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Nanophotonics

Controlled compression, amplification and frequency up‐conversion of optical pulses by media with time‐dependent refractive index

Alexander Gabriel Löhr, Misha Ivanov, Margarita Khokhlova

Published Mar 8, 2023• 3 citations
Publisher

Abstract

Control over the time dependence of the refractive index of a material allows one to modify and manipulate the properties of light propagating through it. While metamaterials provide a promising avenue in this context, another route has been extensively explored by the ultrafast community - the so-called molecular modulators. Indeed, impulsively-aligned diatomic molecules provide a unique medium, where periodic rotational revivals induced by a pump pulse persist for tens of picoseconds, offering an excellent opportunity for the controlled modification of the refractive index and, therefore, of femtosecond laser pulses propagating through these media. Here we present an analytical theory which describes this process and stumble across a novel mechanism revealing exponential transformations of the probe pulse - its compression, amplification and frequency up-conversion. In particular, our analytical results predict the generation of amplified ultrashort (about 20 fs) ultraviolet pulses centered around 550 nm, starting with near infrared input pulses centered on 1 μm of about 30 fs duration, under very realistic experimental conditions.

DOI
10.1515/nanoph-2022-0818

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Control over the time dependence of the refractive index of a material allows one to modify and manipulate the properties of light propagating through it. While metamaterials provide a promising avenue in this context, another route has been extensively explored by the ultrafast community - the so-called molecular modulators. Indeed, impulsively-aligned diatomic molecules provide a unique medium, where periodic rotational revivals induced by a pump pulse persist for tens of picoseconds, offering an excellent opportunity for the controlled modification of the refractive index and, therefore, of femtosecond laser pulses propagating through these media. Here we present an analytical theory which describes this process and stumble across a novel mechanism revealing exponential transformations of the probe pulse - its compression, amplification and frequency up-conversion. In particular, our analytical results predict the generation of amplified ultrashort (about 20 fs) ultraviolet pulses centered around 550 nm, starting with near infrared input pulses centered on 1 μm of about 30 fs duration, under very realistic experimental conditions.
We present a simple and intuitive model based on the impulse response of linear electrical systems for describing the propagation of optical pulses through a dynamic Fabry–Perot resonator whose refractive index changes with time. Our model shows that the adiabatic wavelength conversion process in resonators results from a scaling of the round-trip time with index changes. For pulses longer than the cavity round-trip time, we find that more energy can be transferred to the new wavelength when the input pulses are slightly detuned from the cavity resonance and the refractive index does not change too rapidly. In fact, the optimum duration of index changes scales with the photon lifetime of the resonator. We describe the evolution of the shape and spectrum of picosecond pulses inside a resonator under a variety of input conditions and with the magnitude and duration of index variations. We also apply our general theory to the case of pulses whose widths are shorter than the round-trip time and derive an analytical expression for the output field under quite general conditions. This analysis reveals a shifting of the spectral comb as well as compression of the temporal pulse train that depends on the both the magnitude and sign of the index change. Our results should find applications in the area of optical signal processing using resonant photonic structures.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
Recent progress has been made in the theoretical and experimental study of the amplification of optical signals without population inversion (AWI) of the participating electronic levels. Induced coherence among appropriate levels in the active medium is the necessary condition for obtaining AWI. Similarly, the generation of wave packet states in atoms and molecules also relies on the coherent superposition of several states. It is feasible, therefore, that AWI is possible in a system which has been excited into a wave packet state. We have thus demonstrated experimentally such amplification in an extended sample of sodium dimers and we term this process wave packet amplification (WPA). An important characteristic of WPA is that the gain is doubly phase-sensitive—it is modulated at both the wave packet oscillation period and the optical period. The former time-dependence is a result of the periodic revivals of the pump-induced electronic polarization and the latter optical phase-sensitivity is a manifestation of the coherent nature of the molecular wave packet. The experiments to be described use a time-resolved upconversion method to detect the change in energy of a 50 fs probe pulse after it passes through a sodium heat pipe that has been pumped with another 50 fs pulse. The maximum saturated energy gain in this system is four and corresponds to all of the available energy being transferred from the wave packet to the probe pulse.
Investigations of controlled modifications of dispersive properties of atomic media and of propagation of short laser pulses have recently become a dynamically developing field of theoretical and experimental researches. In this lecture a brief overview is presented of basic physical phenomena underlying modifications of a group velocity of a pulse propagating in an optically modified medium. In particular, the possibilities of slowing down this velocity to zero and of retrieving the stopped pulse are discussed.
Abstract Ultrashort, coherent light pulses in the extreme ultraviolet (XUV) wavelength region are excellent tools for a wide range of experiments. These XUV pulses are in particular used to characterize electron dynamics. Additionally, the high photon energy enables quantum control of short-lived transitions in atoms. These transitions are of interest for ultrafast quantum control as the bandwidth of the control pulses needs to be less than the transition frequency. Coherent XUV pulses would be even more useful if the tools to control and manipulate them existed. Presently, however, no modulators exist for these frequencies, which significantly reduces the number of possible ultrafast optics experiments and applications in the XUV regime. This Ph.D. tutorial addresses this problem and focuses on the control of XUV light in time and space. To enable control of XUV light we have developed a method for opto-optical modulation (OOM), which modulates the phase of XUV light emitted from a gas of atoms. The atoms are resonantly excited with a coherent XUV pulse generated through high order harmonic generation and emit light after the excitation pulse passed. By shifting the resonance frequencies through the AC Stark shift with a non-resonant infrared control pulse, the phase of the emitted light, and therefore its wavefront, is controlled. With OOM the direction of XUV light emitted from noble gases has been controlled, and the temporal dynamics of the emission studied. By varying the delay between the excitation and the control pulse, the time of redirection was controlled, which enabled high signal to noise study of the temporal dynamics of the emission. Furthermore, a proof-of-principle experiment with two control pulses was performed, resulting in a shaped XUV pulse with controlled duration. The technique of OOM presented in this article is still at a very early stage and in order to obtain complete control of the amplitude and phase of the XUV pulses further development is necessary. Such development would present new opportunities for ultrafast XUV quantum control.