Dipole radiation in a one-dimensional photonic crystal. II. TM polarization

Abstract

As in a recent paper [I. Alvarado-Rodríguez, P. Halevi, and Adán S. Sánchez, Phys. Rev. E 63, 056613 (2001); 65, 039901(E) (2002)], we study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac-delta functions (Dirac-comb SL). However, while in the aforementioned paper the radiation was restricted to the transverse electric (TE) polarization mode, here we focus our attention on the transverse magnetic (TM) mode. Employing the same methodology, again we find that the power spectra are dominated by slope discontinuities. These occur - if at all - at the band edges for on-axis propagation, depending on the dipole's position and orientation. The largest enhancement or inhibition is present for normalized frequencies such that (omegad/c) less, similar 2pi; here, omega is the dipole frequency, c is the speed of light in vacuum, and d is the distance between the barriers. For substantial values of the grating strength considerable enhancement or suppression of the radiated power (in comparison to the free-space value) is obtained. We also find that the power emitted by a gas of randomly oriented dipoles exhibits slope discontinuities at all band edges for on-axis propagation. In comparison with the TE polarization case, the TM polarization exhibits several different qualitative features.

Design and applications of strongly dispersive photonic crystal structures

“…The temporal dispersion of the material can be used to realize dispersion compensation [20], pulse compression [21], pulse shaping [22], and optical delay [23]. The spatial dispersion of photonic crystals covers another set of applications including subwavelength imaging [24][25], beam shaping [26], controlling the radiation pattern [27][28][29], superprism-based demultiplexing [14], and diffraction-free propagation [30][31].…”

On-chip spectrometers for visible and infrared sensing applications

“…Several device ideas based on temporal dispersion of the material have been proposed, including dispersion compensation, 7 pulse compression, 8 pulse shaping, 9 and optical delay. 10 The controllable spatial dispersion in photonic crystals have been proposed for another set of applications such as subwavelength imaging, [11][12] beam shaping, 13 controlling the radiation pattern, [14][15][16] superprism-based demultiplexing, 6 and diffractionfree propagation. [17][18] We have previously demonstrated that the unique dispersive properties of Si-based PCs (i.e., superprism effect, negative diffraction, and negative refraction) can be combined to realize ultra-compact devices for spatial separation of different wavelength channels of an optical signal.…”

Spontaneous-emission rates in finite photonic crystals of plane scatterers

“…In [16], both infinite and finite crystals of planes were considered and their transmission and reflection properties were studied with the use of transfer matrix methods. The infinite crystal was again considered in [17,18,19,20] and named the 'Diraccomb superlattice'. Frequency-dependent emission rates were determined for several positions in the unit cell and both TE- [17,19] and TM-waves [18,20] were considered.…”

“…The infinite crystal was again considered in [17,18,19,20] and named the 'Diraccomb superlattice'. Frequency-dependent emission rates were determined for several positions in the unit cell and both TE- [17,19] and TM-waves [18,20] were considered. The periodicity of infinite crystals makes that Bloch's theorem can be used in the analysis.…”