Superlensing effect in photonic crystals

At the Physics Department of HKUST, a group of researchers has been carrying out work on the superlensing effect in photonic crystals. We are:

  • Che Ting Chan (theorist)
  • Xinhua Hu (theorist)

The lensing effect can be achieved in photonic crystal (PC) slabs, but in many situations, the mechanism can be traced to the self-collimation effect of a square-like constant frequency surface. We show that using a metal-in-dielectric configuration, circular constant frequency surfaces can be obtained, and the lensing effect then obeys fairly well the image-distance relationship characteristic of an n = -1 material.  As a two-dimensional example, far-field imaging is realized in square arrays of silver nanowires in air for transverse-electric waves at 400 nm.  A high resolution of about 100 nm is obtained with a three-layer slab of such PCs.  By varying the matrix, the results are extended to the optic and near-infrared regimes.


[1] Xinhua Hu and C. T. Chan, Appl. Phys. Lett. 85, 1520 (2004).

Imaging with U + V = L is realized in square arrays of silver nanowires (diameter D = 59.9 nm and lattice constant a = 69.9 nm) in air for TE mode (E field perpendicular to the nanowires) at 400 nm (TM mode is forbidden).


Meso-structures by holographic lithography

Holographic lithography combines the techniques of holography and laser-induced polymerization in which a photo-resist is exposed to the interference pattern formed by multiple coherent laser beams.  Regions with high intensity are polymerized, while under-exposed regions are washed away in a post-exposure process, leaving behind a 2D/3D polymerized structure.  This method is very flexible such that various structures, like SC, FCC and BCC, can be fabricated by controlling the beam configurations, intensities, and polarizations.  It can also be extended to aperiodic or quasi-periodic structures using five or more beam configurations.  Furthermore, chiral structures are also possible by using circularly polarized beams.

Continue reading Meso-structures by holographic lithography

Group velocity in strongly scattering media

A wave’s group velocity is one of its most important properties.  It characterizes the speed at which signals can be transmitted.  For waves traveling in a material medium, the group velocity is generally given by the differential slope of the dispersion relation (wave frequency versus wavevector).  However, for resonant or strongly scattering media, this formula breaks down.  In such media the prediction of group velocity thus became a classical problem in the study of waves.  In collaboration with experimentalists at the University of Manitoba and University of Pennsylvania, we have proposed a solution to this classical problem through the use of a “spectral function approach” [1].  In particular, the experimental results on the sonic group velocity, obtained by using the phase averaging method, exhibited very large and peculiar variations which break the theoretical bounds of the so-called effective medium theories, valid in the long wavelength regime.  With no adjustable parameters, the spectral function approach can quantitatively explain all the measured results.  The physical picture which emerges is that in strongly scattering media, wave multiple scattering can lead to a renormalization of the perceived medium property, which in turn can mean a “new” dispersion relation from which the group velocity should be calculated.


Key Publication:

  1.  “Group Velocity in Strongly Scattering Media”, J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. Jing, and D. A. Weitz, Science 271, 634 (1996).

Ultra sound tunneling

Tunneling is generally regarded as a quantum phenomenon.  For example, electrons can tunnel through a thin insulating barrier.  Electromagnetic waves can also tunnel through gaps.  In collaboration with University of Manitoba’s Prof.  John Page, we have demonstrated for the first time that sound waves can also exhibit tunneling [1,2].  This was done by first constructing a photonic crystal consisting of tungsten carbide spheres (0.8 mm in diameter) arranged in face-centered-cubic crystalline structure.  The whole structure was placed in water.  A photonic bandgap is predicted through first-principles calculation with the mid-gap frequency of ~0.8 megahertz.  Sound transmission along the [111] direction of the crystal was measured.  It was seen that the measured transit time of a sonic wavepacket, with its dominant frequency in the gap regime, can be even shorter than that predicted for tungsten carbide (of similar thickness) when the photonic crystal is more than 8 mm thick.  This can be explained by the fact that tunneling is essentially governed by the uncertainty principle, so the transit time across the barrier should be independent of its thickness (although the magnitude of the transmitted pulse packet decreases exponentially with thickness).  For thick barrier it means an extremely “fast” propagation.  This has indeed been confirmed experimentally.  However, there are intrinsic differences between electron tunneling and the tunneling of sound, which was also observed.



Key Publications:

  1. “Ultrasound Tunneling through 3D Phononic Crystals”, S. Yang, J. H. Page, Z. Y. Liu, M. L. Cowan, C. T. Chan and P. Sheng, Phys. Rev. Lett. 88, 104301 (2002).
  2. “The Sound of Silence”, Nature Physics Portal, March 4, 2002.