Orbital angular momentum multiplexing with non-degenerate modes in secondary frequency domain

The Electro-Magnetic (EM) waves with Orbital Angular Momentum (OAM) can achieve high spectral efficiency through multiplexing of different OAM modes. Due to the divergence of the beam angle, only partial phase plane of OAM wave can be received in the long distance transmission. Recently, it is reported that the mapping of different OAM modes to the corresponding frequency shifts in the second frequency domain can be established, so that to efficiently identify the OAM modes with partial phase plane reception. However, not all combinations of arbitrary OAM modes support the one-to-one mapping with frequency shifts in the second frequency domain. In other words, there is degeneracy in the combinations of different OAM modes for multiplexing transmission. Naturally, which combinations of OAM modes can be chosen to avoid the occurrence of the degeneracy in the second frequency domain becomes a fundamental problem. In this paper, the non-degenerate mode of OAM multiplexing is mathematically analyzed and evaluated. Specifically, all the non-degenerate patterns corresponding to the multiplexing combinations are enumerated with OAM numbers less than 7. Moreover, an experiment with 2 OAM modes multiplexing is carried out to illustrate the degeneracy of the OAM mode combination in the second frequency domain.