  The origin of non-dispersive flat band modes for a quasi-one dimensional
square-kagome ladder network is explored analytically by virtue of the real
space renormalization group (RSRG) technique. A section of the eigenstates is
non-diffusive i.e., localized within a cluster of sub-lattice sites partly by
the destructive type of quantum interference and partly by the physical divider
formed by the sites with zero wave function amplitude. By making the amplitude
vanish at the selective sites it becomes possible to confine the incoming
excitation within the trapping cell leading to the formation of compact
localized states. The effective mass of the particle becomes infinitely large
corresponding to those self-localized modes and hence the mobility of the wave
train becomes vanishingly small. This quenched kinetic energy leads to a
momentum independent contribution to a dispersion curve. The present analysis
is corroborated by numerical calculation of spectral landscape and the
corresponding dispersion profile. The application of uniform magnetic flux may
lead to a comprehensive engineering of the position as well as the curvature of
the band. Also, one-to-one mapping between electronic case and photonic case
within the tight-binding framework helps us to study the photonic localization
in an analogous single mode wave guide system. The concept of slow light
eventually introduces the possibility of spatial compression of light energy.
