  We present a novel method to implement time-delayed propagation of radiation
fields in cosmological radiative transfer simulations. Time-delayed propagation
of radiation fields requires construction of retarded-time fields by tracking
the location and lifetime of radiation sources along the corresponding
light-cones. Cosmological radiative transfer simulations have, until now,
ignored this "light-cone effect" or implemented ray-tracing methods that are
computationally demanding. We show that radiative transfer calculation of the
time-delayed fields can be easily achieved in numerical simulations when
periodic boundary conditions are used, by calculating the time-discretized
retarded-time Green's function using the Fast Fourier Transform (FFT) method
and convolving it with the source distribution. We also present a direct
application of this method to the long-range radiation field of Lyman-Werner
band photons, which is important in the high-redshift astrophysics with first
stars.
