Analytic design of an achromatic double grating coupler

A method for designing a double grating for coupling a polychromatic wave out of a waveguide with negligible angular dispersion is presented. It is based on calculating analytically two different grating functions, such that the chromatic dispersion of the first grating function is compensated by the second grating function. It is shown that the usable wavelength range can be increased by more than 2 orders of magnitude relative to conventional grating couplers for typical angular tolerance.