Some features of a promising technology for creating complex profiles of smoothly irregular and stepped integrated optical waveguide structures, namely, the technology of laser printing, are briefly discussed. The relevance and importance of this direction is due to the widespread and promising technology of femtosecond recording, as well as the active use of elements (chips) created in this way in integrated optics and nanophotonics. Three-dimensional photon schemes have a wide range of applications, from quantum information processing and miniature lasers to opto-mechanics and optical fluids. When designing bulk integrated optical structures, complex problems arise, both of a theoretical nature and of numerical simulation of the waveguide propagation of optical radiation, because the guided waveguide modes experience radiation and leakage losses. In this regard, the creation of new methods for theoretical and numerical analysis of waveguide processes, in particular those related to the leakage of modes, is undoubtedly important and relevant in the development of the technology of “laser printing”. Our study shows that, first of all, the radiation outflow process should be considered as a wave process, and models should be built based on wave equations. Constructing a rigorous theory of waveguide leakage processes will make an important theoretical contribution to the theory of integrated optical waveguides and will contribute to improving the technology of “laser printing”. © Springer Nature Switzerland AG 2019.