Line lasing in a two-dimensional lattice of orbital photonic resonators

TL;DR

This work designs a 2D photonic lattice of orbital micropillars (an orbital Lieb lattice) that supports line-lasing modes due to flat dispersion along one axis and dispersive behavior along the perpendicular axis. By combining $s$ and $p$ orbitals, the authors realize independent line modes and demonstrate lasing at the top of the $sp$ antibonding band with a relatively low threshold and polarization aligned perpendicular to the lasing line. They further show phase locking between crossing line lasers, which is explained by an ellipticity-induced coupling between $p_x$ and $p_y$ orbitals, and supported by a driven-dissipative numerical model that includes reservoir blueshifts and dissipative hopping. The findings highlight a pathway to densely packed, line-resolved laser matrices with potential for electrically injected implementations in 2D photonic lattices, leveraging controlled orbital coupling and nonlinear reservoir dynamics.

Abstract

The engineering of specialty lasers with unconventional mode structures is one of the modern challenges in the development of integrated coherent sources. Examples include the use of bound states in the continuum, microlasers with orbital angular momentum, Dirac-band lasers and topological lasers. In this work we engineer a two-dimensional lattice of coupled micropillars with lasing line modes. We use a convenient combination of orbital photonic modes to design photonic bands which are flat in one direction and dispersive in the perpendicular one giving rise to line lasing modes. Such an architecture opens the possibility of implementing densely packed lasing matrices in compact two dimensional lattices.

Figures (6)

• Figure 1: (a) Scheme of two coupled micropillars of different diameter. As schematically depicted on the energy level diagram below, the diameters of the micropillars are designed for the $p_x$ and $p_y$ modes of the large micropillar to be at the energy of the $s$ modes of the smaller micropillar. (b) Arrangement of the overlapping orbitals in the $sp$ bands of the Lieb lattice. (c) Scanning electron microscope image of a typical $sp$ Lieb lattice.
• Figure 2: (a) Eigenvalues of the $sp$ orbital bands computed from a tight binding model with nearest-neighbours. (b) Measured bands at $k_y = -\pi/a$ at low excitation power. Dashed lines display a fit to the eigenvalues of Eq. (\ref{['eq:H_sp']}). (c) Real space emission measured at the energy of the $s$ mode for a $4 \times 4$ lattice. (d) Real space emission measured at the energy of the top of the $sp$ band.
• Figure 3: (a) Sketch of the configuration for the excitation of an horizontal line of the lattice. (b) Integrated intensity of the upper $sp$ mode along the line in which the lattice is excited. The intensity is resolved in linear polarization. (c) Degree of linear polarization computed from (b). (d) Emitted spectrum along a line crossing the center of the excitation spot at low excitation power (0.5 mW). (e) Real-space photoluminescence at the energy of the top of the $sp$ band. (f)-(g) Same as (d)-(e) at an excitation power above the lasing threshold.
• Figure 4: (a) Sketch of the excitation configuration of a vertical line of the lattice. (b) Real-space emission at the energy of the $sp$ lasing mode above threshold. (c) Integrated intensity of the upper $sp$ mode along the line in which the lattice is excited. The intensity is resolved in linear polarization. (d) Degree of linear polarization computed from (c).
• Figure 5: (a) Scheme of the crossed excitation spot along a vertical and a horizontal line. (b) Integrated intensity of the top of the $sp$ band integrated over the sites along the lines in which the lattice is excited. (c) Measured laser emission at the energy of the $sp$ lasing mode above threshold ($P=2P_{th}$). The inset shows a zoomed view of the micropillar at which the two lines cross. (d) Measured spectrum resolved in linear polarization at $P=1.2P_{th}$ for photon energies at the top of $sp$ band at two different spatial points corresponding to the circles in the horizontal and vertical arms in (c). (e) Visibility of the fringes arising from the interference between the two circled sites in (c) when they are overlapped on a CCD camera. Insets show the overlapped images at low and high power. (f) Same as (e) when the power of the vertical excitation spot is kept at 23.2 mW and the power of the horizontal excitation spot is varied.