DOI: 10.4231/w2w3-8h49
title: Dataset associated with Time-Reflection of Microwaves by a Fast Optically-Controlled Time-Boundary

description: &lt;p&gt;When an electromagnetic wave propagates in a medium whose properties are varied abruptly in time, the wave experiences refractions and reflections known as time-refractions and time-reflections, both manifesting spectral translation as a consequence of the abrupt change of the medium and the conservation of momentum. However, while the time-refracted wave continues to propagate with the same wave-vector, the time-reflected wave propagates backward with a conjugate phase despite the lack of any spatial interface. Modulating the refractive index of the medium strongly and periodically in time gives rise to multiple time-reflections and time-refractions, which interfere and yield dispersion bands separated by band-gaps in the momentum. This temporal structure is known as Photonic Time-Crystals. The most intriguing property of Photonic Time-Crystals is that states residing in the momentum gap can have exponentially increasing amplitudes, which draw energy from the modulation. Photonic Time-Crystals offer a plethora of new possibilities for innovative physics and applications, ranging from the generation of pairs of entangled photons and below-threshold Cherenkov radiation to new widely-tunable laser sources at THz frequencies. However, all of these rely on time-reflections: without significant time-reflections there would be no Photonic Time-Crystals. This understanding poses a major challenge: unlike time-refraction which is (almost) always significant, for the time-reflection to be substantial, the refractive index change has to be large (order of unity) and abrupt (occurring within 1-2 cycles of the time-reflected waves). Otherwise, if the index change is insufficiently strong or too slow, then the time-reflection becomes extremely weak, and realizing Photonic Time-Crystals becomes completely impossible.&lt;/p&gt;

&lt;p&gt;In this work, we present the observation of time-reflected microwave pulses at the highest frequency ever observed (0.59 GHz), and the experimental evidence of the phase-conjugation nature of time-reflected waves. Our experiments are carried out in a periodically-loaded microstrip line with optically-controlled picosecond-switchable photodiodes. Our system paves the way to the experimental realization of Photonic Time-Crystals at GHz frequencies.&lt;/p&gt;

&lt;p&gt;&lt;span aptos="" style="font-size:11.0pt;line-height:107%;font-family:"&gt;&lt;!--[endif]--&gt;&lt;/span&gt;&lt;!--[endif]--&gt; This dataset includes all simulation and measurement data presented in both the main manuscript (Figures 2 and 3) and the included supplementary information document (Supplementary Figures 3, 4, 7, 9, 10, and 12). The dataset also includes the python code used to extract the simulated and measured time-reflection and time-refraction coefficients presented in Table 1 in the main manuscript.&lt;/p&gt;

&lt;p&gt;The dataset for Figure 2 contains the measured and simulated response of the time-boundary experiments with a single Gaussian pulse, and the measured results of two sequential pulses fed into the microstrip line in which the amplitude of the first pulse is varied. These results experimentally demonstrate the reflection of electromagnetic pulses from a time interface, and allow the extraction of the measured time-reflection and time-refraction coefficients for comparison to theory and simulation, with good agreement.&lt;/p&gt;

&lt;p&gt;The dataset for Figure 3 contains the measured results of electromagnetic pulses scattered at time interfaces with a single carrier Gaussian input pulse, and an input chirped pulse with a Gaussian envelope and nonlinear phase. These results demonstrate both the frequency translation and phase-conjugation nature of time-reflected waves. They also demonstrate the time-reflection of an electromagnetic pulse with the highest-to-date frequency from an optically-controlled ultra-fast time interface.&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 3 contains the measured dc I-V characteristics of a single high-speed photodiode operating as a switch. These high-speed photodiodes were used in the experimental prototype (periodically-loaded microstrip line) in order to generate a strong time interface.&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 4 contains the measured picosecond rise time of a single high-speed photodiode. This data confirmed that the chosen high-speed photodiodes would enable an abrupt change in the microstrip&#39;s characteristic impedance in order to generate a strong time interface.&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 7 contains the measured and simulated frequency response of the periodically-loaded microstrip line which was used as the experimental prototype in order to generate a strong time interface. Included are the scattering parameters and the corresponding dispersion diagrams of both State 1 (photodiode switch OFF) and State 2 (photodiode switch ON).&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 9 contains the measured and simulated response to an input pulse with the microstrip in State 1. This data was used to extract the spatial-boundary scattering coefficients and characteristic impedance of State 1.&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 10 contains the measured and simulated response to an input pulse with the microstrip in State 2. This data was used to extract the spatial-boundary scattering coefficients and characteristic impedance of State 2.&lt;/p&gt;

&lt;p&gt;The dataset for Supplementary Figure 12 contains the measured and simulated response to an input pulse with the microstrip changing from State 1 to State 2 generating a time boundary. This data was used to extract the time-boundary scattering coefficients presented in Table 1.&lt;/p&gt;

&lt;p&gt;More detailed information can be found in the Readme.txt file included with the dataset.&lt;/p&gt;
description: This dataset includes all data and code associated with manuscript titled "Time-Reflection of Microwaves by a Fast Optically-Controlled Time-Boundary" by Jones et al., which has been accepted for publication in Nature Communications on July 4, 2024.