Experimental Observation of Optical Bound States in the Continuum

We present the experimental observation of bound states in the continuum. Our experiments are carried out in an optical waveguide array structure, where the bound state (guided mode) is decoupled from the continuum by virtue of symmetry only. We demonstrate that breaking the symmetry of the system couples this special bound state to continuum states, leading to radiative losses. These experiments demonstrate ideas initially proposed by von Neumann and Wigner in 1929 and offer new possibilities for integrated optical elements and analogous realizations with cold atoms and optical trapping of particles.

Figure 1

Refractive index profile of the structure used for the demonstration of a BIC. The structure comprises a one-dimensional array of 51 equidistant waveguides in the $x$ direction and two additional waveguides above and below the array. The size of each waveguide is $4\mu \mathrm{m}$ in the horizontal direction and $11\mu \mathrm{m}$ in the vertical direction.

Figure 2

Calculated dispersion relation of the waveguide array (solid curve) indicating a continuum of extended states (Bloch modes) in the $x$ direction, comprising the first band of the array (gray). All of these modes are $y$ symmetric. The circles indicate the propagation constants of the three discrete bound states of the three vertical waveguides in the center of the array. The two bound states above and below the band are $y$ symmetric, but they are disconnected from the band because they reside in the gaps above and below the band, thereby forming ordinary bound states (defect modes). The central discrete state is immersed in the continuous band, but because it is antisymmetric in the vertical direction it is decoupled from the band, thereby forming a BIC.

Figure 3

Light intensity at the output plane of the structure, following proper excitation of the BIC. (a) Light intensity at the output plane when the structure is fully $y$ symmetric. Clearly, no light is leaking into the array. (b) Light intensity at the output plane when the refractive index gradient is introduced by a 30 K temperature gradient across 1 mm (distance between upper and lower thermal contacts). Clearly, the broken symmetry mediates leakage of light into the array.

Figure 4

Power coupled into the continuum states (array modes) as a function of the applied thermal gradient across the structure. The blue dots represent the experimental data, while the red line shows the simulation results.