  The interaction of coherent light with a nonlinear medium is modeled here by
a general quantum anharmonic oscillator. The model is not exactly solvable in a
closed analytical form. But we need operator solutions of the equations of
motion corresponding to these models in order to study the quantum fluctuations
of coherent light in nonlinear media. In the present work we derive approximate
operator solutions. From these solutions we observe that there exists an
apparent discrepancy between the solutions obtained by different techniques. We
compare different solutions and conclude that all correct solutions are
equivalent and the apparent discrepancy is due to the use of different ordering
of the operators. We use these solutions to investigate the possibilities of
observing different optical phenomena in a nonlinear dielectric medium. To be
precise, we have studied quantum phase fluctuations of coherent light in a
third order inversion symmetric nonlinear medium. Fluctuations in phase space
quadrature for the same system are studied and the possibility of generating
squeezed state is reported. Fluctuations in photon number are studied and the
nonclassical phenomenon of antibunching is predicted. We have generalized the
results obtained for third order nonlinear medium and have studied the
interaction of an intense laser beam with a general (m-1)-th order nonlinear
medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the
context of (m-1)-th order nonlinear medium.
