Arbitrary energy-preserving control of the line spacing of an optical frequency comb over six orders of magnitude through self-imaging

Spectral self-imaging (SI) is an efficient technique for controlling the line spacing (LS) of optical frequency combs (OFC). However, the degree of control is relatively limited, since the LS of the output comb must be set to be an integer sub-multiple of the input one. This technique can be extended to achieve arbitrary control of the comb LS by pre-conditioning the input comb with a properly designed spectral phase mask. This way, the output LS can be set to be any desired integer or fractional multiple of the input one. This generalized spectral SI process is intrinsically energy-preserving, which enables passive amplification of individual spectral lines of the comb when the scheme is designed for LS increase. Here we demonstrate the unique capabilities of generalized spectral SI in a simple dedicated fiber-optics platform, based on a frequency-shifting recirculating loop. When seeded with an external CW laser, the loop delivers a frequency comb with an arbitrary and reconfigurable quadratic spectral phase. We report lossless arbitrary control of the LS of the generated OFCs over six orders of magnitude, from the kHz to the GHz range, including passive amplification of individual comb lines by factors as high as 17 dB. The LS control is produced without modifying the features of the frequency comb. Practical applications of this LS control method are discussed.