Momentum nonconserving interaction within a layer of nonlinear material localized in a subwavelength region of the space

Muriel Botey, Jordi Martorell, and Ramon Vilaseca
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya,
Colom 11, 08222 Terrassa, Spain, E-mail:jordi.martorell@upc.es

t has been shown that localization of light within a photonic crystal can be used to enhance the second and third order nonlinear interaction [1]. This light localization and enhancement are larger when defects breaking the perfect periodicity of the lattice are introduced within the structure [2]. These type of structures have been considered, among other things, to enhance the generation of second harmonic (SH) light [3]. Within the defect of the structure, the SH wave is reflected back and then forward again resulting in a large transfer of energy from the fundamental to the forward propagating SH beam. In systems where the nonlinear material is localized in a subwavelength region of space, energy could be transferred directly from the backward SH to the fundamental wave or viceversa in a momentum nonconserving interaction. To properly study the contribution from these later type of interactions, we have considered a very simple geometry where the SH light is reflected back only once by a single mirror that is placed in front of a thin planar layer of nonlinear material.
The output SH light form this type of structure is strongly dependent on the mirror position relative to the location of the layer, and can be inhibited even when the SH intensity within the structure is nonvanishing. This result is in accordance with an experimental observation by Kauranen et al. [4] where SH generation was considered in a single mirror configuration almost identical to the one described above. This apparent contradiction can only be explained if one considers the interaction of the fundamental field with both the forward generated and the reflected SH fields, as well as the interaction of the same total SH field with the incident and reflected fundamental. Moreover, if we consider separately all the possible interactions, we see that the major contribution to this interaction comes from the nonconserving momentum transfer of energy from the reflected SH field back to the incident fundamental. In bulk generation of SH light, the contribution of such terms would vanish, however, in generation from a subwavelength layer momentum is conserved due to the presence of a nearby interface between a linear and a nonlinear material.
In conclusion, we have shown that in order to fully describe the interaction within a layer of nonlinear material localized in a subwavelength region of the space in front of a reflecting boundary it is essential to consider all interactions between the fundamental and the SH fields, including non-conserving momentum terms.

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