A system of a resonant scatterer described as a two-level atom coupled to a circular dielectric waveguide is studied. The system is characterized by the scattering properties of a guided mode (guided transmission and reflection, bulk radiation) and optomechanical properties (propelling force and torque on the scatterer). The results are based on a self-consistent solution of the scattering problem using the Green's functions and cover the cases of scatterers inside and outside waveguides. It is shown that while a scatterer with a fixed dipole orientation gives rise to scattering spectra described by Lorentzian line shapes, an isotropic scatterer can produce non-Lorentzian line shapes. The parameters defining the line shape are analyzed. The complicated line shapes are likely to arise in the coherent characterization of an emerging class of photonic devices based on photon emitters coupled to well-confined modes of dielectric waveguides. It is obtained that the propelling force and axial torque on the scatterer at resonance can be directly expressed in terms of the spontaneous emission coupling factor $(\ensuremath{\beta})$ of the system. The balances of the linear and angular momentum in the system are discussed. Numerical results are presented for strongly confined guided modes which allow efficient mode scattering and conversion of the linear and angular mode momentum to the force and torque, respectively.
Line shapes for both the absolute value and the real and imaginary components of the nonlinear, paramagnetic susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ of a ruby crystal have been measured as a function of the magnetic field and crystal orientation at room temperature and "resonant" conditions, where the
X-band driving frequency coincides with or is very close to the resonance frequencies of an equidistant or nearly equidistant paramagnetic three-level system. Though all measured line shapes were in good qualitative agreement with theoretical line-shape expressions, derived under the assumption of homogeneously broadened, Lorentzian-shaped, single-quantum resonances, a quantitative comparison between theory and experiment exhibited systematic discrepancies, such as too slowly decaying wings for the theoretical curves and too large theoretical amplitudes at "partly resonant" conditions for nearly equidistant three-level schemes. Line-shape measurements for single-quantum resonances of the linear susceptibility contradicted the Lorentzian line-shape assumption, but could satisfactorily be matched by a Gauss-type line shape. Although it was possible to fit the measured single-quantum resonance line shapes also by the convolution of a narrow, Lorentzian line shape with a proper combination of macroscopic inhomogeneous line-broadening effects such as Gaussian distributions of crystal
c-axis orientations and crystal strains, the equivalent procedure for the nonlinear susceptibility resonances did not remove the discrepancy between theory and experiment. Since the approach towards thermal equilibrium within tightly coupled spin systems in solids has, in general, to be described by nonexponential relaxation processes, the line-shape expressions for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ were phenomenologically generalized and formulated in terms of non-Lorentzian-shaped, homogeneous, single-quantum resonances. By using these generalized line-shape expressions, it was possible to achieve a satisfactory quantitative agreement with all experimental results for both the line shapes of single-quantum, linear-susceptibility resonances as well as for the line shapes of the absolute value and the real and imaginary components of the nonlinear-susceptibility resonances.
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.