GaN substrates grown by the ammonothermal method are analyzed by Fast Fourier Transformation Spectroscopy in order to study the impact of doping (both n-and p-type) on their transparency in the near-infrared, mid-infrared, and terahertz spectral range. It is shown that the introduction of dopants causes a decrease in transparency of GaN substrates in a broad spectral range which is attributed to absorption on free carriers (n-type samples) or dopant ionization (p-type samples). In the mid-infrared the transparency cut-off, which for a semi-insulating GaN is at~7 µm due to an absorption on a second harmonic of optical phonons, shifts towards shorter wavelengths due to an absorption on free carriers up to~1 µm at n~10 20 cm −3 doping level. Moreover, a semi-insulating GaN crystal shows good transparency in the 1-10 THz range, while for n-and p-type crystal, the transparency in this spectral region is significantly quenched below 1%. In addition, it is shown that in the visible spectral region n-type GaN substrates with a carrier concentration below 10 18 cm −3 are highly transparent with the absorption coefficient below 3 cm −1 at 450 nm, a satisfactory condition for light emitting diodes and laser diodes operating in this spectral range.