Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics

We present a theory for the analytical design of double-chirped mirrors wit h special dispersion characteristics. A simple analytical equation takes an arbitrarily desired group delay dispersion (that also includes possible hi gher order dispersion) as an input function and gives the chirp law as an o utput, The chirp law determines the local Bragg wavelengths in the mirror. It allows the calculation of the thicknesses of the high-and law-index laye rs if the double chirp of the layers in the front part of the mirror is tak en into account, We use this method to design a highly dispersive double-ch irped semiconductor Bragg mirror and a double-chirped TiO2-SiO2 mirror for higher order dispersion compensation in optical parametric oscillators oper ating in the visible spectral range. The design formulas are applicable to general chirped Bragg gratings and provide insight into the reasons why cer tain dispersion characteristics might be impossible to achieve.