Left Handed Metamaterials and Negative Refraction

Srinivas Sridhar (Physics) and John Derov (Air Force Research Laboratories, Hanscom)

This project is supported by the Air Force Research Laboratories and the National Science Foundation.

For more details see http://sagar.physics.neu.edu.

Naturally available materials that are transparent to electromagnetic (EM) waves can be characterized by a positive refractive index . It was observed recently by David Smith and Sheldon Shultz at UC San Diego that in certain composite metamaterials EM waves bend negatively corresponding to a negative index of refraction . Negative index media exhibit some unusual propagation characteristics of EM waves. The most striking property is that of Left-Handed Electromagnetism (LHE), since the electromagnetic fields E, H, and the wave vector k, form a left-handed triplet set. Consequently the energy flow represented by the Poynting vector is anti-parallel to the wave vector. In contrast for conventional materials form a right-handed set corresponding to Right-Handed Electromagnetism (RHE).

We have fabricated NIM by interleaving arrays of split ring resonators and wire strips. Microwave measurements were carried out in 1-D X-band waveguide and 2-D waveguide setups. From the 1D waveguide results we have determined the crucial material parameters such as complex refractive index, permeability and permittivity ( and ) required to design materials and optimize characteristics for microwave applications. The determined from the waveguide transmission parameters is found to vary from -1.9 to -0.3 in the passband region 9.6 - 10.5GHz. The results show that transmission is optimized for and low . The results suggest that the characteristic properties of the NIM are dependent on the length of the material, choice of the substrate material, and continuity in the wire strips.

Since all physical radiation sources emit their radiation in the form of wave packets, we analyze refraction of electromagnetic wave packets on passing from an isotropic positive (PIM) to an isotropic negative index medium (NIM). We definitively show that in all cases the energy is always refracted negatively. For localized waves, the group refraction is always negative. We accomplish this by treating comprehensively group refraction at a PIM-NIM interface by analytical and numerical treatment of several exhaustive examples: localized wave packets, beams, and also a finite number of plane waves. We focus on physically important quantities such as the energy flow and momentum. In all of the cases we show that the energy and momentum refract negatively. We show that in all cases where the wave group does not extend to infinity in the perpendicular direction of the wave vector, the interference pattern also refracts negatively.

Microwave Photonic Crystals

The metamaterials (NIM) are highly absorptive, and unlikely to be scaled to three dimensions or to smaller sizes suitable for applications at optical frequencies. Our search for novel materials that possess left handed electromagnetism lead to the observation of negative refraction in a new class of materials -metallic photonic crystals. We have demonstrated negative refraction of microwaves in .metallic photonic crystals fabricated using cylindrical copper rods arranged on a periodic lattice. With parallel theory and numerical simulations we showed that the negative refraction observed corresponds to left-handed electromagnetism and arises due to the dispersion characteristics of waves in the periodic medium. The ease of fabrication, control of design parameters, scalability and very low attenuation in the metallic photonic crystal (100 times smaller than that in composite metamaterial ) pave the way for several interesting applications from microwave to optical frequencies. Our main contribution in the field of left handed electromagnetism is in proving its physical reality in both NIM and photonic crystals, a topic which has been recently controversial. The photonic crystal discussed here is a natural extension of the n-disk scatterer that we have been studying as a model system for Quantum Chaos.

Near and far field imaging by negative index and negative permittivity materials

We studied analytically and numerically imaging by Left-Handed Metamaterials. For the far field, the image is "perfect" only for . Away from this value, aberration and caustics will be present and were analyzed. For near field imaging with , the consequences of departure from dielectric matching and losses were analyzed. A paper on this topic has been submitted to the journal Microwave and Optics Technology.

Public recognition of our work

Our work on negative refraction has received considerable attention from the scientific community. Some of the popular venues that have highlighted our work include:

  1. Physics Today, May 2003
  2. AIP News, Number 628 #1, March 13, 2003
  3. Press conference at APS March Meeting, Austin, Texas, March 4, 2003
  4. New Scientist, v.177, p.24, 15 March, 2003

Papers published and submitted

  1. "Near field imaging by negative permittivity media", W.T. Lu and S. Sridhar, submitted to Microwave and Optical Technology (2003)
  2. "Negative index media in microwave waveguide", P. Parimi, P. Vodo, S. Sridhar, J.S. Derov, and B. Turchinetz, submitted to Applied Physics Letters (2003)
  3. "Refraction of electromagnetic energy for wave packets incident on a negative index medium is always negative", W.T. Lu, J. Sokoloff, and S. Sridhar, submitted to Physical Review

Papers in preparation:

  1. "Negative refraction and left-handed electromagnetism in microwave metallic photonic crystal", P. Parimi, W.T. Lu, P. Vodo, J. Sokoloff, and S. Sridhar
  2. "Explicit determination of material parameters of negative index metamaterials", P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, B. Turchinetz, and J. S. Derov
  3. "Far field imaging by negative index media", W.T. Lu and S. Sridhar
  4. "Band structure calculations and negative refraction in two-dimensional metallic photonic crystals", W.T. Lu and S. Sridhar

Invited and Contributed Talks

  1. "Quantum Chaos and Left-Handed Electromagnetism in Microwave Billiards", Colloquium, Univ. of New Mexico, April 18, 2003
  2. "Quantum Chaos and Left-Handed Electromagnetism in Microwave Billiards", Quantum Seminar, Los Alamos National Laboratories, April 17, 2003
  3. "Exploring semiclassics using microwaves", Workshop on "Semi-classical Methods in Physics and Chemistry", Mathematical Sciences Research Institute, Berkeley, April 7-11, 2003
  4. "Left-Handed Light", Northeastern University, Nov.7, 2002
  5. "Left-Handed Light", Raman Research Institute, August , 2002
  6. "Left-Handed Light", Indian Institute of Science, August, 2002

2003 American Physical Society March Meeting, March 3-7, 2003

  1. "Perfect lens" Imaging by Negative Index Media", W. T. Lu, J. B. Sokoloff, S. Sridhar [Session K22.003]
  2. "Refraction of Electromagnetic Energy for Wave Packets Incident on a Negative Index Medium: Always Negative", J. B. Sokoloff, W. T. Lu, S. Sridhar [Session K22.007]
  3. "Microwave Propagation in Negative Index and Artificial Dielectric Media", Patanjali Parimi, Plarenta Vodo, Wentao Lu, Srinivas Sridhar [Session K22.008]
  4. "Statistics of the Eigenfunctions of Chaotic and Disordered Quantum Systems: A Disordered Tight Binding Model Calculation", Prabhakar Pradhan, Wentao T. Lu, S. Sridhar [Session S17.005]
  5. "Spectral Statistics of Microwave Disordered Billiards", Daisuke Sato, Wentao Lu, Prabhakar Pradhan, Srinivas Sridhar [Session S17.006]

PIERS-Progress in Electromagnetics Research Symposium

  1. Pulse Propagation in Left-handed Metamaterials, Artan Kaso and Srinivas Sridhar, PIERS, July 1 - 5, 2002, Cambridge, MA