We investigated the dynamics of photo-induced optical activity of metal chiral gratings on an Si substrate for terahertz (THz) waves. We employed a new technique that enables optical-pump and THz-probe measurements via broadband THz spectroscopy at the microsecond time scale using a low-repetition-rate pump and a high-repetition-rate probe. We revealed that the THz optical activity decays as a result of the carrier diffusion effect because this optical activity is because of the presence of three-dimensional chiral structures of photo-carriers in the Si substrate.
© 2012 Optical Society of America
Recent progress in the design and fabrication of artificial subwavelength structures such as metamaterials has led to the realization of several novel functions for manipulating light [1,2]. In particular, strong optical activity in planar metal chiral structures has been demonstrated in the visible [3–7] and terahertz (THz) regions [8–11]. Because optical activity is a nonlocal optical response, the effect can be enhanced by introducing double layered structures [5,6,12] or three-dimensional chiral structures . Control of the polarization of a THz wave is one of the important applications of these artificial chiral structures because of the lack of effective polarization devices. Chiral structures are also promising as a new route to negative refractive index materials .
Active control of metamaterials is also an important issue, and several attempts at doing so have been reported for THz metamaterials [14–17]. The modulation speed of such active metamaterials is important for their application as THz modulators. In conventional schemes for photo-controlled devices, the carrier lifetime determines the modulation speed. For example, using a semiconductor substrate with a short carrier lifetime, a THz modulation as fast as a few picoseconds has been reported . We have found that optical activity in the THz region is induced by photo-excitation on Si with chiral-patterned metal gratings . In combination with the fabricated metal chiral gratings and photo-generated carrier distribution, three-dimensional chiral metallic structures were formed. Because the optical activity is sensitive to the spatial properties of the distribution of the photo-carriers, it is expected that the dynamics of the induced optical activity depends on fast carrier diffusion rather than carrier recombination [Fig. 1(a)].
In this Letter, we investigated the temporal responses of the transmittance and polarization-rotation spectra of photo-excited metal chiral gratings on an Si substrate to clarify the dominant factor determining the decay time. A new method of phase-locked optical-pump and THz-probe time-domain spectroscopy was developed to detect the microsecond time scale response because the carrier lifetime is long. It was revealed that the carrier diffusion effect governs the decay process of the THz optical activity in such photo-induced artificial chiral structures.
Two-dimensional, 100 nm-thick gold chiral gratings with a 100 μm period were fabricated on a high-resistance Si substrate (resistivity ) . Because the lifetime of the photo-carriers in such substrates is a few microseconds, it is difficult to measure the dynamics of the THz response with the conventional femtosecond-laser-based optical-pump and THz-probe method with optical path length delay tuning . Therefore, we developed a new time-domain THz spectroscopy scheme based on the combination of synchronized low-repetition-rate optical pumping and high-repetition-rate THz probing.
Figures 1(b) and 1(c) show the schematic descriptions of this technique. A Ti:sapphire-based femtosecond-laser system (RegA9000, Coherent, Inc.) is used as the light source. The output from a mode-locked Ti:sapphire oscillator with a 76 MHz repetition rate, a center wavelength of 800 nm, and a pulsewidth of 140 fs is divided into two beams. One is divided again and used for the generation and detection of the THz radiation with optical rectification and electro-optic (EO) sampling using ZnTe crystals . The other is used as a seed pulse for a Ti:sapphire regenerative amplifier with a repetition rate of 120 kHz and a pulsewidth of 200 fs. The repetition rate of the regenerative amplifier is created as a fraction of that of the oscillator. The output of this regenerative amplifier is used for excitation of the chiral grating samples. Here, the pump pulse excites the sample every 8.3 μs, and the THz pulses probe the effect of the photo-excitation every 13 ns.
The observed THz electric field () is expressed as , where is the electric field without photo-excitation, is the electric field change due to photo-excitation, is the delay time of the probe pulse, which is controlled by the delay stage shown in Fig. 1(b), and is the time after the pump pulse excitation. Because the probe THz pulses are generated with a period of , takes discrete values that are expressed as , where is the time between the pump pulse and the first THz pulse and is the number of THz pulses following the pump pulse excitation. In this experiment, was on the order of a few picoseconds while time was in the scale from nanoseconds to microseconds. The dynamics were determined by fixing the delay stage and measuring with an oscilloscope at a certain as a function of from the EO sampling signals. By repeating this measurement with different delay times , was obtained as a function of both and . Then by combining the obtained and , the full dynamics of the THz waveform were retrieved. The temporal response in the frequency domain, , was obtained by performing a Fourier transform. By applying this method to both the and components using wire grid polarizers , the dynamics of the THz polarization rotation could also be obtained.
In conventional optical-pump and THz-probe measurements, time-domain waveforms are obtained using the THz-TDS technique at certain fixed ’s, where both and are scanned using optical delay stages. The range of is limited by the length of the delay stage. In contrast, this new method can directly determine the -dependence of at a certain using high-rep THz probe pulses, and an electronic sampling method. It should be noted that the dynamics at the ultrafast () time scale can be also measured simply by adding another optical delay stage for tuning .
Figure 2 shows the experimental results for the dynamics of the transmittance and polarization rotation spectra of a photo-excited metal chiral sample. The horizontal axis is the frequency of the THz wave, and the vertical axis is the time after the photo-excitation. The horizontal cross sections are the transmission spectra or polarization rotation spectra at certain times, while the vertical cross sections are the dynamics of the transmittance or polarization rotation at the specific frequencies that are denoted by the arrows.
The dynamics of the differential transmission are shown at the right-hand side of Fig. 2(a), where is the complex transmittance coefficient. The decay curve of the transmittance can be fitted to exponential decaying functions with two components: , where and are the decay times of each component and and are their amplitudes. The faster component is approximately 300 ns and the slower component is approximately 3 μs. This result indicates that there is another mechanism in addition to the carrier lifetime involved in the decaying dynamics of the THz response of the photo-excited metal chiral gratings. Figure 2(b) shows the temporal profiles of the optical activity. A polarization rotation as large as 1.5° at approximately 1 THz is observed just after the photo-excitation. In contrast to the transmittance, the polarization rotation decays with only one exponential component. The decay time is approximately 250 ns, and is close to the faster decay time () of the transmittance.
These results clearly show that the carrier diffusion effect affects the optical activity. When the metal chiral grating on the Si substrate is excited by light, a chiral structure of the photo-carrier distribution is generated in the semiconductor substrate . The transmittance drastically decreases because of the THz absorption of the photo-carriers, while polarization rotation occurs because of the light-induced three-dimensional chirality. Because the chiral shape of the carrier distribution is essential for three-dimensional chirality, the optical activity disappears when the carrier diffusion effect makes the distribution uniform. In contrast, the transmittance depends on the carrier density at the surface of the Si substrate rather than the spatial properties of the carriers. Thus, the differential transmittance initially decays by the carrier diffusion in the direction normal to the sample surface, and then later decays because of the finite carrier lifetime.
In order to confirm the validity of this interpretation, numerical simulations were performed. The carrier diffusion effect was taken into account and the carrier density distribution in the Si substrate at each time was calculated by solving the diffusion equation,1), is the carrier density and is the diffusion Coefficient, which is assumed to be . The carrier distribution becomes uniform within tens of nanoseconds [Fig. 3(a)], which is much faster than the lifetime (). Thus, we neglected the finite lifetime effect in this calculation. The THz transmittance and polarization rotation were calculated by assuming that the refractive index profile is determined by the carrier density distribution. Commercial software (DiffractMod, RSoft, Inc.) that employs the rigorous coupled wave analysis method was used for this calculation. The change in the refractive index is described by the Drude model, and the carrier density is expressed as a plasma frequency in the Drude model . Figures 3(b)–3(e) show the results of the calculated spectra and their temporal profiles. Because carrier lifetime is neglected here, the transmittance does not perfectly decay, while polarization rotation decays by the effect of carrier diffusion. This feature is consistent with the experimental results.
It should be noted that the mechanism of photo-control of the THz optical activity is quite different from the conventional scheme for the active control of THz metamaterials, where the carrier recombination lifetime limits the response speed of the modulation. The carrier diffusion effect can, therefore, be used to control the THz response at a high speed beyond the carrier lifetime .
In conclusion, we examined the dynamics of the THz response in photo-excited metal chiral gratings. We revealed that the THz response decays because of both the carrier diffusion effect and carrier recombination. Because the photo-induced THz optical activity is sensitive to the shape of the carrier distribution, the carrier diffusion effect crucially controls their dynamics. In addition, the response speed is much faster than the carrier lifetime. We also developed a low-rep optical pump and high-rep THz probe technique that enables the measurement of time- and frequency-resolved spectra at a microsecond time scale and in the THz frequency region.
We are grateful to Prof. T. Sekitani and Prof. T. Someya for the sample preparation, and Prof. Y. Svirko, Dr. H. Tamaru, and Dr. K. Yoshioka for fruitful discussions. This research was supported by the Photon Frontier Network Program, the Global COE Program “the Physical Sciences Frontier,” Special Coordination Funds for Promoting Science and Technology of the Ministry of Education, Culture, Sports, Science and Technology, Japan, KAKENHI (20104002), and Research Fellowships for Young Scientist (N. K.) from the Japan Society for the Promotion of Science (JSPS). ADVANTEST F5112+VD01 and Cadence Virtuoso at the VLSI Design and Eduction Center (VDEC) in the University of Tokyo were used for the sample fabrication.
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