Tunable subwavelength slit lenses based on the manipulation of refractive index of medium

A nanoslit array is introduced on the silicon waveguide, and the phase difference is controlled by the slit width to satisfy the function of the focusing lens. If keep the designed width and depth of the slit in accordance with the focusing effect unchanged, when the incident wavelength changes, the focal position must change accordingly, and the dispersion effect is significant. In order to achieve the achromatic effect, the refractive index of the surrounding medium is changed while changing the wavelength. Finally, the refractive index of the surrounding medium which can keep the focal length constant at the wavelength of 1550-1950nm is obtained, and the equation that the change of the refractive index and the wavelength of the medium makes the focal length constant is obtained. The achromatic effect can be effectively achieved, and applications range of achromatic metalens from imaging in optical communications to telescopes in the astronomical field.