Jerome V. Moloney

There has been considerable recent interest in the phenomenology of high harmonic generation (HHG) in topological insulators. We study HHG in the Qi-Wu-Zhang (QWZ) model for a Chern insulator, which satisfies spatial inversion symmetry but breaks time-reversal symmetry. The QWZ model is particularly interesting because it combines rich physics with unique simplicity. Our theoretical approach is based on the semiconductor Bloch equations, and we present two distinct numerical methods for simulating HHG which are immune to topological obstruction of the Bloch phase. We obtain highly converged HHG spectra in both trivial and topological phases of the QWZ model, and we use these results to investigate spectral characteristics which have been proposed as signatures of band topology. We derive a simple relationship between harmonic ellipticity and material Berry curvature for two-band systems, and we show that this can be used for accurate prediction of the helicity of emitted harmonics. While this clarifies the relationship between ellipticity and Berry curvature, it also uncovers limitations that restrict the scope of ellipticity as an indicator of topological phase. More generally, our findings contribute to the important discussion surrounding topological signatures in HHG spectra. Beyond that, we also observe a dual plateau structure of the HH spectrum in the topological phase which is absent in the trivial phase, but the origin of this phenomenon is not topological. Rather, the multiple plateaus are clearly attributed to the interference of HHG originating from different regions of the full two-dimensional Brillouin zone (BZ). As a consequence, our study reinforces the importance of including the entire BZ for accurate modeling of HHG in solids.

The semiconductor Bloch equations (SBEs) are a well-established model for optical interactions in condensed matter. In particular, the SBEs in the electromagnetic length gauge preserve the band picture of periodic crystals and thus provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. For materials with broken inversion or time-reversal symmetry, the length gauge SBEs involve complex transition dipole moments (TDMs), which depend on the choice of Bloch gauge. The numerical and conceptual complications resulting from this gauge freedom have impeded interpretation and key applications of HHG, such as the tomographic reconstruction of crystal band structure. We derive gauge invariant SBEs (GI-SBEs) that contain only gauge invariant structural quantities: the absolute value of TDMs, the shift vector, and for more than two bands a triple product of TDM phases. The GI-SBEs provide insight into the physics of HHG in solids with broken inversion symmetry, which we demonstrate in gapped graphene.

Mode-locked vertical external cavity semiconductor lasers are a unique class of nonlinear dynamical systems driven far from equilibrium. We present a novel, to the best of our knowledge, experimental result, supported by rigorous microscopic simulations, of two coexisting mode-locked V-cavity configurations sourced by a common gain medium and operating as independent channels at angle controlled separated wavelengths. Microscopic simulations support pulses coincident on the common gain chip extracting photons from a nearby pair of coexisting kinetic holes burned in the carrier distributions.

In the long-wave infrared (LWIR) range, where, due to wavelength scaling, the critical power of Kerr self-focusing P_cr in air increases to 300-400 GW, we demonstrate that without external focusing a train of picosecond CO₂ laser pulses can propagate in the form of a single several-centimeter diameter channel over hundreds of meters. The train of 10 µm pulses, for which the total energy ≥20 J is distributed over several near-terawatt picosecond pulses with a maximum power ≤2P_cr, is generated naturally during short pulse amplification in a CO₂ laser. It is observed that the high-power 10 µm beam forms a large diameter “hot gas” channel in the ambient air with a ≥ 50 ms lifetime. Simulations of the experiment show that such filamentation-free self-channeling regime has low propagation losses and can deliver multi-Joule/TW-power LWIR pulses over km-scale distances.

We derive gauge invariant semiconductor Bloch equations (GI-SBEs) that contain only gauge invariant band structure; shift vectors, and triple phase products. The validity and utility of the GI-SBEs is demonstrated in intense laser driven solids with broken inversion symmetry and nontrivial topology. The GI-SBEs present a useful platform for modeling and interpreting light-matter interactions in solids, in which the gauge freedom of the Bloch basis functions obscures physics and creates numerical obstacles.

For electro-optical modeling in solids, the transition dipole phase and the related Berry connection carry important symmetry information about the system. This is especially important in the extremely nonlinear optics regime. One example is the even order harmonic intensity in high harmonic generation from solids. Semiconductor Bloch equations are widely used as theoretical model of this phenomenon. Recently, what has been denoted as the “random-phase problem” or “random gauge” in density-functional theory has gained increasing attention, since it complicates phase sensitive modeling within this framework. Here, we propose and evaluate a phase-sensitive approximation based on a triple dipole product as a solution to this problem. We further evaluate the approximation in a semiconductor Bloch equations model for high harmonic generation in GaAs and compare it to the twisted parallel transport gauge.

Higher-order optical harmonics entered the realm of nanostructured solids being observed recently in optical gratings and metasurfaces with a subwavelength thickness. Structuring materials at the subwavelength scale allows us toresonantly enhance the efficiency of nonlinear processes and reduce the size of high-harmonic sources. We report the observation of up to a seventh harmonic generated from a single subwavelength resonator made of AlGaAs material. This process is enabled by careful engineering of the resonator geometry for supporting an optical mode associated with a quasi-bound state in the continuum in the mid-infrared spectral range at around λ = 3.7 μm pump wavelength. The resonator volume measures ~0.1 λ ³ . The resonant modes are excited with an azimuthally polarized tightly focused beam. We evaluate the contributions of perturbative and nonperturbative nonlinearities to the harmonic generation process. Our work proves the possibility to miniaturize solid-state sources of high harmonics to the subwavelength volumes.

We demonstrate a 1.5 GHz broadband laser system based on a passively mode-locked Vertical-External-Cavity Surface-Emitting-Laser (VECSEL) for high speed nonlinear imaging. The 300 nm wide supercontinuum generated via photonic crystal fiber (PCF) coupled with pulse shaping by means of multiphoton intrapulse interference phase scan (MIIPS) allows us to procedurally filter out spectral windows of interest for nonlinear imaging applications as well as compress the resulting pulses to their transform-limited duration. The intrinsically high repetition rate our system is operating at matches the typical fluorescence lifetime of many biological samples, making it an ideal source for rapid nonlinear bio-imaging while mitigating the risks of photobleaching and photodamage.

We use microscopic many-body models based on first principle density functional theory to investigate the high harmonic generation (HHG) in monolayer transition metal dichalcogenides (ML-TMDCs) at the example of MoS₂. A two-dimensional bandstructure model is utilized that allows for the realistic inclusion of Coulomb correlations. It is shown that for off-resonant mid-IR excitation Coulomb correlations lead to a dramatic enhancement of HHG intensity by up to two orders of magnitude. For resonant excitation near the fundamental excitonic resonance the Coulomb interaction leads to dressed harmonics. These have a sub-floor of broad spectral contributions. The amplitude of these contributions is about four to six orders of magnitude below the peak. The width scales linearly with the exciting field and can reach hundreds of meV.