Far-infrared slab lensing and subwavelength imaging in crystal quartz

Abstract

We examine the possibility of using negative refraction stemming from the phonon polariton response in an anisotropic crystal to create a simple slab lens with plane parallel sides, and show that imaging from such a lens should be possible at room temperature despite the effects of absorption that are inevitably present due to phonon damping. In particular, we consider the case of crystal quartz, a system for which experimental measurements consistent with all-angle negative refraction associated with the phonon polariton response have already been demonstrated. Furthermore, we investigate the possibility of subwavelength imaging from such materials, and show that it should be possible for certain configurations.

Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride

“…Investigations into other polar van der Waal's materials 26 such as MoS 2 , may further extend the spectral range where natural HMs are found. 25,39 These efforts may lead to the development of disruptive technologies such as the nanoscale equivalent of an optical fiber, due to the volume-bound confinement of sub-diffraction modes within hBN. Impact in areas such as enhanced molecular spectroscopy, 40 nanophotonic circuits, 37 tailored thermal emission sources, 41,42 flat optics, 43 and super-resolution imaging 12,44 is also anticipated.…”

Tunable all-angle negative refraction using antiferromagnets

“…In terms of a slab lens, this is significant in the case where the material parameters are such that both the object and image can be very close to (i.e., within the near field of) the crystal surfaces, since in this case subwavelength imaging should be possible. We would expect this behavior close to the resonance frequency ω ⊥ [22], in which case propagation across the crystal would be in the form of nearly collimated beams [44]. Thus, both the more general possibility of a slab lens with tunable "focal length" and that of obtaining subwavelength imaging close to ω ⊥ warrant further investigation.…”

“…Thus, even in the presence of an external field in the configuration of Fig. 1, a single antiferromagnet crystal with parallel sides should act as a slab lens similar to that obtained from an indefinite permittivity medium [7,15,17,22]. An object placed on one side of such a lens will project an intermediate image within the slab and a final image on the other side of it.…”

“…3, except that corresponding to frequency C, show propagation into the antiferromagnet with low absorption. The degree of absorption in indefinite (hyperbolic) media is most often represented by a figure of merit (FOM) defined as [8,11,22,23] FOM = |Re(k 2z )|/Im(k 2z ). Note that, according to this definition, the FOM is dependent on incident angle.…”

“…In addition, the intrinsic layered structure of graphite has been shown to lead to an indefinite permittivity in the ultraviolet region [16]. At far-infrared frequencies, the phonon response in certain natural anisotropic crystals can also lead to an indefinite permittivity tensor, so that all-angle negative refraction is possible around the optic phonon frequencies in such crystals [17][18][19][20][21][22][23].…”