Tailoring Optical Nonlinearities via the Purcell Effect

Abstract

We predict that the effective nonlinear optical susceptibility can be tailored using the Purcell effect. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies. For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved.PACS numbers: 42.50. Ct,42.70.Qs Optical nonlinearities have fascinated physicists for many decades because of the variety of intriguing phenomena that they display, such as frequency mixing, supercontinuum generation, and optical solitons [1,2]. Moreover, they enable numerous important applications such as higher-harmonic generation and optical signal processing [2,3,4]. On a different note, the Purcell effect has given rise to an entire field based on studying how complex dielectric environments can strongly enhance or suppress spontaneous emission from a dipole source [5,6,7,8,9]. In this Letter, we demonstrate that the Purcell effect can also be used to tailor the effective nonlinear optical susceptibility. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity, in which the refractive index is shifted by an amount proportional to intensity. This effect occurs in most materials, modeled here as originating from the presence of a collection of two-level systems. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies.In hindsight, the modification of nonlinearities through the Purcell effect could be expected intuitively: optical nonlinearities are caused by atomic resonances, hence varying their strengths should influence the strengths of nonlinearities as well. Nevertheless, to the best of our knowledge, this interesting phenomenon has not thus far been described in the literature. Moreover, as we show below, it displays some unexpected properties. For example, while increasing spontaneous emission strengthens the resonance by enhancing the interaction with the optical field, it actually makes the optical nonlinearity weaker. Furthermore, phase damping (e.g., through elastic scattering of phonons), which is detrimental to most optical processes, plays an essential role in this scheme, because in its absence, these effects disappear.A simple, generic model displaying Kerr nonlinearity is a two-level system. Its susceptibility has been calculated to all orders in both perturbative and steady state limits [2]. However, this derivation is based on a phenomenological model of decay observed in a homogeneous medium, and does not necessarily apply to systems in which the density of states is stron...

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