We investigate the usefulness of the wide-angle Fast Fourier Transform-based
beam propagation method (FFT-BPM) to investigate important and quite involved problems in the propagation of optical beams. The incident transverse electric (TE) and
transverse magnetic (TM) optical beams at the critical angle on a dielectric interface are
investigated. Major numerical difficulties associated with the singularity of the transverse
derivative of the step-like refractive index at the interface plane (for the TM case) are
circumvented via an ‘‘equivalent-index’’ formalism. An arc-tangent function is used to
approximate the abrupt change of the refractive index at the interface, such that the
singular derivative is eliminated, and the TM problem is transformed to an equivalent TE
one with no singular behavior. Further, the propagation of a rectangular incident pulse on
an interface at the critical angle is also studied. In this investigation, the large shift of the
lateral field and the standing wave pattern resulting from the incident and reflected fields
are investigated and justified by simple calculations. A new phenomenon, called ‘‘spatial
transient’’ is discussed, concerning the substantial spatial evolution of the pulse over very
short propagation distance (fraction of the wavelength). Finally, a parametric study of a plasmonic-type sensor in the Kretschmann configuration is presented using the proposed
FFT-BPM to ensure its validity in studying such subwavelength-based phenomenon. |
