Phase-resolved techniques are integral to modern optics. As an important example, time-domain THz spectroscopy is used to analyze phenomena ranging from exciton formation [1], the dynamics of an electron-hole plasma [2] to magnetic excitations [3]. While those techniques have been advanced to bandwidths beyond 100 THz [4,5], progress toward the visible is, e.g., hampered by the lack of sufficiently short probe pulses. For phase-retrieval at optical frequencies, therefore, alternative concepts are necessary, many of which rely on spectral interferometry [6–8]. In its common heterodyne embodiment, a signal pulse is superimposed with a local oscillator, which allows to trace the phase-difference with respect to such a reference. This concept is particularly useful to analyze the weak coherent response typical of, e.g., four-wave mixing experiments.

In this Letter, we demonstrate an alternative scheme of spectral interferometry. It proves versatile to detect transient amplitude and phase changes in ultrafast pump-probe type configurations. After transmission through the sample, a probe pulse of center frequency $2\omega$ is superimposed with an $\omega$ pulse from the same laser source, and thereby generates an electrical signal reflecting $\omega /2\omega$ quantum interference control of currents [9] in a semiconductor detector. A Fourier transform of the resulting two-color field cross-correlation reveals the electric field of the $2\omega$ pulse as well as any pump-induced modifications of the $2\omega$ field. We test these ideas for two examples of transient semiconductor optical phenomena. In particular, the excitonic resonance of bulk CdTe serves as a testbed for the transient response of a narrowband optical resonance. In addition, we study the mutual interaction of copropagating $2\omega$ probe and optical pump pulses in ZnSe and extract field modifications related to two-photon absorption and cross-phase modulation.

The optical source is a 250 kHz regenerative amplifier (Coherent RegA 9040) delivering 40 fs, 7 μJ pulses at 1.55 eV (800 nm). While a portion of 2 μJ is reserved as an optical pump, the remainder is fed into an OPA to generate 60 fs, 0.8 eV (1550 nm) signal pulses referred to as fundamental pulse $\omega$. This near-infrared light is frequency doubled in a BiBO crystal. As sketched in Fig. 1(a), the $\omega$ and $2\omega$ pulses are passed through a two-color Michelson interferometer, which ensures full control over the relative timing of the co-polarized harmonically related components. Despite a compact design with 6 cm arms, it is possible to insert a microscope cryostat into the $2\omega$ arm. Also the pump pulse is loosely focused onto the sample with an adjustable relative timing [cf. Fig. 1(a)]. As a result, we conceptionally perform 1.55 eV pump-$2\omega$ probe experiments as a function of the time $t_D$ elapsed since excitation. Performing such an experiment with the established approach, involving spectral resolution within the $2\omega$ probe, would therefore extract a transmission change $\mathrm{\Delta }{T}_{2\omega }(\nu ,t_D)$. For the present interferometric technique, instead, the transmitted $2\omega$ pulse is superimposed with a time-delayed $\omega$ pulse and focused onto a 50 μm wide bar of electrically contacted low temperature grown GaAs. Its room temperature bandgap $E_G=1.42\mathrm{eV}$ satisfies $\hslash \omega <E_G<2\hslash \omega$. Phase-stable superpositions of such $\omega$ and $2\omega$ pulses induce a coherently controlled lateral electrical current according to [10]

 

Fig. 1. (a) Experimental setup: the RegA output is split up for use as a pump and as a seed of an OPA generating the $\omega$ pulse. A BiBO generates $2\omega$ while a two-color interferometer controls the $\omega /2\omega$ time delay $\tau$. Another delay line adjusts the pump-$2\omega$ delay $t_D$. (b) Photocurrent signal of a contacted LT-GaAs bar upon interferometric variation of $\tau$ while $2\omega$ is transmitted through a CdTe thin film ($T=7\mathrm{K}$). Inset: closeup at $\tau \approx 200\mathrm{fs}$. (c) Spectral domain results derived from a comparison of the data in (b) to a measurement without a sample. The CdTe has a field transmission $\mathrm{\Delta }E/E(\nu )$ (black) and induces a phase retardation $\mathrm{\Delta }\mathrm{\Phi }(\nu )$ (blue).

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To demonstrate the capabilities of the method, we analyze two classes of semiconductor optical nonlinearities. We start with the excitonic resonance of bulk CdTe and its pump induced transient changes. CdTe is chosen as its excitonic interband transitions conveniently lie within the $2\omega$ spectrum. A 370 nm thin CdTe specimen glued to a fused silica substrate is cooled to $T=7\mathrm{K}$ in a cryostat positioned in the $2\omega$ interferometer arm. Figure 1(b) shows the current interferogram for the CdTe sample without optical excitation. Remarkably, we still detect interferometric oscillations of the photocurrent beyond $\tau =100\mathrm{fs}$ where no temporal overlap between $\omega$ and $2\omega$ is expected. This finding reflects the free induction decay of the excitonic polarization induced by the $2\omega$ pulse. By comparison with a reference interferogram $I_S(\tau )$ when the $2\omega$ beam is transmitted through the substrate only, we derive the CdTe induced changes to the $2\omega$ field [cf. Fig. 1(c)]. The relative field amplitude change $\mathrm{\Delta }E/E=E_{2\omega ,0}(\nu )/E_{2\omega ,S}(\nu )-1$ (black curve) shows a prominent dip around $\omega =384\mathrm{THz}$ ($\hslash \omega =1.587\mathrm{eV}$) reflecting the ground state exciton transition. Around the same frequency, the phase change $\mathrm{\Delta }\mathrm{\Phi }={\mathrm{\Phi }}_{2\omega ,0}(\nu )-{\mathrm{\Phi }}_{2\omega ,S}(\nu )$ (blue) shows a dispersive lineshape as expected from such a resonance.

We now turn to results for transient spectroscopy of the exciton. The sample is excited with 0.5 μJ, 1.55 eV pump pulses to generate carrier densities of $2\times {10}^{18}{\mathrm{cm}}^{-3}$ mainly by absorption of the high-energy tail of this broadband pulse. The resulting pump induced changes are shown in Fig. 2 for various positive and negative $t_D$. The signal $\mathrm{\Delta }I(\tau )$ [cf. Fig. 2(a) and 2(d)] decays on a timescale of $\approx 130\mathrm{fs}$ related to the exciton dephasing time. This fast decoherence is probably connected to the elevated carrier density excited by $2\omega$ and the pump as well as considerable strain of the CdTe thin film mounted on fused silica. The Fourier transform results show a pump induced bleaching of the exciton transition in the field transmission [Fig. 2(b)] and in the phase data [Fig. 2(c)]. The decay of the bleaching strength for increasing positive $t_D$ is mainly related to carrier recombination. In contrast, pronounced spectral oscillations are observed at slightly negative delay times $t_D$ where $2\omega$ precedes the pump [cf. Fig. 2(e) and 2(f)]. Here the probe induced free induction decay is perturbed by the pump as previously studied, e.g., in bulk GaAs [12]. Intuitively, a pump induced dephasing of the excitonic polarization starting at a certain delay $|t_D|$ induces spectral oscillations with a period of $\mathrm{\Delta }\nu =1/|t_D|$. Spectral oscillations of the same frequency are also well resolved in the phase response [cf. Fig. 2(f)]. While the latter result is not unexpected, it previously remained unresolved.

 

Fig. 2. Transient spectroscopy of CdTe ($T=7\mathrm{K}$). (a) pump induced photocurrent change $\mathrm{\Delta }I(\tau )$. (b), (c) Fourier transform results for the pump induced change of the field transmission $\mathrm{\Delta }E/E(\nu )$ and phase retardation $\mathrm{\Delta }\mathrm{\Phi }(\nu )$ for various positive pump-$2\omega$ delay times $t_D$. Panels (d) to (f) display the corresponding results for several negative $t_D$.

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Finally, we present results for 1.55 eV pump, $2\omega$ probe experiments in 2 mm thick ZnSe at room temperature. While its bandgap $E_G=2.7\mathrm{eV}$ satisfies $2\hslash \omega <E_G$, transient signals during time-overlap can be expected due to two-photon absorption involving one pump and one probe photon. In addition, group velocity dispersion and cross-phase modulation affect the interaction. The pump induced amplitude and phase change of a weak $2\omega$ field in ZnSe at various pump delay times and a pump intensity of $I_P\approx 10\mathrm{GW}/{\mathrm{cm}}^{-2}$ are shown in Fig. 3. For pulses overlapping at the sample surface ($t_D=0$) we observe a pronounced pump induced absorption especially for the low energy components within the $2\omega$ spectrum centered at 387 THz. This negative going signal is much less pronounced on the high frequency wing beyond 395 THz because the group velocity mismatch to the pump at 375 THz effectively reduces the interaction length. Instead we detect a positive $\mathrm{\Delta }E/E$ for slightly positive $t_D$. It reveals a slight blue-shift of the $2\omega$ spectrum related to cross-phase modulation induced by the pump (note that for $t_D>0$ the probe overlaps with the trailing edge of the pump so that $d{I}_P/dt<0$). In line with the amplitude data in Fig. 3(a), also the pump induced phase changes in panel (b) are most pronounced for the low frequency components around $t_D\approx 0$. Simulations based on the nonlinear propagation equation for Gaussian pulses reproduce many aspects of the experiment with reasonable values of the nonlinear refractive index ($\gamma =1.7\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$) and a two-photon absorption coefficient of $\beta =3.5\mathrm{cm}/\mathrm{GW}$. From the simulations we learn that the amplitude changes are mainly related to two-photon absorption while the phase change is predominantly governed by cross-phase modulation. The group velocity mismatch and dispersion effects in ZnSe lead to the larger influence of the pump on the low energy part of the $2\omega$ probe spectrum for all delay times.

 

Fig. 3. Transient spectroscopy of 2 mm bulk ZnSe at room temperature. Pump induced amplitude (a) and phase changes (b) for different delay times $t_D$ observed for a 1.55 eV pump irradiance of $I_P\approx 10\mathrm{GW}/{\mathrm{cm}}^{-2}$. The grey shaded area in (a) shows the $2\omega$ spectrum in arbitrary units.

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In conclusion, we combine amplitude- and phase-resolution at optical frequencies with femtosecond time-resolution to sensitively trace transient semiconductor optical nonlinearities. The use of other modelocked laser sources and/or detector crystals can easily extend the concept to other optical frequencies. Future studies will focus on optical nonlinearities that mainly manifest as transient phase-retardations—phenomena inaccessible with conventional time-resolved spectroscopy.