Extracting the electron-boson spectral function α²F(ω) from infrared and photoemission data using inverse theory

We present a method for extracting the electron-boson spectral function α²F(ω) from infrared and photoemission data. This procedure is based on inverse theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several families of high-T_c superconductors. Principal limitations of extracting α²F(ω) from experimental data will be pointed out. We directly compare the IR and angular-resolved photoemission spectroscopy α²F(ω) and discuss the resonance structure in the spectra in terms of existing theoretical models.