1. Introduction

The generation of phase-locked laser pulses is one of the recent important breakthroughs in optical physics and photonics. Since both the amplitudes and the phase of light play important roles in atomic and molecular control, attosecond science, and photochemical reactions [1–5], the characterization of electric field waveforms is of great importance. Frequency-resolved optical gating (FROG), or spectral phase interferometry for direct electric field reconstruction (SPIDER) are used for such characterization [6, 7], in which ambiguity in the absolute phase remains. Recently, direct observation of the electric field waveform is reported using an attosecond streaking method [5], whereas it is difficult to apply this method to weak oscillator-based light sources.

In the terahertz frequency range, phase-locked electromagnetic fields are commonly generated and detected by using photoconductive antennas [8] or electro-optic crystals [9]. In the generation process, both techniques use difference frequency generation (or optical rectification) in materials, and therefore, the carrier envelope phase slip (CEP-slip) of the generated pulses is exactly zero, even if lasers without CEP stabilization are used. This property allows for the observation of the electric field waveforms of terahertz pulses as well as for the generation of precise frequency combs in the low terahertz region [10], making possible many advanced applications. Such technologies enable not only terahertz time-domain spectroscopy, but also phase-sensitive nonlinear spectroscopy [11–13], terahertz imaging [14], etc.

Because these terahertz techniques have various advantages over incoherent spectroscopy, many researchers are attempting to extend applicability toward higher frequencies [15, 16]. We have recently shown that the spectrum can be expanded to the near-infrared region (including the telecommunication wavelength region) by using an organic nonlinear crystal or air plasma, both of which can realize broadband phase matching [17, 18]. The results demonstrate the strong capability of few-cycle lasers to generate broadband frequency combs with zero CEP-slip, or, equivalently phase-locked electromagnetic pulses. However, methods for the characterization of electric field waveform, which can also be applicable to relatively weak light sources (e. g. Ti-sapphire oscillator), have not been devised. In particular, such methods which also ensure high compatibility with the current high-frequency electronics are required, since the near-infrared region would likely be used by the next generation of optoelectronics [1].

In this paper, we demonstrate that photoconductive antennas, which are often used in the terahertz region, can be applied to electric-field detection of light pulses at least up to near-infrared region. The setup requires only simple electronics, and can be used as a powerful new method in applications such as electric field monitoring, near-infrared time-domain spectroscopy, information-communication technologies, and coherence tomography. Since photoconductive antennas are compatible with electrical circuits, it could also bridge the gap between high-frequency electronics and near-infrared optical technologies, paving the way to the visible wavelengths.

As the detection bandwidth of the electromagnetic waves is determined by the duration of gating pulses and the material response time, we chose a commercial sub-5-fs ultrashort laser (VENTEON) for gating [19], and a low-temperature-grown GaAs for the antenna substrate. Photoexcited carriers in the substrate have a fast decay time of about 0.1 ps. The calculation shows the increase of the sensitivity at high frequency with decreasing gate-pulse duration (Fig. 1(a)). The sensitivity finally approaches to the Fourier transform of an exponential decay, which drops slowly with 1/ω at high frequency. Even though the carrier decay rate is much lower than the frequency of the electric field, the much faster rise time, which is determined by the gate pulse duration of the laser, enables the detection of high frequency components. This characteristic is a key to realizing smooth and broadband electric field detection, and is important for evaluating waveforms of electromagnetic transients. Therefore, photoconductive antennas are promising devices for the detection of high-frequency electric fields.

 

Fig. 1 (a) Calculated and observed sensitivity spectrum of the photoconductive antenna gated with 5-fs laser pulses. The pink, red and orange curves represent the calculated sensitivity for Gaussian gate pulses with pulse duration of 2 fs, 4 fs, and 5 fs respectively. The blue curve represents the measured sensitivity, and the dotted curve represents the raw spectrum before calibration. (b) Schematic of the experimental setup for ultrabroadband terahertz generation and detection. NCM: negative chirp mirror; BS: beam splitter; WP: wedge pair; PC antenna: photoconductive antenna; PM: parabolic mirror.

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In the calculation of the sensitivity, we used several simple assumptions. In the detection process using a photoconductive antenna gated with ultrashort laser pulses, photoexcited carriers are accelerated by the electric field of the incident electromagnetic field, upon which they generate observable dc current. Using envelope function I(t) of the gate pulses and the decay dynamics of the number of excited carriers n(t) = n₀ exp[−t/τ] for t > 0 and n(t) = 0 for t < 0, the total number of excited carriers can be written as

2. Experiment

To experimentally demonstrate the high-frequency detection process outlined above, we used difference frequency generation in a DAST crystal with the thickness of 150 μm to generate strong near-infrared pulses [17]. Figure 1(b) shows our experimental setup. The output of sub-5-fs laser was irradiated onto a DAST crystal, which was tilted in order to increase the efficiency of generation of high-frequency phase-locked infrared pulses. The polarization of the incident laser was set parallel to the b-axis of DAST crystal (with s–polarization), and the angle of incidence was 40 degrees from the normal. The generated terahertz wave had p-polarization (parallel to the a–axis of DAST crystal). The phase matching condition for the generation of 180-THz component at normal incidence is satisfied at the edge of laser spectrum as shown in the reference [17]. The tilting of the DAST crystal moves the phase matching frequency to lower energy where the intensity of the laser is higher, because the effective refractive index of generated light decreases as the angle is tilted from the a–axis. Si with 10-μm Ge on top was placed after the DAST crystal to cut the excitation laser above 200 THz. We used the detection antenna (Hamamatsu photonics) in reflection geometry in order to reduce the influence of absorption as well as group velocity dispersion in the substrate. In this setup, the excited carriers in the antenna substrate were accelerated by the electric field of phase-locked pulses to yield observable dc current.. The penetration depth of the laser to the GaAs substrate is about 1.6 μm [20], which is sufficiently thin compared with the coherent length of near-infrared detection. The current is amplified using current and lock-in amplifiers and collected with an analog-to-digital converter implemented in a computer.

3. Results and discussion

Figure 2 summarizes the obtained results. In the inset of Fig. 2(a), we can clearly observe extremely fast oscillations as a function of time delay as shown. The Fourier transformed spectrum of the waveform ranges to nearly 180 THz, demonstrating the responsibility of the PC antenna up to the frequency (corresponding to a wavelength of 1666 nm). The sensitivity of the photoconductive antenna gated with a 5-fs laser can be estimated by comparing the obtained Fourier transform spectrum with the intensity-calibrated spectrum of the generated infrared pulses. The result (shown in Fig. 1) indicates close agreement with the calculated sensitivity of the photoconductive antenna gated with 4- to 5-fs laser pulses, while the decaying sensitivity above 180 THz makes the spectral portion currently unusable for the spectroscopy applications. It is noteworthy that the simple assumptions made in the calculation of sensitivity hold even at such extremely high frequencies.

 

Fig. 2 (a) Observed waveform of a near-infrared pulse generated from a DAST crystal and detected with a photoconductive antenna. Inset shows a magnification of the oscillatory component. (b) Fourier transform of the obtained waveform. The spectrum extending up to 180 THz can be seen. A sharp absorption due to the CO₂ in air is also observed at 70 THz.

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The obtained experimental results demonstrate that photoconductive antennas are promising devices for future applications based on electric field detection of infrared pulses, and might be used as infrared oscilloscopes. If we use shorter pulses, which have become available recently [5], the detection of higher-frequency component, even in the visible region, will be possible in principle.

Using this setup, near-infrared time-domain spectroscopy as well as phase control of infrared pulses can be easily demonstrated. Here, we measure the transmission spectrum of a polystylene film, which is a standard material for the calibration of Fourier transform infrared spectrometers. From the results summarized in Fig. 3, we can observe absorption lines that correspond closely to those obtained with conventional Fourier transform infrared spectrometry (see Fig. 3(a)). The results confirm that the observed terahertz waveform is in fact proportional to the electric field of the generated infrared pulses. The difference in the depth of the absorption lines is probably due to the limited dynamic range of our setup compared with the FTIR instruments. Slight shift of the peak frequencies might originate from the precision of the delay stage, which could be calibrated by this kind of absorption measurements.

 

Fig. 3 (a) Measured electric field waveform transmitted through a polystyrene film with a thickness of 40 μm and the reference waveform. (b) Intensity transmittance spectrum (time domain) calculated from the ratio of Fourier transforms of observed waveforms shown in (a). The result observed using a conventional Fourier transform infrared spectrometer is also shown. (c) The time-frequency image obtained from the windowed Fourier transform of the waveform transmitted through polystyrene film shown in (a). The window function is a Hanning function with a window size of 300 fs, scanned at 10-fs steps. The solid and dotted lines represent the peak positions of the sample and reference time-frequency images, respectively.

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The phase-sensitive property of the demonstrated infrared time-domain spectrometer is an important advantage over conventional Fourier transform infrared spectrometers. To obtain phase information, we applied windowed Fourier transform to the observed terahertz waveform (Fig. 3(b)). The reference waveform already exhibits a chirp due to the group velocity dispersion in DAST, Si and Si:Ge. Upon inserting the polystyrene film (Fig. 3(b)), all the frequency components of the pulse are delayed due to finite refractive indices (>1) of the film.

Characterization and manipulation of chirp are key to achieving coherent control of photoinduced phenomena, such as attosecond pulse generation [1, 4]. In the infrared frequency range, the chirp of the light pulses can be controlled using materials with either negative or positive group velocity dispersion. As fused silica has negative group velocity dispersion in this frequency range, we can control the pulse durations of the waveforms simply by changing the thickness of fused silica plates through which the light pulses are transmitted (see Fig. 4(a)). The time-windowed Fourier transform images shown in Fig. 4(a) demonstrate the control of phase profiles (chirping) with the use of fused silica plates, illustrating the pulse monitoring capability of our setup. The pulse duration was compressed down to about 20 fs, which could be made even shorter by using a wedged pair of fused silica plates or a pulse shaping technique. Naturally, the waveforms shown in Fig. 4 provide information about the refractive index dispersion of fused silica [21]. We show the obtained refractive index dispersion as well as the extinction coefficients in Fig. 4(b), demonstrating the capabilities of this near-infrared time-domain spectrometer. Note that in the calculation of the refractive index dispersion, we assumed n = 1.4251 at 110 THz.

 

Fig. 4 (a) Time-frequency images obtained from the windowed Fourier transform of observed waveforms transmitted through two fused silica plates, a single fused silica plate, and no fused silica plates. Dotted curves represent the peak positions of the time-frequency images. (b) The corresponding waveforms. Note that each spectrum in (a) and each waveform in (b) are shifted by 2.4 ps per fused silica plate. (c) Obtained complex refractive index dispersion of the fused silica plate. Real and imaginary parts are shown in red and orange dots, respectively. Dashed curve represents the Sellmeier equation for fused silica take from the reference [21].

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4. Conclusions

In summary, we observed the electric field waveforms of infrared pulses by using a photoconductive antenna gated with 5-fs laser pulses. The observed waveforms demonstrate the phase-sensitive detection of electromagnetic fields of infrared pulses for frequencies up to 180 THz. The demonstrated capabilities of pulse monitoring and near-infrared time-domain spectroscopy suggest the possibility for a wide range of applications in optics and photonics. Since the sensitivity of detection of electric fields is predicted to be smooth over a broad frequency range, this method could evolve into a powerful technique for observing the electric fields of phase-locked light pulses, possibly including the visible or ultraviolet regions as well.