  Topologically quantized response is one of the focal points of contemporary
condensed matter physics. While it directly results in quantized response
coefficients in quantum systems, there has been no notion of quantized response
in classical systems thus far. This is because quantized response has always
been connected to topology via linear response theory that assumes a quantum
mechanical ground state. Yet, classical systems can carry arbitrarily amounts
of energy in each mode, even while possessing the same number of measurable
edge modes as their topological winding. In this work, we discover the totally
new paradigm of quantized classical response, which is based on the spectral
winding number in the complex spectral plane, rather than the winding of
eigenstates in momentum space. Such quantized response is classical insofar as
it applies to phenomenological non-Hermitian setting, arises from fundamental
mathematical properties of the Green's function, and shows up in steady-state
response, without invoking a conventional linear response theory. Specifically,
the ratio of the change in one quantity depicting signal amplification to the
variation in one imaginary flux-like parameter is found to display fascinating
plateaus, with their quantized values given by the spectral winding numbers as
the topological invariants.
