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Register a new userPower coupling losses for misaligned and mode-mismatched higher-order Hermite-Gauss modes
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This paper analytically and numerically investigates misalignment and mode-mismatch induced power coupling coefficients and losses as a function of Hermite Gauss (HG) mode order. We show that higher-order HG modes are more susceptible to beam perturbations when, for example, coupling into optical cavities: the misalignment and mode-mismatch-induced power coupling losses scale linearly and quadratically with respect to the mode indices respectively. As a result, the mode-mismatch tolerance for the $mathrm{HG}_{3,3}$ mode is reduced to a factor of 0.28 relative to the currently-used $mathrm{HG}_{0,0}$ mode. This is a potential hurdle to using higher-order modes to reduce thermal noise in future gravitational-wave detectors.
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This note describes the analytical derivation of the response of bullseye detectors to optical beats between higher-order spatial modes of the Laguerre-Gauss form, and subsequently the Hermite-Gauss form. Also included is a comparison with numerically calculated beat coefficients, and a simple example of the use of the resulting beat coefficients in simulating a mode mismatch sensor for a Fabry-Perot cavity.
The gravitational waveform of a merging stellar-mass binary is described at leading order by a quadrupolar mode. However, the complete waveform includes higher-order modes, which encode valuable information not accessible from the leading-order mode alone. Despite this, the majority of astrophysical inferences so far obtained with observations of gravitational waves employ only the leading order mode because calculations with higher-order modes are often computationally challenging. We show how to efficiently incorporate higher-order modes into astrophysical inference calculations with a two step procedure. First, we carry out Bayesian parameter estimation using a computationally cheap leading-order-mode waveform, which provides an initial estimate of binary parameters. Second, we weight the initial estimate using higher-order mode waveforms in order to fold in the extra information from the full waveform. We use mock data to demonstrate the effectiveness of this method. We apply the method to each binary black hole event in the first gravitational-wave transient catalog GWTC-1 to obtain posterior distributions and Bayesian evidence with higher-order modes. Performing Bayesian model selection on the events in GWTC-1, we find only a weak preference for waveforms with higher order modes. We discuss how this method can be generalized to a variety of other applications.
We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100W, the same regime that will be used by 2nd generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical type LG33 mode with a purity of order 97% at a power of 83W, the highest power ever reported in literature for a higher-order LG mode.
Mode-locking is predicted in a nanolaser cavity forming an effective photonic harmonic potential. The cavity is substantially more compact than a Fabry-Perot resonator with comparable pulsing period, which is here controlled by the potential. In the limit of instantaneous gain and absorption saturation, mode-locking corresponds to a stable dissipative soliton, which it very well approximated by the coherent state of a quantum mechanical harmonic oscillator. This property is robust against non-instantaneous material response and non-zero phase-intensity coupling.
The different dynamical behaviors of the Hermite-Gaussian (HG) modes of mode-locked nanolasers based on a harmonic photonic cavity are investigated in detail using a model based on a modified Gross-Pitaevskii Equation. Such nanolasers are shown to exhibit mode-locking with a repetition rate independent of the cavity length, which is a strong asset for compactness.The differences with respect to conventional lasers are shown to originate from the peculiar gain competition between HG modes, which is investigated in details. In the presence of a saturable absorber, the different regimes, i. e. Q-switching, Q-switched mode-locking, and continuous-wave (cw) mode locking, are isolated in a phase diagram and separately described. Mode-locking is found to be robust against phase-intensity coupling and to be achievable in a scheme with spatially separated gain and absorber.
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