High-order Sideband Generation Research Articles

Tunable UV ∼ IR frequency comb generation via high-order sideband generation

We propose the generation of a widely tunable UV-to-IR frequency comb by high-order sideband generation (HSB) spectrum emitted from semiconductors. In our theoretical simulations, we demonstrate the high-order sideband signals of two series (2m Ωseed + (2n + 1) ωdriver, and (2m + 1) Ωseed + 2 nωdriver ), where m and n are integers of a seed pulse and a driver laser frequency, respectively. The simulations also reveal the intensity of HSB scale with the driver laser power, both perturbatively and non-perturbatively. We find that the harmonic position and spacing of the high-order sideband emission can be controlled by varying the seed pulse and driver photon energies. In the experiment, we applied a visible ( ℏΩseed = 3.1 eV, ∼400 nm) seed pulse and mid-infrared (MIR, ℏωdriver = 0.4 eV, 3.1 μm) driver pulses to ZnSe target. Our experimental observations confirmed the UV (4.7 eV, 263 nm and 3.9 eV, 317 nm) HSB generation.

Dephasing of Strong-Field-Driven Excitonic Autler-Townes Doublets Revealed by Time- and Spectrum-Resolved Quantum-Path Interferometry.

Understanding dephasing mechanisms of strong-field-driven excitons in condensed matter is essential for their applications in quantum-state manipulation and ultrafast optical modulations. However, experimental access to exciton dephasing under strong-field conditions is challenging. In this study, using time- and spectrum-resolved quantum-path interferometry, we investigate the dephasing mechanisms of terahertz-driven excitonic Autler-Townes doublets in MoS_{2}. Our results reveal a dramatic increase in the dephasing rate beyond a threshold field strength, indicating exciton dissociation as the primary dephasing mechanism. Furthermore, we demonstrate nonperturbative high-order sideband generation in a regime where the driving fields are insufficient to dissociate excitons.

Investigation of spectro-temporal high-order sideband generation from transition metal dichalcogenides [Invited

High-order sideband generation (HSG) in semiconductors under intense terahertz fields has been extensively studied, because it provides essential information for studying ultrafast dynamics in strong-field-dressed quantum materials. In particular, transition metal dichalcogenides (TMDCs), characterized by their unique band structures, provide an exemplary semiconductor system to explore the influence of material band structure on strong-field-induced modulation of HSG. In this work, we investigate the spectro-temporally resolved HSG from different bulk TMDC materials. Our results reveal distinct temporal HSG spectra, which can be attributed to the different absorption behaviors of these materials. Simulations based on the strong-field approximation and Floquet theory can well reproduce the experimental observations. Our work also delves into the spectro-temporal interference that emerges when neighboring harmonic orders overlap in the HSG spectrum. This work enhances our understanding of high-order sideband dynamics in strong-field-dressed semiconductors, offering insights for applications in spectrum- and phase-resolved ultrafast measurements.

Multiple plateaus of high-sideband generation from Floquet matters

We theoretically report that high-order sideband generation (HSG) from Floquet matters driven by a strong terahertz light while engineered by weak infrared light can achieve multiple plateau HSG. The Floquet-engineering systems exhibit distinctive spectroscopic characteristics that go beyond the HSG processes in field-free band-structure systems. The spatial-temporal dynamics analyses under Floquet-Bloch and time-reversal-symmetry theories clarify the spectra and its odd-even characteristics in the HSG spectrum. Our work demonstrates the HSG of Floquet matters via Floquet engineering and indicates a promising way to extract Floquet material parameters in future experiments.

Explicit formula for high-order sideband polarization by extreme tailoring of Feynman path integrals

High-order sideband generation (HSG), as an analogue of the interband processes in high-harmonic generation (HHG) in solids, is a nonperturbative nonlinear optical phenomenon in semiconductors that are simultaneously driven by a relatively weak near-infrared (NIR) laser and a sufficiently strong terahertz (THz) field. We derive an explicit formula for sideband polarization vectors in a prototypical two-band model based on the saddle-point method. Our formula connects the sideband amplitudes with the laser-field parameters, electronic structures, and nonequilibrium dephasing rates in a highly nontrivial manner. Our results indicate the possibility of extracting information on band structures and dephasing rates from high-order sideband generation experiments with simple algebraic calculations. We also expect our approach to be useful on the quantitative understanding of the interband HHG.

Reconstruction of Bloch wavefunctions of holes in a semiconductor.

A central goal of condensed-matter physics is to understand how the diverse electronic and optical properties of crystalline materials emerge from the wavelike motion of electrons through periodically arranged atoms. However, more than 90 years after Bloch derived the functional forms of electronic waves in crystals1 (now known as Bloch wavefunctions), rapid scattering processes have so far prevented their direct experimental reconstruction. In high-order sideband generation2-9, electrons and holes generated in semiconductors by a near-infrared laser are accelerated to a high kinetic energy by a strong terahertz field, and recollide to emit near-infrared sidebands before they are scattered. Here we reconstruct the Bloch wavefunctions of two types of hole in gallium arsenide at wavelengths much longer than the spacing between atoms by experimentally measuring sideband polarizations and introducing an elegant theory that ties those polarizations to quantum interference between different recollision pathways. These Bloch wavefunctions are compactly visualized on the surface of a sphere. High-order sideband generation can, in principle, be observed from any direct-gap semiconductor or insulator. We thus expect that the method introduced here can be used to reconstruct low-energy Bloch wavefunctions in many of these materials, enabling important insights into the origin and engineering of the electronic and optical properties of condensed matter.

Tunable high-order sideband generation in a coupled double-cavity optomechanical system.

Tunable high-order sideband generation has important applications in the realization of the optical frequency comb with a varying spectral region (corresponding to the sideband range) and frequency resolution (corresponding to the sideband interval). In this paper, we propose a theoretical scheme to tune both the range and the interval of the high-order sidebands in a coupled double-cavity optomechanical system, which consists of an optomechanical cavity and an auxiliary cavity. Our proposal can be realized by driving the optomechanical cavity with a control field and a probe field simultaneously, driving the auxiliary cavity with a pump field. Furthermore, we assume that the frequency detuning between the control field and the probe field (the pump field) equals ωb/n (ωb/m), where ωb is the mechanical frequency, m and n are integers. When n = m = 1, we find that the sideband range can be effectively enlarged by increasing the pump amplitude or the photon-hopping coupling rate, or by decreasing the auxiliary cavity damping rate. When n = 1 and m > 1, the output spectrum consists of a series of integer-order sidebands, fraction-order sidebands, and the sum and difference sidebands, and the sideband interval becomes ωb/m and can be diminished by simultaneously increasing m and the pump amplitude.

Observation of nonlinear dynamics in an optical levitation system

Optical levitation of mechanical oscillators has been suggested as a promising way to decouple the environmental noise and increase the mechanical quality factor. Here, we investigate the dynamics of a free-standing mirror acting as the top reflector of a vertical optical cavity, designed as a testbed for a tripod cavity optical levitation setup. To reach the regime of levitation for a milligram-scale mirror, the optical intensity of the intracavity optical field approaches 3 MW cm−2. We identify three distinct optomechanical effects: excitation of acoustic vibrations, expansion due to photothermal absorption, and partial lift-off of the mirror due to radiation pressure force. These effects are intercoupled via the intracavity optical field and induce complex system dynamics inclusive of high-order sideband generation, optical bistability, parametric amplification, and the optical spring effect. We modify the response of the mirror with active feedback control to improve the overall stability of the system.

Fraction-order sideband generation in an optomechanical system.

We propose a scheme for generating a new kind of sideband, i.e., the fraction-order sideband, in an optomechanical system. In the conventional scheme of high-order sideband generation [Opt. Lett.38, 353 (2013)OPLEDP0146-959210.1364/OL.38.000353], the sideband interval has a minimum frequency limitation, which is equal to the mechanical frequency ωb, and this limits the precision of the sideband comb. With our proposed fraction-order sidebands, the sideband interval can break that limitation and reach ωb/n (n is an integer). The scheme we propose can be realized by driving the optomechanical system with three laser fields, including a control field (ωc) and two probe fields (ωp, ωf), in which the detuning between ωc and ωp is equal to the mechanical frequency ωb, while the detuning between ωc and ωf is equal to ωb/n. In this case, we find that not only the integer-order (high-order) sidebands, but also the fraction-order sidebands, and the sum and difference sidebands between the integer- and fraction-order sidebands, will appear in the output spectrum. Moreover, the sideband interval becomes ωb/n, and it can be decreased by increasing n. Our work paves the way to achieve a tunable optical frequency comb based on the optomechanical system.

Magnon-induced optical high-order sideband generation in hybrid atom-cavity optomagnonical system.

The nonlinearity of magnons plays an important role in the study of an optomagnonical system. Here in this paper, we focus on the high-order sideband and frequency comb generation characteristics in the atom coupled optomagnonical resonator. We find that the atom-cavity coupling strength is related to the nonlinear coefficients, and the efficiency of sidebands generation could be reinforced by tuning the polarization of magnons. Besides, we show that the generation of the sidebands could be suppressed under the large dissipation condition. This study provides a novel way to engineer the low-threshold high-order sidebands in hybrid optical microcavities.

Saturable nonlinearity-induced high-order sideband generation in a parity–time symmetric double-cavity system

A coupled active–passive double-cavity system with balanced effective gain and loss provides a powerful platform for sideband generation. In different input limits, we explore the gain-saturation nonlinearity of the active cavity with regard to sideband generation. Using a perturbation method, we give an explicit analytical expression for second-order sideband generation (SSG), showing a conversion efficiency of over 80% and pump powers as low as ∼μW. A remarkable mode-splitting is also observed during the SSG process in the unbroken parity–time () symmetry phase. With change in the system parameters, our numerical method shows that high-order sideband generation (HSG) in the unbroken phase is controllable, including increasing its amplitude and changing its order number, especially when switching HSG between perturbative and non-perturbative regimes. In the broken phase, field localization effect leads to a stronger output spectral intensity than that in the unbroken phase.

Subband picture of high-harmonic generation in solids

We propose a novel picture of high-harmonic generation (HHG) in solids based on the concept of temporally changing band structures. To demonstrate the utility of this picture, we focus on the high-order sideband generation (HSG) caused by strong terahertz (THz) and weak near-infrared (NIR) light in the context of pump-probe spectroscopy. We find that the NIR frequency dependence of the HSG indicates the existence of new energy levels (sub-bands) around the band-gap energy, which have multiple frequencies of THz light. This sub-band picture explains why the HSG intensity becomes a non-monotonic function of the THz light amplitude. The present analysis not only reveals the origin of the plateau structure in HHG spectra, but also provides a connection to other high-field phenomena.

Parity-time-symmetry–enhanced sideband generation in an optomechanical system

Optical high-order sideband generation, creating new frequencies with equal spectral separation, has developed potential applications in optical communication and metrology. Here, we investigate the generation of optomechanically induced high-order optical sideband spectra in an optical parity-time ($\mathcal{PT}$) -symmetric system. The system consists of an active optical mode, a passive optical mode, and a mechanical mode, where the mechanical mode is optomechanically coupled with the passive optical mode. Based on numerical analysis, the $\mathcal{PT}$-symmetric system enhances sideband spectra in both amplitude and number of sidebands. With certain parameters, forty sidebands head up on both sides of the control field near the exceptional point. The capability to generate optical high-order sidebands and control light propagation in micro- and nanomechanical systems may open up a promising perspective for complex integrated $\mathcal{PT}$ devices.

Difference frequency sideband generation in semiconductors

In this paper, a near-infrared (NIR) laser (with frequency ωNIR) exciting and an intense mid-infrared (MIR) bichromatic laser (with frequencies ω1 and ω2) driving scheme is proposed in semiconductors. It is predicted that if the frequency difference between the two components of the MIR laser, i.e. Ω = ω1-ω2, is in dozens of GHz frequency range, the emitting light contains spectra with frequencies ω = ωNIR + NΩ, where N is integer. In analogy with high-order THz sideband generation (HSG) in semiconductors, this phenomenon is named difference frequency sideband generation (DSG). Similar to the HSG case, the emitted sideband spectrum in DSG exhibits a nonperturbative plateau, where the intensity of the sideband remains approximately constant up to a cutoff frequency. The location of the cutoff frequency and its relationship with the frequency detuning of the NIR laser are discussed via the semi-classical saddle-point method.

Highly Sensitive Charge Sensor Based on Atom-Assisted High-Order Sideband Generation in a Hybrid Optomechanical System.

Realizing highly sensitive charge sensors is of fundamental importance in physics, and may find applications in metrology, electronic tunnel imaging, and engineering technology. With the development of nanophotonics, cavity optomechanics with Coulomb interaction provides a powerful platform to explore new options for the precision measurement of charges. In this work, a method of realizing a highly sensitive charge sensor based on atom-assisted high-order sideband generation in a hybrid optomechanical system is proposed. The advantage of this scheme is that the sideband cutoff order and the charge number satisfy a monotonically increasing relationship, which is more sensitive than the atom-free case discussed previously. Calculations show that the sensitivity of the charge sensor in our scheme is improved by about 25 times. In particular, our proposed charge sensor can operate in low power conditions and extremely weak charge measurement environments. Furthermore, phase-dependent effects between the sideband generation and Coulomb interaction are also discussed in detail. Beyond their fundamental scientific significance, our work is an important step toward measuring individual charge.

Optical frequency combs from high-order sideband generation.

We report on the generation of frequency combs from the recently-discovered phenomenon of high-order sideband generation (HSG). A near-band gap continuous-wave (cw) laser with frequency fNIR was transmitted through an epitaxial layer containing GaAs/AlGaAs quantum wells that were driven by quasi-cw in-plane electric fields FTHz between 4 and 50 kV/cm oscillating at frequencies fTHz between 240 and 640 GHz. Frequency combs with teeth at fsideband = fNIR + nfTHz (n even) were produced, with maximum reported n > 120, corresponding to a maximum comb span > 80 THz. Comb spectra with the identical product fTHz × FTHz were found to have similar spans and shapes in most cases, as expected from the picture of HSG as a scattering-limited electron-hole recollision phenomenon. The HSG combs were used to measure the frequency and linewidth of our THz source as a demonstration of potential applications.

High-order sideband generation in a two-cavity optomechanical system with modulated photon-hopping interaction

The high-order sideband generation in a two-cavity optomechanical system is discussed, where photon hopping between the two cavity modes is modulated sinusoidally. We show that the high-order sideband generation can be induced originating from two processes: the parametric frequency conversion between the photon–photon interactions and the nonlinear optomechanical interactions between the photon–phonon interactions. Both the modulation amplitude and frequency of photon hopping between the two cavities have flexible manipulation on the high-order sideband generation at the low pump power level. With the modulation amplitude varying, we are able to obtain a robust comb-type spectral structure and a weak spectral structure, which can be amplified by tuning the modulation frequency. Selective generation of particular sidebands may also been achieved via transforming the modulation frequency when the parametric conversion process is dominant. Moreover, the dependence of the high-order sideband generation on other important parameters is also discussed in detail, including the cavities linewidthes, the frequency detuning of the two input laser fields and the intensity of control field. These results may provide further insights into the understanding of the high-order sideband generation, and find applications in optical frequency converters and optical frequency combs.

Magnon-induced high-order sideband generation.

Magnon Kerr nonlinearity plays a crucial role in the study of an optomagnonical system and may bring many interesting physical phenomena and important applications. In this Letter, we report the investigation of high-order sideband generation induced by magnon Kerr nonlinearity in an optomagnonical system, which is still unexplored in this emerging research field. We uncover that the microwave driving field plays a significant role in manipulating the generation and amplification of the higher-order sidebands and, more importantly, the sideband spacing can be regulated by controlling the beat frequency between the pump laser and the probe laser, which is extremely eventful for the spacing modulation of the sideband frequency comb. Based on the recent experimental progress, our results will deepen our cognition into optomagnonical nonlinearity and may find fundamental applications in optical frequency metrology and optical communications.

Coherent detection of THz-induced sideband emission from excitons in the nonperturbative regime

Strong interaction of a terahertz (THz) wave with excitons induces nonperturbative optical effects such as Rabi splitting and high-order sideband generation. Here, we investigated coherent properties of THz-induced sideband emissions from GaAs/AlGaAs multiquantum wells. With increasing THz electric field, optical susceptibility of the THz-dressed exciton shows a redshift with spectral broadening and extraordinary phase shift. This implies that the field ionization of the $1s$ exciton modifies the THz-dressed exciton in the nonperturbative regime.

Tunable high-order-sideband generation and carrier-envelope-phase–dependent effects via microwave fields in hybrid electro-optomechanical systems

We investigate the high-order-sideband generation (HSG) in a hybrid cavity electro-photomechanical system in which an optical cavity is driven by two optical fields (a monochromatic pump field and a nanosecond Gaussian probe pulse with huge numbers of wave cycles), and at the same time a microwave cavity is driven by a monochromatic ac voltage bias. We show that even if the input powers of two driven optical fields are comparatively low the HSG spectra can be induced and enhanced, and the sideband plateau is extended remarkably with the power of the ac voltage bias increasing. It is also shown that the driven ac voltage bias has profound effects on the carrier-envelope-phase--dependent effects of the HSG in the hybrid cavity electro-photomechanical system. Our research may provide an effective way to control the HSG of optical fields by using microwave fields in cavity optomechanics systems.