The ultrafast reflectivity switching presented in Fig. 2 is due to the novel ultrafast material modification controlled by intense synthesized light field in real-time. The first step for proving and understanding the underlying physics of the frequency dependent reflectivity switching in real time is to extract the modulated material reflectivity due to the strong light field interaction. This can be obtained by dividing the reflected probe pulse spectrum (black curve in Fig. 2d) by the intrinsic reflectivity of fused silica, then, deconvolute the result from the measured spectrogram in Fig. 2a. The obtained spectrogram, plotted in Fig. 3a, represents the transient reflectivity change of the fused silica material induced by the strong field of the driver pulse in frequency and time domains. This transient material modification (Fig. 2a and b) happens in a frequency range far from its higher harmonics spectral range, indicating that the observed reflectivity modulation (in Fig. 2a and b) is not a result of the spectral interference between the high harmonic generation frequencies33.
From Fig. 3a, we extracted the average amplitude of the reflectivity oscillation at different frequencies and plotted it in the blue line in Fig. 3b. The offset values of the reflectivity modulation as a function of frequency are plotted in the red curve. Each value at a particular frequency corresponds to the offset from zero point of the temporal oscillation, whereas the amplitude values determine how strong the reflectivity oscillations will be as a function of pump-probe time delay for that specific frequency. In addition, the reflectivity of fused silica in the equilibrium state (no influence of the pump pulse) is plotted in the black line. Comparing the frequency oscillation (Fig. 3b) to the spectrum of pump pulse in Fig. 2d (black line), we can observe that the reflectivity peaks do not overlap with the spectrum intensity peaks of the pump pulse, proving that the observed reflectivity modulations seen in our experiment are not due to the interference between the probe and pump pulses. Furthermore, the observed reflectivity oscillations (Fig. 2a,b and Fig. 3a) at any particular frequency are distinct and have steady amplitudes within a time delay range much longer than the pulse’s coherence time34, indicating that again this modulation is not induced due to the conventional interference between the pump and probe pulses.
Moreover, it is clear in Fig. 2a and b and Fig. 3a that for each frequency the reflectivity is oscillating in a periodic oscillation in time associated with that frequency. Also, the oscillation amplitude is controlled by the proximity to an individual resonance frequency in the excited dielectric permittivity induced by the intense pump field. Thus, such ultrafast reflectivity switching can be explained by the interference of the bound-electron resonances, which causes a transient modification of the fused silica dielectric constant (\(\epsilon )\), refractive index, and its reflectivity in the strong field.
The reflectivity modulation of the dielectric system in a strong field can be expressed as
$${R}_{m}\left(\omega \right)=\frac{{\left[1-n\left(\omega \right)\right]}^{2}+{\kappa }^{2}\left(\omega \right)}{{\left[1+n\left(\omega \right)\right]}^{2}+{\kappa }^{2}\left(\omega \right)}$$
1
where \(\tilde{n}=\pm \sqrt{{\tilde{\epsilon }}_{r}}=n\left(\omega \right)+i\kappa \left(\omega \right)\) is the refractive index, \({\tilde{\epsilon }}_{r}\) is the relative permittivity. For a particular frequency \({\omega }_{0}\), the electric fields of pump and probe pulses in the time domain can be expressed as
$${E}_{pump}={A}_{0}{e}^{i{\omega }_{0}t}$$
2
$${E}_{pro}={A}_{1}{e}^{i{\omega }_{0}(t+N{\Delta }t)}$$
3
where \({A}_{0}\) and \({A}_{1}\) are the electric field amplitudes of the pump and probe pulses, respectively. In our experiment \(A={A}_{0}/{A}_{1}\tilde10\). \({\Delta }t\) is the time delay step (100 as), \(N{\Delta }t\) denotes the Nth delay step.
After Fourier transformation, we can write Eqs. 2 and 3 in the spectral domain as
$${\tilde{E}}_{pump}={A}_{0}\delta (\omega -{\omega }_{0})$$
4
$${\tilde{E}}_{pro}={A}_{1}\delta \left(\omega -{\omega }_{0}\right){e}^{i\omega N{\Delta }t}$$
5
and,
$$\frac{{\tilde{ E}}_{pump}}{{\tilde{ E}}_{pro}}=A{e}^{-i\omega N{\Delta }t}$$
6
.
Assuming that the material polarizability, modified by the strong field interaction, affects the propagation of the probe pulse, so the electric field of the probe pulse can be expressed as
$$\nabla {\tilde{E}}_{pro}=-{\omega }^{2}{\mu }_{0}\left({{\epsilon }_{0}\tilde{E}}_{pro}+{\tilde{P}}_{pump}+{\tilde{P}}_{pro}\right)=-{\omega }^{2}{\mu }_{0}{\epsilon }_{0}{\tilde{E}}_{pro}\left(1+{\chi }_{1}{\prime }+{\chi }_{2}{\prime }\right)$$
$$=-{\omega }^{2}{\mu }_{0}{\epsilon }_{0}{\tilde{\epsilon }}_{\text{r}}{\tilde{E}}_{pro}$$
7
where
$${\tilde{\epsilon }}_{\text{r}}=1+{\chi }_{1}{\prime }+{\chi }_{2}{\prime }$$
8
$${\chi }_{1}^{{\prime }}=A{e}^{-i\omega N{\Delta }t}{\omega }_{p}^{2}{\sum }_{k=\text{1,2},\dots }\frac{{f}_{k}}{{{{\omega }_{0,k}}^{2}-\omega }^{2}-i\omega {\varGamma }_{k}}$$
9
$${\chi }_{2}^{{\prime }}={\omega }_{p}^{2}{\sum }_{j=\text{1,2},\dots }\frac{{f}_{j}}{{{{\omega }_{0,j}}^{2}-\omega }^{2}-i\omega {\varGamma }_{j}}+C$$
10
where \({\mu }_{0}\) and \({\epsilon }_{0}\) are the permeability and permittivity in vacuum. \({\tilde{P}}_{pump}\) is the pump-induced material polarization coupled to \({\tilde{P}}_{pro}\), whereas the latter is the material polarization caused by the probe pulse (note, the intensity of the probe pulse is too weak to induce polarizability change in the system). Eqs. 9 and 10 show that the susceptibility \({\chi }_{1}{\prime }\) (or \({\chi }_{2}{\prime }\)) corresponding to \({\tilde{P}}_{pump}\) (or \({\tilde{P}}_{prop}\)) can be expressed as a combination of multiple Lorentz resonators upon the pump excitation, where \({\omega }_{0,j}\), \({\varGamma }_{j}\), and \({f}_{j}\)(or \({\omega }_{0,k}\), \({\varGamma }_{k}\), and \({f}_{k}\)) are the natural frequency, damping rate, and strength of the jth (kth) resonator. C is a constant that represents the effect of resonances far from the spectrum range of interest. \({\omega }_{p}^{2}=\frac{{e}^{2}{n}_{e}}{m{\epsilon }_{0}}\) is the square of the plasma frequency, m is the free electron mass. Here, we assume one active electron per molecule in the fused silica, \({n}_{e}=2.2\times {10}^{28}\) m−3.
Accordingly, we utilized Eqs. 9 and 10 to simulate the experimentally measured reflectivity modulation spectrogram of fused silica (shown in Fig. 2a) using our pump pulse field (which is shown in Supplementary Information Fig. S1). The simulation results of the measured spectrograms (Fig. 2a and b) can capture all the measured reflectivity modulation features, as shown in Fig. 3c and d, respectively, by considering the spectral phase of the pump pulse, as explained in the Supplementary Information. The obtained calculated spectrograms, shown in Fig. 3c and d, are in good agreement (Standard deviation = 1.37% and 2.1%) with the measured spectrogram in Fig. 2a, b. The fitting parameters for \({\chi }_{2}{\prime }\) and \({\chi }_{1}{\prime }\), are listed in Table 1 and Table 2 (Supplementary Information).
Based on the experiment and theoretical results, the observed ultrafast reflectivity switching of fused silica can be attributed to the multiphoton resonances in the dielectric permittivity of the fused silica excited by our unique high-intensity and broadband near-single-cycle pump pulse. The novelty in our pump pulse is that it has strong field strength to induce the multiphoton excitation without damaging the fused silica system since it contains only 1.5 field cycles. Moreover, our pump pulse spans over 1.5 octaves, allowing for multiphoton excitation of fused silica with different photon combinations from the UV, Visible, and NIR spectral regions. Also, the short pulse duration of the pump pulse (2.7 fs) implies that all the photons in the pump pulse are almost in phase, which is a key for inducing the reflectivity switching in the sub-femtosecond time scale. Note, the weak intensity optical pulse (at the same level as our probe pulse intensity) will not induce the multiphoton excitation, thus no temporally oscillation or reflectivity modulation would be observed.
Additionally, the presented reflectivity modulation spectrograms in Fig. 2a and b carries the signature of the broadband pump pulse spectral phase dispersion. Therefore, the presented experiment can be utilized as an accurate methodology for characterizing the ultrashort laser pulses and its spectral phase dispersion directly and with a high resolution (see Fig. S2b) which is beyond the capability of the typical ultrashort pulse characterization techniques (i.e., frequency-resolved optical gating). Moreover, this transient modification can be engineered by controlling the laser pulse waveform (spectral phase) to achieve a tunable refractive index of natural material (i.e., fused silica) by high intensity ultrashort lasers, which is only possible in metamaterials35,36, opening the door for a vast range of applications in ultrafast photonics.
Ultrafast optical information encoding.
As demonstrated experimentally in Fig. 2, the light-induced phase transition of the fused silica allows us to switch between an ON and OFF state of the reflected light signal following the driver field. Consequently, the reflectivity modulation and the switching alterability can be controlled by tailoring the driver field waveform. Accordingly, we demonstrate next the control of the switching signals using on-demand complex synthesized waveforms generated by ALFS 4,32,37. Figure 4a (I), b (I), and c (I), show some of the measured reflectivity modulation spectrograms—after subtracting background spectrum — triggered by three different synthesized light fields. The integrated intensities of the reflected spectra at different instances of time (above zero amplitude) are plotted in Fig. 4a (II), b (II), and c (II). Note, the light signal can also be measured by photodiode detector instead of the spectrometer to directly detect the integrated intensity signal. The light signal switches from ON to OFF states uniformly every half-cycle of the driver field. By setting a certain intensity amplitude threshold (60%) in Fig. 4a (II), b (II), and c (II)—which easily can be experimentally implemented or programmed in the photodetector —the number of the detected light signals (above this threshold) and the switching alternative-time varies depending on the shape of the driver waveform. Figure 4a (III), b (III), and c (III) show the signals above the 60% threshold, and the insets in the top (contains 22 slots) represent the signal status (OFF or ON) in black and white in real-time at each half cycle of the driver field. Using the first waveform, the signal switches ON and OFF three times with a time separation of 4.5 fs and 3.6 fs. This switching time interval is controlled to be 3.6 and 1.8 fs (as shown in Fig. 4b(II)) using the second waveform. Moreover, the number of the switching signal increases to four by using the third waveform with 1.8, 1.8, and 3.6 fs time period separations between the signals as shown in Fig. 4c (III).
Remarkably, this capability of controlling the light signal switching (ON/OFF) allows the ultrafast data encoding with synthesized light waveforms32, which are beyond the reach of conventional ultrafast pulses field. Accordingly, the reflected signal above the threshold will be detected “ON status” and presents the binary code “1”. The reflected signal below the threshold— will not be detected by the photodetector and hence will have an “OFF status”— representing the binary code “0”. The number of coding bits that the light field can carry equals twice of the number of the driver light field cycles. Some of the examples of binary encoding using the synthesized waveforms are shown in the insets of Fig. 4a (III), b (III), and c (III). Remarkably, the presented experiments are conducted in ambient conditions at room temperature which promises viable engineering of the demonstrated light field encoding to stabilize the long-anticipated ultrafast photonics.
In a potential ultrafast light field encoding process (illustrated in Fig. S3), the data will be encoded on the synthesized light waveforms generated by the ALFS32 (or any pulse shaping device), which will act as an "encoder" device. Then, the synthesized waveform (which is considered to be the encoded laser beam) will carry the data from the transmitter to the receiver station. Next, the encoded laser beam will be focused on the dielectric together with another beam (decoder laser beam). Finally, the reflected decoder laser beam from the dielectric will be detected by a photodetector. After setting a certain predefined threshold, the photodetector will read the coded data in the 1 & 0 binary form. The light field encoding can be obtained using multicycle pulses, which are provided by the commercial laser systems available in the market, in combination with pulse shaping and light field synthesis technology3,4,32,37−39. Notably, this demonstrated optical switching occurs in ambient conditions allowing a simple realistic architecture of a potentially realistic compact optical switch integrated on a photonic chip. Moreover, the data encoding on ultrafast light waveforms, in contrast to the encoding provided by modern electronic sources using a microwave, would significantly enhance the data processing and transformation speed for light-time distances.
In conclusion, the light-field induced phase transition of dielectric system in strong field enables switching the reflected light signal ON and OFF with attosecond switching speed. The light field tailoring and shaping with high resolution allow us to demonstrate the attosecond optical switching control and data binary encoding by synthesized laser pulses. This work paves the way to develop an ultrafast optical-based switches, and to transfer data with petahertz speed and beyond, which can carry information to the deep space opening a new era in communication and information technology.