Dynamical control of the emission of a square microlaser via symmetry classes

A major objective in photonics is to tailor the emission properties of microcavities which is usually achieved with specific cavity shapes. Yet the dynamical change of the emission properties during operation would often be advantageous. The implementation of such a method is still a challenging issue. We present an effective procedure for the dynamical control of the emission lobes which relies on the selection of a specific coherent superposition of degenerate modes belonging to different symmetry classes. It is generally applicable to systems exhibiting pairs of degenerate modes. We explored it experimentally and analytically with organic square microlasers, which emit narrow lobes parallel to their sidewalls. By means of the pump polarization, emission lobes are switched on and off selectively with an extinction ratio better than $1/50$.

Figure 1

Experimental far-field intensity distributions of a square microlaser. A photograph of the cavity is superimposed to indicate the orientation. (a) Circular pump polarization, side length $a=120\mu \mathrm{m}$. (b) Linear pump polarization, side length $a=180\mu \mathrm{m}$. Due to technical reasons, the accessible angles for Fig. 1 were limited to $[-{15}^{\circ },{195}^{\circ }]$; the full polar plot was created by duplicating the data. [(c) and (d)] Perspective images of a square microlaser pumped from above with $a=120\mu \mathrm{m}$ for linear pump polarization parallel to the direction of observation. The camera is equipped with a notch filter at 532 nm. (d) The dashed white line indicates the cavity contours. (c) With additional white light illumination.

Figure 2

Schematic drawings of wave vectors (black solid lines) inside a square cavity. Each wave function in Table 1 is composed of eight plane waves. Their corresponding wave vectors belong to two different subsets presented in (a) and (b) where (b) is obtained from (a) by a $\pi /2$ rotation. Each subset is dynamically closed, i.e., a ray remains in its subset after reflections at the sidewalls. If the angle of incidence $\alpha$ is close to the critical angle (${\alpha }_c\simeq {42}^{\circ }$), then emission takes place at a grazing angle while maintaining good confinement. The complementary angle of incidence $\pi /2-\alpha$ is significantly larger than ${\alpha }_c$. Thus the ray is confined inside the cavity by total internal reflection, leading to negligible emission. Consequently, emission (red dashed arrows) occurs along the $x$ direction in (a) and along the $y$ direction in (b). The pump polarization is indicated by a green doublesided arrow. The pump efficiency depends on the angle $\beta$. It is maximal for a plane wave with $\beta =\pi /2$. In the case of a pump polarization along the $y$ direction, $\beta$ is slightly larger in (b) than in (a), and hence configuration (b) is enhanced by stimulated emission.

Figure 3

Geometry of the setup. The pump beam (vertical thick green arrow) impinges vertically on the cavity. The microlaser emits in the cavity plane (horizontal thick red arrows). The emission is collected by a lens in the far field at azimuthal angle $\phi$. The thin arrows indicate the polarization states.

Figure 4

Experimental spectrum of a 200-$\mu \mathrm{m}$ large square microlaser. The pump is linearly polarized parallel to one pair of sidewalls, and the observation direction is parallel to the pump polarization. The pump intensity is about twice the lasing threshold. Inset: Threshold curve for pump polarization parallel (solid red line) and perpendicular (dotted blue line) to the direction of observation. The maximum intensity of the spectrum is plotted versus the pump intensity, which is normalized to the laser threshold at $3.0\mathrm{MW}{\mathrm{cm}}^{-2}$.

Figure 5

Far-field intensity distributions calculated analytically with the Kirchhoff integral (see Appendix pp1) based on different superpositions of ${\psi }_{A_1}$ and ${\psi }_{B_2}$ as indicated below each figure. We used $(m_x,m_y)=(444,398)$, which corresponds to ($k_x=1.16259\times {10}^5{\mathrm{cm}}^{-1}, k_y=1.04336\times {10}^5{\mathrm{cm}}^{-1}$). (a) ${\psi }_{+}={\psi }_{A1}+{\psi }_{B2}$. (b) ${\psi }_{-}={\psi }_{A_1}-{\psi }_{B_2}$. (c) ${\psi }_{A_1}$.