arXiv subjects

T. Sh. Misirpashaev

Publications and source records attributed to T. Sh. Misirpashaev.

5 recordsLinked to original sources

arXiv1997

Lasing Threshold and Mode Competition in Chaotic Cavities

The lasing threshold is studied of a multi-mode chaotic cavity (linear size D >> wavelength λ) coupled to the outside through a small hole (linear size d << λ). For sufficiently weak absorption by the boundaries, the statistical distribution of the threshold is wide, its mean value being much less than the pumping rate needed to compensate the average loss. The average number N_{nc} >> 1 of non-competing excited modes is proportional to the square root of the pumping rate. We use the classical model of spatial hole burning to account for mode competition and find a reduction in the average number of excited modes to N =3^{1/3} N_{nc}^{2/3}.

chao-dyn↗

arXiv1997

Spontaneous Emission in Chaotic Cavities

The spontaneous emission rate Γof a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing N wavechannels, the distribution of Γis given by P(Γ) \propto Γ^{N/2-1}(Γ+Γ_0)^{-N-1}, where Γ_0 is the free-space rate. For small N the most probable value of Γis much smaller than the mean value Γ_0.

chao-dyn↗

arXiv1996

Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant $ε= ε'+iε''$. Depending on the sign of $ε''$, the medium is absorbing or amplifying. The transmitted intensity decays exponentially $\propto\exp(-L/ξ)$ as the waveguide length $L\to\infty$, regardless of the sign of $ε''$. The localization length $ξ$ is computed as a function of the mean free path $l$, the absorption or amplification length $|σ|^{-1}$, and the number of modes in the waveguide $N$. The method used is an extension of the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar to non-unitary scattering matrices. Asymptotically exact results are obtained for $N\gg1$ and $|σ|\gg1/N^2l$. An approximate interpolation formula for all $σ$ agrees reasonably well with numerical simulations.

cond-mat↗

arXiv1996

Reflectance Fluctuations in an Absorbing Random Waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $γ$ per mean free path. Two distinct regimes are identified. The regime $γN^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $γN^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-γN$.

cond-mat↗

arXiv1996

Localization of Light: Dual Symmetry between Absorption and Amplification

We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $ε$, and show that dual systems, which differ only in the sign of the imaginary part of $ε$, have the same localization length. Paradoxically, absorption and stimulated emission of radiation suppress the transmittance of the waveguide in the same way.

cond-mat↗