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Abstract
We constructed a system that can generate phase-controlled terahertz (THz) pulses using a fan-out periodically poled lithium tantalate crystal and an optical pulse shaper containing a spatial light modulator. The phase of each THz frequency components could be controlled by manipulating the delay time of the corresponding optical pulses. Using the system, we generated arbitrarily group-velocity-dispersion-controlled THz pulses, where the chirp parameter was 2.53 ps2/rad between 0.6 and 1.5 THz. In addition, we generated arbitrarily carrier-envelope-phase-controlled THz pulses in the same system. Phase-controlled THz pulses may be useful for applications such as dispersion compensation.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
A terahertz pulse is an ultrashort pulse that contains many spectral components covering more than one octave in the range 0.1–10 THz. When such an ultrashort pulse passes through an optical component such as a waveguide, the phase of the spectral components of the ultrashort pulse is shifted due to dispersion of the components. Therefore, the temporal waveform of the ultrashort pulse is distorted by the phase shift. An experimental setup using THz pulses is composed of several optical components. After propagating through the experimental setup, the temporal waveform of the THz pulses is also distorted. For example, Anthony et. al. showed temporal waveforms of a THz pulse after passing through a THz fiber made of Zeonex [1]. The pulse duration of the temporal waveform of the THz pulse was a few ps before propagating in 50 mm of the THz fiber. After propagating in the THz fiber, the pulse duration was broadened to more than 10 ps.
To avoid distortion of the temporal waveforms, a dispersion compensation technique is used. In this technique, the phases of the spectral components of the ultrashort pulse are pre-shifted in order to obtain the desired ultrashort pulses after propagating through the experimental setup [2,3]. Therefore, to realize dispersion compensation, a phase control technique is needed.
The phase shift caused by dispersive elements such as optical components is mainly explained by the Group Delay Dispersion (GDD). GDD is a quadratic phase shift with respect to frequency. The temporal width of the THz pulse strongly depends on GDD. Moreover, carrier envelope phase (CEP) is an important parameter. CEP is the phase of the carrier frequency with respect to the peak of the pulse envelope. In other words, CEP is a frequency-independent phase offset of the spectral phase. This means that when the same phase shift is added to the whole spectrum of a broadband pulse, the CEP is shifted. When a THz pulse passes through an optical component, the phase velocity and group velocity of the THz pulse are different, and thus the CEP is shifted. Because a THz pulse contains only a few cycles and has a broad spectral bandwidth covering more than one octave, the temporal waveform of the THz pulse strongly depends on the CEP. For example, CEP is important in THz scanning-tunneling microscopy (THz-STM) [4]. Field emission of electrons from a metal nanotip depends on CEP. Thus, CEP control is an important technique. Therefore, the GDD and CEP should be arbitrarily controlled.
A system that can control both the CEP and GDD for a few-cycle THz pulse is useful for dispersion compensation. In the optical region, a pulse compressor is used for compensation of GDD [5]. A pulse compressor can be constructed using angular dispersive optical components such as prisms and gratings. In THz region, unfortunately, to the best of our knowledge, there are no appropriate dispersive optical components because typical materials such as silicon have a constant refractive index in the THz region [6]. Moreover, there are no appropriate THz grating because it has to have a bandwidth over one octave in THz region. Thus, a THz pulse compressor cannot be constructed using typical materials. Techniques of controlling only the CEP or GDD for broadband THz pulses covering more than one octave have been reported. For example: the CEP was controlled by using prism wave plates [7]. GDD was controlled by using a hybrid waveguide [8], an optical pulse shaper that controls the instantaneous polarization state and intensity [9], and a chirped aperiodically poled crystal [10]. A technique for controlling both the CEP and GDD of THz pulses with a 0.2 THz bandwidth has also been reported [11]. In another method, THz pulses can be generated by combining multi-frequency components of THz waves [12]. The method is promising in that the phase of the broadband THz pulse can be controlled by manipulating the phase of each frequency component. The authors of that report demonstrated that only the amplitude of THz pulses with a 0.2 THz bandwidth could be controlled by manipulating the amplitude of each frequency component. However, a technique for controlling both the CEP and GDD of a broadband THz pulse has not yet been reported.
In this work, we constructed a system that can control both the CEP and GDD of a broadband THz pulse whose bandwidth is more than one octave. The system is composed of an optical pulse shaper and a fan-out periodically poled crystal. We generated multi-frequency THz components from the crystal, which was pumped by optical pulses from the optical pulse shaper. The phase of each THz frequency component could be controlled by using the optical pulse shaper. When multi-frequency THz components were combined, a phase-controlled THz pulse was obtained. Using the system, we generated a GDD-controlled THz pulse. In addition, we generated a CEP-controlled THz pulse with the same system.
2. Concept
Figure 1 shows a concept for generating phase-controlled THz pulses. The system is composed of an optical pulse shaper, a fan-out periodically poled (PP) crystal, a THz-beam splitter (THz-BS), and an off-axis parabolic mirror (OAP). The fan-out PP crystal pumped by the optical pulses generates spatially separated multi-frequency THz components. The THz-BS reflects THz waves but transmits optical pulses. Optical pulses generated by a femtosecond laser are input to the optical pulse shaper. The optical pulse shaper consists of gratings, lenses, and a spatial light modulator (SLM) [2,3,13,14]. Individual optical frequency components of the optical pulse are angularly dispersed by the gratings and lenses and are manipulated by the SLM displaying a two-dimensional spatial pattern (side view in Fig. 1). Because lenses can compensate for Fresnel diffraction, we placed image relay lenses after the optical pulse shaper to relay the image at the SLM surface to the center of the crystal. The optical pulses from the optical pulse shaper are focused vertically in the form of a one-dimensional beam onto the fan-out PP crystal via a cylindrical lens (not shown). After reflection by the THz-BS, a THz pulse can be obtained by focusing the light to a point with an off-axis parabolic mirror (OAP). The bandwidth of the THz pulse depends on the bandwidth of the multi-frequency THz components generated from the fan-out PP crystal. When the bandwidth of the multi-frequency THz components is more than one octave, a broadband THz pulse can be obtained.
Fig. 1. A concept for generating phase-controlled THz pulses. THz-BS: THz beam splitter; SLM: spatial light modulator.
We explain below how to control the phase of each THz frequency component by using the optical pulse shaper. The optical pulse shaper is placed in front of the fan-out PP crystal in order to vary the delay time of each optical pulse in the horizontal direction. The delay time causes a phase shift of the THz frequency components. The phase shift of the THz waves, Δϕ, at frequency f is
where Δt is the delay time of the optical pulse. Therefore, the phase of each THz frequency component can be controlled by manipulating Δt of the corresponding pump pulses by using the optical pulse shaper. As a result, the phase-controlled THz pulses can be generated by using the optical pulse shaper and the fan-out PP crystal.Further, we considered the design of the fan-out PP crystal and the direction of the generated THz pulse to precisely control the phase of the THz pulses. First, we considered the spectral bandwidth, Δω, of the THz frequency component generated by a PP crystal pumped by a point pump beam. Here, Δω is a spectral component whose phase can be independently controlled by the optical pulse shaper. A narrower Δω allows us generate THz pulses with a phase profile closer to the desired profile. Therefore, we can generate a more precisely phase-controlled THz pulse by using a narrower Δω. Δω is given by [15]
where N(=L/Λ) is the number of domains in the PP crystal, L is the length of the PP crystal, and f(Λ) is the center frequency of the THz waves. Also, f(Λ) is given by [16] where c is the speed of light, Λ is the inverse period, and nTHz and nopt are the refractive indexes in the crystal at THz frequencies and a wavelength of about 800 nm, respectively. Note that the plus sign means forward THz waves, and the minus sign means backward THz waves. In general, the PP crystal simultaneously generates forward and backward THz waves [15,16]. The forward THz wave is generated in the same direction as the pump pulses. Conversely, the backward THz wave is generated in the opposite direction. Therefore, in this paper, we used only the backward THz waves in Eq. (3) because their bandwidth is narrower than the forward waves.Second, we considered the spectral bandwidth of THz frequency components generated by the crystal when pumped by a finite-width pump beam. In the conventional fan-out PP crystal, the wavelength of the THz frequency component varies linearly along the lateral direction [17]. When the conventional fan-out PP crystal is pumped by a pump beam having a finite beam width, the bandwidth in the frequency region of the THz frequency component from each position on the conventional fan-out PP crystal is different. Thus, the bandwidth of phase-controllable frequency components is not the same at each THz frequency. In particular, it is indicated that the phase of higher frequency components is coarsely controlled because the bandwidth of phase-controlled frequency components becomes broader with higher frequency. To avoid this problem, we prepared a fan-out PP crystal that emits THz waves whose frequency varies linearly and continuously across the lateral direction. When the designed fan-out PP crystal was pumped by a pump beam with a finite beam width, the bandwidth in the frequency region of the phase-controllable frequency components generated by the designed fan-out PP crystal was the same at each THz frequency. Thus, the phase of higher THz frequency components could be controlled more precisely. Consequently, the designed fan-out PP crystal and backward THz waves allow us to more precisely control the phase of the generated THz pulses.
3. Experimental setup
The experimental setup is shown in Fig. 2. The setup is composed of two subsystems: one for generating a phase-controlled THz pulse, and one for detecting it. The femtosecond laser system (Vitara-T, Coherent Inc.) produced 40 fs pulses at a repetition rate of 80 MHz and a wavelength centered on 810 nm. The average output power was 600 mW. The output of the femtosecond laser pulses was split into two components by a beam splitter (BS) to serve as pump and probe pulses. The diameter of the pump beam used to generate THz pulses was expanded to 5 mm (FWHM), corresponding lateral length of the designed fan-out PP crystal, by using a beam expander. The pump pulse was tailored by an optical pulse shaper to control the phase of the generated THz pulses. We constructed the optical pulse shaper based on a two-dimensional liquid-crystal-on-silicon SLM (LCOS-SLM), which is able to modulate the phase and spectral intensity individually [2,3,13,14,18,19]. The optical pulse shaper was a conventional 4f pulse shaping arrangement in a reflection geometry consisting of a grating (1500 grooves/mm), a cylindrical lens (f = 100 mm) and an LCOS-SLM (Hamamatsu, X13138-type, 1272 × 1024 pixels) [13]. The specifications of the optical pulse shaper are as follows: the wavelength range was 770-830 nm and the wavelength resolution was 0.25 nm. Again, because lenses can compensate for Fresnel diffraction, we placed image relay lenses after the optical pulse shaper to relay the image at the LCOS-SLM surface to the center of the crystal. The THz-BS is that Indium Tin Oxide (ITO) film deposited on quartz block. Through the THz-BS (transmittance of 91% in optical region), optical pulses with an average power 310 mW were vertically line focused onto the designed fan-out PP crystal with a cylindrical lens (Tsurupica, f = 100 mm) to generate spatially separated multi-frequency components of backward THz pulses (side view in Fig. 2). We compensated for dispersion of optical elements in the path of the pump pulses by using the optical pulse shaper in order to increase the THz signal intensity. As a result, the temporal duration of the optical pulses in the crystal was compressed to 40 fs. We used the designed fan-out PP lithium tantalate (PPLT) crystal (length = 10 mm, width = 5 mm, height = 1 mm) continuously tunable from 0.15 to 1.65 THz, corresponding to an inverse period Λ from 235.13 µm to 21.38 µm [see Eq. (3)]. In this case, nTHz=6.4 and nopt=2.1 [20].
Fig. 2. Experimental setup for generation of phase-controlled THz pulses. LCOS-SLM, liquid-crystal-on-silicon spatial light modulator; OAP, off-axis paraboric mirror; PPLT, periodically poled lithium tantalate; BS, bean splitter.
In the THz detection configuration, the spatially separated multi-frequency components were collimated with the cylindrical lens, reflected by the ITO mirror, and focused onto a Photo Conductive Antenna (PCA) for detection by using an off-axis parabolic mirror (EFL = 50.8 mm). The average power of a probe pulses was 10 mW. We evaluated the THz pulses with a conventional THz-TDS system. The PCA is a photoconductive dipole antenna (Hamamatsu, G10620-12) with a 5 µm photoconductive gap. A delay stage was inserted in the path of the probe pulses to avoid distortion of the imaging relation between the LCOS-SLM surface and the designed fan-out PP crystal. Using the probe pulses with the delay stage, the temporal waveforms of the backward THz pulses were obtained by sampling the signal. The path of the backward THz pulses was filled with dry air to avoid water vapor absorption. The humidity in the path was 5% at room temperature (T = 297 K).
Here, we explain how to control the phase of the THz pulses with the optical pulse shaper. We divided the pump beam from the optical pulse shaper into 22 areas along the lateral direction of the crystal. The length of each area was 200 µm, corresponding to 16 pixels on the LCOS-SLM. The pump pulse of each area was delayed independently by the optical pulse shaper. First, we measured temporal waveforms of generated THz waves pumped by each area. By calculating the temporal waveforms by using the fast Fourier transformation (FFT), we obtained the phase and amplitude spectra. The phase can be shifted by the delay of the pump pulse (see Eq. (1)). Therefore, we generated the desired phase-controlled THz pulses by appropriately adjusting the delay of each pump pulse. For instance, when the entire phase of a THz pulse is set to a constant value, transform-limited (TL) THz pulses can be generated. Conversely, when the phase of a THz pulse is set based on a quadratic function with respect to frequency, GDD-controlled THz pulses can be generated. The quadratic function is described by ϕ(2)=β(f-f0)2, where β is a chirp parameter, and f0 is the center frequency.
4. Results and discussions
First, to check the tunability of the phase of THz frequency components generated by the crystal, we measured the generated THz waveforms by changing the position of a partial pump beam by using the optical pulse shaper. The width of the partial pump beam was approximately 200 µm. From the temporal waveforms of the generated THz waves, amplitude spectra were calculated by the FFT, as shown in Fig. 3(a). We obtained generated THz frequency components between 0.6 and 1.5 THz. The amplitude of each spectrum was different because the profile of the pump beam was Gaussian. We observed hardly any other THz frequency components whose frequency was below 0.6 THz or above 1.5 THz due to the low optical pulse energy at an edge of the crystal. Next, we evaluated the phase shift of each frequency at 0.6, 1.0, and 1.5 THz, respectively. The phase shifts can be controlled by the delay time of the pump pulses, as shown in Fig. 3(b). The experimental values show good agreement with the calculated values from Eq. (1). The maximum amount of phase shift reached more than 2π at all frequencies. Therefore, the phase of each frequency from 0.6 to 1.5 THz can be arbitrarily manipulated.
Fig. 3. (a) Spectra of THz signals generated by the crystal by changing the position of a partial pump beam. (b) Phase shift as a function of delay time of the pump pulses corresponding to each THz frequency component.
To demonstrate our system, we generated GDD-controlled THz pulses with an optical pulse shaper. Figure 4(a) shows the temporal waveforms of the phase-controlled or unshaped THz pulses generated using the system. The temporal waveform indicated by the black dotted line was an unshaped THz pulse. The temporal waveform indicated by the black solid line was generated when the entire phase of a THz pulse was set to zero at 10.5 ps. The temporal waveform indicated by the blue line was generated when the phase was set based on the quadratic function with β=2.53 ps2/rad and f0=1 THz. In addition, the temporal waveform indicated by the red line was generated when the phase was set to the quadratic function with β=-2.53 ps2/rad. The temporal width of the black line was smaller than that of the blue and red lines. The amplitude of shaped THz pulse was decreased in comparison with that of the unshaped pulse. This is a problem that should be improved in future. Figure 4(b) shows the phase spectra obtained by FFT of the temporal waveforms shown in Fig. 4(a). The phase of the black dotted line in Fig. 4(b) indicated the unshaped pulse. The phase of the black solid line in Fig. 4(b) was nearly zero between 0.6 and 1.5 THz. Thus, we confirmed that the temporal waveform of the black line indicated a TL THz pulse with CEP = 0. The phase spectra of the blue and red solid lines showed good agreement with the calculated profiles (broken lines) at 0.6-1.5 THz. Figure 4(c) shows the amplitude spectra of phase-controlled or unshaped THz pulses. The amplitude of the shaped THz pulse was decreased by half in comparison with that of the unshaped pulse. Therefore, we demonstrated that both TL and arbitrarily chirped THz pulses can be generated in the system.
Fig. 4. (a) Temporal waveforms of the unshaped, transform-limited, positive and negative chirped THz pulses, respectively. (b) Phase spectra obtained by Fourier transformation of temporal waveforms shown in Fig. 4(a). Broken lines are the calculation value. (c) Amplitude spectra obtained by Fourier transformation of temporal waveforms shown in Fig. 4(a).
Next, we demonstrated that CEP-controlled THz pulses could be generated by the same system. Figure 5(a) shows the temporal waveforms of THz pulses generated by the system when the CEP of the THz pulse was set to CEP = 0, +π/2, and -π/2, respectively. A change of the temporal waveform was clearly observed. In particular, the signs of the temporal waveforms were opposite when the difference in CEP was π. In addition, we confirmed only the internal phase was changed without changing the pulse envelope. Figure 5(b) shows the phase spectra obtained by FFT of the temporal waveforms shown in Fig. 5(a). We found that the phase of the whole spectra is almost the desired constant value. This indicated that the CEP-controlled THz pulses were TL pulses. Figure 5(c) shows the amplitude of a CEP-controlled THz pulse. The overall amplitude spectra were not changed when the CEP was controlled. Therefore, we were able to control the CEP of the generated broadband TL THz pulse.
Fig. 5. (a) Temporal waveforms of THz pulses with CEP equal to 0, +π/2, and -π/2, respectively. Broken line is the envelope of the THz pulses. (b) Phase spectra of corresponding CEP-controlled THz pulses. (c) Amplitude spectra of corresponding CEP-controlled THz pulses.
The highest frequency of the generated THz pulses was limited by absorption in the crystal. The crystal was made of lithium tantalate. The absorption of lithium tantalate in the THz frequency regime becomes larger with higher frequency [21]. Fortunately, the absorption becomes smaller at lower temperature, such as below room temperature [20,22]. Therefore, the bandwidth of the THz pulses generated by the system can be increased when the crystal is cooled. At the same time, it is expected that the amplitude of the generated THz pulse may be increased because of lower absorption.
The number of areas is limited by the number of pixels in the SLM (=1024) or the bandwidth of the THz spectrum generated by the optical pulse. Therefore, the number of areas is limited by the latter in our case. The bandwidth was 0.1 THz in Fig. 3(a), which was limited by absorption in the PP crystal. By cooling the PP crystal, the bandwidth can be made narrower, to 0.017 THz, for example [20]. Thus, the number of areas can be increased to 5-times more (=22 × 5 = 110). The reciprocal of the number of areas gives the spectral resolution, which limited the precision of CEP/GDD.
CEP/GDD is also limited by the phase shift in the THz region. The phase shift is limited by the maximum/minimum delay time of the optical pulse controlled by the optical pulse shaper. The maximum/minimum delay time can be calculated by referring to [2]. The maximum delay time is 7 ps. It is the delay time at which the intensity of the optical pulse decreases to half. The lower the frequency, the longer the delay time required for a larger phase shift. Therefore, the maximum phase shift is 26 rad at 0.6 THz. The minimum delay time is less than 7 fs, which was calculated by using parameters of our optical pulse shaper. The higher the frequency, the shorter the delay time required for a smaller phase shift. Therefore, the minimum phase shift is 0.025 rad at 1.5 THz. The CEP can be changed between ±π. In Fig. 1, the maximum amount of phase shift reached more than 2π at all frequencies. Therefore, CEP can be an arbitrary value. The precision of the CEP is limited by the minimum phase shift, which is 0.025 rad. The precision of GDD is limited by the minimum phase shift. The maximum GDD is limited by the maximum phase shift. However, in Fig. 4(b), the phase shift at 0.6 THz was less than 10 rad. It was caused by arriving time of an optical pulse that was exists at nearly 5 ps. Thus, GDD-controlled THz pulses cannot be broadened before 5 ps. When we add appropriate phase shifts while considering the arrival time of the optical pulse, the THz pulse shaper has the potential to generate large-GDD THz pulses with GDD = 4.05 ps2/rad, which is 1.6-times larger than GDD = 2.53 ps2/rad.
5. Conclusions
We constructed a system that can generate phase-controlled THz pulses by using the optical pulse shaper and the designed fan-out PPLT crystal. We used the designed fan-out PPLT crystal and backward THz waves to precisely control the phase of the generated THz pulse. Using the system, we generated TL THz pulses with CEP = 0. GDD-controlled THz pulses could also be generated by the same system. The chirp parameter of the GDD-controlled THz pulses reached 2.53 ps2/rad between 0.6 and 1.5 THz. In addition, CEP-controlled THz pulses could be generated. The CEP of the generated THz pulse can be shifted over π/2 range. Phase-controlled THz pulses may be useful for dispersion compensation. In addition, GDD-controlled THz pulses may be useful for several applications, such as THz radar [10].
With this system, the amplitude of the THz pulses can be modulated also possible using the intensity modulation of the pump pulses by the optical pulse shaper [2,3,13,18,19]. The amplitude of the THz spectra is proportional to the intensity of optical pulses. The amplitude modulation of THz pulses may be useful for full control of the temporal waveform of THz pulses because a THz pulse is completely characterized by the phase and amplitude calculated from the FFT.
Acknowledgment
We thank A. Hiruma and T. Hara for their encouragement.
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