform for direct and arbitrary temporal shaping of broadband THz light pulses. The technique is based on an array of line photoexcitations of charge carriers within an otherwise homogeneous semiconductor embedded within a parallel plate waveguide. The spatially periodic charge distributions locally modulate the THz dielectric function, mapping each photoexcited line in the array directly to a reflected single-cycle THz pulse. By tuning the spatial distribution of the line excitations, arbitrarily shaped THz pulse sequences can be created from a single THz input pulse with relatively little intrinsic loss. We demonstrate synthesis of multi-cycle THz waveforms, 8-bit digital pulse sequences, and THz frequency combs with control over amplitude, central frequency, and linewidth.
© 2017 Optical Society of America
The temporal shaping and encoding of information on a terahertz (THz) lightwave is key to achieving Tb/s wireless data transfer rates [1–3]. At the same time, THz time-domain spectroscopy has evolved from measuring the broadband linear response of materials to highly nonlinear, coherent manipulations of quantum systems requiring advanced control over the pulse field profile [4–7]. Given a robust, broadband control scheme over the THz pulse amplitude and phase, multiple phase-locked THz pulse sequences can be generated and used to manipulate quantum states in the same manner as microwave pulses are currently used in multi-pulse nuclear magnetic resonance (NMR) spectroscopy . Passive shaping of THz fields accomplishes this in a static manner using spectral filters, including plasmonic [9,10], metamaterial [11,12], or photonic structures . Extensions of these methods to active mode operation provide tunability over the targeted modulated bandwidth, often through pulsed photoexcitation; however, commonly only in the vicinity of the engineered resonance [14–23] or photonic bandgap [24,25]. More direct approaches to narrowband THz generation have been heavily developed by low-temperature-operated quantum cascade lasers [26,27] and by tunable difference frequency mixing of optical pumps in a nonlinear crystal , such as in injection-seeded THz-wave parametric generation (IS-TPG) . These methods, however, offer a limited amount of control over the output central frequency and bandwidth.
In order to achieve broadband THz waveform envelope control, spatial or temporal shaping of femtosecond optical pump pulses driving THz generation in an electro-optic crystal or a photoconductive antenna has been applied [30–32]. Though very versatile, the damage threshold of programmable optics used to perform optical pulse shaping, such as spatial light modulators (SLMs), often limits the total amount of pump energy available to generate the THz pulse train and therefore limits the output THz power. Schemes that use photoconductive gated antennas to generate THz waves from temporally shaped optical pulses, while simple, are inherently limited by current saturation in the semiconductor. Nonlinear optical methods for generating intense single-cycle THz pulses with photon quantum conversion efficiencies at or exceeding 100% now exist, such as tilted pulse front optical rectification in [33–35]; waveform synthesis techniques that operate directly in the THz domain are desirable to take advantage of these high power sources. In this work, we demonstrate a flexible platform for arbitrary shaping of THz waveforms driven by such intense, single-cycle THz pulses.
The pulse-shaping method is based on spatially patterned photoinjected charge carrier distributions inside a semiconductor-filled THz parallel-plate waveguide (PPWG), which we have previously demonstrated as a versatile platform to modulate the amplitude , propagation direction, pulse delay , mode coupling , and frequency content of THz pulses . Input THz pulses, polarized perpendicular to the plates, are efficiently coupled into the dispersionless TEM mode of the PPWG and interact with the optically injected photoconductive regions. Importantly, these regions can be sub-THz wavelength in their spatial extent due to the much smaller diffraction limit of the defining optical pump pulse and small diffusive spread in the picoseconds after injection. In this work, we create a one-dimensional metal–dielectric line array within the waveguide that controllably and reversibly creates replicas of an incident single-cycle THz pulse, with a temporal spacing between replicas governed by the periodicity of the lines. We demonstrate multi-cycle envelope-engineered pulses with control over the frequency, linewidth, and phase, as well as encoding of a digital 8-bit binary sequence onto a THz waveform.
The experiment uses a THz single-cycle pulse generated by tilted pulse-front optical rectification in a crystal [33,40]. This pulse couples into a tapered aluminum PPWG , as illustrated in Fig. 1(a). A 10 mm thick float-zone silicon beam splitter (BS) at 45° is placed before the PPWG and redirects 65% of the reflected signal (red) for detection performed with electro-optic sampling in a ZnTe crystal. A window etched in the top tapered aluminum plate permits the 1070 nm pump pulse from an optical parametric amplifier to photoexcite the embedded sample. Figure 1(b) shows a side view of the embedded Si wafer; gold and indium-tin oxide (ITO) coatings confine the THz light for dispersionless propagation in the transverse electro-magnetic (TEM) mode. In the low carrier density regime where all frequency components of the THz pulse are below the photoinduced plasma frequency , the finite conductivity of the optically transparent ITO dominates the waveguide loss through the power absorption coefficient , where is the refractive index at THz frequencies inside silicon, is the vacuum permittivity, is the waveguide thickness, and is the sheet resistance of the ITO layer . The photon energy of the pump (1.16 eV) is tuned just above the bandgap energy of silicon (1.12 eV) to take advantage of the penetration depth , injecting charge carriers uniformly through the thickness of the silicon to avoid scattering into higher order modes . In our operation regime, the photoinduced charge carrier densities () are kept 1 order of magnitude lower than the threshold for mobility reduction due to electron–hole scattering . Furthermore, the fluence employed () is still 3 orders of magnitude below the optical damage threshold for silicon excited at a wavelength of 1060 nm with 100 fs pulses . A shadow mask placed atop the transparent ITO layer ( transmission at 1070 nm) spatially shapes the photoexcitation to induce a periodic photoconductivity modulation along the THz propagation direction, creating a zero-gap, one-dimensional metal–dielectric photonic crystal structure with a sharp transmission and reflection enhancement (compared to uniform illumination) at a frequency , where is an integer, the vacuum speed of light, and is the periodicity of the array [39,45]. We note the complex-valued index modulation () is intrinsically different from a distributed Bragg reflector, which is based solely on index modulation and exhibits a gap in the photon density of states. Furthermore, the predominant single-cycle character of the transmitted pulse inhibits the pulse-shaping ability in transmission mode, thus all experiments are performed in reflection configuration.
3. RESULTS AND DISCUSSION
An example of the input and reflected THz waveforms are shown in Fig. 2(a), where the black line is collected from the air–Si interface reflection inside the tapered PPWG. A digital sequence (red curve) of (111101) is created, with 1 denoting a photoexcited line and 0 an unexcited line, as shown in the inset diagram. The amplitude of the THz reflection from each individual line (1% here) increases with charge carrier density and, therefore, pump fluence, providing a way to gray-scale adjust the relative peak amplitude of each pulse in the waveform. The Gaussian spatial intensity profile of the pump pulse illuminating the entire one-dimensional array is then imprinted along the time axis of the synthesized waveform. The shadow mask period () and line width () used are 160 and 20 μm, respectively. The blue curve shows finite-difference time-domain (FDTD) simulation results using the aforementioned experimental parameters and using the experimental reference electric field profile as an input field. We use a Gaussian spatial pump intensity profile to replicate the experimental conditions and reproduce the experimental results with good agreement.
Generating a waveform composed of 12 pulse replicas with the aforementioned parameters leads to the synthesis of a frequency comb with line separation . The incident broadband electric field amplitude (black, top) and reflected frequency comb (red, top) presented in Fig. 2(b) demonstrate the clear spectral reshaping induced by a 10 μJ near-infrared (NIR) pump pulse. The blue curve shows that the FDTD simulations reproduce the spectrum of the synthesized waveform very well with a faster decay of experimental reflection in frequency due to guiding losses. The bandwidth of the incident pulse determines the highest harmonic achievable for a given line separation as well as the frequency range where single-harmonic synthesis can be achieved. The red curve in the lower panel shows the associated spectral phase of the reflected waveform in the vicinity of the first three resonances with high and low frequency ranges omitted due to low signal.
The frequency comb can be tuned continuously within the input THz pulse bandwidth by adjusting the lattice pitch (). Figure 3 shows the effect of tuning the lattice pitch from 160 μm (black curve) to 60 μm (pink curve) with a constant line width () and line number (12). Consequently, the first-order resonance is shifted from 0.27 to 0.73 THz, as shown in the inset. The input bandwidth determines how short the input pulse is in time and thus how closely lines can be brought together before replicas start overlapping temporally. When the overlap is significant, envelope reshaping can occur, as can be observed in the peaked oscillations at early times of the 60 μm (pink) data set. For the largest pitch of 160 μm, where multiple resonances lie within the input pulse bandwidth, a gradual drift can be seen in the carrier envelope phase of each replica from 14 to 47 ps. This evolution in the carrier envelope phase is due to the dispersion induced within the photoexcited regions in the vicinity of the plasma frequency . When a single resonance is present within the input bandwidth and is far enough from the plasma frequency (e.g., the waveform in Fig. 3), the resulting waveform is purely monochromatic and has envelope characteristics solely governed by the pump intensity profile.
Bandwidth tuning of the THz waveforms is achieved simply by adjusting the number of photoexcited lines in the array. As the pump intensity profile is narrowed, using an adjustable slit just above the shadow mask, fewer lines are injected, resulting in fewer pulse replicas and broader bandwidth. Linewidth tuning, as shown in Fig. 4, becomes evident as the pump spatial extent is broadened from 0.12 mm (black) to 2.45 mm (green) with the inset showing the synthesized electric field time traces. We observe excellent agreement between the waveform envelope extent and the time equivalent of the spatial extent of the slit opening (horizontal black lines, inset). The full extent of the illumination (green) generates a 20-cycle THz waveform with a linewidth of at a 274 GHz central frequency, or a spectral purity of 8%, which rivals commercially available THz bandpass filters. The Gaussian profile of the pump is again responsible for the lower electric field values at early and late times. The minimum linewidth achieved is limited only by the number of lines etched in the sample shadow mask and by the size of the optical port etched in the aluminum tapered PPWG [Fig. 1(a)].
Numerical simulations were performed using commercially available FDTD software (Lumerical) to further understand the limitations of the technique. By tuning the plasma frequency, , of a set of 12 lines of 20 μm width with a 160 μm period up to 19 THz, the reflected waveform is tuned from a multi-cycle to a single-cycle waveform [Fig. 5(a)]. In the scenario where the plasma frequency is significantly greater than the input THz pulse bandwidth, the transmission coefficient of individual lines becomes the limiting factor to the total number of pulses an array can contain. The reflected peak amplitude of the th line in the array scales as , where is the incident field amplitude and is the individual line reflection coefficient. The peak field reflection coefficient can reach up to 65% at . Provided that is of the order of 1%, as in our experiments, light can traverse the entire array and back without significant loss compared to the first line reflection. The spectral amplitude reflection plotted in Fig. 5(b) shows the continuous transition between and electron density regimes. Vertical cuts in Fig. 5(b) show the corresponding reflection spectra in Fig. 5(c) for the datasets presented in Fig. 5(a). We can see that, as the plasma frequency reaches 10 THz (black line), a broadband background reflection becomes evident and even more pronounced as reaches 19 THz (solid blue line). Transfer matrix calculations corresponding to a constant 25% field reflection off a single 20 μm thick photoinjected slab are shown in Fig. 5(b) by the dashed white curve. When the frequency is increased, higher plasma frequencies are required to achieve the same amount of reflection, as expected. The good agreement between this curve and the resonant peak roll-off from FDTD simulations confirms the Drude response of the media is responsible for the frequency dependence of the peak reflectivity and not disorder in the array.
Finally, each line in the photoexcited array can be independently addressed to individually modulate the replica pulses in the THz waveform. Thus, information can be encoded into the pulse train using binary 1s (pulse present) and 0s (pulse absent), as demonstrated in Fig. 6. The top-most waveform (purple) shows all eight field cycles in the “1” state, with subsequent data sets displaying binary sequences that spell “McGill” in 8-bit binary American Standard Code for Information Interchange (ASCII). The shadow mask has a 160 μm pitch with 20 μm wide lines and is pumped with 10 μJ pulse energy. Again, variations in peak field amplitudes, or gray-scaling, is caused by the inhomogeneous pump intensity distribution. For demonstration purposes, the array is limited to 8 cycles, or bits, though in the regime FDTD simulations indicate that 32 bits could be encoded with peak fields ratio between the first and last electric field cycle due to the enhanced THz transmission on resonance  (see Supplement 1). It is worth noting that using a pump fluence that increases with the number of lines can help circumvent diminishing signals as the number of photoinjected lines increases. Furthermore, the high transmission ratio of this device enables recycling of the incident single-cycle pulse when operating in the non-depleting regime. By cascading these arrays it is then possible to generate multiple bit sequences from a single input pulse.
We have demonstrated temporal shaping of broadband THz light using spatially controlled photoinjected charge carriers inside a PPWG. THz waveforms were synthesized from of a single incident THz pulse using periodic one-dimensional arrays, creating frequency combs that are completely tunable in frequency, bandwidth, amplitude, and chirp. Moreover, individually addressing each line excitation in the array allows on–off keying of information onto a THz pulse train. In leveraging high peak field THz pulses, this platform can be used to arbitrarily tailor multi-cycle pulse sequences for quantum control schemes of meV scale excitations in matter, or to encode information for THz wireless transmission anywhere within the input bandwidth. The all-optical nature of this device makes it fully reversible and reconfigurable after charge-carrier recombination. This refresh rate could be pushed to the gigahertz range using direct bandgap semiconductors with shorter carrier lifetimes, such as GaAs, using two-photon excitation to ensure uniform illumination through the PPWG.
Natural Sciences and Engineering Research Council of Canada (NSERC); Fonds de Recherche du Québec—Nature et Technologies (FRQNT).
See Supplement 1 for supporting content.
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