1. Introduction

The measurement of ultrafast optical response has been an essential tool for understanding the nonlinear behavior of materials, including graphene [1], semiconductors such as InP [2], and artificial semiconductor-based saturable absorbers such as GaAs/AlGaAs [3]. In addition, it is important to understand the mechanism of ultrafast optical response occurring, for example, in the photo-induced transient absorption of nonlinear crystals such as ZnTe [4] and lithium niobate [5,6], and in laser ablation [7]. Femtosecond-laser-based time-resolved spectroscopy (fs-TRS) is a basic technique for evaluating the ultrafast optical response of a sample with fs-order temporal resolution [2–6]. Conventionally, pump and probe pulses are required for fs-TRS. The pump pulse and probe pulses are used to excite the sample and measure the ultrafast response of the sample, respectively. The pump and probe pulses typically should be non-coaxially focused on the sample to avoid damaging the detector by the intense pump pulse. Commonly, coaxially-focused-fs-TRS can be achieved by using a spectral [8] or polarization [5] filters. However, spatial beam separation to control temporal delay between the pump and probe pulses was still required even the filters are used.

Coaxial fs-TRS with temporal pulse separation of the pump and probe pulses has the potential to be an effective system for easily obtaining the ultrafast optical response of a sample. Conventional fs-TRS is difficult to apply to waveguides such as optical fibers because non-coaxial beams are difficult to focus on the input of waveguides with high-efficiency coupling and long-term stability. Moreover, the interaction length between the pump and probe pulses with coaxial fs-TRS can be longer than that of conventional pulses. Owing to the long interaction length, the signal-to-noise ratio (SNR) of ultrafast optical response can be increased. Also the spatial resolution can be improved [9]. Therefore, co-axial-type fs-TRS has the potential to be used for easily obtaining ultrafast optical response with high SNR and long-term stability.

In this letter, we propose a novel co-axial fs-TRS based on a pump–probe technique with a color-selective multi-pulse (CSMP) generated by a spatial-light-modulator-based optical pulse shaper (SLM-OPS). The SLM-OPS can control the temporal waveform and delay of an optical pulse by modulating the phase of each spectral component of the laser spectrum [10,11]. Previously, we reported that six temporal-delay-controlled CSMPs could be generated by an SLM-OPS [12]. In this case, we divided the entire laser spectrum into two segments to form pump and probe pulses as a color-selective double pulse (CSDP). Thus, we can generate co-axial propagating pump and probe pulses as CSDP without spatial beam separation. In addition, we easily removed exclusively the pump pulse using a spectral filter because the pump and probe pulses were composed of different spectral components. As a result, the coaxial CSDP-based fs-TRS that controls the time delay between pump and probe pulses can be achieved by combing the SLM-OPS and spectral filter without spatial beam separation of the pump and probe pulses. In this case, temporal waveform of probe pulse was evaluated by a conventional cross-correlator with a reference pulse which can be removed by time-stretched method [8] (see discussion). As a proof of concept, we applied the proposed method to evaluate the photo-induced transient absorption of a nonlinear crystal.

2. Concept

Figure 1 shows the schematic of the proposed coaxial time-resolved spectroscopy with color-selective double pulses. Unlike the previous report [12], a CSDP was composed of the compressed pump and chirped probe pulses because the time window of the ultrafast pump-probe measurement was limited by the pulse duration of the probe pulse [8]. The chirped probe pulse enabled obtaining the ultrafast optical response of the sample in a single scan. The SLM-OPS enables the application of chirp and temporal delay to the probe pulse without requiring additional mechanical components in the proposed method. To generate a CSDP, we divided the entire spectrum into two segments and applied different group delay dispersions (GDD) and time delays to each spectral segment using the SLM-OPS. The phase function of the probe pulse is, ϕ(ω) = ϕ₁(ω-ω₀) + ϕ₂(ω-ω₀), where ϕ₁ is a constant for temporal shift of the probe pulse,  ϕ₂ is a GDD parameter, ω is an angular frequency, ω₀ is an angular frequency of a center wavelength of a laser. In particular, the temporal width of the probe pulse should be sufficiently long to measure the optical response of the sample. In our experiment, the chirped probe and compressed pump pulses were composed of long- and short-wavelength segments, respectively. Next, the acquisition of ultrafast optical response from a sample with a generated CSDP is explained. First, the temporal waveform of the modulated probe pulse, I_{probe w/ pump} (t), which is measured after passing through the sample and a bandpass filter, is obtained. Subsequently, the temporal waveform of the probe pulse is obtained by turning off the pump pulse, I_{probe w/o pump} (t), via intensity modulation using the SLM-OPS [10,11]. Also, the temporal waveform of the residual pump pulse is I_pump (t) obtained by keeping the pump pulse on without reducing the intensity while keeping the probe pulse off. Consequently, the ultrafast optical response of the sample, ΔI(t), can be deduced from the following equation:

 

Fig. 1. Schematic of the proposed coaxial time-resolved spectroscopy with color-selective double pulses. OPS: optical pulse shaper; BPF: bandpass filter.

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3. Experimental setup

The experimental setup is illustrated in Fig. 2. The setup was composed of two subsystems: one for generating a CSDP and the other for detecting it. The fs laser system (Vitara-T, Coherent Inc.) generated 50 fs pulses at the repetition rate of 80 MHz, and the center wavelength was 800 nm. The average power of the fs laser was 400 mW. Using a beam splitter, the output from the laser was split into two components to serve as measurement and reference pulses. The measurement pulse was tailored using an SLM-OPS to generate the CSDP. The SLM-OPS exhibited a conventional 4f pulse-shaping arrangement in a reflection geometry consisting of a two-dimensional SLM (for details, see [12,13]). Owing to its ability to modulate the pulse two-dimensionally, the spectral phase and intensity of the measurement pulses could be independently manipulated [10,11]. Intensity extinction ratio of the SLM-OPS was 33. The SLM-OPS featured a wavelength range of 770–840 nm and a wavelength resolution of 0.25 nm, indicating maximum pulse duration was 3.4 ps. The spectral ranges for the pump and probe pulses were set to 770–820 nm and 820–840 nm, respectively. The CSDP was focused onto a 1-mm-thick ZnTe crystal (110) through a lens (f = 50 mm) to effectively pump the sample for a high energy density. After passing through the sample, the CSDP was collimated with another lens (f = 50 mm), and its pump segment was blocked with a bandpass filter (FB-830, center wavelength = 830 nm, full width at half maximum (FWHM) = 10 nm, Thorlabs). The temporal waveform of the probe part of the CSDP was evaluated using a conventional cross-correlator with a delay stage (OSMS20-85(X), SigmaKoki) and reference pulses (see details, [12]). A power transmittance of the SLM-OPS was 71%. The average power of the pump and probe pulse was 300 and 5 mW, respectively. The temperature of the experimental environment was approximately 296 K.

 

Fig. 2. Experimental setup. SLM-OPS: spatial-modulator-based optical pulse shaper; BPF: bandpass filter; OAP: off-axis parabolic mirror; PMT: photomultiplier; LIA: lock-in amplifier.

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4. Results and discussions

The generation of the CSDP was confirmed in which each pulse was composed of a different preferred spectral component and chirped. Figure 3(a) shows the typical intensity and phase modulation applied with the SLM-OPS. In the pump pulse, GDD of -4,500 fs² centered at 800 nm was applied in the spectral range of 770–820 nm for the dispersion compensation of the lens in front of the samples. In contrast, a GDD of +20,000 fs² centered at 830 nm was applied in the 820–840 nm spectral range to form a temporally stretched probe pulse. A typical temporal waveform of each pulse is shown in Fig. 3(b). The temporal waveform of each pulse was obtained by limiting the intensity of the selected bandwidth using the SLM-OPS. For example, when we limited the intensity in the 820–840 nm spectral range to the lowest possible value, we obtained a pump pulse with a pulse duration of 0.3 ps located at the temporal position of 4.2 ps. It should be noted that the pulse duration of the pump pulse was limited by the cross-correlator rather than Fourier-transform-limitation (<100 fs). A unintended modulation was observed in the tail of the pump pulse because the wavelength component near the boundary of the phase design could not be completely controlled. In contrast, the probe pulse was stretched to 2.0 ps, when we reduced the intensity in the 770–820 nm range. Thus, we confirmed that the CSDP featured the preferred temporal waveform.

 

Fig. 3. (a) Intensity spectrum of the laser and phase spectrum applied using an SLM-OPS. GDD of the probe pulse based on SLM-OPS was +20,000 fs². (b) Typical temporal waveforms of pump and probe pulses using the cross-correlator. Inset: a temporal waveform of probe pulse in detail.

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As a proof of concept, we measured the ultrafast optical response of a ZnTe crystal using the proposed method. Figure 4 (a) shows the typical temporal waveforms of CSDP after passing through ZnTe when the applied GDD of the probe pulse was +17,500 fs². Owing to the intensity modulation of the SLM-OPS, the temporal waveform of the probe pulse was easily obtained with pump pulse illumination, probe pulse without pump pulse, and residual pump pulses, which was dominated by the 820 nm spectral component that has been slightly transmitted through the bandpass filter. Comparing the temporal waveforms, we found that the temporal waveform of the probe pulse was asymmetrically modulated in the presence of pump pulse illumination. The intensity of the probe pulse was modulated by the ZnTe crystal owing to two-photon excitation by pump pulse illumination. The ΔI(t) of ZnTe was easily obtained via Eq. (1) using only the SLM-OPS. ΔI(t) was normalized by the intensity of the temporal waveform of probe pulses, as shown in Fig. 4(b). Owing to the collinear propagation of the pump and probe pulses, we obtained a good SNR through the measurement. The noise level of the waveform was ΔI/I∼0.01. Using the time-stretching method [14], a noise level of a temporal waveform of transient transmission change (ΔT/T) of ZnTe crystal was 0.04. The noise level of the proposed method is 1/4 compared to the previous results [14]. Moreover, minimum ΔI and ΔT was -0.2. Thus, the SNR of the proposed method is four times larger than the previous results. Despite the oscillatory signal [14] shown in Fig. 4(b), the signal clearly shows transient absorption with sub-ps temporal width that is similar to a previously reported finding obtained based on a time-stretching method with a Ti: sapphire regenerative amplifier system [8]. The small oscillatory signal may be due to an unintentional echo pulses generated in some optical components [14]. We confirmed that the proposed method can be used to evaluate transient absorption based on the two-photon excitation of the ZnTe crystal.

 

Fig. 4. (a) Typical temporal waveforms of the probe with pump (red), without pump (blue), and residual pump (green) using the cross-correlator. The GDD of the probe pulse was 17,500 fs². (b) Normalized ΔI of the ZnTe crystal (ΔI/I_probe) calculated from three temporal waveforms in (a).

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Next, we evaluated the temporal waveform of ΔI(t) for each pulse duration of the chirped probe pulse, that is, each time window of the fs-TRS, applying different GDD using the SLM-OPS. In other words, we evaluated the temporal resolution of the measurement because it depended on the probe pulse duration [8]. Figure 5(a) shows pump-probe measurements of ZnTe obtained by changing the probe pulse duration. The temporal width Δt (measured three times) of ΔI(t) estimated as FWHM from fitting of a Gaussian function. The SNR of the longer chirped probe pulse was decreased because intensity of the probe pulse was lower due to a smallest spatial feature on the phase mask of the SLM-OPS. A typical temporal waveform of transient absorption for each time window is shown in Fig. 5(b). Δt decreases with decreasing probe pulse duration; in particular, Δt reached 0.2 ps when the pulse duration of probe pulses was as short as 0.2 ps. It should be noted that Δt has relatively broader variations when the pulse duration of the probe pulse is below 0.3 ps, which is limited by the cross-correlator. To evaluate the validity of the result, we also measured Δt with the conventional fs-TRS (black line in Fig. 5 (b)) and confirmed that the obtained value of 0.18 ± 0.01 ps, which was measured 10 times, was comparable with that measured via the proposed method. In this case, time resolution, τ_res, was explained using the following equation [8], τ_res= (τ₀τ₁)^1/2, where τ₀ and τ₁ were pulse duration of the pump and probe pulses, respectively. We confirmed that minimum Δt was also comparable to time resolution (orange dashed line in Fig. 5(b)). In particular, the small oscillatory signal was appeared when Δt was larger than time resolution. Thus, the effectiveness of the proposed co-axial fs-TRS in obtaining a transient absorption profile was confirmed, and the results were comparable to those obtained via the conventional method.

 

Fig. 5. Pump–probe measurements of ZnTe obtained by changing the probe pulse duration. The dashed line was obtained from the conventional method. (a) Temporal waveform of ΔI(t) of each probe pulse duration. (b) Δt vs pulse duration of the probe pulse.

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Coaxial fs-TRS without beam separation can be constructed by applying the time-stretched method. Indeed, we used a reference pulse divided by an fs laser for the cross-correlator. The proposed method has the potential to be combined with a time-stretched method with a long-optical fiber [8]. Using this method, a probe pulse broadened over nanoseconds by the fiber can be directly measured by an oscilloscope without the cross-correlator. Although high propagation loss of the optical fiber, we can obtain the temporal waveform of transient absorption without the reference pulse by using the time-stretched method. Otherwise, a low-loss dispersive medium, such as a chirped-fiber bragg grating [14], can be used to measure the temporal waveform without loss of the probe pulse. The proposed method has the potential to realize coaxial fs-TRS without any beam separation.

5. Conclusions

We propose a novel coaxial time-resolved spectroscopy based on the pump-probe technique using a CSDP with an SLM-OPS. In the proposed method, a compressed pump and chirped probe pulses were generated as a CSDP. Ultrafast optical response of a ZnTe crystal can be obtained from the temporal waveform of the output probe with a pump, probe without a pump, and residual pump pulse. After calculating the temporal waveforms, we evaluated the two-photon-induced transient absorption of the ZnTe crystal via the proposed method. By decreasing the time window by compressing the pulse duration of the probe pulse, we confirmed that the pulse duration of ΔI(t) reached 0.2 ps. The minimum Δt of the transient absorption was in good agreement with the result obtained via the conventional method. The proposed method has the potential to realize co-axial fs-TRS without the cross-correlator by using the time-stretched method [8,14]. The proposed coaxial fs-TRS can be utilized for easily obtaining a ultrafast response of a sample such as a waveguide and a nonlinear optical fiber.