From: U-LEO-FUJITSU-XP\Leo Date: Mon, 13 Jul 2009 09:35:51 +0000 (-0400) Subject: Made 7 changes missed by ZJ and corrected one error he introduced :P X-Git-Url: http://www.dnquark.com/git/?a=commitdiff_plain;h=refs%2Fheads%2Fmaster;p=spie_book.git Made 7 changes missed by ZJ and corrected one error he introduced :P --- diff --git a/anisotropic_nim_subsects_5.tex b/anisotropic_nim_subsects_5.tex index 5499145..717d942 100755 --- a/anisotropic_nim_subsects_5.tex +++ b/anisotropic_nim_subsects_5.tex @@ -741,7 +741,7 @@ by essentially magnifying subwavelength structures. A {\em hyperlens} is a hollow core cylinder (or half cylinder), made of a strongly anisotropic material, that can function as a -far field subdiffraction +far-field subdiffraction lens.\cite{JacobAlekseyevNarimanov2006,EnghetaHyperlens2006,SmolyaninovHyperlens2007,ZhangHyperlens2007} To understand the origin of subwavelength resolution in the hyperlens, it is useful to consider the imaging problem in the @@ -788,9 +788,9 @@ Ref.~\inlinecite{JacobAlekseyevNarimanov2006}.] We may think of the scattered angular momentum modes as distinct information channels through which the information about the object at the origin is conveyed to the far-field. However, even -though the number of these channels is infinite ($m$ is unbounded -in Eq.~(\ref{eq:besselExpansion})), very little information -is carried over the high-$m$ channels. Fig.~\ref{fig:scattering}(b) shows the exact radial profile +though the number of these channels is infinite [$m$ is unbounded +in Eq.~(\ref{eq:besselExpansion})], very little information +is carried over the high-$m$ channels. Figure~\ref{fig:scattering}(b) shows the exact radial profile of the electric field for $m$=1 and $m$=14. For high values of $m$, the field exponentially decays toward the origin. This suggests that the interaction between a high-$m$ mode and an object placed at @@ -804,7 +804,7 @@ The high-$m$ modes are evanescent within a circle of critical radius called {\em the caustic}. This is because conservation of angular momentum implies that the tangential wave vector of a high-angular-momentum mode increases toward the center ($k_{\theta}r=m=\rm const$). In a medium such as vacuum characterized by a circular -isofrequency curve (see Fig. \ref{fig:dr}(a)), this increase in the tangential component is +isofrequency curve [see Fig. \ref{fig:dr}(a)], this increase in the tangential component is not supported, as both the tangential and radial wave vectors are bounded (see Eq.~(\ref{eq:diff_cutoff}) and related discussion). These incident high-angular-momentum modes simply reflect @@ -837,8 +837,8 @@ in a hollow core dielectric cylinder. It should be noted that the polar dielectric permittivities are -ill defined at the center and any practical realization of -cylindrical anisotropy using metamaterials, can only +ill defined at the center, and any practical realization of +cylindrical anisotropy using metamaterials can only closely approximate the desired dielectric permittivities away from the center (when $r \geq \lambda $). However, numerical simulations show that the effective medium description is adequate @@ -899,7 +899,7 @@ high-$m$ modes in regular dielectrics [see Fig. %\centerline{\scalebox{.85}{\includegraphics{wg_modes_1.pdf}}} \centerline{\scalebox{.43}{\includegraphics{eff_medium_modes.pdf}}} \caption{(a) High-angular-momentum states in an isotropic -dielectric cylinder. (b) high-angular-momentum states in a +dielectric cylinder. (b) High-angular-momentum states in a cylinder made of $ \epsilon_{\theta}>0$, $\epsilon_{r}<0$ metamaterial (in the effective medium approximation); note that the field penetrates to the center. [From @@ -1102,7 +1102,7 @@ specular reflection at the inner core. (c) Absolute value of the field for a Gaussian beam scattering from the layered hyperlens with parameters $rho \approx 4\lambda$, $r_{\rm min} \approx \lambda$, $r_{\rm max} \approx 7 \lambda$, $h \approx \lambda/100$, -$\epsilon_{m} \approx -0.4$, $\epsilon_{d} \approx 2.4$. The ray +$\epsilon_{m} \approx -0.4$, and $\epsilon_{d} \approx 2.4$. The ray trajectory shown in white is calculated using Eq.~(\ref{semiclassical_eq}) and specular reflection at the inner boundary. Note the narrowing of the Gaussian beam and also the motion of the center of the beam along the calculated ray trajectory. @@ -1161,7 +1161,7 @@ within the hyperlens. The rays of light are negatively refracted at the inner curved surface of the hyperlens, which helps in the formation of a beam. Inside the hyperlens, the rays then move in straight lines, almost radially, traveling to the outer interface. -These rays arrive at normal incidence and the beam-like nature in +These rays arrive at normal incidence, and the beam-like nature in the hyperlens is preserved as they emerge into vacuum. Thus, the two point sources give rise to two distinct beams in the far-field, even though they are separated by less than the diffraction limit inside