Adi Pick, Alexander Cerjan, and Steven G. Johnson, "Ab initio theory of quantum fluctuations and relaxation oscillations in multimode lasers," J. Opt. Soc. Am. B 36, C22-C40 (2019)
We present an ab initio semi-analytical solution for
the noise spectrum of complex-cavity microstructured lasers, including
central Lorentzian peaks at the multimode lasing frequencies and
additional sidepeaks due to relaxation-oscillation (RO) dynamics. In
Phys. Rev.
A 91, 063806
(2015) [CrossRef] , we computed the
central-peak linewidths by solving generalized laser rate equations,
which we derived from the Maxwell–Bloch equations by invoking
the fluctuation–dissipation theorem to relate the noise
correlations to the steady-state lasing properties. Here, we
generalize this approach and obtain the entire laser spectrum,
focusing on the RO sidepeaks. Our formulation treats inhomogeneity,
cavity openness, nonlinearity, and multimode effects accurately. We
find a number of new effects, including new multimode RO sidepeaks and
three generalized factors. Last, we apply our formulas to
compute the noise spectrum of single-mode and multimode
photonic-crystal lasers.
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Coefficients of the Single-Mode and Multimode Generalized Rate
Equations [Eqs. (6) and (16)], Expressed in Terms of the Laser Parameters [Cavity
Permittivity, ; Gain Frequency and Bandwidth,
and ; and Pump Intensity and Spatial
Profile, and ] as Well as the Laser Steady-State
Properties [SALT Frequencies ; Mode Amplitudes,
; and Mode Profiles,
]a
Coefficients of the Single-Mode Noise Spectrum
[Eq. (7)], Expressed in Terms of Quantities Obtained from
SALT: the Steady-State Modal Amplitudes,
, and the Oscillator-Equation
Coefficients, , , and , Defined in Table 1
Coefficients of the Single-Mode and Multimode Generalized Rate
Equations [Eqs. (6) and (16)], Expressed in Terms of the Laser Parameters [Cavity
Permittivity, ; Gain Frequency and Bandwidth,
and ; and Pump Intensity and Spatial
Profile, and ] as Well as the Laser Steady-State
Properties [SALT Frequencies ; Mode Amplitudes,
; and Mode Profiles,
]a
Coefficients of the Single-Mode Noise Spectrum
[Eq. (7)], Expressed in Terms of Quantities Obtained from
SALT: the Steady-State Modal Amplitudes,
, and the Oscillator-Equation
Coefficients, , , and , Defined in Table 1