[Paper Review] Evanescent waves in photonic crystals and image of Veselago lens

Alexander L. Efros, C. Y. Li+1 more|arXiv (Cornell University)|Mar 19, 2005

Photonic Crystals and Applications2 references3 citations

TL;DR

This paper demonstrates that evanescent waves in photonic crystals (PCs) with left-handed properties near the Γ-point do not experience amplification, despite negative permittivity and permeability for propagating modes. Instead, evanescent waves decay within the crystal, and only surface modes can amplify them; thus, superlensing arises only in thin lenses with specific boundary conditions, not from left-handed material properties per se.

ABSTRACT

It is shown that negative electric permittivity and magnetic permeability recently discovered in a photonic crystal in the vicinity of the Gamma-point are properties of propagating modes only. The evanescent modes rather decay than increase in the bulk of the crystal though they may be amplified by surface waves. If surface support such waves, the evanescent waves may improve the image of a thin Veselago lens. It is shown that a ``perfect lens'' contradicts to the wave optics and a criterion of ``superlensing'' is formulated.

Motivation & Objective

• To investigate whether evanescent waves (EWs) in a photonic crystal (PC) with negative ε and μ are amplified, as claimed by Pendry's perfect lens theory.
• To clarify the distinction between propagating modes and evanescent modes in PCs with spatial dispersion and their electromagnetic response.
• To assess whether the Veselago lens in a real PC can achieve superlensing via evanescent wave amplification.
• To establish a criterion for superlensing independent of macroscopic electrodynamics and wave optics principles.
• To resolve the contradiction between Pendry's claim of perfect imaging and the divergence problem in the Ziolkowski and Heyman solution.

Proposed method

• Numerical solution of microscopic Maxwell’s equations for a 2D dielectric uniaxial PC to obtain Bloch functions and dispersion relations near the Γ-point.
• Calculation of effective ε and μ from the spatial average of the Bloch functions at k=0, showing negative values only for propagating modes.
• Use of the Fresnel equation and Green’s function decomposition into propagating (Hp) and evanescent (Hev) wave components to analyze field propagation.
• Analytical and computational modeling of the magnetic energy distribution near the focus for both thick and thin PC slabs.
• Comparison of the lateral and perpendicular intensity profiles to assess imaging quality and identify deviations from ideal diffraction-limited focusing.
• Application of the Bessel function J₀ as a model source field to test lateral imaging fidelity under finite slab conditions.

Experimental results

Research questions

• RQ1 Do evanescent waves in a real photonic crystal with negative ε and μ experience amplification, as predicted by Pendry’s perfect lens model?
• RQ2 Can the Veselago lens in a photonic crystal achieve superlensing through evanescent wave amplification, or is this effect an artifact of idealized models?
• RQ3 What is the role of boundary conditions and slab thickness in enabling enhanced imaging (superlensing) in thin PC-based Veselago lenses?
• RQ4 How does the presence of spatial dispersion in the PC affect the validity of macroscopic electrodynamics and the definition of ε and μ?
• RQ5 Does the perfect imaging of a point source contradict fundamental principles of wave optics, regardless of the lens material?

Key findings

• Evanescent waves in the photonic crystal decay in the bulk, despite negative ε and μ for propagating modes, contradicting Pendry’s claim of amplification.
• Only surface waves can amplify evanescent waves, and this effect is significant only in thin lenses with specific termination (e.g., BH surface).
• The thick Veselago lens produces a diffraction-limited focus described by Hₚ, with a Bessel-like lateral profile J₀(y'k₀), consistent with regular lensing, not superlensing.
• The thin lens with a BH surface shows a sharper focus than predicted by Hₚ alone, indicating superlensing due to evanescent wave amplification.
• The observed superlensing is not due to left-handed material properties but to boundary effects and surface wave coupling.
• A criterion for superlensing is established: it requires amplification of evanescent waves, which only occurs under specific geometric and boundary conditions, not in thick slabs or idealized models.