Journal Pre-proof
Optical radiation force circular dichroism spectroscopy F.G. Mitri PII: DOI: Reference:
S0022-4073(19)30982-3 https://doi.org/10.1016/j.jqsrt.2020.106850 JQSRT 106850
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: Revised date: Accepted date:
12 December 2019 20 January 2020 21 January 2020
Please cite this article as: F.G. Mitri , Optical radiation force circular dichroism spectroscopy, Journal of Quantitative Spectroscopy & Radiative Transfer (2020), doi: https://doi.org/10.1016/j.jqsrt.2020.106850
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
JQSRT (2020)
Optical radiation force circular dichroism spectroscopy F.G. Mitria) Santa Fe, New Mexico 87508, USA (Submitted 11 December 2019, revised 20 January 2020)
Highlights - This work introduces the optical radiation force circular dichroism spectroscopy method - This method is defined as the force difference of left-handed and right-handed circularly polarized waves - The example of a perfect electromagnetic circular cylinder is considered - A line source of cylindrically diverging waves with circular polarization is assumed - Radiation force and energy efficiency results are computed and discussed
Abstract This work introduces the method of circular dichroism spectroscopy in the framework of the electromagnetic/optical radiation force theory. This analytical tool is defined here as the difference in radiation force of left-handed and right-handed circularly polarized electromagnetic waves illuminating an object exhibiting rotary polarization. The example of a lossless material, such as the perfect electromagnetic conductor (PEMC) cylinder having a circular geometric cross-section, is considered. The modal expansion method in cylindrical coordinates is used to obtain exact mathematical series expansions for the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation) considering left-handed and right-handed circularly polarized cylindrically diverging waves emanating from a line source. The case of plane progressive waves is recovered when the source is located far from the cylinder. Numerical illustrative results for the dimensionless radiation force functions as well as the scattering, extinction and absorption energy efficiencies and their co-polarized and cross-polarized components are performed with particular emphasis on the size parameter of the cylinder, the dimensionless distance parameter from the line source, and the admittance parameter of the cylinder. The results reveal that the individual radiation force functions for left-handed and right-handed circularly polarized waves can be negative, zero, or positive depending on the cylinder distance from the source. Moreover, the optical radiation force circular dichroism (ORFCD) and the extinction energy efficiency circular dichroism (EEECD) are positive for a negative admittance of the cylinder, while they reverse sign for a positive admittance. While the EEECD shows some form of symmetry versus admittance sign change, the ORFCD does not. The possibility of achieving invisibility cloaking for a small PEMC cylinder is also investigated. The present ORFCD spectroscopy method is applicable to any cylinder material exhibiting rotary polarization such as chiral, topological insulator, plasma, liquid crystal etc. Keywords: Electromagnetic scattering; electromagnetic radiation force; circular dichroism/rotary polarization; PEMC cylinder; circularly polarized waves; multipole expansion method
1. Introduction
[17], stopped-flow [18] and synchrotron radiation [19] spectroscopies. In all these methods the difference of energy extinction (by absorption and scattering [20]) between lefthanded and right-handed circularly polarized wavefields is quantified. As such, the extinction energy efficiency circular dichroism (EEECD) spectra allow studying the shapes of particulate matter and arrangement of atoms [21]. From a theoretical standpoint that could improve structural analyses of unconventional materials by means of radiation forces and scattering of EM/optical waves, it is of some importance to develop a novel spectroscopy method that would complement the state-of-the-art circular dichroismbased techniques available to date. Such an analytical spectroscopy method may be utilized in the realm of optical tweezers and particle manipulation, entailing the subtraction of radiation force spectra of left-handed and right-handed circularly polarized EM/optical waves illuminating an object
Circular dichroism [1] is an interesting property exhibited by some type of materials possessing internal asymmetry that absorb and scatter electromagnetic (EM) and optical radiation based on polarization. During this process, a rotation of the plane of polarization [2-5] (known also as depolarization [6]) is induced, which offers a quantitative tool to characterize particles via spectroscopy. For example, typical information related to the detailed inner structure of proteins, liquid crystals, nucleic acid, nanostructures etc., can be obtained [7]. Previously, such materials have been defined as “optically active” [8] to describe this property. However, this description must be distinguished from active materials containing active sources which radiate EM/optical/acoustical waves [9-12]. Numerous circular dichroism-based techniques exist [13, 14], encompassing electronic [15], magnetic [16], vibrational 1
JQSRT (2020) rly polarized field affects the radiation force by a PEMC cylinder material, since the incident field is a superposition of two dephased TM and TE modes. This topic is relevant in understanding the fundamentals of EM radiation force theory for particles exhibiting rotary polarization (or TM ⇆ TE mode conversion). Moreover, applications in the realm of particle manipulation, stabilization and optical tweezers have considered circularly polarized waves because of their intrinsic properties. The purpose of this analysis is therefore focused on developing an exact analytical formalism for the modeling for the EM/optical radiation force on a circular PEMC cylinder in both left-handed and right-handed circularly polarized field, emanating from a line source of cylindrically diverging waves (see panels (a) and (b) of Fig. 1). The analytical formalism presented in the following is exact, without any approximations related to particle size, such that the Rayleigh, Mie and geometrical optics regimes can be all considered. As such, the ORFCD spectroscopy method can be introduced. In the following, section 2 presents a complete analysis of the scattering used to derive the exact expressions of the radiation force functions and scattering, extinction and absorption energy efficiencies with emphasis on the crosspolarized waves. In section 3, numerical simulations are considered and discussed. Verification and validation stemming from the law of energy conservation applied to scattering are also performed. Finally, section 4 presents the conclusion of this work.
2. Method Consider a line source emitting an electromagnetic (EM) field composed of either left-handed or right-handed circularly polarized cylindrical diverging waves, denoted respectively by LHCP and RHCP (see panels (a) and (b) of Fig. 1). The resulting incident electric field vector is expressed as the combination of a pair (i.e., TE and TM) of linearly polarized components as
Fig. 1. Graphical representation for the interaction of an optical/EM lefthanded circularly polarized field of cylindrical diverging waves emanating from a line source, incident upon an infinitely-long PEMC cylinder having a circular cross-section of radius a. The incident field propagates along the xaxis, perpendicularly to the cylinder z-axis.
allowing rotary polarization. This method is defined here as optical radiation force circular dichroism (ORFCD) spectroscopy. In this paper, the aim is to introduce the ORFCD from a theoretical perspective, stemming from the analysis of the EM/optical scattering by a perfect electromagnetic conductor (PEMC) [22, 23] lossless cylinder [24] chosen as an example. The PEMC material can induce mode conversion (i.e. optical rotation or depolarization) such that both co-polarized and cross-polarized waves are generated in the scattered field [2433]. Other materials such as chiral, plasma and topological insulators exhibit similar properties. As such, the crosspolarized field contributes significantly to the radiation force experienced by the object as shown in the recent works [3436], in which linearly polarized transverse magnetic (TM) wave incidence has been considered. The challenge that remains to be addressed is how a circula
LHCP H 1 kR cyl . div . RHCP Einc E0e it e ie z 01 , H 0 kr0
(1)
where the superscripts LHCP and RHCP correspond to the (+) and (–) signs in the right-hand side of Eq.(1), respectively. E0 is the electric field amplitude and (r,, z) form a cylindrical coordinates system centered on the cylinder as shown in Fig. 1. The parameters e and e z denote the unit vectors along the polar and axial directions, respectively. As shown from
e it is considered, 1 but omitted from the field equations for convenience. H 0 . Eq.(1), a time-dependence in the form of
is the cylindrical Hankel function of the first kind of order zero, k = 1/2/c is the wavenumber in the host medium, is the dielectric permittivity, is the angular frequency and c is
Electronic mail:
[email protected]
2
JQSRT (2020) the speed of light. R is the distance from the center of the line source to an observation point in the transverse plane (xy), and r0 is the distance between the source and the center of the cylinder. The incident waves impinge perpendicularly on the z-axis of an infinitely long cylinder of radius a made of a PEMC material. The medium of wave propagation is homogeneous, non-dissipative and non-magnetic. Application of Graf’s addition theorem (pp. 142-144 in [37]) for cylindrical wave functions (Eq. (2) on p. 360 in [38]), the modal expansion method [39, 40] is used to express Eq.(1) as a mathematical series as,
LHCP cyl . div . RHCP Einc r, r0 ,
r0 r a
1 H
1
n
n
n
n 0
LHCP cyl . div . RHCP Hsca r, r0 , r0 r a
where H n1 is the cylindrical Hankel function of the first kind of order n, H n1 ' is its derivative with respect to the
E0 H 0 kr0 1
argument. The coefficients
TM TE
kr0 J n kr e iJ n kr e z cos n of, polarization, respectively, whereas Cn
i r0 r a
1 H
n
n
n 0
1 n
kr0
E0 H 0 kr0
n 0
H n ka CnTM TM 1
iJ n kr e J n kr e z cos n . '
'
iM
H n1 ' ka CnTM TE J n' ka ,
(7)
H n ka CnTE TE 1
iM
H n1 ka CnTE TM J n ka ,
(8)
H n ka CnTE TE 1
'
i M H n1 ' ka CnTE TM J n' ka ,
E0 H 0 kr0 1
CnTM TE CnTE TE H n1 ' kr e cos n , n 1 H n kr0 i CnTM TM CnTE TM H n1 kr e z n
(6)
1
conversion in the scattered waves (denoted by TM ⇆ TE), an incident circularly polarized field scattered from its surface would enhance the generation of TM and TE mode conversion. This intrinsic property stems from the fact that circular polarization consists of combining two linear TM and TE components that are perpendicular to each other, equal in amplitude, but have a phase difference of π/2. Consequently, the total electric and magnetic vector fields consist of all contributions, including the cross-terms (TM TE and TE TM). The scattered electric and magnetic vector fields expressions are given as,
r0 r a
i M H n1 ka CnTM TE J n ka ,
Since the PEMC cylinder material induces EM mode
TE TM
and Cn
1
(3)
LHCP cyl . div . RHCP Esca r, r0 ,
CnTE TE
H n ka CnTM TM
Based on Maxwell’s equations [41], the incident magnetic vector field is obtained from Eq.(2) as,
r, r0 ,
and
describe those of the scattered cross-polarized waves due to mode conversion. Applying the appropriate boundary conditions for the PEMC cylinder, such that the tangential field components vanish (see Eq.(9) in [24]), the following system of linear equations is obtained as,
' kind and J n is its derivative with respect to the argument.
CnTM TM
correspond to the scattered co-polarized waves for each type
'
function, J n is the cylindrical Bessel function of the first
cyl . div . Hinc
i CnTM TM CnTE TM H n1 ' kr e cos n , CnTM TE CnTE TE H n1 kr e z
n
(5)
n 2 n 0 and ij is the Kronecker delta
LHCP RHCP
E0 H 01 kr0
n 1 H n1 kr0
n 0
(2) where
i
1
(4) 3
(9)
where M is known as the admittance [24] of the PEMC cylinder (i.e., a measure of electromagnetic conduction of the cylindrical material). Based on Eqs.(6)-(9), the scattering coefficients for the copolarized and cross-polarized scattered waves are determined as,
JQSRT (2020)
H n ka
J n ka i M H n1 ka CnTM TM
J n' ka 1
Hn
ka
H n ka 1
'
iM H ' ka , i M H ka iM H ' ka 1 n
1 n
1
CnTM TE
(10)
1 n
J n ka
H n1 ' ka J n' ka
H n1 ka
i M H n1 ka
H n1 ' ka
iM
H n1 ' ka
(continue on page 8)
4
,
(11)
JQSRT (2020)
Fig. 2. Panels (a)-(f) display the plots for the dimensionless radiation force functions [given by Eqs.(19)-(22)] versus the size parameter ka for a PEMC cylinder having an EM admittance M = 0.5. Panels (g) and (h) display the ORFCD components for plane and cylindrically diverging waves, respectively. For each plot, the dimensionless distance source-cylinder kr0 is constant and has the value indicated near each curve. Notice that kr0 is always larger than ka, ensuring the physical validity of the results (i.e., the source is external to the cylinder). When kr0 , the case of plane progressive waves is obtained.
5
JQSRT (2020)
Fig. 3. Panels (a)-(f) display the plots for the scattering, extinction and absorption energy efficiencies [given by Eqs.(26)-(36)] for a PEMC cylinder having an EM admittance M = 0.5. Panel (g) displays the EEECD given by Eq.(40) for cylindrically diverging waves. For each plot, the dimensionless distance source-cylinder kr0 is constant and has the value indicated near each curve. Notice that kr0 is always larger than ka, ensuring the physical validity of the results (i.e., the source is external to the cylinder). When kr0 , the case of plane progressive waves is obtained.
6
JQSRT (2020)
Fig. 4. The same as in Fig. 2, but the EM admittance of the PEMC cylinder is M = +1.
7
JQSRT (2020)
Fig. 5. The same as in Fig. 2, but the EM admittance of the PEMC cylinder is M = –1.
8
JQSRT (2020)
J n ka CnTE TE
J n' ka H n1 ka H n ka 1
'
iM H ka i M H ' ka , iM H ka ' i M H ka 1 n
1 n
1 n
CnTE TM
H n1 ' ka
0
(12)
cyl . div ., x
iM H ka i M H ' ka 1 n
Ycyl.div ., x
Knowing the mathematical expressions for the total (i.e., incident + scattered) electric and magnetic field components, the derivation for the longitudinal (i.e., along the x-axis) radiation force per-length and its dimensionless function (or efficiency) can be accomplished for each type of polarization LHCP or RHCP as [42, 43],
E
inc
(14)
, Hinc , E zinc , H zinc ,
... denotes the real part of a complex number, the superscript * denotes a complex conjugate, the subscript in Eq.(14) indicates that the far-field limits (i.e., kr ) of the field components are used, dS Lrd er , where L is the length of a cylindrical surface enclosing the cylinder, r is the radial distance to a point in the polar plane, and e r cos e x sin e y , is the normal unit vector pointing outwardly to the surface of the cylinder, and
2 ka
2 Y p. p. w., x kr0
J kr J n
0
n 1
kr0 Yn kr0 Yn 1 kr0
n 0
TM TM nTM 1 2 nTM TM nTM TM 1 2 nTM 1 1 nTE1TE 1 2 nTE TE nTE TE 1 2 nTE1TE TE TM TE TM TE nTM TE 1 2 nTM 1 2 1 n 1 n nTE TM 1 2 nTE1TM nTE1TM 1 2 nTE TM TM nTM TM nTE1TM nTE TM nTM 1 TM TM TE TM TM n 1 nTE TM nTM 1 2 n TM TE TE TE TE TE TM TE n 1 n n 1 n TE nTM TE nTE1TE nTE TE nTM 1
LHCP cyl . div . RHCP , Hinc , z
c LHCP FcylRHCP . div ., x 2aLI 0
1 2 1 H 0 kr0
CnTM TE CnTE TM .
(16)
For the circular cylinder of radius a, the longitudinal dimensionless radiation force function (or efficiency) is defined as,
of a matrix. Eqs.(11) and (13) also demonstrate that
LHCP RHCP
F ex.
(13)
1 n
E inc* H sca E sca H inc* z , , z , , S 1 sca* sca inc* sca F E z , H , E , H z , , 2c sca inc* sca sca* E , H z , E , H z , dS
1 n 1, n 0, 0 otherwise
the longitudinal component of the force vector is obtained after algebraic manipulation and can be recast as an exact partial-wave series expansion, LHCP F RHCP
,
n
(15)
where the mathematical symbol ... indicates the determinant
where Ecyl .div. inc
cos n cos cos d 2 0
J n ka
H n1 ' ka J n' ka H n1 ka
1 n
H n ka 1
2
(17) where
nTM TM CnTM TM ,
e x and e y are
nTM TE CnTM TE ,
the unit Cartesian vectors along the x-axis and y-axis, respectively. Using the property of the angular integral,
nTE TE CnTE TE ,
nTM TM CnTM TM ,
nTM TE CnTM TE ,
nTE TE CnTE TE ,
nTE TM CnTE TM ,
nTE TM CnTE TM , I 0 E0
2
2,
...
denotes the imaginary part of a complex number, and 9
,
JQSRT (2020)
Y pLHCP . p . w ., x is the radiation force function for the case of a left-
TE YcylTE. div ., x
handed circularly polarized field of plane progressive waves (p.p.w.), which is expressed as,
1 2 1 H 0 kr0
2 Y p.p. w., x ka
TM TM n
TM nTM nTE TE nTE1TE 1
n 0
nTE TM nTE1TM
nTM TE
2 ka
TE nTM 1
TM TM TM TM TM TM TM TM n 1 n n 1 n TM TE TM TE TM TE TM TE n 1 n n 1 n 2 nTE TE nTE1TE nTE TE nTE1TE TE TM TE TM TE TM TE TM n 1 n n 1 n TM TE TE TE TM TM TE TM n 1 n n 1 2 n TE TM TM TM TE TE TM TE n n 1 n n 1
.
cyl . div ., x
TE TE
, cyl . div ., x
Ycyl .div., x Ycyl .div., x Y
,
Y
2 ka
(19)
2 TM TM Y p. p. w., x kr0
J kr J n
0
n 1
0
n 1
kr0 Yn kr0 Yn1 kr0
(21)
2 ka
2 , Y p. p. w., x kr0
J kr J n
0
n 1
kr0 Yn kr0 Yn1 kr0
n 0
TM TE TM TE TE nTM TE 1 2 nTM 2 1 n n 1 1 nTE TM 1 2 nTE1TM nTE1TM 1 2 nTE TM , TM nTM TM nTE1TM nTE TM nTM 1 TM TM TE TM TM nTE TM nTM n 1 n 1 2 TM TE TE TE TE TE TM TE n 1 n n 1 n TE nTM TE nTE1TE nTE TE nTM 1
TM YcylTM.div ., x
n
n 0
1 2 1 H kr0 0
where,
1 2 1 H 0 kr0
J kr J
, cyl . div ., x
For convenience, Eq.(17) can be re-expressed as the sum of three distinct contributions resulting from the co-polarized waves components (denoted by the superscripts TM TM and TE TE, respectively), and a cross-polarized factor one (denoted by the superscript ) related to mode conversion. It follows that, TM TM
nTE1TE 1 2 nTE TE nTE TE 1 2 nTE1TE ,
(18)
Y
2 TE TE Y p. p. w., x kr0
(22) TM TM
and the expressions for Y p . p . w., x ,
kr0 Yn kr0 Yn 1 kr0
n 0
TM nTM 1 2nTM TM nTM TM 1 2 nTM1TM , 1 (20)
TE Y pTE. p . w., x ,
appearing in Eqs.(20)-(22) [corresponding progressive waves (p.p.w)] are given as,
Y
TM TM p . p . w .,x
2 ka
,
and
Y p. p.w., x
to
plane
TM TM n
TM nTM 1
n 0
TM TM 2 nTM TM nTM nTM TM nTM , 1 1
(23)
10
JQSRT (2020)
Y
TE TE p . p . w., x
2 and
Y
2 ka
TE TE n
n 0
TE TE n 1
TE TE n
nTE1TE
TE TE n
TE TE n 1
,
,
TM TM TM TE TE TE TE TM Qsca Qsca Qsca Qsca Qsca Qsca ,
(24)
(31) TM TM ext
Q
, p . p . w., x
2 ka
TE TM n
nTE1TM
nTM TE
n 0
.
Q
Q
n
n
2
n 0
TM TM 2 n
TM TM 2 n
Q
TM TE Qsca
2 ka
n n
2
n 0
TM TE 2 n
TE TE Qsca
TE TM sca
Q
,
Qsca
2 ka
2 ka 4 ka
4 ka
n
2
n
n
2
n
n 0
n 0
n 0
TE TM 2 n
nTE TM , (29)
2
2
2
n
n
2
n 0
n
n
n
n
2
TE TM n
nTM TE (34)
2
TM TE n
,
n 0
ext
ext
Q Q Q , ext
sca
ext
(35) (36)
H n kr0 1
n
H 01 kr0
.
(37)
Notice that lim n 1 , and the infinite plane wave kr0
nTE TE ,
(33)
and
,
TE TE 2 n
n nTE TE , 2
n
abs
result is recovered. Now that all the physical observables are defined in exact partial-wave series expressions, the radiation force circular dichroism (RFCD) efficiency for cylindrically diverging waves emanating from a line source is obtained from Eqs.(17) and (19) as (continue on page 12),
(28)
nTM TE nTE TE nTM TM nTE TM TE TM nTM TM nTE TE nTM TE n
n n
n 0
(32)
n 0
ext
(27)
2
n 0
n nTM TM ,
n
, TM TM TE TE Q Q Q Q ,
nTM TE , 2
2 ka
4 ka
(26)
, ext
The analysis is further extended to derive the expressions for the energy efficiencies (or cross-sections), such as the scattering, extinction and absorption efficiencies. Those quadratic observables are useful in the study of the scattering and radiation force since they validate/verify the results from the standpoint of energy conservation. Stemming from the previous exact formalisms [44] for the scattering by a PEMC [24] or a chiral [8] cylinder, series expansions for the scattering, extinction and absorption energy efficiency factors have been derived analytically and are given as follows,
2 ka
TE TE ext
(25)
2 ka
TE nTM 1
TM TE TM TE TM TE TM TE n 1 n n 1 n TE TM TE TM TE TM TE TM 2 n n 1 n n 1 nTM TE nTE1TE nTM TM nTE1TM 2 TE TM TM TM nTE1TE nTM TE n 1 n
TM TM sca
2 ka
nTM TE nTM TM nTE TE , nTE TM nTM TM nTE TE (30)
11
JQSRT (2020)
Fig. 6. Panels (a)-(f) display the plots for the dimensionless radiation force functions [given by Eqs.(19)-(22)] versus the dimensionless source-cylinder distance kr0 for a PEMC cylinder having an EM admittance M = 0.5. Panels (g) and (h) display the ORFCD components for plane and cylindrically diverging waves, respectively. For each plot, the dimensionless cylinder size is ka and has the value indicated near each curve. Notice that kr0 is always larger than ka, ensuring the physical validity of the results (i.e., the source is external to the cylinder).
12
JQSRT (2020)
Ycyl .div ., x Ycyl .div ., x Ycyl .div ., x
3. Numerical results and discussions
Ycyl,.div ., x Ycyl,.div ., x 1 2 1 H kr0 0
4 ka
2 Y p. p. w., x kr0
J kr J n
Eqs.(38) and (40) establish the core of the ORFCD and EEECD spectroscopy formalisms for any cylindrical particle allowing rotary polarization in the field of circularly polarized plane progressive waves. In this analysis, a non-absorptive PEMC cylinder with a circular cross-section is considered and the host medium is air with a dielectric constant 1. The radiation force efficiencies for the cylindrically diverging left-handed and right-handed circularly polarized waves as well as the energy efficiencies related to scattering, extinction and absorption are computed. A MATLAB numerical platform is utilized for the simulations. Emphasis is given on varying the size parameter ka of the cylinder, the dimensionless distance from the source kr0 and the EM admittance parameter M. The mathematical series representing the components of the longitudinal radiation force function and energy efficiencies are truncated according to a convergence criterion that was enforced to ensure accuracy , and negligible numerical error. The convergence criterion is
0
n 1
kr0 Yn kr0 Yn 1 kr0
n 0
nTE TM 1 2 nTE1TM nTE1TM 1 2 nTE TM TE TM TE TM TE nTM TE 1 2 nTM 1 2 n1 1 n TM nTM TM nTE1TM nTE TM nTM 1 TM TM TE TM TM n 1 nTE TM nTM n 1 2 TM TE TE TE TE TE TM TE n 1 n n 1 n TE nTM TE nTE1TE nTE TE nTM 1
chosen such that Nmax = round[ka + 4 3 ka + 55], leading to a negligible relative numerical error in the order of ~10–14. This maximum truncation order is larger than the one used previously for plane progressive waves [45] (i.e., Nmax = round[ka + 4.05 3 ka + 2] ) because near the source (i.e., kr0 ~ ka), adequate convergence requires adding a larger number of multipoles in the series. Moreover, in all the computations, the condition kr0 > ka has been enforced, suggesting that the source is always external to the cylinder core, which warrants the physical validity of the results. First, a PEMC cylinder is considered with an EM admittance factor M = 0.5. Panel (a) of Fig. 2 displays the results for the longitudinal radiation force function for the copolarized waves TM TM given by Eq.(20) versus ka, for six different values of kr0 (= 1, 2, 4, 6, 10 and ). In the
(38) where Y p . p . w., x is obtained from Eq.(18) [or Eq.(25)] as,
Y p. p. w., x Y p. p. w., x Y p. p. w., x Y p. p,. w., x Y p. p,. w., x Y p. p. w., x 4 ka
TM TM
Rayleigh regime for which ka 0.5, Ycyl . div ., x is maximal. As
ka increases and approaches kr0, it diminishes, vanishes, and turn negative as the source is moved close to the cylinder. When the source is moved to infinity, i.e., kr0 , the plane
TE nTE1TM nTM TE nTM 1
TE TM n
n 0
nTM TE nTE1TE nTM TM nTE1TM 4 TE TM TM TM nTE1TE nTM TE n 1 n
TM TM
.
progressive wave limit is reached, and Ycyl . div ., x is always positive. TE TE
(39)
This is not the case for the plots of Ycyl . div ., x shown in panel
In terms of energy related to scattering and absorption, the extinction circular dichroism efficiency is obtained from Eq.(35) as,
(b) of Fig. 2. Ycyl . div ., x is positive for all values of kr0,
, ext
Qext Q
8 ka
TE TE
suggesting that this component always acts in the direction of wave motion, and induces a repulsive force. As ka increases, TE TE Ycyl decreases, but increases significantly as ka . div ., x
, ext
Q
approaches kr0.
n 2
n
,
TM TE n
.
Panel (c) of Fig. 2 shows the plots for Ycyl . div ., x representing
(40)
the cross-terms or mode conversion occurring between the TM and TE polarizations for the LHCP cylindrical wave field. The
n 0
,
plots corresponding to kr0 = 1, 2, 4 and 6 show that Ycyl . div ., x is always negative, which contributes to the generation of a pulling force component toward the source. For kr0 = 10, 13
JQSRT (2020)
Fig. 7. Panels (a)-(f) display the plots for the dimensionless radiation force functions [given by Eqs.(19)-(22)] versus the EM admittance parameter of a Rayleigh PEMC cylinder illuminated by circularly polarized cylindrical diverging waves at ka = 0.1. Panels (g) and (h) display the ORFCD components for plane and cylindrically diverging waves, respectively. For each plot, the dimensionless parameter kr0 has the value indicated in the legend.
14
JQSRT (2020)
Fig. 8. Panels (a)-(f) display the plots for the extinction energy efficiency factors for a Rayleigh PEMC cylinder in circularly polarized cylindrical diverging waves at ka = 0.1. Panel (g) displays the EEECD given by Eq.(40) for cylindrically diverging waves. For the small PEMC cylinder, the results show that the extinction energy efficiency factors are negligibly affected as M and kr0 vary (i.e., all the plots are quasi-superimposed). The solid dashed (black) lines in panels (d) and (f) correspond to the absorption energy efficiency.
15
JQSRT (2020)
Ycyl ,.div ., x is negative for ka < 3, and vanishes around ka = 3. It
results are displayed in panels (a)-(g) of Fig. 3 for all components. In all the cases, and since the PEMC cylinder is lossless, the absorption efficiencies vanish, as required by energy conservation. Panels (a) and (b) of Fig. 3 show that the extinction
becomes positive as ka increases further, and vanishes again around ka = 8.9. Beyond that limit, and as kr0 approaches ka,
Ycyl,.div .,x becomes negative near the source.
TM TM
efficiencies Qext
The plots for the total radiation force function Ycyl . div ., x for
to that of Ycyl . div ., x shown in panel (a). That is, Ycyl . div ., x is maximal and positive in the Rayleigh regime. It vanishes as the source approaches the PEMC cylinder surface, and becomes negative as the source is located nearby it. For plane
,
Panel (e) of Fig. 2 displays the plots for Ycyl . div ., x corresponding to the interaction of TM and TE polarizations assuming a RHCP cylindrical diverging wave field. The TE TE
,
scattering Qsca and extinction Qext efficiencies versus ka, which are equal and positive, in agreement with energy
behavior of Ycyl . div ., x is somewhat similar to Ycyl . div ., x shown ,
in panel (b), such that Ycyl . div ., x > 0 for all the values of kr0. The plots for the total radiation force function Y
,
scattering Qsca and extinction Qext efficiencies for LHCP cylindrically diverging waves, which are equal, but negative. This suggests that the interference between TM and TE modes in the interaction of LHCP cylindrically diverging waves with the PEMC cylinder has the tendency to reduce the total scattering. Panel (d) on the other hand, displays the plots for the total
progressive waves, Ycyl . div ., x is always positive.
cyl . div ., x
+
with previous results of linearly polarized waves (See Eqs.(27) and (28) in [24]). These physical observable are always positive. Panel (c) of Fig. 3 shows the plot for the interference
(d). The behavior of Ycyl . div ., x versus ka is somewhat similar
,
TM TM
, amount to Qsca
TM TE TE TE TE TM and Qsca + Qsca , respectively, which agrees Qsca
the LHCP cylindrically diverging waves are displayed in panel TM TM
TE TE
and Qext
conservation, i.e., Qabs 0 . Notice that the PEMC cylinder material is totally reflecting of the EM waves. Only circumferential creeping waves are scattered in the medium of wave propagation [46-48] and no losses can occur in its core material. As the incident field circular polarization changes from
for
the case of RHCP cylindrically diverging waves are displayed
in panel (f). The variations of Ycyl . div ., x versus ka display also TE TE
some similarities with those of Ycyl . div ., x shown in panel (b),
,
LHCP to RHCP, the interference scattering Qsca
suggesting a repulsive force on the PEMC cylinder using RHCP cylindrically diverging waves for all values of kr0. Comparison of panel (f) with panel (d) shows that the sense of circular polarization has a significant effect on the behavior of the force (i.e., repulsive vs. attractive) experienced by the cylinder. The ORFCD is computed as well, and panel (g) of Fig. 2
and
,
extinction Qext efficiencies become positive, as shown in panel (e) of Fig. 3. Comparison of panel (e) with panel (c) ,
,
,
,
shows that Qsca = Qext = Qsca = Qext , for all the values of kr0. Panel (f) of Fig. 3 shows the plots for the total scattering
displays the plot of Y p . p .w., x for plane waves. As shown in
and extinction Qext efficiencies for RHCP cylindrically Qsca
panel (g), Y p . p . w., x is not affected by the variations of kr0
diverging waves versus ka, which are equal and positive, in
agreement with energy conservation, i.e., Qabs 0 . Subsequently, the EEECD for cylindrically diverging waves
and is independent of it. Furthermore, Y p . p . w., x < 0 for this particular value of the EM cylinder admittance M (= 0.5), and approaches zero as ka increases. A negative ORFCD for plane waves suggests that the radiation force induced by a RHCP plane wave-field is larger than the one induced by LHCP plane waves. Subsequently, the ORFCD for cylindrically diverging waves
is evaluated via Qext , which amounts to Qsca as shown in panel (g) of Fig. 3. Qext < 0 for all the selected kr0 values versus ka, suggesting that extinction by a RHCP cylindrically diverging wave-field is larger than the one induced by LHCP cylindrically diverging waves. Negative EEECD is consistent with numerous experimental studies and findings in analytical chemistry [49], liquid chromatography [50], nucleic acids research [51], biological chemistry, spectroscopy etc. and used as a powerful method in particle characterization. The effect of increasing the EM admittance is investigated, and the radiation force efficiencies and ORFCD components are computed for a PEMC cylinder with M = +1. The corresponding results are displayed in panels (a)-(f) of Fig. 4. The change in the EM admittance alters the radiation force functions, however, some similarities with the results shown in Fig. 2 occur. Concerning the ORFCD, panel (h) of Fig. 4
Ycyl .div ., x is evaluated, and panel (h) of Fig. 2 displays the plots at the selected kr0 values. Some similarity arises between the plots of panel (h) and those displayed in panel (c) for
Ycyl,.div ., x . However, in panel (h), Ycyl .div ., x < 0 for all values of kr0. This also suggests the radiation force induced by a RHCP cylindrically diverging wave-field is larger than the one induced by LHCP cylindrically diverging waves. The scattering, extinction and absorption energy efficiencies are also computed for a lossless PEMC cylinder with an EM admittance M = 0.5 versus ka at different values of kr0, and the 16
JQSRT (2020) shows
that
Ycyl .div ., x changes
sign
for
the
Finally, the effect of varying the admittance of the PEMC cylinder is examined for a Rayleigh (ka = 0.1) and Mie (ka = 5) cylinder, respectively. The radiation force and extinction energy efficiency components are computed in the range –5 M 5 for three values of kr0. For the Rayleigh PEMC cylinder case, kr0 is chosen so that the cylinder is near (kr0 = 0.2), midway (kr0 = 1) and far (kr0 = 10) from the source.
curve
corresponding to kr0 = 10; it is negative for ka < 6, vanishes near ka 6 and turns positive as ka further increases. Moreover, it vanishes again near ka 8.25, and becomes negative as kr0 (= 10) approaches ka. For plane progressive waves (i.e., kr0 ), Ycyl . div ., x < 0 in the range 0 < ka 10.
TM TM
Panel (a) of Fig. 7 displays the plots for Ycyl . div ., x , which
The effect of altering the sign of the admittance is also examined, and numerical computations for the radiation force functions for M = –1 are displayed in panels (a)-(h) of Fig. 5. Visual inspection and comparison with the panels of Fig. 4 show the even functions property, such that TM TM TE TE , , cyl . div ., x
Y
TM TM TE TE , , cyl . div ., x
ka, M Y
show symmetry versus the axis M = 0. Notice that M = 0 corresponds to the case of a perfect magnetic cylinder where the effect of the cross-polarized waves vanishes. Near the TM TM
source (kr0 = 0.2), panel (a) shows that Ycyl . div ., x can be negative in the range –0.5 M 0.5. When kr0 (= 1) TM TM
increases, Ycyl . div ., x exhibits negative values in a smaller
ka, M .
TM TM
range. For a large distance (kr0 = 10) Ycyl . div ., x > 0 for all the
On the other
values of M.
hand, the ORFCD for plane waves is an odd function such that
Y p. p. w., x ka, M Y p. p. w., x ka , M .
TE TE
Panel (b) shows the plots for Ycyl . div ., x where symmetry also
Notice,
occurs with respect to the axis M = 0. This is somewhat
however, that Ycyl . div ., x is neither even nor odd such that
TE TE
Ycyl .div ., x ka , M Ycyl .div ., x ka , M .
i.e.,
Next, the variations of the radiation force functions as well as the ORFCD versus kr0 are investigated for a PEMC cylinder having an EM admittance of M = 0.5. Three different dimensionless sizes are considered, namely, ka = 0.1, 1 and 5, respectively. The results are displayed in panels (a)-(h) of Fig. TM TM cyl . div ., x
TE TE
source, Ycyl . div ., x becomes negative for M < –1.8 (or M > 1.8). TE TE
Otherwise, Ycyl . div ., x is always positive for all the values of M as kr0 increases. ,
The plots for Ycyl . div ., x are displayed in panel (c), where an
the cylinder,
asymmetry arises with respect to the axis M = 0. For positive
vanishes before it turns positive as kr0 increases.
values of M, Ycyl . div ., x < 0, while for negative values of M, the
As the source is moved away from
Y
TE TE TE TE Ycyl Near the . div ., x kr0 , M Ycyl . div ., x kr0 , M .
is negative.
6. Panel (a) shows that near the source Y TM TM cyl . div ., x
TM TM
expected since Ycyl . div ., x (and Ycyl . div ., x ) is an even function;
,
opposite occurs. For M = 0, this component related to the interference of TM and TE modes vanishes, which is expected for a material lacking rotary polarization. Panel (d) shows the total radiation force function assuming a LHCP cylindrical diverging wave field. Near the source at kr0
TE TE
Panel (b) shows, however, that Ycyl . div ., x > 0 for all values of kr0. As for the interference term for LHCP cylindrically diverging waves, panel (c) shows that the cases when ka = 0.1 ,
and 1, Ycyl . div ., x < 0, contributing to a negative pulling force , cyl . div ., x
component. As ka increases (= 5), Y
= 0.2, Ycyl . div ., x displays negative values for 0.25 < M < 3.5.
is negative when
Also, for the case where kr0 = 1, Ycyl . div ., x is negative over a
the source is located nearby the cylinder, vanishes around kr0 6.5, and becomes positive as kr0 further increases. The behavior of the total radiation force function for LHCP cylindrically diverging waves is shown in panel (d) where
narrow range 0.6 < M < 1.4. As the source moves away from
the cylinder, Ycyl . div ., x is positive. ,
Ycyl ,.div ., x is only negative near the cylinder. As the incident
Panel (e) displays the plots for Ycyl . div ., x , where for positive
field is changed to a RHCP cylindrically diverging waves, the
values of M, Ycyl . div ., x > 0, while for negative values of M,
,
,
, , Ycyl . div., x < 0. Similarly to panel (c), Ycyl . div ., x vanishes for M =
radiation force component Ycyl . div ., x is always positive as shown in panel (e). It also contributed to a pushing/repulsive force as shown in panel (f). The ORFCD for plane progressive waves is displayed in panel (g), which clearly shows total independence of the parameter kr0. In all the cases,
0. The plots for the total radiation force function assuming a RHCP cylindrical diverging wave field are shown in panel (f).
Y p . p . w., x < 0 for the PEMC cylinder with M = 0.5. The
Near the source at kr0 = 0.2, Ycyl . div ., x displays negative values
curves in panel (h) also show that the ORFCD of cylindrically diverging waves is also negative.
Ycyl .div ., x is negative over the range –1.4 < M < –0.6, while
for –3.5 < M < –0.25. Also, for the case where kr0 = 1,
Ycyl .div ., x > 0 for kr0 = 10. 17
JQSRT (2020)
Fig. 9. The same as in Fig. 7, but ka = 5.
18
JQSRT (2020)
Fig. 10. The same as in Fig. 8, but ka = 5.
19
JQSRT (2020) both LHCP and RHCP waves, which could be useful in optical manipulation and in studying the mechanical effects of EM waves on particles exhibiting rotary polarization. In this analysis, a rigorous analytical formalism is developed and examplified for a lossless PEMC circular cylinder using the modal expansion method in partial-wave series in cylindrical coordinates. Mathematical expressions for the EM radiation forces (per-length) as well as the scattering, extinction and absorption energy efficiencies are derived without any approximations. The incident illuminating field is either composed of LHCP or RHCP cylindrical diverging waves. Numerical computations are performed with particular emphases on the size parameter of the cylinder, its distance from the source and EM admittance parameter. Several conditions are predicted where the PEMC cylinder located nearby the source can experience a pulling negative force in opposite direction of wave propagation. Should some conditions related to the size parameter, source distance and admittance parameter be met, the PEMC cylinder becomes irresponsive to the linear transfer of momentum, and experiences zero force. In addition, the possibility of EM cloaking is also predicted for a Rayleigh PEMC cylinder illuminated by LHCP or RHCP waves. Furthermore, both the ORFCD and EEECD alternate between negative or positive values depending on the EM admittance. This effect may be used in spectroscopy methods in particle characterization and classification. The results show that the numerical predictions are in total agreement with the law of energy conservation. It is important to note here that the radiation force expressions developed here are not restricted to the case of a PEMC cylinder, but can be used for any cylindrical material exhibiting polarization rotation such as a chiral, topological insulator or plasma cylinder to name a few cases. Concerning cylindrical particles with geometrical crosssections deviating from the circular one, recent investigations have addressed part of this challenge for various cases of illuminations with linearly polarized fields [52-55]. It would be interesting to further investigate the ORFCD and EEECD methods for the characterization of elliptical cylinders with smooth and corrugated surfaces, and the influence of either LHCP or RHCP waves on the radiation forces for a PEMC cylinder. Moreover, the analysis to consider the effects of boundaries/corners on the ORFCD and EEECD for a PEMC cylinder would be of interest, and the scope of the previous works on homogeneous particles [56, 57] could be extended for this purpose. Also, multiple scattering effects [52, 58, 59], which are significant in the presence of two or more cylinders, affect the ORFCD and EEECD spectroscopy methods. Further analyses are warranted to carefully examine potentially novel effects in radiation force and EM cloaking arising from those emergent phenomena.
The ORFCD for plane progressive waves is displayed in panel (g), which exhibits positive or negative values when the admittance is negative or positive, respectively. Similarly, the ORFCD for cylindrical diverging waves displayed in panel (h) reveals positive or negative variations versus negative or positive admittance, respectively, which is the largest near the source. The extinction energy efficiency factors are also computed, and the results are displayed in panels (a)-(g) of Fig. 8 for the Rayleigh (i.e., small) PEMC cylinder at ka = 0.1. Notice that in all the plots, the extinction factors are minimally affected by the change of the source-cylinder dimensionless distance (i.e., all the plots are superimposed for the three selected values of TM TM
TE TE
kr0). Panels (a) and (b) show that Qext and Qext are symmetric with respect to the axis M = 0 and are always positive. The interference extinction factor displayed in panel (c) exhibits positive and negative values for negative and positive admittance, respectively, while the total extinction assuming a LHCP cylindrical diverging waves is always positive as required by energy conservation and shown in panel (d). The solid dashed line in panel (d) [also in panel (f)] corresponds to the absorption efficiency, which is zero as expected. An interesting observation is noted for M = +1 for
all values of kr0, where Qext 0. This effect suggests the feasibility of EM cloaking of a Rayleigh PEMC cylinder in LHCP waves where extinction is nearly zero. Panel (e) for the interference extinction factor for RHCP waves varies between negative and positive values as M varies similarly, and vanishes for M = 0. Panel (f) shows the total extinction energy efficiency factor for RHCP waves, where also the possibility of achieving EM cloaking is predicted for M = –1. The EEECD for the Rayleigh PEMC cylinder is displayed in panel (g), where positive and negative values are computed while M varies, respectively, from negative to positive numbers. Thus, it can be concluded that the EEECD effect is highly sensitive to the EM admittance parameter, which can be used as a potential means in particle characterization of particles allowing rotary polarization. Additional computations versus admittance are performed for a larger Mie PEMC cylinder with ka = 5 at three different values of kr0 (= 5.1, 6 and 10). The corresponding results for the radiation force functions and extinction efficiency factors are displayed in the panels of Figs. 9 and 10, respectively. Although the plots in the panels of Fig. 9 display somewhat similar behaviors with the Rayleigh case shown in Fig. 7, the amplitudes are smaller. On the other hand, the panels in Fig. 10 for the Mie PEMC cylinder exhibit significantly different characteristics, quite distinct from the Rayleigh case presented in Fig. 8. Particularly, panels (d) and (f) in Fig. 10 do not predict any cloaking effect, which only occurs for the small PEMC cylinder. Moreover, the distance from the source affects the extinction efficiency factors distinctively.
References
4. Conclusion and some perspectives
[1] Berova N, Nakanishi K, Woody RW. Circular Dichroism: Principles and Applications. New York, USA: Wiley; 2000. [2] Arago DFJ. Mémoire sur une modification remarquable qu’éprouvent les rayons lumineux dans leurs passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique. Mém Cl Sci Math Phys 1811;1:93–134.
This work introduces a method of spectroscopy, termed here optical radiation force circular dichroism (ORFCD). This technique is based on subtracting the radiation forces of 20
JQSRT (2020) [3] Herschel JFW. On the Rotation Impressed by Plates of Rock Crystal on the Planes of Polarization of the Rays of Light as Connected with Certain Peculiarities in Its Crystallization. Transactions of the Cambridge Philosophical Society 1820;1:43–51. [4] Pasteur L. Memoires sur la relation qui peut exister entre la forme crystalline et al composition chimique, et sur la cause de la polarization rotatoire. Compt Rend Séances Acad Sci 1848;26:535-8. [5] Kauznman WJ, Walter JE, Eyring H. Theories of Optical Rotatory Power. Chemical Reviews 1940;26:339-407. [6] Beckmann P. The depolarization of electromagnetic waves: Golem Press; 1968. [7] Fasman GD. Circular Dichroism and the Conformational Analysis of Biomolecules: Springer US; 1996. [8] Bohren CF. Scattering of electromagnetic waves by an optically active cylinder. J Colloid Interface Sci 1978;66:105-9. [9] Mitri FG. Optical Bessel tractor beam on active dielectric Rayleigh prolate and oblate spheroids. J Opt Soc Am B 2017;34:899-908. [10] Mitri FG. Extinction cross-section suppression and active acoustic invisibility cloaking. Journal of Physics D: Applied Physics 2017;50:41LT01. [11] Mitri FG. Extinction cross-section cancellation of a cylindrical radiating active source near a rigid corner and acoustic invisibility. J Appl Phys 2017;122:174901. [12] Mitri FG. Active electromagnetic invisibility cloaking and radiation force cancellation. Journal of Quantitative Spectroscopy and Radiative Transfer 2018;207:48-53. [13] Ranjbar B, Gill P. Circular Dichroism Techniques: Biomolecular and Nanostructural Analyses- A Review. Chemical Biology & Drug Design 2009;74:101-20. [14] Chemes LB, Alonso LG, Noval MG, de Prat-Gay G. Circular Dichroism Techniques for the Analysis of Intrinsically Disordered Proteins and Domains. In: Uversky VN, Dunker AK, editors. Intrinsically Disordered Protein Analysis: Volume 1, Methods and Experimental Tools. Totowa, NJ: Humana Press; 2012. p. 387-404. [15] Berova N, Bari LD, Pescitelli G. Application of electronic circular dichroism in configurational and conformational analysis of organic compounds. Chemical Society Reviews 2007;36:914-31. [16] Mason WR. Magnetic Circular Dichroism Spectroscopy: Wiley; 2007. [17] P J Stephens a, Lowe MA. Vibrational Circular Dichroism. Annual Review of Physical Chemistry 1985;36:213-41. [18] Bayley P, Anson M. Stopped-flow Circular Dichroism: A rapid kinetic study of the binding of a sulphonamide drug to bovine carbonic anhydrase. Biochemical and Biophysical Research Communications 1975;62:717-22. [19] Miles AJ, Wallace BA. Synchrotron radiation circular dichroism spectroscopy of proteins and applications in structural and functional genomics. Chemical Society Reviews 2006;35:39-51. [20] van de Hulst HC. Light scattering by small particles: John Wiley and Sons, Inc.; 1957. [21] Ianeselli A, Orioli S, Spagnolli G, Faccioli P, Cupellini L, Jurinovich S, et al. Atomic Detail of Protein Folding Revealed by an Ab Initio Reappraisal of Circular Dichroism. Journal of the American Chemical Society 2018;140:3674-82. [22] Lindell IV, Sihvola AH. Perfect Electromagnetic Conductor. Journal of Electromagnetic Waves and Applications 2005;19:861-9. [23] Sihvola A, Lindell IV. Perfect electromagnetic conductor medium. Annalen der Physik 2008;17:787-802. [24] Ruppin R. Scattering of Electromagnetic Radiation by a Perfect Electromagnetic Conductor Cylinder. Journal of Electromagnetic Waves and Applications 2006;20:1853-60. [25] Ahmed S, Naqvi QA. Electromagnetic Scattering from a Perfect Electromagnetic Conductor Cylinder Buried in a Dielectric Half-Space. Progress In Electromagnetics Research 2008;78:25-38. [26] Ahmed S, Naqvi QA. Electromagnetic Scattering from Parallel Perfect Electromagnetic Conductor Cylinders of Circular Cross-Sections Using an Iterative Procedure. Journal of Electromagnetic Waves and Applications 2008;22:987-1003. [27] Ahmed S, Naqvi QA. Electromagnetic scattering from a two dimensional perfect electromagnetic conductor (PEMC) strip and PEMC strip grating simulated by circular cylinders. Opt. Communications 2008;281:4211-8. [28] Ahmed S, Naqvi QA. Directive EM Radiation of a Line Source in the Presence of a Coated PEMC Circular Cylinder. Progress In Electromagnetics Research 2009;92:91-102. [29] Ghaffar A, Yaqoob MZ, Alkanhal MAS, Ahmed S, Naqvi QA, Kalyar MA. Scattering of electromagnetic wave from perfect electromagnetic
conductor cylinders placed in un-magnetized isotropic plasma medium. Optik 2014;125:4779-83. [30] Fiaz MA. Investigating the reduction of cross-polarized Gaussian beam scattering from a PEMC buried cylinder coated with a topological insulator. Appl Optics 2018;57:7830-6. [31] Ahmad A, Fiaz MA. Scattered field from a PEMC cylinder buried below rough interface using extended boundary condition method. Optik 2019;193:162572. [32] Hamid AK, Cooray F. Scattering from a Buried PEMC Cylinder due to a Line Source Excitation above a Planar Interface Between Two Isorefractive Half Spaces. Advanced Electromagnetics (AEM) 2019;8:16. [33] Hamid AK, Cooray F. Scattering from a Buried PEMC Cylinder Illuminated by a Normally Incident Plane Wave Propagating in Free Space. Advanced Electromagnetics (AEM) 2019;8:1-7. [34] Mitri FG. Electromagnetic radiation force on a perfect electromagnetic conductor (PEMC) circular cylinder. Journal of Quantitative Spectroscopy and Radiative Transfer 2019;233:21-8. [35] Mitri FG. Optical radiation force expression for a cylinder exhibiting rotary polarization in plane quasi-standing, standing, or progressive waves. Journal of the Optical Society of America A 2019;36:768-74. [36] Mitri FG. Induced radiation force of an optical line source on a cylinder material exhibiting circular dichroism. Journal of the Optical Society of America A 2019;36:1648-56. [37] Graf JH. Ueber die Addition und Subtraction der Argumente bei Bessel'schen Functionen nebst einer Anwendung. Mathematische Annalen 1893;43:136–44. [38] Watson GN. A Treatise on the Theory of Bessel Functions. London: Cambridge University Press; 1922. [39] Strutt JW (Lord Rayleigh). The theory of sound. New York: Dover publications; 1945. [40] Morse PM, Feshbach H. Methods of theoretical physics. New York: McGraw-Hill Book Co.; 1953. [41] Maxwell JC. A Treatise on electricity and magnetism. Oxford, UK: Clarendon Press; 1873. [42] Gouesbet G, Grehan G. Generalized Lorenz-Mie Theories. 1st ed: Springer, Berlin; 2011. [43] Mitri FG. Radiation force and torque of light-sheets. Journal of Optics 2017;19:065403. [44] Mitri FG. Generalization of the optical theorem for monochromatic electromagnetic beams of arbitrary wavefront in cylindrical coordinates. Journal of Quantitative Spectroscopy and Radiative Transfer 2015;166:81-92. [45] Wiscombe WJ. Improved Mie scattering algorithms. Appl Optics 1980;19:1505-9. [46] Franz W, Deppermann K. Theorie der Beugung am Zylinder unter Berücksichtigung der Kriechwelle. Ann. der Physik 1952;445:361-73. [47] Franz W, Beckmann P. Creeping waves for objects of finite conductivity. IRE Transactions on Antennas and Propagation 1956;4:203-8. [48] Franz W, Klante K. Diffraction by surfaces of variable curvature. IRE Trans Antenn Prop 1959;7:68-70. [49] Pandoli O, Massi A, Cavazzini A, Spada GP, Cui D. Circular dichroism and UV-Vis absorption spectroscopic monitoring of production of chiral silver nanoparticles templated by guanosine 5′-monophosphate. Analyst 2011;136:3713-9. [50] Khalid S, Rodger PM, Rodger A. Theoretical Aspects of the Enantiomeric Resolution of Dimetallo Helicates with Different Surface Topologies on Cellulose Columns. Journal of Liquid Chromatography & Related Technologies 2005;28:2995-3003. [51] Li HJ, Epstein P, Yu SS, Brand B. Investigation of huge negative circular dichroism spectra of some nucleoproteins. Nucleic Acids Research 1974;1:1371-84. [52] Mitri FG. Electromagnetic binding and radiation force reversal on a pair of electrically conducting cylinders of arbitrary geometrical crosssection with smooth and corrugated surfaces. OSA Continuum 2018;1:521-41. [53] Mitri FG. Optical radiation force (per–length) on an electrically conducting elliptical cylinder having a smooth or ribbed surface. OSA Continuum 2019;2:298-313. [54] Mitri FG. Radiation force and torque on perfect electrically–conducting (PEC) corrugated circular and elliptical cylinders in TE or TM polarized plane progressive waves with arbitrary incidence. Journal of Quantitative Spectroscopy and Radiative Transfer 2019;235:15-23. [55] Mitri FG. Radiation force and torque on an elliptical cylinder illuminated by a TE-polarized non-paraxial focused Gaussian light sheet with
21
JQSRT (2020)
[56]
[57]
[58]
[59]
arbitrary incidence. Journal of the Optical Society of America A 2020;37:265-75. Mitri FG. Scattering cross-section of a cylindrical conducting particle illuminated by electromagnetic plane waves near a conducting quarterspace. Journal of Quantitative Spectroscopy and Radiative Transfer 2018;215:77-83. Mitri FG. Acoustic radiation force of attraction, cancellation and repulsion on a circular cylinder near a rigid corner space. Applied Mathematical Modelling 2018;64:688-98. Mitri FG. Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles. Journal of Quantitative Spectroscopy and Radiative Transfer 2018;206:142-50. Mitri FG. Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles. Journal of Modern Optics 2019;66:1347-57.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Statement
FG Mitri has conceptualized the methodology, its validation, data curation, and writing of the paper in its entirety.
22