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We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of
two-level atoms, based on a self-consistent solution of the Maxwell-Bloch
equations in the mean field and single-atom density matrix approximations. This
makes it possible to correctly take into account the effects caused by the free
motion of atoms in a gas, which lead to a nonlinear dependence of the
spectroscopic signal on the atomic density even in the absent of a direct
interatomic interaction (e.g., dipole-dipole interaction). Within the framework
of this approach, analytical expressions for the light field were obtained for
an arbitrary number of resonant waves and arbitrary optical thickness of a gas
medium. Sub-Doppler spectroscopy in the transmission signal for two
counterpropagating and co-propagating waves has been studied in detail. A
previously unknown red shift of a narrow sub-Doppler resonance is predicted in
a counterpropagating waves scheme, when the frequency of one wave is fixed and
the frequency of the other wave is varied. The magnitude of this shift depends
on the atomic density and can be more than an order of magnitude greater than
the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz
shift). The found effects, caused by the free motion of atoms, require a
significant revision of the existing picture of spectroscopic effects depending
on the density of atoms in a gas. Apart of fundamental aspect, obtained results
are important for precision laser spectroscopy and optical atomic clocks.