We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear systems of optical phonons. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell’s equations and leads to phenomena such as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. [Proc. Natl. Acad. Sci. U. S. A. 115, 12148 (2018)], which demonstrated light amplification in a resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.
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Efficient computation of coherent multimode instabilities in lasers using a spectral approach
Coherent multimode instabilities are responsible for several phenomena of recent interest in semiconductor lasers, such as the generation of frequency combs and ultrashort pulses. These techonologies have proven disruptive in optical telecommunications and spectroscopy applications. While the standard Maxwell-Bloch equations (MBEs) encompass such complex lasing phenomena, their integration is computationally expensive and offers limited analytical insight. In this paper, we demonstrate an efficient spectral approach to the simulation of multimode instabilities via a quantitative analysis of the instability of single-frequency lasing in ring lasers, referred to as the Lorenz-Haken (LH) instability or the RNGH instability in distinct parameter regimes. Our approach, referred to as CFTD, uses generally non-Hermitian Constant Flux modes to obtain projected Time Domain equations. CFTD provides excellent agreement with finite-difference integration of the MBEs across a wide range of parameters in regimes of non-stationary inversion, including frequency comb formation and spatiotemporal chaos. We also develop a modal linear stability analysis using CFTD to efficiently predict multimode instabilities in lasers. The combination of numerical accuracy, speedup, and semi-analytic insight across a variety of dynamical regimes make the CFTD approach ideal to analyze multimode instabilities in lasers, especially in more complex geometries or coupled laser arrays.
more » « less- NSF-PAR ID:
- 10474843
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 25
- Issue:
- 11
- ISSN:
- 1367-2630
- Format(s):
- Medium: X Size: Article No. 113030
- Size(s):
- ["Article No. 113030"]
- Sponsoring Org:
- National Science Foundation
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SUMMARY Along age-progressive hotspot volcano chains, the emplacement rate of igneous material varies through time. Time-series analysis of changing emplacement rates at a range of hotspots finds that these rates vary regularly at periods of a few to several tens of millions of years, indicative of changing melt production within underlying mantle plumes. Many hotspots exhibit at least one period between ∼2 and 10 Myr, consistent with several proposed mechanisms for changing near-surface plume flux, and thus melting rate, such as small-scale convection, solitary waves and instability formation in tilted plume conduits. Here, we focus on quantifying instability growth within plumes tilted by overlying plate motion. Previous studies using fluids with constant or temperature-dependent viscosity suggest that such instabilities should not form under mantle conditions. To test this assertion, we use a modified version of the finite element code ASPECT to simulate 400 Myr of evolution of a whole-depth mantle plume rising through the transition zone and spreading beneath a moving plate. In a 2-D spherical shell geometry, ASPECT solves the conservation equations for a compressible mantle with a thermodynamically consistent treatment of phase changes in the mantle transition zone and subject to either a temperature- and depth-dependent linear rheology or a temperature-, depth- and strain-rate dependent non-linear rheology. Additionally, we examine plume evolution in a mantle subject to a range of Clapeyron slopes for the 410 km (1–4 MPa K–1) phase transitions. Results suggest that plume conduits tilted by >67° become unstable and develop instabilities that lead to initial pulses in the transition zone followed by repeated plume pulsing in the uppermost mantle. In these cases, pulse size and frequency depend strongly on the viscosity ratio between the plume and ambient upper mantle. Based upon our results and comparison with other studies, we find that the range of statistically significant periods of plume pulsing in our models (∼2–7 Myr), the predicted increase in melt flux due to each pulse (3.8–26 × 10−5 km3 km−1 yr−1), and the time estimated for a plume to tilt beyond 67° in the upper mantle (10–50 Myr) are consistent with observations at numerous hotspot tracks across the globe. We suggest that pulsing due to destabilization of tilted plume conduits may be one of several mechanisms responsible for modulating the melting rate of mantle plumes as they spread beneath the moving lithosphere.
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We demonstrate for the first time, to our knowledge, the occurrence of a
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Non-Hermitian optics is a burgeoning field at the intersection of quantum physics, electrodynamics, and nanophotonics. It provides a new perspective of the role of gain and loss in optical systems. Leveraging the advanced designs inspired by non-Hermitian physics, classical optical platforms have been widely investigated to unveil novel physical concepts, such as parity-time symmetry and exceptional points, which have no counterparts in the conventional Hermitian settings. These investigations have yielded a plethora of new phenomena in optical wave scattering, optical sensing, and nonlinear optical processes. Non-Hermitian effects also have a profound impact on the lasing behaviors in the semiclassical framework of lasers, allowing for novel ways to engineer single-mode lasers, chiral laser emission, laser noise, linewidth, etc. Furthermore, over recent years, there has been increasing interest in the explorations of non-Hermitian physics in quantum optics, which addresses photon statistics, entanglement, decoherence, and quantum sensing in non-Hermitian systems. In this review, we review the most recent theoretical and experimental advances in non-Hermitian optics and photonics, covering the significant progress in both classical and quantum optics regimes.
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Pulse train instabilities have often given rise to confusion and misinterpretation in ultrafast pulse characterization measurements. Most prominently known as the coherent artifact, a partially mode-locked laser with a non-periodic waveform may still produce an autocorrelation that has often been misinterpreted as indication of a coherent pulse train. Some modern pulse characterization methods easily miss the presence of a coherent artifact, too. Here, we address the particularly difficult situation of a pulse train with chirp-only instability. This instability is shown to be virtually invisible to autocorrelation measurements, but can be detected with frequency-resolved optical gating, spectral phase interferometry for direct electric-field reconstruction, and dispersion scan. Our findings clearly show that great care is necessary to rule out a chirp instability in lasers with an unclear mode-locking mechanism and in compression experiments in the single-cycle regime. Among all dynamical pulse train instabilities analyzed so far, this instability appears to be the best-hidden incoherence and is most difficult to detect.
