From ed7e567d330eabac5f7681b5deb396a56d57c899 Mon Sep 17 00:00:00 2001 From: "U-LEO-FUJITSU-XP\\Leo" Date: Wed, 24 Jun 2009 21:00:29 -0400 Subject: [PATCH] Semiclassical gaussian image had (abc) labels made larger to correlate with the previous (spiral) figure; figures were moved around a bit; hl imaging figure got move to top of page --- anisotropic_nim_subsects_5.tex | 50 +++++++++++++++++++++------------------- semiclass_gaussian.pdf | Bin 685641 -> 201151 bytes 2 files changed, 26 insertions(+), 24 deletions(-) diff --git a/anisotropic_nim_subsects_5.tex b/anisotropic_nim_subsects_5.tex index 611e067..903dde2 100755 --- a/anisotropic_nim_subsects_5.tex +++ b/anisotropic_nim_subsects_5.tex @@ -832,6 +832,18 @@ used for dielectric permittivities. A low-loss cylindrically anisotropic material can also be achieved by metallic inclusions 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, such as metamaterial structures, 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 +and that the hyperlens functions even in the case where the inner radius is no greater than a wavelength.\cite{JacobAlekseyevNarimanov2006} The +hyperlens functions in the channeling regime where a smaller inner +radius aids in higher resolution. + + \begin{figure}[t] \centering \scalebox{0.34}{\includegraphics{fig2_metacylinder.pdf}}\\ @@ -848,18 +860,6 @@ Ref.~\inlinecite{JacobAlekseyevNarimanov2006}.]} -It should be noted that the polar dielectric permittivities are -ill defined at the center and any practical realization of -cylindrical anisotropy, such as metamaterial structures, 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 -and that the hyperlens functions even in the case where the inner radius is no greater than a wavelength.\cite{JacobAlekseyevNarimanov2006} The -hyperlens functions in the channeling regime where a smaller inner -radius aids in higher resolution. - - - As before, we focus on extraordinary waves (TM modes, with the magnetic field along the axis of the cylinder). @@ -967,7 +967,7 @@ image (e.g., further magnification) by conventional optics. -\begin{figure} +\begin{figure}[t] \centerline{\scalebox{0.45}{\includegraphics{image_resolution_b.pdf}}} \caption{(a) Schematics of imaging by the hyperlens. Two point sources separated by $\lambda/4.5$ are placed within the hollow core @@ -987,17 +987,6 @@ Ref.~\inlinecite{JacobAlekseyevNarimanov2006}.]} \subsubsection{Semiclassical treatment} -\begin{figure}[tb] -\centering \scalebox{0.54}{\includegraphics{fig1_spiral_2.pdf}} -\caption{Trajectories of two rays incident on the hyperlens with -different impact parameters, calculated using the analytical -expression in Eqs.~(\ref{semiclassical_eq}--\ref{semiclassical_eq_theta0}). (a) $\eta$ = 0.1. (b) $\eta$ =0.5. Note the strong -spiraling behavior. (c) ``Channeling regime'' for large $\eta$ ($\eta$ =100), -where rays travel in straight lines radially. Note that all rays -travel towards the center. [From -Ref.~\inlinecite{JacobNarimanov2007}.]} \label{spiral} -\end{figure} - The above results were obtained by numerically propagating fields through the cylindrical layered structure. There exists, however, an analytic approach to analyzing light propagation in the @@ -1082,6 +1071,19 @@ choose an inner radius of $\lambda$, outer radius $7\lambda$, thickness of layers $\lambda/100$, $N=600$ layers, and impact parameter $\rho=2.4\lambda$ at an operating wavelength of 700~nm. + +\begin{figure}[tb] +\centering \scalebox{0.54}{\includegraphics{fig1_spiral_2.pdf}} +\caption{Trajectories of two rays incident on the hyperlens with +different impact parameters, calculated using the analytical +expression in Eqs.~(\ref{semiclassical_eq}--\ref{semiclassical_eq_theta0}). (a) $\eta$ = 0.1. (b) $\eta$ =0.5. Note the strong +spiraling behavior. (c) ``Channeling regime'' for large $\eta$ ($\eta$ =100), +where rays travel in straight lines radially. Note that all rays +travel towards the center. [From +Ref.~\inlinecite{JacobNarimanov2007}.]} \label{spiral} +\end{figure} + + \begin{figure}[t] \centering \scalebox{0.4}{\includegraphics{semiclass_gaussian.pdf}} diff --git a/semiclass_gaussian.pdf b/semiclass_gaussian.pdf index 629f918053d721b548fbcac6cdcb8aee1b2699a2..4508fdf9bb1035cc7b310fa12277b85db96304fa 100755 GIT binary patch delta 160177 zcmb@t1ymf*wl6#(NFWfBV8I=NGq?l@A-D|gu0aL}?j0aNf;$0%1s~kqf(8i*E`w!o zcV~F>|DSulbKkl5t@o|_eLcNa)$Fd`yXsfFc6aT)`^PRzM=owGD?1N27|ajmg3t(X zNz;IZgt&!;xm0MtT$(hfE8IN%Tyiu9H2lH>G+=(AIBn(!{BZ%4fFM5~4fkIMjUyh; z-xY3dAu#WMp$QA||2qu~<`epN8V{I9;J?s#1bF^;8kkp@n_u`Z8t^Z{C~iD_|K5;a zkdNoz1cLCSK!|SqiFm>|CJ^v#QmQ-1OCU5|3c;O+FvNRxtQ5HSh?Wg zyn4l@Ve4Z>0~Y2|b+PjJ8%A(K^aF}FV17Y<9$_9yK^|dlDJeei8$L;)H$0L&GH-;1 z1*E0H;;;DLNXhU^@k&X*k&zbW=i`4PBP8^OTSiz?QbvgPjr5y@-3J^5s8P^3ncJb{ zC|Nn$xV@th;!dbSC$x~K5e9Q<(C`Y0i@UnHSeZfbaJ=TsO-+~0Oij0KK+hWr!P#gs zG}dOz@7}$BjtDfz41I!0i>ZRyhu2Dmi(8hjQh?D09$cXt#4CM*%k`o@IEkB=`@|%S z%jx52xTisuoZ@lqhbRw@#=Q 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