This article gives a class of solution of Maxwell equations which implies the solution of arbitrary ho-lomorphic hypercomplex functional with brief discussion of their physical meaning. It exhibites some wider nature than classical electromagnetic theory:(1) An electromagnetic field may spread non-periodically and may have the holographic nature and free shape.(2) The electromagnetic field may spread more slowly, equally or more quickly than light speed.(3) The electromagnetic field may spread in arbitrary curved direction.(4) There is a branch electromagnetic field in in-tergrowth space. An intergrrowth world may exist.This article also makes an inference and a description about the example of the above-mentioned strange electromagnetic field. It relates to some hard-to-explain phenomena through different physical models.