Interference-induced enhancement of intensity and energy of a quantum optical field by a subwavelength array of coherent light sources

Abstract

Recently, we have showed a mechanism that could provide a great transmission enhancement of the light waves passed through subwavelength aperture arrays in thin metal films not by the plasmonpolariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone. We now present a quantum reformulation of the model. The Hamiltonian describing the interference-induced enhancement of the intensity and energy of a multimode quantum optical field is derived. Such a field can be produced, for instance, by a subwavelength array of coherent light sources.PACS numbers: 03.70.+k, 03.75.-b, 03.50.-z Since the demonstration of enhanced transmission of light through a subwavelength metal apertures in the study [1], the phenomenon attracts increasing interest of researchers working in the field of nanooptics and nanophotonics [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. It is generally accepted [25] that the excitation and interference of plasmon-polaritons play a key role in the process of enhancement in the most of experiments (see, the recent reviews [26,27]). Recently, we have showed a mechanism that could provide a great transmission enhancement of the light waves passed through subwavelength aperture arrays in thin metal films not by the plasmon-polariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone [28]. According to the model, the beams generated by multiple, subwavelength apertures can have similar phases and can add coherently. If the spacing of the apertures is smaller than the optical wavelength, then the phases of the multiple beams are nearly the same and beams add coherently (the light power and energy scales as the number of light-sources squared, regardless of periodicity). If the spacing is larger, then the addition is not so efficient, but still leads to enhancements and resonances (versus wavelength) in the total power transmitted. The analysis [28] is based on calculation of the energy flux (intensity) of a beam array by using Maxwell's equations for classic, non-quantum electromagnetic fields. The enhancement mechanism was interpreted as a non-quantum analog of the superradiance emission of a subwavelength ensemble of atoms (the light power and energy scales as the number of light-sources squared, regardless of periodicity) predicted by the Dicke quantum model [29]. We now present a quantum reformulation of our model. The Hamiltonian describing the interference-induced enhancement of the intensity and energy of a multimode quantum optical field is derived. Such a field can be produced, for instance, by a subwavelength array of coherent light sources.With the objective of quantizing the electromagnetic (EM) field, it is convenient to begin with consideration of the Hamiltonian of a classical (non-quantum) EM field based on Maxwell's equations. The detailed description of the problem can be found i...