Elena I. Smotrova

Optical Theorem Helps Understand Thresholds of Lasing in Microcavities With Active Regions

Within the framework of the recently proposed approach to view the lasing in open microcavities as a linear eigenproblem for the Maxwell equations with exact boundary and radiation conditions, we study the correspondence between the modal thresholds and field overlap coefficients. Macroscopic gain is introduced into the cavity material within the active region via the “active” imaginary part of the refractive index. Each eigenvalue is constituted of two positive numbers, namely, the lasing wavenumber and the threshold value of material gain. This approach yields clear insight into the lasing thresholds of individual modes. The Optical Theorem, if applied to the lasing-mode field, puts the familiar “” condition on firm footing. It rigorously quantifies the role of the spatial overlap of the mode E-field with the active region, whose shape and location are efficient tools of the threshold manipulation. Here, the effective mode volume in open resonator is introduced from first principles. Examples are given for the 1-D cavities equipped with active layers and distributed Bragg reflectors and 2-D cavities with active disks and annular Bragg reflectors.

Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes

Lasing modes in cyclic photonic molecules (CPMs) composed of several identical thin semiconductor microdisks in free space are studied in a linear approximation. Maxwells equations with exact boundary conditions and the radiation condition at infinity are considered as a specific eigenvalue problem that enables one to find natural frequencies and threshold gains. It is demonstrated that careful tuning of the distance between the disks in CPMs is able to drastically reduce the lasing thresholds of the whispering-gallery modes having small azimuth indices.

Spectra, thresholds, and modal fields of a kite-shaped microcavity laser

We investigate the lasing spectra, threshold gain values, and emission directionalities for a two-dimensional microcavity laser with a “kite” contour. The cavity modes are considered accurately using the linear electromagnetic formalism of the lasing eigenvalue problem with exact boundary and radiation conditions. We develop a numerical algorithm based on the Muller boundary integral equations discretized using the Nystrom technique, which has theoretically justified and fast convergence. The influence of the deviation from the circular shape on the modal characteristics is studied numerically for the modes polarized in the cavity plane, demonstrating opportunities of directionality improvement together with preservation of a low threshold. These advantageous features are shown for the perturbed whispering-gallery modes of high-enough azimuth orders. Other modes can display improved directivities while suffering from drastically higher threshold levels. Experiments based on planar organic microcavity lasers confirm the coexistence of Fabry–Perot-like and whispering-gallery-like modes in kite-shaped cavities and show good agreement with the predicted far-field angular diagrams.

Lasing frequencies and thresholds of the dipole supermodes in an active microdisk concentrically coupled with a passive microring

The lasing spectra and threshold values of material gain for the dipole-type supermodes of an active microdisk concentrically coupled with an external passive microring are investigated. TE polarized modes are treated accurately using the linear electromagnetic formalism of the 2-D lasing eigenvalue problem (LEP) with exact boundary and radiation conditions. The influence of the microring on the lasing frequencies and thresholds is studied numerically, demonstrating threshold reduction opportunities. This is explained through the analysis of the mode near-field patterns and the degree of their overlap with the active region, as suggested by the optical theorem applied to the LEP solutions.

Ultralow Lasing Thresholds of

Cyclic photonic molecules (CPMs) composed of an even number of identical submicron-size circular-disk active resonators in free space are studied in two dimensions. Cold-cavity lasing frequencies and threshold values of material gain are extracted from an electromagnetic eigenvalue problem with exact boundary and radiation conditions. We show that assembling several small cavities in a tightly packed CPM efficiently lowers the thresholds of optically coupled nonwhispering-gallery modes of the lowest values (i.e., 0 and 1) of the azimuth index in each cavity provided that high antisymmetry is arranged

pi

A numerical study is presented of several lowest in frequency modes in a spiral microlaser. The modes in an arbitrarily shaped active cavity are considered as solutions to the two-dimensional eigenproblem for the Muller boundary-integral equations. After discretization using the Nyström-type algorithm, the eigenvalues are found in terms of frequency and material-gain threshold.

-Type Supermodes in Cyclic Photonic Molecules Composed of Submicron Disks With Monopole and Dipole Modes

The lasing spectra and thresholds of a selectively pumped photonic molecule composed of two microdisks is investigated using effective index approximation and full-wave 2-D electromagnetic equations. The lasing eigenvalue problem formulation is used to find modal frequencies and threshold values of material gain. The influence of the optical coupling between active and passive microdisks on the lasing eigenvalues and directionalities of emission is studied. It is shown that for strong coupling the effect of making one of the resonators passive leads to the doubling of the threshold.

Optical fields of the lowest modes in a uniformly active thin subwavelength spiral microcavity

We present a theoretical design for a single-mode, truly subwavelength terahertz disk laser based on a nanocomposite gain medium comprising an array of normal-metal/ferromagnetic (FM) point contacts embedded in a thin dielectric layer. Stimulated emission of light occurs due to spin-flip relaxation of spin-polarized electrons injected from the FM side of the contacts. Ultrahigh electrical current densities in the contacts and a dielectric material with a large refractive index, neither condition being achievable in conventional semiconductor media, enables the thresholds of lasing to be overcome for the lowest-order modes of the disk, making single-mode operation possible.

Optical coupling of an active microdisk to a passive one: effect on the lasing thresholds of the whispering-gallery supermodes

The lasing spectra and thresholds of selectively activated photonic molecule (PM) composed of two microdisks have been investigated. 3-D boundary problem for Maxwell equations is reduced to 2-D one with effective index method. Further in-plane 2-D problem is analysed accurately. Lasing eigenvalue problem (LEP) formulation is used to find naturals frequencies and threshold gains. The influence of the second microdisk on lasing spectra and thresholds has been studied. Dependences of frequencies and thresholds on distance between resonators are presented.

Subwavelength terahertz spin-flip laser based on a magnetic point-contact array

The lasing modes in a thin kite-shaped active microcavity are considered as solutions to a specifically tailored two-dimensional (2-D) linear eigenvalue problem for the Maxwell equations with exact boundary and radiation conditions. This problem is reduced to the set of Mullers boundary integral equations discretized using the adequate quadrature formulas. The eigenvalues are found numerically as the roots of the corresponding determinantal equation. The results of the study of mode lasing thresholds, spectra and light emission directivities are presented.