For the past two decades, researchers have explored dielectric cavities like spheres and disks, which support long-lived modes called whispering gallery modes (WGMs) due to total internal reflection along the cavity's boundary. WGMs in microcavities with high-Q and small mode volume are crucial for applications like low-threshold lasers, optical frequency combs, biosensors, and optical gyroscopes. However, the isotropic emission of 2D disk cavities limits their directional light emission. The rotational symmetry of the disk shape restricts practical applications of the photonic devices because of their isotropic emission which lacks directionality in far-field emission and difficulty in free space out-coupling. To overcome this problem, deformation of the disk cavity has been mainly attempted; however, the approach cannot avoid Q-degradation owing to the broken rotational symmetry.

Fig. 1. Ray trajectories, 2D refractive index profiles, and 3D nanohole distributions of a center-shift (CS) limaçon TC and the corresponding homogeneous limaçon cavity. (a) Well-ordered ray trajectory in the CS limaçon TC exhibiting similar caustic to a uniform disk. Curved blue lines are transformed images of the Cartesian grid lines in the original virtual space, and the red line is the boundary of a CS limaçon TC. (b) Two-dimensional CS limaçon TC and its refractive index profile. (c) Chaotic ray trajectory in the homogeneous limaçon cavity. The ray is launched with the same incident angle as in (a). Straight blue lines are grid of the Cartesian coordinates. (d) Homogeneous limaçon-shaped cavity having the same shape as the CS limaçon TC and its refractive index.

As another approach, in 2016, Prof. Muhan Choi at Kyungpook National University, South Korea, and his collaborators presented the transformation cavity (TC) which has deformed shape and spatially varying refractive index designed by conformal transformation optics (TO). Since TO encodes the effect of a coordinate transformation into refractive index distribution, it enables the TC inherits the feature of a circular cavity. However, in order to apply the scheme to optical devices, deep-subwavelength scale nanostructures are required for satisfying effective medium approximation, but the fabrication of the nanostructure is a highly challenging task. For this reason, the experimental demonstration has remained in the microwave regime.

In the recently published paper Yong-Hoon Lee, Honghwi Park, Inbo Kim, Sang-Jun Park, Sunghwan Rim, Byoung Jun Park, Moohyuk Kim, Yushin Kim, Myung-Ki Kim, Won Seok Han, Hosung Kim, Hongsik Park, Muhan Choi. Shape-tailored whispering gallery microcavity lasers designed by transformation optics[J]. Photonics Research, 2023, 11(9): A35, the authors reported a limaçon-shaped TC semiconductor laser that operates at the optical communication wavelength regime as a first demonstration of a TC-based light source. A 500 nm-thick InGaAsP-based multi-quantum-well wafer was vertically etched to form the nanoholes with a diameter of 60 nm, and the spacing between each nanohole is distributed between 100 to 240 nm depending on the local refractive index. Due to this nanohole distribution designed by TO and effective medium approximation, Q-spoiling caused by the boundary deformation is recovered. As a result, the lasing threshold of TC laser is reduced to one third of that of a corresponding homogeneous cavity laser with the same deformed shape, and comparable to that of a homogeneous microdisk (i.e., circular) laser.

Fig. 2. (a) SEM image of the fabricated CS limaçon TC laser. (b) Lasing curves of the three cavity lasers for comparison.

Comment from Prof. Choi:
"Because of some difficulties in fabrication, the first experiment of TC was conducted in the microwave regime, but here, we have just demonstrated the TC operating at optical communication regime, and presented lasing action of the TC for the first time. So far, our design approach has mainly focused on conformal equivalence between simply connected cavity regions, that is, the considered mappings are connecting two flat spaces. For future work, we are studying ligthwave dynamics in curved space by utilizing the transformation between curved space and flat space."