Lucia Florescu

Semiclassical theory of lasing in photonic crystals

We present a theoretical analysis of laser action within the bands of propagating modes of a photonic crystal. Using Bloch functions as carrier waves in conjunction with a multiscale analysis, we derive the generalized Maxwell–Bloch equations for an incoherently pumped atomic system in interaction with the electromagnetic reservoir of a photonic crystal. These general Maxwell–Bloch equations are similar to the conventional semiclassical laser equations but contain effective parameters that depend on the band structure of the linear photonic crystal. Through an investigation of steady-state laser behavior, we show that, near a photonic band edge, the rate of stimulated emission may be enhanced and the internal losses are reduced, which leads to an important lowering of the laser threshold. In addition, we find an increase of the laser output along with an additional narrowing of the linewidth at a photonic band edge.

Inversion formulas for the broken-ray Radon transform

We consider the inversion of the broken-ray Radon transform, a problem that arises in the context of inverse transport theory in optical tomography. We derive inversion formulas which allow the recovery of the scattering and absorption coefficients of the radiative transport equation in the single-scattering regime. Our results are illustrated with numerical simulations.

Single-scattering Optical Tomography: Simultaneous Reconstruction of Scattering and Absorption

We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiply-scattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.

Nonreciprocal broken ray transforms with applications to fluorescence imaging

Abstract Broken ray transforms (BRTs) are typically considered to be reciprocal, meaning that the transform is independent of the direction in which a photon travels along a given broken ray. However, if the photon can change its energy (or be absorbed and re-radiated at a different frequency) at the vertex of the ray, then reciprocity is lost. In optics, non-reciprocal BRTs are applicable to imaging problems with fluorescent contrast agents. In the case of x-ray imaging, problems with single Compton scattering also give rise to non-reciprocal BRTs. In this paper, we focus on tomographic optical fluorescence imaging and show that, by reversing the path of a photon and using the non-reciprocity of the data function, we can reconstruct simultaneously and independently all optical properties of the medium (the intrinsic attenuation coefficients at the excitation and the fluorescence frequency and the concentration of the contrast agent). Our results are also applicable to inverting BRTs that arise due to single Compton scattering.

Single-Atom Lasers in Photonic Crystals

We present a quantum theory of a coherently pumped two-level atom in a photonic crystal, coupled to both a multi-mode wave-guide channel and a high quality micro-cavity embedded within the photonic crystal. The cavity field characteristics are highly distinct from that of a corresponding high Q cavity in ordinary vacuum. If the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence, enhanced, inversionless, nearly coherent light generation occurs when the photon density of states jump between the Mollow spectral components is large. The spectrum of the cavity field is also investigated and showed to be narrower than in the case of a conventional cavity. Moreover, enhanced, non-classical light generation is possible, if the cavity field is tuned on resonance with a Mollow sideband.