IACS Institutional Repository

Indian J. Phys. 82 (6), 659-661 (2008) 
Vol. 82 • No. 6 • June 2008 
(CONTENTS 
Proceedings (Part II) of the ffh Biennial Conference of the Physics Academy 
of the North East (PANE) held at Department of Physics, Gauhati University, 
Guwahati-781 014, Assam, India during March 1-2,2007. 
FrontTitle 653 
Advisory Board and Editors 655-656 
From Editor's Desk 657 
Front Contents 659-661 
Foreword 
DILIP KUMAR CHOUDHURY AND BUDDHADEB BHATTACHARJEE 663-664 
Direct derivation of Sagnac effect 
K D KRORI, SABITA DUTTA AND KANIKA DAS 665-672 
Nucleocosmochronology of Dergaon meteorite 
P DUTTA, K DUORAH AND H L DUORAH 673-678 
Cavity-modified laser induced fluorescence of a blended system 
of polymer film 
R CHANGMAI AND G D BARUAH 679-683 
Microstructures, stress, strain and surface characterization of TD 
polycrystalline CdS thin films 
K KUNJABALI SINGH AND H L DAS 685-693 
[ Cont'd on next page ] 
660 Contents 
Electrical transport and magnetic properties of La086Ag0 ^(Mn^ Al )Oq 
compounds 
S K SRIVASTAVA, MANORANJAN KAR AND S RAVI 695-699 
Influence of cooling rate on the properties of ferromagnetic shape 
memory alloy 
SlDANANDA S A R M A AND A SRINIVASAN 7 0 1 - 7 0 6 
Synthesis and optical characterization of CdS nanocomposites 
R DEVI, P K KALITA, P PURKAYASTHA AND B K SARMA 707-713 
Fabrication of silver/cross-linked polyvinyl alcohol nanoparticles by 
hydrothermal method 
S DEB AND D SARKAR 715-718 
Naphthacene and pentacene based organic thin film transistors with 
L a ^ as the gate insulator 
K KONWAR, P GOGOI AND B BAISHYA 719-722 
Comparative studies on optical parameters of CdTe and ZnO thin films 
G WARY AND A RAHMAN 723-728 
Application of projection operator method to define basis functions 
for use in photoemission calculations 
B ZOLIANA AND R K THAPA 729-734 
Effect of collision geometry on the multiplicity of secondary charged 
particles emitted from 84Kr-AgBr interactions at 950 MeV/A 
B BHATTACHARJEE, B DEBNATH AND S SENGUPTA 735-740 
Hardness study of titanium nitride thin films deposited on bell-metal 
by cylindrical magnetron sputtering 
SANKAR MONII BORAH, ARUP RATAN PAL, HEREMBA BAILUNG 
AND JOYANTI CHUTIA 741-746 
Proton induced X-ray emission (PIXE) and proton induced y-ray 
emission (PIGE) studies of some medicinal plants of north east India 
K NOMITA DEVI, H NANDAKUMAR SARMA AND SANJIV KUMAR 747-752 
Type-ll seesaw in SO(10) theories with spontaneous CP violation 
KBORA 753-759 
Vector model of quantum inteference laser 
FARZANA B HAZARIKA AND G D BARUAH 761-766 
Contents 661 
Algebraic approach : study of vibrational spectra of some linear 
triatomic molecules 
NIRMAL KUMAR SARKAR, JOYDEEP CHOUDHURY AND 
RAMENDU BHATTACHARJEE 767-772 
X-ray and infrared spectroscopic studies of the molecular structure of 
3-(2,4-dichlorophenyl)-1 -phenylprop-2-en-1 -one 
MANISHA PHUKAN AND B K SARMA 773-777 
Form factors and charge radii of light and heavy flavoured mesons in 
a QCD inspired quark model with two loop static potential 
NAMITA SHARMA BORDOLOI AND D K CHOUDHURY 779-787 
Quark contribution in the evolution equation of the scaling violation of F^  
ABHIJEET DAS AND A SAIKIA 789-794 
Field effect transistor from dispersion polymerized aniline 
J BHADRA AND D SARKAR 795-799 
Interaction of loosely bound radioactive and stable nuclei via elastic 
scattering and fusion cross sections 
KKALITA 801-805 
Forthcoming Publications 807--808 
Notes for Contributors 809-812 
Our Special Publications 813-814 


English

Front Contents

Srivastava, S K

Kar, Manoranjan

Ravi, S

Electrical Transport and Magnetic Properties of La0.86Ag0.15 (Mn1-y Aly)O3 Compounds

Bora, K

Indian J. Phys. 82 (6), 753-759 (2008) 
Type-II seesaw in SO(10) theories with spontaneous 
CP violation 
KBora 
Department of Physics, Gauhati University Ouwahati 781 014 Assam Indwi 
E mail kalpanaO* gauhati ac in 
Abstract We propose a possibility of spontaneous CP-violation (SCPV) at high scale in a SUSY SO(10) 
theory The model is L-R symmetric SUSY SO(10) with 10 and 126 dimensional Higgs generating fermion masses, 
and the CP phase is generated through complex VEV of B-L breaking 126 Higgs The model can have potential 
applications in explaining fermion masses, v masses via type- II seesaw mechanism and Leptogenesis as well 
Keywords Susy So(10), spontaneous CP violation, GUTs 
PACS Nos. 11 15 Ex, 11 30 Er, 11 30 Pb, 12 10 Kt 
1. Introduction 
Understanding fermion masses and mixings is one of the longstanding challenges of 
theoretical particle physics. The various neutrino oscillation experiments have now 
established that neutrinos have masses, and that they mix among themselves Grand 
Unified Theories (GUTs) provide a powerful tool for understanding fermion masses, and 
relations among them. 
CP violation (CPV) was discovered experimentally about four decades ago, but its 
origin still remains one of the fundamental open questions in particle physics. CPV is 
directly observed only in the decays of the Kaons and B-mesons. At least four aspects of 
CPV are observed in nature - CPV in quark sector [1,2], in lepton sector, generation of 
BAU (baryon asymmetry of the Universe), and strong and SUSY CP problems. In this 
paper, we shall address its manifestation in the first two cases only. 
Within the premises of the standard model (SM) model, neutrinos are massless, so 
there is no mixing and no CPV in the neutrino sector. However, the existence of v 
masses is a well established fact now, and hence any theory which can explain them 
would also imply CPV in leptonic (CPV-L) sector in principle. The latter might be detected 
©2008IACS 
754 KBora 
in future experiments to be performed at neutrino factories. Indirect evidence for the CPV-
L may also be provided by forthcoming experiments on v -less ftp decay (majorana 
phases). Existence of matter dominated Universe is another evidence of CPV, but it has 
been established that within the SM, it is not possible to generate observed BAUt partly 
due to smallness of CPV in SM (CKM phase). This provides motivation for considering 
new sources of CPV beyond the SM-CKM mechanism (e.g. through CPV from SUSY 
breaking sector). In gauge theories, there are two possibilities of CPV - explicit (hard) CP 
breaking at the Lagrangian level through complex Yukawa couplings (as in SM), or 
spontaneous (soft ) CP breaking by the vacuum via complex VEV (SCPV). 
SCPV at higher scales seems to be an interesting proposition to explain the origin of 
CPV in nature since all the couplings of the Lagrangian are real due to CP invanance at 
the Lagrangian level. CP is broken only through phases in VEV [3,4]. There has been 
quite significant amount of works in literature addressing the question of SCPV, an 
incomplete list is given as [5-11]. It has been a known difficulty with SUSY theories that 
they cannot generate CP breaking spontaneously. This is because they lead to a real 
CKM matrix. A recent analysis [12] of the present experimental data provides clear evidence 
for a complex CKM matrix. These experimental findings [13] of the Y angle inspires to 
ask the question if we can have a SUSY extension of the SM with SCPV and a complex 
CKM matrix. In fact some work has already been done in this line [6-10]. There they 
introduce extra vector-like quark which mixes with standard quarks and lead to a non-
trivial phase in 3x3 CKM matrix [7], VEV of 126 Higgs in SUSY SO(10) theory is complex 
[6], or add extra Higgs [8], extension of SM with a SU(2)L singlet quark and a singlet 
Higgs field [11], has been considered. Issues of yukawa sector fits as well as problem of 
CKM CP violation in the minimal setup has been discussed in detail in [14] also. 
2. Motivation for the present work 
In the present work, we have attempted to find a possible model to generate a CP phase 
spontaneously in L-R symmetric SUSY SO(10) theory, in particular in context of generating 
neutrino masses and mixings via type-ll seesaw mechanism. In the framework of SO(10) 
GUT SCPV was first discussed in [15]. In the present model, B-L symmetry is broken by 
a 126 dim Higgs, which also contributes to fermion masses along with a 10 dim Higgs 
[16,17]. This theory seems to be too attractive to generate small masses - it has a right 
handed majorana neutrino (RHMN) to implement see-saw mechanism, naturally contains 
B-L symmetry needed to keep the RHMN below the Planck scale, provides a group 
theoretical explanation of why neutrinos are majorana particles, has automatic R-parity 
conservation which leads to natural conservation of baryon and lepton number symmetry 
prior to symmetry breaking, provides a simple mechanism for explaining origin of matter 
in the Universe etc. It has been shown that type-l see-saw predictions of this model are 
in contradiction with experiments [16,18]. Then, type-ll see-saw [19] for neutrino masses 
[20] was suggested to explain the data. In [21] b-x unification was used to explain the 
masses and mixings. In [22], CPV was introduced thorough complex Yukawa couplings 
(of course this list is incomplete!), and it was found that compatibility with data requires 
Type-ll seesaw in SO(10) theories with spontaneous CP violation 755 
CKM phase to be outside the first quadrant (whereas the SM CKM phase is in first 
quadrant). It implies tnat to understand CPV in this minimal SO(10) model, one must 
have a non-CKM source for CPV So it would be interesting to see how CPV can be 
generated in this model to explain v masses and mixings, along with generation of BAU 
through Leptogenesis with the minimal modification. Attempts have already been made in 
this direction [23,24], but they included 120-dim Higgs and CP is violated through complex 
Yukawa couplings. 
In the present work, we propose a different scenario We show that if assume SCPV 
at higher scales in minimal SUSY SO(10) theory (with 10+126 Higgs) with complex VEV 
for B-L breaking 126 Higgs, one can't have a nontnvial CPV phase So we propose that if 
we include two 126 Higgs bosons, one with real VEV and the other with a complex VEV, 
one can have a nontnvial value of CPV phase by some fine-tuning in the Higgs coupling 
constants of the Lagrangian. Now since the theory has SU(4)C symmetry at higher scales, 
the CKM phase in the baryonic quark mass matrix will be related to CP phases in the 
leptonic sector as well And since heavy RH maprana neutrino mass matrix will be complex 
(due to complex VEV on 126 Higgs) the model has the potential to explain BAU also It 
should be noted that CPV may be generated, in general by assigning VEV of any Higgs 
to be complex. But advantage of 126 having complex VEV is that, it appears in mass 
relations of fermions, to correct them, through induced VEV of triplet of 126 So it can 
directly generate CKM-CP violation in the quark sector and leptonic sector We would like 
to stress that we are not attempting to comment on other issues such as strong CP, 
SUSY CP problems etc, which can be solved may be by imposing some additional 
symmetries on the Lagrangian, or via some other mechanism This lies beyond the scope 
of this paper. 
Now, we would like to present the distinguishing features and novelties of our work, as 
compared to some of the recent works in this line: 
1. In [23,24], CP is introduced through complex Yukawa couplings, whereas we 
use SCPV. 
2. In [9], SUSY SO(10) -> SM via intermediate SU(5), while here we have used 
SU(2)L x SU(2)R x SU(4)C as the intermediate symmetry, although the breaking 
is single step {i.e. Mv = MR[M]) 
3. In [8], they add extra Higgs/Higgs+fermions to the SM, white here we have 
added extra 126 Higgs to the SUSY SO(10) theory, with VEV of one of the 126 
as real, and that of the other as complex. At the same time, we propose that it 
be applied for specific model building purpose (for neutrino masses). 
3. The model 
We consider the SUSY SO(10) theory, with 45(A) + 54(S) dim Higgs field breaking SO(10) 
down to the L-R symmetric group SU(2)Lx SU(2)Rx U(1)(B.L)x SU(4)C (G2213), and the 
minimal Higgs set 10 + 126 + 126 that couple to matter and also break the G2213 group 
756 KBora 
to G31 SU(3)C x U(1)em ) [17] (these details are well established, but for the sake of 
completeness, we shall review them briefly here). The Majorana mass of heavy RH neutrino 
owes its origin to the breaking of local B-L symmetry, therefore MR ~ Mseesaw ~MB,L [25] 
Local B-L symmetry provides a natural way to understand smallness of RH neutrino mass 
compared to Mpl . With G2213 one can understand parity violation in nature. 126 (A) 
leaves R-panty as an exact symmetry, and explains why neutralino can act as stable 
dark matter component [26]. In a generic SO(10) with 126 getting VEV, one gets two 
contributions to masses - type-l see-saw and type-ll see-saw (from induced VEV of the 
triplet of 126 Higgs). The superpotential also contains Planck scale induced non-
renormalizable terms (more than dim-3), to give induced VEV to triplet of 126 (for type-ll 
see-saw). If these are not included, 210 Higgs is needed, but getting DTS is not very 
simple [27] here. The superpotential of the theory contains three parts, 
W = Wf + Ws + Wpt Wf = h^^.H + f^^.A (1) 
where, Wf generates mass of matter, with (2,2,1) of 10 dim H and (2,2,15) of 126 dim 
Higgs acquiring VEV. The Ws contains scalar Higgs contribution, and is 
W$ = (fiH + AS)HH + /z sS2 + JlsS? +»AA2+ nAAA + XAAAA + A5' (SAA + SAA) + XASA2 (2) 
The Wp is planck-scale induced part of the superpotential 
V8/r WP=^-APAA2H Mt PI 
(3) 
Now from the superpotential, the F-term (Higgs part) of the potential can be constructed 
|2 
as "-i. dw 
V = 
where a 's are the Higgs scalars, 
dW 
dA 
dW 
dA 
dW 
ds 
dW 
BA 
+ D- term (4) 
and it is easy to see that < A > AAAH term from 
dW 
dA will contribute induced VEV to 
Z (2, 2, 15) of 126 Higgs, to correct mass relations of fermions, while AA HH from 
dW\2 i —\ 
-rx\ term will contribute induced VEV to triplet 4(3,1,10] for type-ll see-saw 
mechanism. 
Next, we shall consider how the breakings of higher symmetries is realized through 
VEVs of Higgs along different directions. In a SUSY theory, the ground state should have 
zero energy, so both F-flatness and D-flatness conditions must be satisfied. The latter is 
Type-ll seesaw in SO(10) theones with spontaneous CP violation 757 
ensured by the presence of both I and I The F-flatness cond.t.ons, with the scalars 
acquiring VEVs as follows are • 
<S>= diag(k,k,k,k,k,k,k',k'Xk'), <r A>- iuxdiag(bb,b,c,c) (5) 
<A>=vRe'u, <4>=v R e" \ (6) 
(7) Fs' l£ = 2fisk + 3As/f2 + A* M6*'" + x°v"e "')~ A^ ' ° 
| ^ « 2nsk' + 3As/c'2 + ^ (v2Re2'" + ^ e 2 '") A , ^ * 0 (8) 
F„ — - = -2bvA+A,x0vR-2MAk^0 (9) <W _ , 2 
dc ~2CA^ + A j ^ ~ ^ ^ " ° (10) 
db 
dW „_ , .
 2 
^ = A ^ e " 0 1 4 A, (x0b+ c ) ^ e - ' " + 2A^ (y0* + k')vRe" = 0 (11) 
F^ = ^ ^ 8 " -f A, (xob f c ) ^ e ' " 4 2As'(y0/c + k')vBe "' = 0 (12) 
where x0 and y0 are appropriate C-G coefficients, due to involvements of different groups 
These constraints must give a non-trivial solution for the CPV phase. The F^ and FA 
constraints can be written as 
(>UB)cosa + /(>4-B)sina = 0 (13) 
(/4 + B)cosa + /(B-/4)sina = 0 (14) 
where constants A and B involve various Higgs couplings and VEVs etc It is easy to 
see that these equations give only the trivial solutions a = 0 and a = n/2 These values 
of a have also to be satisfied simultaneously by the Fs constraints, 
F, : cos2a = A , T S
 2
 s
 (15) X b
2 
kAcz 
-2nsk + : 
2KW2R 
-2fxsk' + 
Usk2 
3As/c'2 F
*> • c °s2« = ffr-2—~ (16) 
758 KBora 
Eqs (13-16) are the new results of our present work, which implies that one cant 
have a nontnvial value of the CPV phase in a L-R symmetric minimal SUSY SO(10) 
theory, where CP has been broken spontaneously at high scale by the complex VEV of 
126Higgs. 
4. New proposal 
To overcome this difficulty, therefore, we propose that in the model, we have two 126 
Higgses, ^ and A^% such that one of them acquires a real VEV while the other one a 
complex VEV, 
< 4, >= vRe'l(X, < A, >= e vR (17) 
here e is a fine tuning parameter, which can be adjusted to get a desired nontnvial value 
of CPV phase at higher scales (see Eqs (15-17)) Note that this is not possible in a 
theory with one Higgs (126), or with two 126s with same VEVs (real or complex) The 
part of the new superpotential generating fermion masses will look like, 
Wf = hatPaVb + ^atWaVbAi + hatPaVb** ' <18) 
Since the VEV of a 126 Higgs is complex, the fermion mass matrices as well as the 
heavy right handed majorana mass matrix will be complex There will be now new relations 
among fermion masses, with a new parameter f in the theory (the theory is quasi-
mimmal in that sense), and a new type-ll see-saw formula The fitting of femion masses 
including neutrino masses at GUT scale according to these new relations can be done 
This analysis is going to be very involved and can be taken up in future works We would 
like to point out that since VEV of the 126 Higgs occurs in the masses of quarks as 
well, we have CKM-CP violation as well in the theory So, the CKM-CP violation as well 
as CPV in the neutrino masses is the manifestation of SCPV at higher scales, since 
VEV of 126 Higgs which is complex, is ~MGUT. 
5. Discussion and conclusion 
To conclude, we have presented a novel mechanism of generating CP spontaneously at 
higher scales in a L-R symmetric SUSY SO(10) theory, which can be further applied in 
context of neutrino masses and mixings, and leptogenesis. Eq. (17) is the new idea 
proposed here for the first time, in this work, which together with Eqs similar to (13-16) 
can give a nontnvial CP violating phase (other than 0 or n/2 ) in this quasi-minimal 
theory. The numerical analyses of fermion masses using GUTs and CKM phase is available 
in literature [14, 20, 21, 22] , but here we have addressed a more fundamental question 
- if CPV phase is at all allowed in a grand unified theory by the potential? Of course 
further investigations, as far as its applications and implications of this idea are concerned, 
are needed, which can be taken up in future works. 
Acknowledgment 
The author thanks M. K. Panda for a primer on GUTs. 
Type-ll seesaw in SO(10) theories with spontaneous CP violation 759 
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[27] D G Lee and R N Mohapatra Phys Lett B324 376 (1994)

Type-II Seesaw in SO(10) Theories with Spontaneous CP Violation

Raghuwanshi, Sanjeev Kumar

Talabattula, Srinivas

Indian J. Phys. 82(10) 1373-1383(2008) 
Applications of degenerate/non-degenerate modes coupling 
in an optical waveguide 
Sanjeev Kumar Raghuwanshi* and Srinivas Talabattula 
Applied Photonics Laboratory, Department of Electrical Communication Engineering, 
Indian Institute of Science, Bangalore-560 012, India 
E-mail : sanjeevkr@ece.iisc.ernet.in 
Received 25 April 200?\ accepted 22 April 2008 
Abstract : Mutual coupling between optical modes is essential in the design of integrated optic devices. In 
this paper we have described how optical energy couples between modes within and between optical 
waveguides. It has been implicitly assumed so far in the literature that the modes, once formed are unchanging 
except perhaps through attenuation due to absorption. In reality, simple mechanisms can lead to significant 
energy exchange among the various modes of a structure. Coupled mode theory describes this energy exchange 
and serves as the primary tool for designing optical couplers, switches and filters. We have explored a coupling 
technique that describes the scalar electromagnetic field of a perturbed waveguide in terms of a superposition 
of modes of the ideal waveguide. In this paper, various applications of degenerate/non-degenerate modes 
coupling in an optical waveguides are discussed with examples. We have also applied our degenerate coupled 
mode theory to analyse the co-directional waveguide coupler. The coupling period of the power is verified by 
Beam Propagation method. 
Keywords : Optical waveguide structure, coupled mode theory approach. 
PACS Nos. : 42.79.Dj, 42.79.-e 
1. Introduction 
Consider two proximate single mode optical waveguides. In each waveguide there are 
two waves, one propagating in the forward direction and one in the backward direction. 
Energy transfer, i.e. coupling, can occur if the evanescent field from one waveguide 
extends into the core of the neighboring waveguide. The degree to which two modes 
exchange energy depends on the design of the coupler and the mode structure of the 
two waveguides. For example, it seems plausible in the structure that the forward wave 
in one waveguide (A+) will primarily couple to the forward wave in the adjacent 
waveguide (8+). We have restricted our discussion to planar or rectangular waveguides 
'Corresponding Author © 2 « » I ACS 
m 
1374 Sanjeev Kumar Raghuwanshi and Srinlvas Talabattub 
in the whole paper. We have followed the development of the coupled mode theory as 
described by Yariv [1]. Consider the planar step index waveguide structure, with film 
index n, of thickness h, and substrate and cover indices ns and n0 respectively [7]. 
The waveguide can support a finite number of guided modes and an infinite number of 
radiation modes. 
In fact this paper is the proof of our Beam Propagation method results with 
coupled mode theory approach [2] for coupling period. The agreements of the results 
are excellent. When two orthogonal modes have identical values of propagation 
constant /?, we must use degenerate perturbation methods for solving the equation of 
motion. Non-degenerate coupled modes theory applies when two modes with different 
/3s are coupled. Non-degenerate mode generally display weak coupling. There are many 
examples of structures where two modes with identical propagation constants are 
coupled. This leads to degenerate coupling and a different approach is required to solve 
the problem. The primary equation for mode coupling is given by [1-19] 
^ e x p { y ( / 3 / z + a ; f ) } ~ ^ e x p { - y ( / 3 / z ~ a ; f ) } + c.a 
Here Af is the amplitude for mode j and $y(x) is the normalized amplitude distribution 
for mode j and also A", A \ Ppen are the backward wave, forward wave and perturbation 
terms respectively. Others terms has usual meaning as in optical waveguide. The 
detailed derivation and implications of this equation can be found elsewhere [3,7]. We 
explore non-degenerate coupling first. 
2. Non-degenerate coupling case : coupling due to a dielectric perturbation 
We begin with the simple case of a perturbed single mode waveguide and see how 
a dielectric defect can couple a mode's forward wave to its backward wave. Consider 
the symmetric slab waveguide shown in Figure 1. 
z*-e z—a 
Figure 1. A dielectric waveguide with a notch defect in it acta aa a perturbation to the guided modea. 
1375 
The waveguide consists of a guiding film index, n1f of thickness ht surrounded 
by a cladding index, n2. A small dielectric notch of depth /i/10 and length 2a in the 
core region perturbs the waveguide structure. Assume that the waveguide is a single 
mode structure and that for z > a there is no backward traveling wave, A~\z > a) = o. 
The mode expects to see an index of n^ when it gets to the notch region but instead 
finds the index is n2. This is a perturbation. To begin our analysis, we must determine 
the unperturbed modes of the waveguide. We can describe the eigenmode of the 
symmetric waveguide as [7], 
#y = Cexp{ - 7 (x - /? /2 ) } x>h/2 
- ~ cosKX , sinKX uif% ^ ^ u,r> $ = C — or -—ZTZ -h/2<x<h/2 y
 coStf/i/2 sm«/7/2 
^ = C e x p { 7 ( x + h /2 ) } x < ~ / ) / 2 . (2) 
where the coefficient, C is chosen to normalize the power in the waveguide to a value 
of 1 W per unit length. Here 7 refer to the attenuation coefficients in the cover and 
substrate respectively and « is the transverse component of wave propagation constant 
in the guiding film. The specific values of «, 7 and (3 are determined from the 
eigenvalue equation [7] for this structure once /?, n^ and n2 are specified. We assume 
this has been done and all eigenvalues are known. To determine the coupling, we must 
describe the perturbation term. In this example, the polarization perturbation, Pm{x) is 
the product of the change in dielectric constant e0 \nl ~ n i 2 ) ar>d the electric field of 
the forward wave £,(*) 
Ppe^x)« ^ ( x ) = e0 (n\ -n*)\ A+$(x)exp{-/(02-u>t)} + c.c. 
2 
0.4/)< x < 0 . 5 f t , - a < z < < 
= 0 elsewhere. (3) 
Notice that the perturbation term exists only in the notch region. Everywhere else in 
the waveguide the mode sees an index distribution that it would normally see without 
the perturbation. The amplitude eq. (1) of motion becomes 
d2 + -
1376 Sanjeev Kumar Raghuwanshi and Srinivas Talabattula 
cos/ex f 
dx [cos Kh/2) 
Mo ("! " " i l l
 A+ exp {_ . (/Jr _ uf)j + 1J |c(i 
* ' 0.4/1 
= jr(A+ exp{-7(/?z-u/f)} + c.c.), (4) 
where r is the coupling constant defined as 
J - . ^ W - ^ T l c f " " * ]"tfx,fo, - a < * < a 
0JJ C0S/C/7/2J 
= 0, elsewhere. • (5) 
Notice that the coupling constant is determined by the overlap of the coupled modes 
in the perturbation region. In this one-dimensional problem, we only integrate over the 
x coordinate to determine the coupling coefficient. Multiplying both sides of eq. (4) 
byexp{/(/3z-u;f)} yields an equation of motion for the amplitudes 
*£• exp (2//?z) - 5 £ + c.c. = }rA\ (6) 
To solve eq. (6), we must integrate both sides. The first term average to a small value 
when integrated over a distance large compared to (2/?)~1. Thus to first order we can 
drop the A~1 term, leaving the simplified equation of motion 
»£- + c*-irA+. (7) 
which, when integrated over z and applying the initial condition that A$ = A ( -a) , has 
solution 
^ = y4+(-a)exp(-yTz). (8) 
Thus we see that the amplitude of the field does not change (to first order) but the 
perturbation (a small region of lower index material) alters the phase of the wave. The 
forward wave in the region of the perturbation will be (note K is negative) 
E(z) = A*(-%exp{-j(f3 + r)z}. 
- a < z < a (9) 
To find a first order solution for A", we must assume that the forward wave, A+, does 
not change, so ^ / f o - 0 - Except for a slight phase change, this is true. The 
coupling equation becomes 
?£- /Wl+exp(-2/7?z). -a<z<a (10) 
uZ 
1377 
This can be directly integrated, nothing that 
A~{a) = 0, 
to yield 
/ r ( - a ) = - i ^ s i n ( 2 / 3 a ) . (11) 
To first order, the coupling of the forward wave to the backward is maximized when 
2/3a = (q + 1 /2)w, where q is an integer. In terms of a, the maximum reflections 
occurs when, 
(<7 + 1/2)7T a
-—w~ <12> 
The behavior of this structure is similar to that of a half wave dielectric stack used to 
make mirrors. Similarly, choosing a quarter wavelength for a will minimize the reflected 
term. The maximum amplitude of the reflection depends on y$% which is usually 
small. Generally speaking, maximum coupling will occur between a forward and 
backward wave when the spatial frequency of the perturbation is approximately 2/3. 
2.1. Coupling due to a symmetric notch in a slab waveguide : 
Consider the symmetric slab waveguide shown in Figure 3(a). A notch is symmetrically 
located about z = 0. In this waveguide, we will determine the normalized modes of the 
structure and calculate the coupling between the fundamental TE mode and the other 
TE modes of the structure. Assume that A = 1.3jjm, n, = 3 . 5 andn2 =3 .498. The 
first step is to determine the normalized modes of the ideal waveguide. We find the 
eigenvalues K and 7 using following equations [7] 
tan * % = J (For even modes) (13) 
= =
-
:
" - (For odd modes) (14) 
There are two even modes and two odd modes supported by this structure. Numerically 
evaluated values for « and (3 for each of mode are listed in Table 1. 
The electric field distribution for the modes are given by [7] 
$y = C e x p { - 7 ( x - f ? / 2 ) } x > / ) / 2 
cos/ex
 c sin KX 
ry
~~co&Kh/2 o r sin/cft/2 
g„ = C w » * ^ orC Z ^ ^ - / 7 / 2 < x < / ) / 2 
£ / = Cexp{7(x + /7/2)} x < - f t / 2 . (15) 
1378 Sanjeev KumarRaghuwanshiandSrinivas Talabattula 
We know every variable in these equations except the normalization coefficient, C. To 
normalize, we must adjust the amplitude, C, to satisfy [7] 
f*n(*)K(x)dx=^jL6i (16) 
The necessary values of C are listed in Table 1. These mode amplitudes will produce 
a normalized power of 1 W/cm width in the slab waveguide. Figure 2, shows the 
calculated mode distributions, for the four normalized modes taken from this data. 
Table 1. Propagation coefficients for the four allowed modes. 
Mode designation 
TE0 
TEt 
TE2 
TE3 
K - • c m * 1 
1335.12 
2658.1 
3949.8 
5158.45 
0 -> cm"1 
169157 
169142 
169117 
169084 
Normalization amplitude 
(v/cm) 
99.7 
197.2 
287.7 
353.3 
Having found the modes of the ideal waveguide, we can now calculate the coupling 
constant for each pair of modes. The polarization perturbation in this example is 
generated by the electric field of the TE0 mode in the dielectric notches. Explicitly, the 
perturbation is (for 9 p m <| x 1 1 0 p m and -a<z<a) 
Ppetx(x)~eo("t-"t)Eo(x,z,t) 
= - 2 . 6 4 7 X 1 0 ~ 1 3 cos (1335.12x) ~ Af exp{-y {0z - u>t)} + c.c. (17) 
Knowing Ppert, we can next calculate the coupling coefficients between the modes. 
Plugging the result into eq. (1), the formula for the general coupling coefficient between 
the TE0i and TEj mode is 
0.5/? -0.5/? 1 
J -2 .647 x1(T1 3 COS (1335.12x)#,+ J -2 .647x1(T 1 3 COS (1335.12x)^dx\. 
0.45/? -0.45/7 J 
(18) 
There are two integrals because there are two dielectric regions in the perturbation. By 
symmetry, we can see that modes TE, and TE3 will not couple to mode TEQ. The 
product of an even and odd function in a symmetric integral always yields a null result. 
Therefore two of the coupling coefficients equal zero. The only mode that the TEQ mode 
can couple to is the even symmetry TE2 mode. The coupling coefficient will be 
10 
75 
5 
-6 
-7.5 
«-' = 
0 1000 2000 3000 4000 5000 
(a) 
400 
200 
0 
-200 
-WO 
-0.002 -0.001 0 0001 Q002 
cm 
(b) 
400 
200 
I o 
-200 
-400 
-0.002 -0001 0 Q0O1 O002 
cm 
(c) 
-0.002 -0.001 0 
cm 
(d) 
0001 0002 
400 
200 
I o 
-200 
-400 
-0002 -0001 0 0001 0002 
cm 
<•) 
400 
300 
' 0 
-200 
-400 
mm*m*mmmmmw*m——*m 
M M M * A * M M I a li II 1 1 1 1 
-01002 -0.001 0 0001 0002 
cm 
(0 
Figure 2. (a) Waveguide in Figure 3(a), supports both even {TEQ, TEg.) and odd (7H1f TEJ modes, (b) (c) Even 
modes, (d) (e) Odd modes. (0 The four mode amplitudes are plotted on the same scale. 
0.5/) 
r w = 2 £ f -2.647X10-13 C08(1335.12X)287.7 ° ° ? i f ^ f * L dx O J v ' cos (3949.8/7/2) 0.45/1 
13B0 Sanjeev Kumar Raghuwanshi and Srinivas Talabattuia 
= - 3 . 9 1 2 cm \ (19) 
The coupled mode equation relating the TE2 mode to the TEQ mode is then, 
0A
*
 tf/(*«+«') _ 2 * L e-J(k*-*t) + c c 
9z dz 
- j r ^ e - ' ^ ^ \ (20) 
multiplying both sides byexp{y ( /? 2 z-u ; f ) } converts the equation to 
a£ ji** - ^L
 + c.c. = /roa*+e-'(*-*)*. dz ~ az ™" '-*•*- (21) 
Integrating over z from - a to a, the first term on the left hand side averages to zero 
to first order. The amplitude of mode TE2 at the end of the perturbation, assuming 
that /£( -a) = 0, is 
K (a) = 2jr{ 02 
= 7 
(ft-A) 
(7.83 
4o"sin(/Jo-02)a 
I 40 A>"sin(/3o-/?2)
a
- (22) 
Squaring this amplitude gives the actual power in the mode. The power in mode TE2 
as a function of perturbation length is shown in Figure 4(a). The coupling length ranges 
from 0 to 0.1 cm in the plot. We can see that a small fraction (<4%) of the mode 
energy transfers into mode TE2 at the optimum interaction length. 
3. Degenerate mode coupling 
There are many examples of structures where two modes with identical propagation 
constants are coupled. This leads to degenerate coupling and a different approach is 
required to solve the problem. Various examples are shown in Figures 3(b), (c). 
Consider the coupled slab waveguide structure is shown in Figure 3(d). The coupler 
consists of two identical step index waveguides with core thickness of 10 ^m situated 
approximately 4 p,m from each other. To calculate the coupling between the waveguides, 
we must first determine the eigenmodes of the uncoupled waveguides. Using techniques 
[7], 0 was found to be at A = 1 pm, 0 = 94227 cnrT1 (Figure 5(a)) and the normalized 
mode for the right-hand waveguide is [7] 
$ y = C e x p { - 2 8 4 0 ( x - 0 . 0 0 1 2 ) } x > 0 . 0 0 1 2 cm 
. - cos 1942 (x - 0.0007) 
*> = ° COS1942X0.0005 0 0 0 0 2 * * * 0 0 0 1 2 Cm 
Applications of degenerate/non-degenerate modes coupling in an optical waveguide 1381 
$ y = C exp {+2840 (x - 0.0002)} x < 0.0002 cm (23) 
Figure 3. (a) A symmetric waveguide is perturbed by a dielectric notch on the top and bottom of the guiding film. 
(b) A directional coupler can be made by placing two waveguides Jn close proximity to one another for a finite 
distance, (c) The coupled waveguides are separated in the y-directkm by a distance of 2a and are 2b wide, (d) 
Two identical slab waveguides are separated by 4 /im. 
The amplitude for the left-hand mode is identical in form, requiring only appropriate 
offset of the coordinates. The modes are norm#teed according to eq. (16). Two 
identical slab waveguides are separated by 4 ixm. t h e eigenmode for one of the slabs 
is superimposed on the right waveguide, as shown in Figure 5(b). Eq. (16) was 
numerically evaluated, yielding C = 433.56. 
In this example, we assume that initially the mode energy is completely 
contained in the right hand waveguide. The perturbation therefore only exists in the core 
of waveguide S, equaling 
Ppen(x) = # ( * )e 0 ( " I - n? ) [~ A+e-^*-^ + ex:. - 0 . 0 0 1 2 < x < -0 .0002 , 
* 0 Elsewhere (24) 
1382 Sanjeev Kumar Raghuwanshi and Srinwas Taiabattula 
0 002 004 006 008 01 
Couplng Length (cm) 
02 04 06 06 1 
Propagation Distance (cm) 
Figure 4. (a) The power transfer from one mode TEQ to mode TEz as a function of notch length in Figure 3(a) 
The coupling varies periodically with notch length, (b) The power in the original waveguide couples back and 
forth between the two waveguides. The coupling period for the power is approximately 0.4 cm. 
The coupling coefficient is found from 
we* 
-0.0002 
p
 = ~
o0 
4 
f (1.52 -1.4992) $a(x)^(x)c/x 
-0 0012 
= 3.6214 cnT1 (25) 
More details data regarding this calculation of coupling coefficient is available with the 
authors. So how does this result compare to the BPM (Beam propagation method) 
simulation [19]. Since this is a degenerate coupled system, there will be strong 
coupling. The amplitude will couple periodically back and forth between the waveguides 
[8]. The power is proportional to the square of the amplitude. Therefore we would 
predict the power would couple back and forth as [1-8], 
I A\2=A* cos(rz)2. (25) 
Figure 4(b) shows how the power couples back and forth between the waveguides. By 
inspection, we see that the spatial coupling period is approximately 0.4 cm, which is 
exactly what we observed in the BPM work [19]. 
4. Conclusions 
In this paper we have explored some applications of amplitude coupling between two 
waveguides based on a scalar theory. We found that coupling is maximized when the 
propagation coefficient, 0 for the two modes is equal. We can enhance the coupling 
Applications of degenerate/non-degenerate modes coupling in an optica/ waveguide 1383 
Figure 5. (a) For the waveguide Figure 3(d), there is only one allowed mode, which occurs near K •• 1942.12. 
(b) The eigenmode for one of the slabs is superimposed on the right waveguide. 
between dissimilar waveguides by using phase matching technique. The coupling of 
radiation from a waveguide into free space is an important problem in optoelectronics. 
Please note that the more details data are available only with authors of this paper, 
regarding the detail derivation of coupled mode equations for various cases. Reader 
should have basic knowledge about integrated optical waveguide to understand this 
paper. Details of derivation are omitted everywhere to avoid any difficulty to understand 
the mode coupling phenomena. The calculation is difficult because the guided modes 
couple to free space modes, which are not normalizable. The design of such couplers 
is as much an art as it is an engineering task. 
References 
[1) 
[2] 
[3] 
[4] 
[5] 
(6) 
[7] 
[81 
[9] 
[10] 
mi 
[12J 
[13] 
[14] 
[15] 
[16] 
[17] 
[18] 
[19] 
A Yariv IEEE J. Quantum Electron. 9 919 (1973) 
S K Raghuwanshi, T Srinivas and A Selvarajan J. Indian Inst Sci. 86 667 (2006) 
S K Raghuwanshi and S Talabattula, XXXII OSI Vdodara, India (2007) 
W H Louisell Coupled Mode and Parametric Electronics (New York : John Wiley and Sons) (1960) 
A W Snyder J. Opt. Soc. Amer. 62 1267 (1972) 
A W Snyder and J D Love Optical Waveguide Theory (London : Chapman and Hall) (1983) 
D Marcuse Theory of Dielectric Optical Waveguides (New York : Academic Press) (1974) 
A Hardy and W Streifer IEEE J. Lightwave Technol. 5 1135 (1985) 
S L Chuang IEEE J. Lightwave Technol. 6 294 (1988) 
W Streifer, M Osinski and A Hardy IEEE J. Lightwave Technol. 5 1 (1987) 
H A Haus, W P Huang, S Kawakami and N A Whitaker IEEE J. Ligtwave Technol. 5 16 (1987) 
H A Haus and W Huang Proc. IEEE7B 1505 (1991) 
A A Hardy IEEE J. Quantum Electron. 34 1109 (1998) 
A W Snyder, Y Chen and A Ankiewicz IEEE J. Lightwave Technol. 7 1400 (1989) 
K Yasumoto Opt. Lett. 7 503 (1993) 
W P Huang, S T Chu and S K Chaudhuri IEEE J. Quantum Electron. 28 184 (1992) 
W P Huang J. Opt. Soc. Amer. 3 963 (1994) 
H A Haus, W P Huang and A W Snyder Opt. Lett. 14 1222 (1989) 
A N Kireev and T Graf IEEE J. Quantum Electron 39 866 (2003)

Applications of Degenerate/Non-Degenerate Modes Coupling in an Optical Waveguide

Nandan, H

Chandola, H C

The Ideas of Dual Description of Quantum Chromodynamics

Shikha, Prajwalit

Sinha, V K

Dubey, J D

Indian J. Phys. 82(12) 1665-1669(2008) 
-JPP"1 
An evaluation of plasmon frequency associated with charge 
carriers for heavy electron systems 
Prajwalit Shikha1*, V K Sinha2 and J D Dubey1 
department of Physics, Vinobha Bhave University, Hazanbag-825 301, Jharkhand, India 
department of Physics, St. Columba's College, Hazaribag-825 3011 Jharkhand, India 
E-mail prajwahtshikha<// 'yahoo co.m 
Received 27 February 2008, accepted 29 September 2008 
Abstracts : We present an evaluation of the plasmon frequency associated with charge carriers of heavy 
electron systems using the theoretical model of Millis, Lavagna and Lee. For such systems, there are two types 
of plasmon frequencies - one is related with the uncorrelated conduction electrons which gives high plasmon 
frequency, and the other is low plasmon frequency which depends upon the Fermi temperature T, and the total 
carrier density n which is the sum of the carrier densities nc and /?,due to conduction and /-electrons respectively. 
Keyowrds : Plasmon frequency, uncorrelated conduction electrons, Fermi temperature, heavy electron 
systems. 
PACS Nos. : 71.27.+a, 71.45.Gm, 72.30.+q, 73.50.Mx 
1. Introduction 
Heavy electron systems are electrically conducting materials with peculiar low temperature 
properties that distinguish them from ordinary metals [1,2]. 
In these systems there are two types of electrons : 
(i) Conduction electrons whose role is dominant below Fermi temperature 7>; 
(ii) ^-electrons whose role is dominant above 7>. 
At high temperature, these systems behave as a weakly interacting collection of 
/"-electron moments and conduction electrons with quite ordinary masses. At low 
temperatures, the f-electron moments become strongly coupled to the conduction 
electrons and to one another, and the conduction electron effective mass (rrf) is 10 
to 100 times larger the bare electron mass (m). The enhancement of the effective mass 
^ — ~ © 2008 IACS 
Corresponding Author 
1666 Prajwalit Shikha, VKSinha andJD Dubey 
can be assigned to the presence of localized f electrons in all heavy electron systems. 
These may be Ce ions with 4f electrons or U or Np ions with 5f electrons. Prominent 
examples are CeAI3f CeCu2Si2, CeCu6, UBe13l UPt3, UCd11f D^n17 and NpBe13. The 
4f or 5f electrons interacting with the bands of the delocalized electrons (d or s) can 
be considered as the "heavy electron" [3,4] of these systems. For the electromagnetic 
response of heavy electron systems, the optical experiments and the analysis of the 
experimental data give the value of the scattering rate and the plasmon frequency 
associated with the charge carriers. For CeAI3, Awasthi [5] have obtained the real part 
of optical conductivity o{u>) [= ^ ( u ) + b2(u>)] from Kramers-Kronig analysis of the 
excitation spectrum data. 
In this paper, we report the evaluation of the plasmon frequency of various heavy 
electron systems. These systems possess two types of plasma frequency [6,7]. One 
is the high plasma frequency and is concerned with the uncorrected conduction 
electrons. The other is the low plasma frequency and depends upon the Fermi 
temperature TF and the total carrier density n (= nc + nf), where n and nf are carrier 
densities due to conduction and f electrons respectively. 
2. Method of calculation 
We have used the theoretical formulation of Millis et al [6,7] which is based on a study 
of the low temperature properties of the lattice Anderson Hamiltonian, in the Kondo 
limit. It describes a band of nearly free electrons hybridizing with a very highly 
correlated band of electrons. In the absence of this hybridization, each f electron is 
confined to one lattice site localized orbitals which are far below the Fermi energy. This 
model is believed to contain the essential physics of heavy electron systems. It has 
a nonmagnetic ground state that behaves like a Fermi liquid with large effective mass. 
For the evaluation of <x(u\T), scattering must be taken into account. There are 
two pbssible sources of scattering of electrons in these systems. One is the scattering 
of electrons from the impurities and the other is the scattering from boson fluctuations. 
This latter turns out to be in some ways analogous to electron-phonon scattering. One 
can apply Matthiesen's rule [8] in which the resistivities due to different scattering 
mechanism are to be added. Thus, if in the presence of impurities only the conductivity 
is a/ and in the presence of boson only the conductivity is ob then the total 
conductivity is given by 
Matthiessen's rule is believed to be valid when the various scattering mechanism are 
not momentum dependent and are weak. 
At sufficiently low temperatures, only impurity-scattering is relevant. To compute 
the corresponding impurity component afaj) of <r(ujfT)t the disorder must be coupled 
into the system. Millis and Lee [6] obtained 
An evaluation ofplasmon frequency associated with charge carriers for heavy electron systems 
a/(u;) = [ne2/mt)] [r,/ {l + (m*/mb)2 u;2rf}] 
= [na2 /m-] | r ; /{i
 + (Wr;)2}] (2) 
introducing the definition,
 T]jrl =m*/m. 
Freytag and Keller [9] calculated the dynamical conductivity for heavy electron 
systems, taking into account the effect of impurity scattering within a mean field 
approximation of the Anderson Hamiltonian They obtained a dynamical conductivity 
characterized by a narrow low-frequency - Drude peak superimposed on a broad 
background with a minimum near k^Tk presumably due to a mixture of the broadened 
mterband transition and the Drude behaviour of the conduction electrons Two 
characteristic plasma frequencies are then expected . the one at high frequency is 
given by 
u2p = 4TT nce2/mb. (3) 
This identifies the uncorrected conduction electrons. The other is at low frequency and 
associated with the heavy plasmons, given by 
^ = >/|e(1 + n f / n c ) ] x r f (4) 
where T* is the renormalized Fermi temperature (usually identified with Tk) and nc and 
nf are the carrier densities due to conduction and f electrons respectively 
To include the scattering from bosons (a*,), application of Matthiessen's rule leads 
to the result that the conductivity is simply formed by adding the c-electron self-energy 
due to electron-boson interactions. Moreover, because the f electrons are dispersionless 
in this approach, the applied model is not Galilean invariant. Keeping in mind that the 
umklapp process can occur at all nonzero temperatures and interpreting the imaginary 
part of the c-electron self-energy as a temperature and frequency-dependent scattering 
rate 1 flwriuj). Millis and Lee [6] found 
1/r(o/, T) = 1/r, 4- (m*/Nmb) • (v2 + n2T2)/ef. (5) 
At T s 0, and for u < uc% where 
»
2c=Nef(mbfm*)lTh (6> 
the impurity scattering dominates and eq. (2) applies. For larger w, one finds 
<T,(UJ) ~ab~ (ne2/mb)(VN(m* mb)ef ~ ne2/mbW. (7) 
Therefore for u > u)c the conductivity becomes very small and approximately independent 
of frequency. 
1668 Prajwalit Shikha, VKSinha andJDDubey 
Now consider the case 7 = 0 , and w = 0. The resistivity p = a"1 and after 
averaging eq. (5) over the energies of thermally excited electrons, one gets 
p = (mjne2)(l/r f 4m*n2T2/3Nmbef). (8) 
3. Results and discussion 
We have calculated the plasma frequency of different heavy-electron-systems using the 
two relations given in eqs. (3) and (4), at the renormalized Fermi temperature 7*. The 
heavy electron plasmon mode reflects not only the heavy quasiparticle mass (rri/m) 
but also the renormalized Coulomb screening The other plasmon frequency is the 
unscreened heavy plasmon and is associated with the spectral weight functions and 
narrow Drude like behaviour of the conduction electrons. The results are given in Table 
1 where the calculated ratio of the effective mass to ordinary mass of the electron in 
these heavy-electron-systems are also given. 
Table 1. Plasmon frequency of different heavy electron systems 
Heavy 
electron 
systems 
CeCu2Si2 
CeAI3 
CeCu6 
CePd, 
UPt, 
UBe,3 
URu2Si2 
UCu5 
U2Zn17 
UPd?Al3 
rrf/m 
220 
1620 
1300 
370 
450 
1100 
180 
250 
500 
150 
u>;(eV) 
using eq (3) 
9 371 
3 453 
3 856 
6412 
6 552 
1 756 
11 073 
8.790 
6216 
11 348 
- ; ( e V ) 
using eq (4) 
10 446 
4 204 
4 053 
7 559 
5 296 
2 361 
9 563 
7 344 
6519 
12 698 
T* (Kelvin) 
11 340 
4 564 
4 400 
8210 
5 700 
2 560 
10 380 
7.974 
7 07 
13 79 
We have also studied the temperature dependence of resistivity p{T) for two 
heavy-electron-systems UPt3 and CeAI3 and have been calculated using eq. (8), and 
are given in Table 2 from 5 to 300 K. The CeAI3 compound has a hexagonal crystal 
structure and its resistivity displays T2 dependence up to 7 = 0.3 K. Our calculation 
gives pQ = 0.95 \i£l cm. The experimental value [10] is po = 0.76 \iQ cm. The actinide 
UPt3 also has a hexagonal structure and displays an anisotropic resistivity. The 
resistivity is different for ab plane and along the hexagonal c axis. It is also found to 
follow the T2 behaviour. Our calculated results for UPt3 for c axis are very much near 
to [p(7)]exp at oaxis. 
An evaluation ofplasmon frequency associated with charge carriers for heavy electron systems 1669 
Table 2. Temperature dependence of resistivity />{T) for UPt3 and CeAl, 
T 
(Kelvin) 
5 
10 
50 
100 
150 
160 
170 
180 
P(T) for 
UPt3(M,flcm) 
126 
21 2 
32 8 
78 3 
80 4 
82 6 
84 5 
86 2 
P(T) for 
CeAI3 (\itt cm) 
150 2 
162 6 
2108 
200 5 
180 4 
172 4 
168 3 
164 6 
T (Kelvin) 
190 
200 
220 
240 
260 
280 
300 
i>(T) for 
UPt3(MS>cm) 
88 5 
90 2 
92 0 
94 3 
96 5 
97 2 
99 8 
P(T) for 
CeAI3 (\iU cm) 
160 5 
158 2 
156 0 
153 9 
150 2 
148 0 
147 0 
Acknowledgment 
We are grateful to the teachers of the University Department of Physics, Vinoba Bhave 
University, Hazaribag, for the support and the encouragement provided for this work We 
are also grateful to the Department of Computer Applications of the St Columba's 
College, Hazaribag for the computation work. PS is further grateful to her husband Sri 
Ajay Kumar and the entire family for the moral and financial support provided. 
References 
[1] H R Otto, H Rudigier, P Delsing and Z Fisk Phys Rev Lett 55 1595 (1985) 
[2] Z Fisk, D W Hess. C J Pethick, D Pines, J L Smith, J D Thompson and J O Willis Science 239 33 (1988) 
[3] PALee.TMRice.JWSerene.LJShamandJWWilkinsCommenfsCondens Matter Phys 12 99(1986) 
[4] T M Rice Phys Scr T19 246 (1987) 
[5] A M Awasthi, L. Degiorgi, G Gruner, Y Dalichaouch and M B Maple Phys Rev B48 10692 (1993) 
[6] A J Millis and P A Lee Phys Rev B35 3394 (1987) 
[7] A J Millis, M Lavagna and P A Lee Phys Rev B36 864 (1987) 
[8] N W Ashcroft and N D Mermin Solid State Physics p 323 (India Harcourt Asia PTE Ltd ) (2001) 
[9] R Freytag and J Keller Z Phys B80 241 (1990)

An Evaluation of Plasmon Frequency Associated with Charge Carriers for Heavy Electron Systems

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Price : Rs. 100.00; US $. 40.00 (332 pages, 
illustrated) 
Date of Publication : December, 1999 
VI. Physics and Technology of Accelerators : A 
Special Issue of Indian Journal of Physics on 
the occasion of Golden Jubilee of India's 
Independence 
Guest Editor : Debashis Basu 
Price : Rs. 100.00; US $. 40.00 (236 pages, 
illustrated) 
Date of Publication : December, 1999 
VIL Recent Trends in Statistical Physics: A Special 
Issue of 
Indian Journal of Physics 
Guest Editor : J K Bhattacharjec 
Price : Rs. 100.00; US $. 40.00 (140 pages, 
illustrated) 
Date of Publication : August, 1998 
VIII. XI DAE Symposium of High Energy Physics 
: A Special 
Issue of Indian Journal of Physics 
Guest Editor : Ranabir Dutt and Asim K Ra\ 
Price : Rs. 300.00; US $. 100.00 (395 pages. 
illustrated) 
Date of Publication : February, 1997 
IX. Lectures of Theoretical Physics Seminai 
Circuit 11990-92] : A Special Issue of Indian 
Journal of Physics 
Guest Editors : C K Majumdar and Partha 
Ghosh 
Price : Rs. 80.00; US $. 35.00 (100 pages, 
illustrated) 
Date of Publication : November, 1993 
X. Commemoration Volume on Professo? 
Meghnad Sana: Birth Centenary [ 1893-19931 
Editors : H Bancrjee and S P Sen Gupta 
Price : Rs. 140.00; US $. 40.00 (240 pages, 
illustrated) 
Date of Publication : December, 1993 
XI. High Temperature Superconductivity 
Lectures of 
Theoretical Physics Seminar Circuit [1989-
90] : A Special Issue of Indian Journal of 
Physics 
Editors : B K Chaudhuri and S P Sen Gupta 
Price : Rs. 80.00; US $. 30.00 (220 pages, 
illustrated) 
Date of Publication : March. 1992 
XII. Commemoration Volume on Professor C V 
Raman: 
Birth Centenary 11888-19881 
Editor : S P Sen Gupta 
Price : Rs. 50.00; US $. 25.00 (225 pages, 
illustrated) 
Date of Publication : July, 1989 
(Please contact us for all these Special Publications) 


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Index (Author & Subject)

Indian J. Phys. 81 (1), 9-11 (2007) ^ ^ ^ 
INDIAN W 
JOURNAL <>f\ 
PHYSICS i 
Vol. 81 • No. 1 • January 2007 
ONTENTS 
I 
Front Title 3 
Advisory Board and Editors 5-6 
From Editor's Desk 7 
Front Contents 9-11 
Proceedings of the Symposium on Condensed Matter Days - 2005 
(CMDAYS-05) organised by the Department of Physics, Berhampur 
University, Berhampur-760 007, Orlssa, India held at the St Vincent Retreat 
at Gopalpur on-sea,lndia during August 29-31, 2005 
Foreword 
KALYAN KUNDU AND G S TRIPATHY 13 
Invited Papers 15-32 
Electron transport in barrier delta-doped coupled quantum well structures 
TSAHU 17-23 
Heavy-fermion systems 
PRASANTA K MISRA 25-31 
Contributed Papers 33-166 
Thermodynamic properties and alloying behaviour of liquid binary alloy : CdZn 
S M RAFOJE AND ASHWANI KUMAR 35-39 
Ab-initio study of optical conductivity of BJZy nano-composite system 
DEBNARAYAN JANA, LI-CHYONG CHEN, CHUN WEI CHEN AND KUEI-HSIEN CHEN 41-45 
[ Cont'd, on next page ] 
10 
Contents 
Study of magnetism and hybridization through ultrasonic attenuation in cuprate 
systems 
K C BISHOYI, G C ROUT AND S N BEHERA 47-53 
Study of superconductivity and antiferromagnetism gaps in cuprates 
S K PANDA AND G C ROUT 5 5 ~ 6 1 
Dielectric and electrical properties of NaBa2V5015 ceramic 
BANARJI BEHERA, P NAYAK AND R N P CHOUDHARY 63-67 
Structural and optical properties of ZnS nanostructured films synthesized via 
RF-magnetron sputtering technique 
P K GHOSH, SK F AHMED, U N MAITI AND K K CHATTOPADHYAY 69-73 
Study of DM interaction in triangular lattice 
UMA BHAUMIK 75-81 
Low energy ion irradiation induced modifications in Co/Pt bi-layers 
SANJUKTA GHOSH, D KANJILAL AND T SOM 83-87 
Optical and electrical properties of chemically grown ZnS quantum dots 
A K BORDOLOI, D MAHANTA, S K DOLUI AND A CHOUDHURY 89-93 
Synthesis of hydroxyapatite at low temperature 
T R RAUTRAY, V VIJAYAN AND S PANIGRAHI 95-98 
Analysis of human bone and teeth 
T R RAUTRAY, SATRUJIT MISHRA, S K PATNAIK, V VUAYAN AND S PANIGRAHI 99-102 
AC impedance analysis of modified PbTi03 ceramic 
K PRASAD, LILY, K KUMARI AND C K SUMAN 103-108 
Vogel-Fulcher like dielectric response in Pb[(Mg,Zn)1/3Nb2^]03 ceramic 
S N CHOUDHARY, K PRASAD, A KUMAR AND R N P CHOUDHARY 109-116 
Dielectric relaxation in tungsten-bronze Pb2Bi3NdTi5018 ferroelectric 
C K SUMAN, K PRASAD AND R N P CHOUDHARY 117-123 
Electrical resistivity of liquid K-Rb-Cs alloys 
P N GAJJAR, S R MISHRA AND A R JANI 125-129 
Growth and characterization of tungsten substituted molybdenum disulfide 
A K SHAH AND P N GAJJAR 131-135 
[ Cont'd, on next papa ] 
Contents 11 
Theoretical investigation of shear viscosity of some less simple liquid metals 
MITESH JOSHI, MANJUL KUMAR, P N GAJJAR, B Y THAKORE AND A R JANI 137-141 
BaTia4Zr06O3 solid solution : phase formation kinetics and ^reaction mechanism 
through solid oxide reaction 
S K ROUT AND S PANIGRAHI i 143-147 
Dielectric study on sol gel derived BTZ film deposited by spin coating technique 
S K ROUT, T BADAPANDA, E SINHA AND S PANIGRAHI * 149-153 
Transition metal doped ZnS nanoparticle systems and th#ir response to swift 
heavy ion irradiation 
U DAS, D MOHANTA, F SINGH, A TRIPATHI, D K AVASTHI AND A CHOUDHURY 155-159 
Superconducting parameters of metals and alloys : HFP technique 
JAYPRAKASH YADAV AND S M RAFIQUE 161-165 
Forthcoming Publications 167 
Notes for Contributors 169-172 
Our Special Publications 173-174 
Contents from back, cover (Cont'd) 176

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Front Contents

Electrical Transport and Magnetic Properties of La<SUB>0.86</SUB>Ag<SUB>0.15</SUB> (Mn<SUB>1-y</SUB> Al<SUB>y</SUB>)O<SUB>3</SUB> Compounds

Type-II Seesaw in SO(10) Theories with Spontaneous CP Violation

Applications of Degenerate/Non-Degenerate Modes Coupling in an Optical Waveguide

The Ideas of Dual Description of Quantum Chromodynamics

An Evaluation of Plasmon Frequency Associated with Charge Carriers for Heavy Electron Systems

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Front Contents

Structural and Magnetic Properties of Pb<SUP>4+</SUP> Substituted Li-Ferrites

6,371

8,071