When an emitter ensemble interacts with the electromagnetic field,
dipole-dipole interactions are induced between the emitters. The magnitude and
shape of these interactions are fully determined by the specific form of the
electromagnetic field modes. If the emitters are placed in the vicinity of a
nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional
form of these modes makes the analytical evaluation of the dipole-dipole
interaction cumbersome and numerically costly. In this work, we provide a full
detailed description of how to successfully calculate these interactions,
outlining a method that can be easily extended to other environments and
boundary conditions. Such exact evaluation is of importance as, due to the
collective character of the interactions and dissipation in this kind of
systems, any small modification of the interactions may lead to dramatic
changes in experimental observables, particularly as the number of emitters
increases. We illustrate this by calculating the transmission signal of the
light guided by a cylindrical nanofiber in the presence of a nearby chain of
emitters.Comment: 14 pages, 5 figures, comments welcom