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 (executable)
--- 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
 
 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
 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
 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
 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
 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
 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
 
 
 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
 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
 %\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
 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 $rho \approx 4\lambda$, $r_{\rm min}
 \approx \lambda$, $r_{\rm max} \approx 7 \lambda$, $h \approx \lambda/100$,
 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.
 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.
 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
 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