超级军网隐身！经查系纯理论突破。
来源：百度文库 编辑：超级军网 时间：2024/04/25 04:08:11
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物理评论快报
确实是很NB的杂志。
确实是很NB的杂志。
粗看了一下，大概是在相对介电常数和磁导常数合适时，对于一个空心圆柱体电磁波逆向散射趋于零，纯理论讨论，没有实验，更别提应用了。
ms最近物理学界对隐身很感兴趣阿，去年还有一个被评为nature年度十大的，用等离激元的，个人认为那个技术含量更高，应用前竟更广（不仅仅在隐身方面）
ms最近物理学界对隐身很感兴趣阿，去年还有一个被评为nature年度十大的，用等离激元的，个人认为那个技术含量更高，应用前竟更广（不仅仅在隐身方面）
我也不是学物理的，不过查了一下，这杂志很牛。不过没有给出文章名字不好查询，所以无缘拜读了。
Therefore, the imperfect cloak, even with its parameters deviated far from the ideal parameters, still can be made completely invisible with the monostatic detection as long as it satisfied the impedance requirement.”
Since almost all current radars belong to the monostatic class, Chen explained that this research can offer a more realistic alternative for engineers. In the future, applications of invisible cloaks could include military uses such as making planes and weapons invisible to radar, enabling the possibility of looking out walls as if they were windows, and hiding ugly factories for aesthetic reasons.
Since almost all current radars belong to the monostatic class, Chen explained that this research can offer a more realistic alternative for engineers. In the future, applications of invisible cloaks could include military uses such as making planes and weapons invisible to radar, enabling the possibility of looking out walls as if they were windows, and hiding ugly factories for aesthetic reasons.
原帖由 railgun 于 2007-10-20 20:24 发表
粗看了一下，大概是在相对介电常数和磁导常数合适时，对于一个空心圆柱体电磁波逆向散射趋于零，纯理论讨论，没有实验，更别提应用了。
ms最近物理学界对隐身很感兴趣阿，去年还有一个被评为nature年度十大的，用 ...
不是纯理论探讨。是基于一种新材料展开的有实用性的前瞻研究。这是浙大和麻省理工一起研究的一个课题。目前已经做成功了微波波段的二维隐身实验。
而且文章的确发表在全球顶尖的物理学杂志上。真实性已经不用怀疑了。对文章有兴趣而且可以免费进数据库的同学自己去查看吧。关键词在下面
Electromagnetic Wave Interactions with a Metamaterial Cloak
Hongsheng Chen, Bae-Ian Wu, Baile Zhang, and Jin Au Kong
Phys. Rev. Lett. 99, 063903 (2007)
Cited 1 times
查到这个文章了，的确是浙大的Hongshen Chen。这个杂志这么牛，7点几，比我发的高一倍，大概真的是牛人了……
这材料出来了么，只有数值计算阿，实验发了么
原帖由 红水兵 于 2007-10-20 20:56 发表
不是纯理论探讨。是基于一种新材料展开的有实用性的前瞻研究。这是浙大和麻省理工一起研究的一个课题。目前已经做成功了微波波段的二维隐身实验。
而且文章的确发表在全球顶尖的物理学杂志上。真实性已经不用怀疑 ...
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这文章发一篇，1万的奖学金就到手了，能发prl做梦都笑醒了
原帖由 逍遥 于 2007-10-20 21:00 发表
查到这个文章了，的确是浙大的Hongshen Chen。这个杂志这么牛，7点几，比我发的高一倍，大概真的是牛人了……
原帖由 railgun 于 2007-10-20 21:10 发表
这文章发一篇，1万的奖学金就到手了，能发prl做梦都笑醒了
偶们这里很久以前1万就取消了，一般的SCI太多了。他那个东西评价很高，不在乎1万了。
前几年的电视里播了一条消息，日本人开发了一种隐身衣，能够通过磁场的折射还是什么原理使人体透明化。不过因为是实验产品，效率还很低下，不知道现在到什么水平了？
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哪个是要钱的，一篇文章20刀，那个文章在这有个连接
http://lilybbs.net/file/D_Physics/PhysRevLett_99_063903.pdf
俺也不是干这个方向的
http://lilybbs.net/file/D_Physics/PhysRevLett_99_063903.pdf
俺也不是干这个方向的
原帖由 逍遥 于 2007-10-20 21:10 发表
我查到这个文章，但下不来，那个PRL的网站不知道怎么回事情。不过科学发现有什么不代表马上可以应用，本菜做的东西自己都觉得屁用没有。
另外，我觉得楼主可以修改帖子名字了，呵呵。这不是一般的小杂志，虽然不一 ...
原帖由 balzac 于 2007-10-20 21:14 发表
前几年的电视里播了一条消息，日本人开发了一种隐身衣，能够通过磁场的折射还是什么原理使人体透明化。不过因为是实验产品，效率还很低下，不知道现在到什么水平了？
那种隐身衣是给卡通迷们cosplay用的。只能在一个特定方向上通过投影仪实现隐身效果。基本原理类似，你站在投影仪的画面里时，观众可以忽略你而关注投影仪的画面。技术含量很低，基本没有军事应用价值。
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prl才1万，prb才800
原帖由 逍遥 于 2007-10-20 21:13 发表
偶们这里很久以前1万就取消了，一般的SCI太多了。他那个东西评价很高，不在乎1万了。
那个（文章下载）是要钱的，一篇文章20美元。
aps的文章是要收费滴
除非学校买了数据库
除非学校买了数据库
原帖由 逍遥 于 2007-10-20 21:23 发表
这些字没看明白
原帖由 balzac 于 2007-10-20 21:14 发表
前几年的电视里播了一条消息，日本人开发了一种隐身衣，能够通过磁场的折射还是什么原理使人体透明化。不过因为是实验产品，效率还很低下，不知道现在到什么水平了？
衣服透明化的设备早就有了:D ~
隐身目前主要是靠外形，这个绕射有点玄……;funk
所以才那摸NB
原帖由 红水兵 于 2007-10-20 21:26 发表
那个（文章下载）是要钱的，一篇文章20美元。
哦，也不显示要钱就一空白半死机状态，不厚道。偶一般都只进免费全文网站，要不发邮件给图书馆去馆际互借……
去就去lilybbs.net 物理系版看吧，超大不支持pdf
原帖由 逍遥 于 2007-10-20 21:23 发表
这些字没看明白
另外您给的链接我进去还是一片空白，麻烦您发我邮箱好不好？
原帖由 railgun 于 2007-10-20 21:29 发表
去就去lilybbs.net 物理系版看吧，超大不支持pdf
我的邮箱关超大什么事情啊？您手上有现成的吗？
地址
原帖由 逍遥 于 2007-10-20 21:31 发表
我的邮箱关超大什么事情啊？您手上有现成的吗？
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week ending
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
Electromagnetic WaveInteractionswithaMetamaterial Cloak
1,2, 2 2 1,2
Hongsheng Chen, * Bae-Ian Wu, Baile Zhang, and Jin Au Kong
1
The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310058, China
2
Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
(Received 19 January 2007; published 6 August 2007)
We establish analytically the interactions of electromagnetic wave with a general class of spherical
cloaksbasedonafullwaveMiescatteringmodel.Weshowthatforanidealcloakthetotalscatteringcross
section is absolutely zero, but for a cloak with a specific type of loss, only the backscattering is exactly
zero, which indicates the cloak can still be rendered invisible with a monostatic (transmitter and receiver
in the same location) detection. Furthermore, we show that for a cloak with imperfect parameters the
bistatic (transmitter and receiver in different locations) scattering performance is more sensitive tot
p pt=t than nttt.
DOI: 10.1103/PhysRevLett.99.063903 PACS numbers: 42.25.Fx, 41.20.Jb
Recently, invisibility cloaking has received much atten- lossofgenerality,weassumetheinnersphere(r<R1)has
tion [1–11]. The design process for the cloak is mostly a permittivity of1 and permeability of1. The cloak
based on a coordinate transformation [4]. An optical con- (R1 <r<R2) is a kind of rotationally uniaxial media
formal mapping method has also been used for the design characterized by
of a medium that creates perfect invisibility in the ray
tracing limit [6]. The design approach in Ref. [4] startedrrtr^r^tIrrtr^r^tI;
from Maxwell’s equations, which indicated such cloaking (1)
should be effective at all frequencies. Cummeret al. dem-
onstratedthefullwavecylindricalcloakingbutwithpurely where I r^r^^^^^ ,t andt are the permittivity
numerical calculations that donot provide asmuch insight and permeability along the^ and^ direction,rr and
into the physicsas ananalytical approach [2].The analyti-rr are the permittivity and permeability along the r^
cal demonstrations reported so far are mostly in the geo- direction, and both of them are functions of r
metricalopticslimitorintheelectrostaticormagnetostatic expressions for the wave propagation inside the cloak are
limit [4–6]. Since both of the two limiting cases include firststudied.Forsourcefreecases,wedecomposethefields
approximationsinMaxwell’stheory,itisverynecessaryto into TE and TM modes (with respect to r^) by introducing
demonstrate analytically whether perfect invisibility, the scalar potentials,TM andTE:
which can be characterized by a zero cross section, is
achievable under any wavelength condition. Furthermore, BTM 5r^TM;
none of the methods reported in [4–6] provides analytical
11
solutions on how sensitive the nonideal cloaks are to the DTM f5 5r^TMg;i!
materialperturbationsaswellashowgoodthecloaksarein (2)
11
terms of bistatic scattering. BTE f5 5r^TEg;i!
In this Letter, the interactions of electromagnetic wave
with the cloaks are analytically established based on a full DTE 5r^TE:
wave Mie scattering model [12–14]. Since the cloak is
Using Eqs. (1) and (2) and after some algebraic manipula-
both anisotropic and inhomogeneous [4], the Mie scatter-
tions,wecan obtain thewave equations for and :
ing theory isextended tobeapplicable tothis special case, TM TE
and then the analytical expressions of the electromagnetic
fieldinthewholespacearerigorouslycalculated.Weshow
that for an ideal cloak with the parameters specified in
Ref. [4], the total scattering cross section is absolutely
zero. Furthermore, the performance and sensitivity of the
cloak with nonideal parameters are quantitatively calcu-
lated and the physics behind the phenomenon are
interpreted.
Figure1showsthatanEx polarizedplanewavewithunit
ik0z
amplitude, Ei xe^ , is incident upon the coated sphere
p
alongthez^direction.k0 !00 isthewavenumberin FIG. 1. Configuration of scattering of plane wave by a spherei!t
air. The time dependence of e is suppressed. Without coated with a cloak.
0031-9007=07=99(6)=063903(4) 063903-1 (C) 2007 The American Physical Society
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
Electromagnetic WaveInteractionswithaMetamaterial Cloak
1,2, 2 2 1,2
Hongsheng Chen, * Bae-Ian Wu, Baile Zhang, and Jin Au Kong
1
The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310058, China
2
Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
(Received 19 January 2007; published 6 August 2007)
We establish analytically the interactions of electromagnetic wave with a general class of spherical
cloaksbasedonafullwaveMiescatteringmodel.Weshowthatforanidealcloakthetotalscatteringcross
section is absolutely zero, but for a cloak with a specific type of loss, only the backscattering is exactly
zero, which indicates the cloak can still be rendered invisible with a monostatic (transmitter and receiver
in the same location) detection. Furthermore, we show that for a cloak with imperfect parameters the
bistatic (transmitter and receiver in different locations) scattering performance is more sensitive tot
p pt=t than nttt.
DOI: 10.1103/PhysRevLett.99.063903 PACS numbers: 42.25.Fx, 41.20.Jb
Recently, invisibility cloaking has received much atten- lossofgenerality,weassumetheinnersphere(r<R1)has
tion [1–11]. The design process for the cloak is mostly a permittivity of1 and permeability of1. The cloak
based on a coordinate transformation [4]. An optical con- (R1 <r<R2) is a kind of rotationally uniaxial media
formal mapping method has also been used for the design characterized by
of a medium that creates perfect invisibility in the ray
tracing limit [6]. The design approach in Ref. [4] startedrrtr^r^tIrrtr^r^tI;
from Maxwell’s equations, which indicated such cloaking (1)
should be effective at all frequencies. Cummeret al. dem-
onstratedthefullwavecylindricalcloakingbutwithpurely where I r^r^^^^^ ,t andt are the permittivity
numerical calculations that donot provide asmuch insight and permeability along the^ and^ direction,rr and
into the physicsas ananalytical approach [2].The analyti-rr are the permittivity and permeability along the r^
cal demonstrations reported so far are mostly in the geo- direction, and both of them are functions of r
metricalopticslimitorintheelectrostaticormagnetostatic expressions for the wave propagation inside the cloak are
limit [4–6]. Since both of the two limiting cases include firststudied.Forsourcefreecases,wedecomposethefields
approximationsinMaxwell’stheory,itisverynecessaryto into TE and TM modes (with respect to r^) by introducing
demonstrate analytically whether perfect invisibility, the scalar potentials,TM andTE:
which can be characterized by a zero cross section, is
achievable under any wavelength condition. Furthermore, BTM 5r^TM;
none of the methods reported in [4–6] provides analytical
11
solutions on how sensitive the nonideal cloaks are to the DTM f5 5r^TMg;i!
materialperturbationsaswellashowgoodthecloaksarein (2)
11
terms of bistatic scattering. BTE f5 5r^TEg;i!
In this Letter, the interactions of electromagnetic wave
with the cloaks are analytically established based on a full DTE 5r^TE:
wave Mie scattering model [12–14]. Since the cloak is
Using Eqs. (1) and (2) and after some algebraic manipula-
both anisotropic and inhomogeneous [4], the Mie scatter-
tions,wecan obtain thewave equations for and :
ing theory isextended tobeapplicable tothis special case, TM TE
and then the analytical expressions of the electromagnetic
fieldinthewholespacearerigorouslycalculated.Weshow
that for an ideal cloak with the parameters specified in
Ref. [4], the total scattering cross section is absolutely
zero. Furthermore, the performance and sensitivity of the
cloak with nonideal parameters are quantitatively calcu-
lated and the physics behind the phenomenon are
interpreted.
Figure1showsthatanEx polarizedplanewavewithunit
ik0z
amplitude, Ei xe^ , is incident upon the coated sphere
p
alongthez^direction.k0 !00 isthewavenumberin FIG. 1. Configuration of scattering of plane wave by a spherei!t
air. The time dependence of e is suppressed. Without coated with a cloak.
0031-9007=07=99(6)=063903(4) 063903-1 (C) 2007 The American Physical Society
week ending
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
1 @2 1 @ @ 1 @2 cosX
cM sinTM fdn nktrR1
2 2 2 2 2SR @r r sin @ @ r sin @ ! n
1M 1
2fnkrRgPcos; kt 0; (3) n t 1 nSR (9)
sinX
cN fdn krR
TE n t 1
p
!0
where kt !tt; (SR) denotes the anisotropic ratio of nN
the cloak, for TM wave,SRt=r, and for TE wave,fng 1
n kt r R1 Pn cos ;SRt=r. Using the separation of variables methodni2n1 p
and assuming frgh, we get h as har- where an nn1 , n 1;2;3;...,00=0,im
monic functions: h e , g as associated pMNMNMN
k ! . Tn , Tn , dn , dn , fn , and fn are
m 1 1 1
Legendre polynomials: g Pncos, and fr as the
unknown expansion coefficients. n,n andn
solution of the following equation:
represent the Riccati-Bessel functions of the first, the@2 nn1 second, and the third kind, respectively [15]. Using
2
ktSR fr 0: (4) Eq. (2), the electromagnetic fields in the three regions
2 2
@r r
can be expanded in terms of the corresponding scalar
potentials [16]. By applying the boundary conditions at
R2
If we take the parameters suggested in [4]:t0 R , the surface, we can get four equations at r R and four
2 R1 1
2 2rR1 R2rR1rt 2 ,t0 , andrt 2 , then equations at r R2. Note that there are two equations at
r R2R1 r
2
r r R1 given by:
for both TE and TM modes, we getSR 2 .rR1tNNN
Therefore, the solution of Eq. (4)is
cn nk1R1 dn n0fnn0 (10)1
fr ktrR1bnktrR1; (5)tMMM
cn nk1R1 dn n0fnn0: (11)1
where bn is the spherical Bessel function. From the above
analysis, we see that the solutions of Eq. (3) in the cloak We see n0 0 andn0 is an infinite term for all
layer are composed of a superposition of Bessel functions, n 1.Sincethefieldinthehiddensphereshouldbefinite,
associatedLegendrepolynomials,andharmonicfunctions. N M
fn and fn must be kept zero. We see the field in the
Inordertomatchtheboundaryconditionsonthespheri-
hidden object is decoupled with those in the other regions.
cal surface, the incident fields are expanded in terms of
From the other four equations at the boundary of r R2,
spherical harmonics. With the solutions of Eq. (3) for the
we can calculate the following coefficients:
cloak layer, we can get the scalar potentials, respectively,
0 0
=
for the incident fields (r>R2), the scattered fields (r>M n 0 n t t 0 n 0 n t
Tn (12)
0 0
R2), the internal fields (r<R1), and the fields of the cloakn0 ntt=0n0 nt
layer (R1 <r<R2), to be of the form:
0 0
= N n 0 n t t 0 n 0 n t
Tn (13)
cosX 0 0
i 1n0 ntt=0n0 nt a k rPcos;
TM n n 0 n
!
n
(6) i =
sinXM t 0
i 1
dn a (14) a k rPcos; n 0 0
TE n n 0 n =
!0 n n 0 n t t 0 n 0 n t
i =N t 0
dn an 0 0 ; (15)
=
cosX n 0 n t 0 t n 0 n t
sM 1 a Tnk rPcos;
TM n n 0 n
! p
n where0 k0R2,t ktR2R1, andtt=t.If
R2 R2
sinX (7)t ,t , thent ,t .
sN 1 0 R2R1 0 R2R1 0 0 a Tnk rPcos;
TE n n 0 n
!0 n Using the Wronskians for the spherical pairs of solutions,
the above four equations are simplified to be:MNM tN t
Tn Tn 0;dn an;dn an:
cosX
intM 100 cn k rPcos;
TM n 1 n
!
n (16)
(8)
sinX
intN 1 It is very interesting to see that the scattering coefficients, cn k rPcos;
TE n 1 n
!0 n TMN
n andTn ,areequaltozero.Theexactlyzeroscattered
063903-2
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
1 @2 1 @ @ 1 @2 cosX
cM sinTM fdn nktrR1
2 2 2 2 2SR @r r sin @ @ r sin @ ! n
1M 1
2fnkrRgPcos; kt 0; (3) n t 1 nSR (9)
sinX
cN fdn krR
TE n t 1
p
!0
where kt !tt; (SR) denotes the anisotropic ratio of nN
the cloak, for TM wave,SRt=r, and for TE wave,fng 1
n kt r R1 Pn cos ;SRt=r. Using the separation of variables methodni2n1 p
and assuming frgh, we get h as har- where an nn1 , n 1;2;3;...,00=0,im
monic functions: h e , g as associated pMNMNMN
k ! . Tn , Tn , dn , dn , fn , and fn are
m 1 1 1
Legendre polynomials: g Pncos, and fr as the
unknown expansion coefficients. n,n andn
solution of the following equation:
represent the Riccati-Bessel functions of the first, the@2 nn1 second, and the third kind, respectively [15]. Using
2
ktSR fr 0: (4) Eq. (2), the electromagnetic fields in the three regions
2 2
@r r
can be expanded in terms of the corresponding scalar
potentials [16]. By applying the boundary conditions at
R2
If we take the parameters suggested in [4]:t0 R , the surface, we can get four equations at r R and four
2 R1 1
2 2rR1 R2rR1rt 2 ,t0 , andrt 2 , then equations at r R2. Note that there are two equations at
r R2R1 r
2
r r R1 given by:
for both TE and TM modes, we getSR 2 .rR1tNNN
Therefore, the solution of Eq. (4)is
cn nk1R1 dn n0fnn0 (10)1
fr ktrR1bnktrR1; (5)tMMM
cn nk1R1 dn n0fnn0: (11)1
where bn is the spherical Bessel function. From the above
analysis, we see that the solutions of Eq. (3) in the cloak We see n0 0 andn0 is an infinite term for all
layer are composed of a superposition of Bessel functions, n 1.Sincethefieldinthehiddensphereshouldbefinite,
associatedLegendrepolynomials,andharmonicfunctions. N M
fn and fn must be kept zero. We see the field in the
Inordertomatchtheboundaryconditionsonthespheri-
hidden object is decoupled with those in the other regions.
cal surface, the incident fields are expanded in terms of
From the other four equations at the boundary of r R2,
spherical harmonics. With the solutions of Eq. (3) for the
we can calculate the following coefficients:
cloak layer, we can get the scalar potentials, respectively,
0 0
=
for the incident fields (r>R2), the scattered fields (r>M n 0 n t t 0 n 0 n t
Tn (12)
0 0
R2), the internal fields (r<R1), and the fields of the cloakn0 ntt=0n0 nt
layer (R1 <r<R2), to be of the form:
0 0
= N n 0 n t t 0 n 0 n t
Tn (13)
cosX 0 0
i 1n0 ntt=0n0 nt a k rPcos;
TM n n 0 n
!
n
(6) i =
sinXM t 0
i 1
dn a (14) a k rPcos; n 0 0
TE n n 0 n =
!0 n n 0 n t t 0 n 0 n t
i =N t 0
dn an 0 0 ; (15)
=
cosX n 0 n t 0 t n 0 n t
sM 1 a Tnk rPcos;
TM n n 0 n
! p
n where0 k0R2,t ktR2R1, andtt=t.If
R2 R2
sinX (7)t ,t , thent ,t .
sN 1 0 R2R1 0 R2R1 0 0 a Tnk rPcos;
TE n n 0 n
!0 n Using the Wronskians for the spherical pairs of solutions,
the above four equations are simplified to be:MNM tN t
Tn Tn 0;dn an;dn an:
cosX
intM 100 cn k rPcos;
TM n 1 n
!
n (16)
(8)
sinX
intN 1 It is very interesting to see that the scattering coefficients, cn k rPcos;
TE n 1 n
!0 n TMN
n andTn ,areequaltozero.Theexactlyzeroscattered
063903-2
week ending
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
0
10 tan( )=0.01
1.5 δ
1
tan(δ)=0.1
1
tan(δ)=1
0.5
-5
z 0 0 10
-0.5
-1
-1 -10
10
-1.5
z
-1 0 1
x x
-15
FIG. 2 (color online). Ex field distribution and Poynting vec- 10
0 30 60 90 120 150 180
tors due to an Ex polarized plane wave incidence onto an ideal
Scattering angle (degree)
cloak with R1 0:50 and R20.
FIG. 3 (color online). Normalized differential cross sections
field indicates the reflectionless behavior of the perfect for a cloak (R1 0:50, R20) with a specified loss tangent
cloak [4]. It should be noted that our mathematical dem- introduced in each component of the permittivity and perme-
onstration is applicable to any wavelength condition. ability. The inset shows the Ex field for the case of tan 0:1.
Figure 2 shows the calculated electric fields and the
Poynting vectors due to an Ex polarized plane wave inci-MN
Tn Tn , andnnj180], which is very
dence onto a cloak with R1 0:50 and R20 (0
different from conventional scattering from regular parti-
denotes the wavelength in free space). We see that the
cles [12]. The calculated field distribution in the xz plane
hidden object is completely hide from the waves, corrob-
for the spherical cloak with tan 0:1 (Fig. 3, inset) is
orating the effectiveness of the cloak proposed in [4].
similar to the simulation results of a cylindrical cloak with
There is no on-axis ray problem [4] here since the
the same type of loss [2]. However, our analytical calcu-
Poynting power becomes zero as the field penetrate deep
lation showsthat only the spherical cloak in this particular
into the cloak [2].
lossy case exhibits exactly zero backscattering. This
The most interesting thing is that Eqs. (12)–(15)give
unique property of the spherical cloak indicates the
further information. For example, it is known that loss is
cloaked object can stillcompletely hide from amonostatic
often an important issue. When the electric and magnetic
loss tangents are introduced, the scattering coefficients radar detection.MN Since the constitutive parameters for a perfect cloak are
Tn and Tn become nonzero. In Fig. 3, we plot the
very difficult to realize, nonideal material parameters are
bistatic scattering as a function of the scattering angle
more often used in the measurements [1,2]. Hence, it is
for the loss tangent of 0.01, 0.1, and 1, respectively. The
worthwhiletostudyhowtheimperfectmaterialparameters
vertical axis represents the normalized differential cross
2 2
jS1j jS2j quantitatively affect the performance of the cloak. We
sections, 2 2 , 2 2 , where S1 and S2 are defined
k R k R
0 2 0 2
calculate the normalized scattering cross section Qsca
by [12]:
2 PM 2N 2
2 n2n1jTn j jTn j ast changes underk R
X2n1MN 0 2
R2
S1TnnTnn; three cases: (Case I) keept0 RR constant; (Case
nn1 2 1
n p
(17) II) keep the impedancett=t0 constant; and
X2n1MN q
tt R2
S2TnnTnn: (Case III) keep the refractive index nt
00 R2 R1
nn1
n
constant. The results are shown in Fig. 4(a), where the
In the above two equationsn andn are related to horizontal axist is normalized by the ideal parameter
1
Pncos R2
the associated Legendre functions byn sin0 R .Weseethat whent isequal totheideal parame-
2 R1
1
dPncos
andn d ,respectively[15].Fortheconfigu- ter, the correspondingt in the three cases are all equal to
R2
ration shown in Fig. 1, S1 and S2 represent the0 R , and Qsca is equal to 0, meaning the cloak is
2 R1
scattering patterns in the yz and xz planes, respectively.
perfect. Whent slightly changed from the ideal parame-M
ThetwocurvesofS1andS2overlapbecauseTn ter, Qsca in Case I and Case II increase from zero moreN
Tn .FromFig.3weseethatthescattered powerincreases rapidlythanthatinCaseIII.ThisisbecauseinCaseIII,the
as the loss increases. A more interesting phenomenon is refractive index is kept constant, and the direction of
that the backscattering magnitude is always zero [because Poynting vector inside the cloak is mostly close to the
063903-3
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
0
10 tan( )=0.01
1.5 δ
1
tan(δ)=0.1
1
tan(δ)=1
0.5
-5
z 0 0 10
-0.5
-1
-1 -10
10
-1.5
z
-1 0 1
x x
-15
FIG. 2 (color online). Ex field distribution and Poynting vec- 10
0 30 60 90 120 150 180
tors due to an Ex polarized plane wave incidence onto an ideal
Scattering angle (degree)
cloak with R1 0:50 and R20.
FIG. 3 (color online). Normalized differential cross sections
field indicates the reflectionless behavior of the perfect for a cloak (R1 0:50, R20) with a specified loss tangent
cloak [4]. It should be noted that our mathematical dem- introduced in each component of the permittivity and perme-
onstration is applicable to any wavelength condition. ability. The inset shows the Ex field for the case of tan 0:1.
Figure 2 shows the calculated electric fields and the
Poynting vectors due to an Ex polarized plane wave inci-MN
Tn Tn , andnnj180], which is very
dence onto a cloak with R1 0:50 and R20 (0
different from conventional scattering from regular parti-
denotes the wavelength in free space). We see that the
cles [12]. The calculated field distribution in the xz plane
hidden object is completely hide from the waves, corrob-
for the spherical cloak with tan 0:1 (Fig. 3, inset) is
orating the effectiveness of the cloak proposed in [4].
similar to the simulation results of a cylindrical cloak with
There is no on-axis ray problem [4] here since the
the same type of loss [2]. However, our analytical calcu-
Poynting power becomes zero as the field penetrate deep
lation showsthat only the spherical cloak in this particular
into the cloak [2].
lossy case exhibits exactly zero backscattering. This
The most interesting thing is that Eqs. (12)–(15)give
unique property of the spherical cloak indicates the
further information. For example, it is known that loss is
cloaked object can stillcompletely hide from amonostatic
often an important issue. When the electric and magnetic
loss tangents are introduced, the scattering coefficients radar detection.MN Since the constitutive parameters for a perfect cloak are
Tn and Tn become nonzero. In Fig. 3, we plot the
very difficult to realize, nonideal material parameters are
bistatic scattering as a function of the scattering angle
more often used in the measurements [1,2]. Hence, it is
for the loss tangent of 0.01, 0.1, and 1, respectively. The
worthwhiletostudyhowtheimperfectmaterialparameters
vertical axis represents the normalized differential cross
2 2
jS1j jS2j quantitatively affect the performance of the cloak. We
sections, 2 2 , 2 2 , where S1 and S2 are defined
k R k R
0 2 0 2
calculate the normalized scattering cross section Qsca
by [12]:
2 PM 2N 2
2 n2n1jTn j jTn j ast changes underk R
X2n1MN 0 2
R2
S1TnnTnn; three cases: (Case I) keept0 RR constant; (Case
nn1 2 1
n p
(17) II) keep the impedancett=t0 constant; and
X2n1MN q
tt R2
S2TnnTnn: (Case III) keep the refractive index nt
00 R2 R1
nn1
n
constant. The results are shown in Fig. 4(a), where the
In the above two equationsn andn are related to horizontal axist is normalized by the ideal parameter
1
Pncos R2
the associated Legendre functions byn sin0 R .Weseethat whent isequal totheideal parame-
2 R1
1
dPncos
andn d ,respectively[15].Fortheconfigu- ter, the correspondingt in the three cases are all equal to
R2
ration shown in Fig. 1, S1 and S2 represent the0 R , and Qsca is equal to 0, meaning the cloak is
2 R1
scattering patterns in the yz and xz planes, respectively.
perfect. Whent slightly changed from the ideal parame-M
ThetwocurvesofS1andS2overlapbecauseTn ter, Qsca in Case I and Case II increase from zero moreN
Tn .FromFig.3weseethatthescattered powerincreases rapidlythanthatinCaseIII.ThisisbecauseinCaseIII,the
as the loss increases. A more interesting phenomenon is refractive index is kept constant, and the direction of
that the backscattering magnitude is always zero [because Poynting vector inside the cloak is mostly close to the
063903-3
week ending
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
(a)5 0,andthematerial parameters inthehiddenobject giveno
case I contribution to the outside field. If some perturbations are
4
case II introduced in the relationship of the radial and transverse
case III
material parameters, the solution of Eqs. (4) should be
3
revisited, and the interaction of the outside field with the
Qsca hidden object cannot be omitted.
2
In conclusion, we have demonstrated the interactions of
the electromagnetic wave with the cloaks by rigorously
1
solving Maxwell equations in the spherical coordinate
system. The fields and bistatic scattering cross section of
0
0 0.5 1 1.5 2 2.5 3 a general class of cloaks (ideal and nonideal) have been
t quantitatively solved by the full wave scattering method.
(b)
The physics behind the invisibility of the cloak has been
1 interpreted. Our method was shown to be computational
1
efficient, which is very useful for cloak design and
0.5 applications.
This work was supported by the Chinese NSF under
z0 Grant No. 60531020, the China PSF under Grant
0
No. 20060390331, and the ONR under Contract
No. N00014-01-1-0713.
-0.5
-1
-1
-1 0 1
x
*Corresponding author.
chenhs@ewt.mit.edu
FIG. 4 (color online). (a) Normalized scattering cross section
[1] D. Schurig et al., Science 314, 977 (2006).
of a cloak as functions oft for three different cases: (Case I)
R2 [2] S.A. Cummer et al., Phys. Rev. E 74, 036621 (2006).
keept0 R constant; (Case II) keept0 constant;
2 R1
[3] A. Alu and N. Engheta, Phys. Rev. E 72, 016623
R2
and (Case III) keep nt constant. (b) Ex field distribution
R2 R1 (2005).
R2
and Poynting vectors for Case III with 2 and
t 0 R2R1 t [4] J.B. Pendry, D. Schurig, and D.R. Smith, Science 312,
1 R2 . 1780 (2006).
2 0 R2R1
[5] D.Schurig,J.B.Pendry,andD.R.Smith,Opt.Express14,
9794 (2006).
ideal case, as shown in Fig. 4(b). Therefore, we can con- [6] U. Leonhardt, Science 312, 1777 (2006).
clude that the bistatic scattering performance of the cloak [7] U. Leonhardt, New J. Phys. 8, 118 (2006).
p p [8] A. Hendi, J. Henn, and U. Leonhardt, Phys. Rev. Lett. 97,
is more sensitive tott=t than nttt.
073902 (2006).
However, it should be noted that from Eqs. (12), (13),
[9] A.H. Sihvola, Prog. Electromagn. Res. pier-66, 191
and (17) the cloak in Case II is still invisible with mono-
(2006).
static detection since the matched impedance results in a
[10] G.W. Milton, M. Briane, and J.R. Willis, New J. Phys. 8,
zero backscattering.
248 (2006).
It is important to note that all the above analyses are
[11] D.A.B. Miller, Opt. Express 14, 12457 (2006).
valid independent of the material parameters of the hidden [12] L. Tsang, J.A. Kong, and K. Ding, Scattering of
object.Evenwhenthematerial parametersofthecloakare Electromagnetic Waves: Theories and applications
imperfect, the incident fields still cannot penetrate into the (Wiley, New York, 2000).
hiddenobject,andthescatteredpoweristotallyintroduced [13] J.A. Kong, Electromagnetic Waves Theory (EMW
by the cloak itself. This unusual phenomenon is based on Publishing, Cambridge, MA, 2005).
[14] B.A. Kemp, T.M. Grzegorczyk, and J.A. Kong, Phys.
the assumptionthat the material parameters ofthecloak in
Rev. Lett. 97, 133902 (2006).
theradialandtransverseaxisalwayshavethesameformof
2 Light Scattering by Small ParticlesrR1 [15] H.C. van de Hulst,rt 2 ,whererepresentsor.Hence,Eqs.(5),
r (Dover, New York, 1957).NM
(10),and(11)alwayshold,leadingtofn 0andfn [16] J.RothandM.J.Digman,J.Opt.Soc.Am.63,308(1973).
PHYSICAL REVIEW LETTERS
PRL 99, 063903 (2007) 10 AUGUST 2007
(a)5 0,andthematerial parameters inthehiddenobject giveno
case I contribution to the outside field. If some perturbations are
4
case II introduced in the relationship of the radial and transverse
case III
material parameters, the solution of Eqs. (4) should be
3
revisited, and the interaction of the outside field with the
Qsca hidden object cannot be omitted.
2
In conclusion, we have demonstrated the interactions of
the electromagnetic wave with the cloaks by rigorously
1
solving Maxwell equations in the spherical coordinate
system. The fields and bistatic scattering cross section of
0
0 0.5 1 1.5 2 2.5 3 a general class of cloaks (ideal and nonideal) have been
t quantitatively solved by the full wave scattering method.
(b)
The physics behind the invisibility of the cloak has been
1 interpreted. Our method was shown to be computational
1
efficient, which is very useful for cloak design and
0.5 applications.
This work was supported by the Chinese NSF under
z0 Grant No. 60531020, the China PSF under Grant
0
No. 20060390331, and the ONR under Contract
No. N00014-01-1-0713.
-0.5
-1
-1
-1 0 1
x
*Corresponding author.
chenhs@ewt.mit.edu
FIG. 4 (color online). (a) Normalized scattering cross section
[1] D. Schurig et al., Science 314, 977 (2006).
of a cloak as functions oft for three different cases: (Case I)
R2 [2] S.A. Cummer et al., Phys. Rev. E 74, 036621 (2006).
keept0 R constant; (Case II) keept0 constant;
2 R1
[3] A. Alu and N. Engheta, Phys. Rev. E 72, 016623
R2
and (Case III) keep nt constant. (b) Ex field distribution
R2 R1 (2005).
R2
and Poynting vectors for Case III with 2 and
t 0 R2R1 t [4] J.B. Pendry, D. Schurig, and D.R. Smith, Science 312,
1 R2 . 1780 (2006).
2 0 R2R1
[5] D.Schurig,J.B.Pendry,andD.R.Smith,Opt.Express14,
9794 (2006).
ideal case, as shown in Fig. 4(b). Therefore, we can con- [6] U. Leonhardt, Science 312, 1777 (2006).
clude that the bistatic scattering performance of the cloak [7] U. Leonhardt, New J. Phys. 8, 118 (2006).
p p [8] A. Hendi, J. Henn, and U. Leonhardt, Phys. Rev. Lett. 97,
is more sensitive tott=t than nttt.
073902 (2006).
However, it should be noted that from Eqs. (12), (13),
[9] A.H. Sihvola, Prog. Electromagn. Res. pier-66, 191
and (17) the cloak in Case II is still invisible with mono-
(2006).
static detection since the matched impedance results in a
[10] G.W. Milton, M. Briane, and J.R. Willis, New J. Phys. 8,
zero backscattering.
248 (2006).
It is important to note that all the above analyses are
[11] D.A.B. Miller, Opt. Express 14, 12457 (2006).
valid independent of the material parameters of the hidden [12] L. Tsang, J.A. Kong, and K. Ding, Scattering of
object.Evenwhenthematerial parametersofthecloakare Electromagnetic Waves: Theories and applications
imperfect, the incident fields still cannot penetrate into the (Wiley, New York, 2000).
hiddenobject,andthescatteredpoweristotallyintroduced [13] J.A. Kong, Electromagnetic Waves Theory (EMW
by the cloak itself. This unusual phenomenon is based on Publishing, Cambridge, MA, 2005).
[14] B.A. Kemp, T.M. Grzegorczyk, and J.A. Kong, Phys.
the assumptionthat the material parameters ofthecloak in
Rev. Lett. 97, 133902 (2006).
theradialandtransverseaxisalwayshavethesameformof
2 Light Scattering by Small ParticlesrR1 [15] H.C. van de Hulst,rt 2 ,whererepresentsor.Hence,Eqs.(5),
r (Dover, New York, 1957).NM
(10),and(11)alwayshold,leadingtofn 0andfn [16] J.RothandM.J.Digman,J.Opt.Soc.Am.63,308(1973).
:victory: :victory:
我是复旦物理系的,但是才大二,很多东西一知半解,我就说说我知道的吧
我们学校前几年从海外回来一个教授,做电磁特异介质的课题,同浙大那边有合作.这个东西看来就是这个项目的延伸.
简单的说就是通过材料的分子级微结构来改变材料的介电常数和磁导率.
可以实现很多特殊的功能,比如电磁信号屏蔽，这个可能可以用在雷达隐身上了。
还有就是可以将透光材料的折射率改变，通过某种特殊的结构，可以让光和电磁波“绕过”想要隐身的物体，从而实现真正意义上的光学隐身。
不过这种东西现在做起来还有很大的难度，就像前面有人提到的，现在基本上还停留在数值计算的程度上。因为就像我前面提到，真正的负折射率材料需要的亚分子级微结构，现在还做不出来。上次老师的报告中提到说目前最好的可以做到50纳米，这是国外的水平。复旦自己没有做过，那个老师是搞理论的。和浙大合作就是让他们制备这种东西，肯定是没有国外的水平了。
现在最顶级的材料也不过就是纳米材料，要想做到真正的原子级，还是不行的。不过这倒是一个不错的方向。如果真搞出来，大家就只有搞引力波雷达或者用高达作战了。。。
我们学校前几年从海外回来一个教授,做电磁特异介质的课题,同浙大那边有合作.这个东西看来就是这个项目的延伸.
简单的说就是通过材料的分子级微结构来改变材料的介电常数和磁导率.
可以实现很多特殊的功能,比如电磁信号屏蔽，这个可能可以用在雷达隐身上了。
还有就是可以将透光材料的折射率改变，通过某种特殊的结构，可以让光和电磁波“绕过”想要隐身的物体，从而实现真正意义上的光学隐身。
不过这种东西现在做起来还有很大的难度，就像前面有人提到的，现在基本上还停留在数值计算的程度上。因为就像我前面提到，真正的负折射率材料需要的亚分子级微结构，现在还做不出来。上次老师的报告中提到说目前最好的可以做到50纳米，这是国外的水平。复旦自己没有做过，那个老师是搞理论的。和浙大合作就是让他们制备这种东西，肯定是没有国外的水平了。
现在最顶级的材料也不过就是纳米材料，要想做到真正的原子级，还是不行的。不过这倒是一个不错的方向。如果真搞出来，大家就只有搞引力波雷达或者用高达作战了。。。
原帖由 zwgy20 于 2007-10-20 21:50 发表
我是复旦物理系的,但是才大二,很多东西一知半解,我就说说我知道的吧
我们学校前几年从海外回来一个教授,做电磁特异介质的课题,同浙大那边有合作.这个东西看来就是这个项目的延伸.
简单的说就是通过材料的分子级微结 ...
高达作战倒不至于。只是可见光波段的侦查失去意义了。但是别的波段还是有办法。比如紫外线波段。从你说的情况看，这个原理的隐身是波长越短，越难工程实现。所以至少还有X射线呢。呵呵
光子晶体结构大小和针对波长有关，俺们这里还有用厘米级铝球做的呢，当然也只能在厘米级波段有效
原帖由 zwgy20 于 2007-10-20 21:50 发表
我是复旦物理系的,但是才大二,很多东西一知半解,我就说说我知道的吧
我们学校前几年从海外回来一个教授,做电磁特异介质的课题,同浙大那边有合作.这个东西看来就是这个项目的延伸.
简单的说就是通过材料的分子级微结 ...
原帖由 railgun 于 2007-10-20 22:04 发表
光子晶体结构大小和针对波长有关，俺们这里还有用厘米级铝球做的呢，当然也只能在厘米级波段有效
完了，以后出门要搞个眼镜戴着，在不停地接受红外、紫外、可视三种光波，要不看不到人，撞了都不知道……
原帖由 zwgy20 于 2007-10-20 21:50 发表
可以实现很多特殊的功能,比如电磁信号屏蔽，这个可能可以用在雷达隐身上了。
选择性透射的蒙皮是不是和这个有关?
比如F22那个雷达罩？
36楼看来也是学这个的，来自哪个学校啊？金属球我们老师说他在香港和人合作做过，现在做的比较多的是工字型二维分形结构，国外那个50纳米的是一字形
据说学理论物理的特别容易发文章——不要做实验。