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Photon momentum driven light-matter interactions

The fundamental conservation laws dictate total energy and momentum of the system of particles should be conserved through the interaction process. For optical excitation, the photon of energy E=ħw is absorbed by an electron, providing its transition to higher energy state, so the total energy of the system is conserved. The photon also carries momentum p=ħw/c, however, in free space, it is ~10^2-10^3 times smaller than that of an electron. Thus, optically allowed transitions are depicted as vertical arrows in energy band diagram - free space photon cannot change an electron momentum. Among most recognizable examples, figure on the left shows energy-momentum space for pure silicon, with its lowest energetically allowed direct transition from G point at ~3.5 eV (350 nm). Below this energy, the transitions are considered momentum-forbidden in Si - it requires an assistance of lattice phonons to change electron momentum and move it horizontally across the reciprocal space of the first Brillouin zone. However, opposite to free space, the momentum of the confined photon shouldn’t be any longer neglected in light-matter interaction. The spatial confinement dr leads to an increase of momentum value by ~ħp/dr, and it becomes comparable to that of an electron when photon is trapped at dr ~0.3-5 nm scales. This means, highly localized optical field can directly change both energy and momentum of an electron, changing the concept of light matter interaction. It makes diagonal transitions on the energy diagram possible.
This effect notably transforms the nature of subsequent light-matter interactions. We demonstrate a dramatic consequence of increase photon momentum for the case of light absorption in Si, turning inefficient indirect electronic transitions into efficient direct transitions across the entire Brillouin zone. This previously unexplored form of light-matter interaction results in a significant enhancement of the semiconductor’s optical properties with a potentially large impact on the fields of optoelectronics, photovoltaics and solar energy conversion.

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Nonlinear optics and multiphoton processes in semiconductors

Identifying strong and fast nonlinearities (both absorption and refraction) for today's photonic applications is an ongoing effort. Materials and devices are typically sought to achieve increasing nonlinear interactions to enhance or enable new photonic effects for generation, detection and manipulation of light. One example of an optical nonlinearity is simultaneous two-photon absorption that occurs in semiconductors, generating a single electron–hole pair in the process. We explore this effect to enable novel chemical sensing and visualization methods and modalities. Inorganic and organic semiconducting systems were historically considered to be excellent candidates for photonic switching because of their relatively large third-order nonlinearities. They have been the subject of extensive studies, both experimental and theoretical in many material-wavelength combinations. However, little attention has been paid to theoretical and experimental predictions for the case where the input wavelengths are vastly different. At the same time, although two-photon processes in a semiconductor are typically weak effects, the rate of absorption increases dramatically when the two photons have very dissimilar wavelengths. A quantum-mechanical model using Keldysh theory successfully predicts the observed scaling relationship between the bandgap, photon energy, and degenerate two-photon absorption (DTA) rate indicating the coefficient increases from zero at the half-bandgap (ħω = Egap/2) to a maximum value at 2/3 of the bandgap. This theory can further be generalized to include the case of non-degenerate two-photon absorption (NTA). Many had assumed that the nonlinear absorption rate depends primarily on the photon energy sum ħω1+ ħω2, and not on the individual scaling factors ħω1,2/Egap. Surprisingly, the nonlinear absorption function exhibits a remarkable singularity when either ħω1,2/Egap becomes small. What many had considered to be the optimal condition for DTA is actually a saddle-point: along the degeneracy line (ħω1/Egap= ħω2/Egap), the absorption is minimum, whereas in the orthogonal direction, it reaches a maximum.
Until recently this intriguing effect has not been widely appreciated yet it holds promise for a host of high impact future applications. Indeed, NTA in wide bandgap semiconductors has been shown to permit the detection of MIR radiation with the help of an additional visible or NIR photon. In NTA, the signal scales linearly with the MIR intensity with detection sensitivities that rival those of cooled MCT detectors and overcomes many previous detection and imaging technical challenges. While operating over a very broad optical bandwidth, the concept does not depend on phase matching, exhibits miniscule polarization dependence, avoids the need for external nonlinear conversion media and does not rely on interferometric gating, hence phase stability, thus offering a simple and robust detection strategy. This discovery enabled several new imaging capabilities - rapid 2D imaging high-definition MIR videography of living organisms in situ as well as three-dimensional yet chemical-selective MIR mapping and, most important, spectral imaging, i.e. high speed acquisition of [xyw] data cube.

 

 
       
 

Excitons at quantum limit

This thrust dives into the mechanisms and origins of long-lived optical excitations in semiconducting systems and it explores effects and processes, related to bound states of electron-hole pairs, i.e. excitons. Excitons holds extraordinary properties and potential:
1. The electron-hole pair is well-recognized as a convenient analog to the hydrogen atom, in which the strong field effects occurs already at moderate field strengths achievable in a laboratory. In contrast, for hydrogen atoms such high fields can only be met near, for instance, white-dwarf stars. We have observed, modelled and explained the behavior of Rydberg excitons, based on the ratio of the exciton binding energy and the external perturbation.
2. Optically created excitons are also a perfect example of composite bosons made of an even number of fermions, as He-4 atoms, Cooper pairs, or alkali-metal atoms. It should behave under some conditions like ideal bosons and can condense into a macroscopic quantum state known as the Bose-Einstein condensate (BEC). Since the electron and hole are strongly bound, their pair bosonic character persists up to high densities and temperatures and, due to the low mass of the particle, their condensate form is expected at higher temperatures, compared to those for atoms. However, ensembles of electrons and holes are complex quantum systems with strong Coulomb correlations, thus, it is non-trivial whether nature chooses a form of exciton BEC. Various systems have been examined in bulk and two-dimensional semiconductors and also in exciton–photon hybrid systems. In our study we focus on paraexcitons, pure spin triplet state, so it is decoupled from the radiation field which makes the coherent ensemble a purely matter-like wave. The large binding energy and long lifetime enable the preparation of cold optically created exciton gas in thermal equilibrium with the lattice. However, collisional loss severely limits the conditions for reaching BEC (similar problem to atomic BEC to realize superfluid He-4). Despite the importance of scattering properties, little information on the scattering cross-section and its mechanisms for paraexcitons are known.

 

 
       
 

Chemical sensitive spectrosopies at low limits

Mediation of energy transfer between light and matter by surface plasmon or field enhancement helped overcome many fundamental hurdles in optical spectroscopy and microscopy, most notably, overcome diffraction limits manyfold and probe matter on single molecule level. When motion of chemical bonds within molecules can be observed in real time in the form of vibrational wave packets prepared and interrogated through ultrafast nonlinear spectroscopy, such nonlinear optical measurements are commonly performed on large ensembles of molecules and are limited to the extent that ensemble coherence can be maintained. Surface plasmon mediated signals allow sensitivities required to detect the motion of a single molecule under ambient conditions. In contrast with measurements in ensembles, the vibrational coherence on a single molecule does not undergo pure dephasing. It develops phase fluctuations with characteristic statistics - time evolution of discretely sampled statistical states. From more application perspective, such sensitivity enhancement enables very simple, fast, all-optical concept for live detection of low amounts of molecules that are common to our daily life, hence important from industrial and environmental perspectives (e.g. in situ ammonia monitoring).
Optically excitations and the response of the material can also be probed directly in the near-field by reading out the time-integrated force between the metal covered tip and the sample. Because the magnitude of the force is dependent on the photoinduced polarization in the sample, such concept exhibits spectroscopic sensitivity. The photoinduced forces are spatially confined on the nanometer scale, which translates into a very high spatial resolution even under ambient conditions and is compatible with a wide range optical excitation frequencies, from the visible to the mid-infrared, enabling nanoscale imaging contrast based on either electronic or vibrational transitions in the sample.

 
       
 

Ultrafast spectroscopy and imaging modalities in THz

THz spectral region is of special interest for condensed matter - it is comprised of many molecular signatures, including low-energy thermal rotations, bending and torsions. When used in pulsed regime and in combination with ultrafast optical exciation, this phase-sensitive concept can directly probe the evolution of real and imaginary parts of dielectric function, hence complex optical conductivity. Moreover, many pulse arrnagement enables multi-dimensional correlation type measurements to probe molecular couplings and its harmonicity, as rich 2D-Raman and 2D THz-THz-Raman.
From application standpoint, not prone to scattering THz pulses offer high penetration yet can probe density and structural properties of media. It makes them powerful imaging tool in both 2D and 3D tomographic fashions and can be utilized in miriad of fields - from biochemistry to stand-off detection of materials. Such visualization concepts and imaging modalities strongly rely on new THz radiation detection strategies that boost sensitivity, spatial resolution, yet allow high definition image quality.