  This paper presents a class of boundary integral equation methods for the
numerical solution of acoustic and electromagnetic time-domain scattering
problems in the presence of unbounded penetrable interfaces in two-spatial
dimensions. The proposed methodology relies on Convolution Quadrature (CQ)
methods in conjunction with the recently introduced Windowed Green Function
(WGF) method. As in standard time-domain scattering from bounded obstacles, a
CQ method of the user's choice is utilized to transform the problem into a
finite number of (complex) frequency-domain problems posed on the domains
involving penetrable unbounded interfaces. Each one of the frequency-domain
transmission problems is then formulated as a second-kind integral equation
that is effectively reduced to a bounded interface by means of the WGF
method---which introduces errors that decrease super-algebraically fast as the
window size increases. The resulting windowed integral equations can then be
solved by means of any (accelerated or unaccelerated) off-the-shelf Helmholtz
boundary integral equation solver capable of handling complex wavenumbers with
a large imaginary part. A high-order Nystr\"om method based on Alpert
quadrature rules is utilized here. A variety of numerical examples including
wave propagation in open waveguides as well as scattering from multiply layered
media demonstrate the capabilities of the proposed approach.
