IACS Institutional Repository

Narasimha Murthy, V N

Kokila, M K

Puttaraja

Shivashankar

Kulkarni, M V

Shivaprakash, N C

,i I , 8 0 (1 0 ). 102 5 -1 027  (2 0 0 6 ) O ' ^ l o t c
Crystal structure of N-methyl-2-(p-octyl phenoxy)benzimidazole
V N NarasimhaMurlhy. M K Kokila and Puttaiaja
D epailm cn l o f  Physics, llan^MliHC U nivcisiiy  Ban^aU)rL-5 hl» OSfi Karnal.ika, liulia 
and
Shivashankai and M V Kulkarni
U cpailm cn i ol C 'hem istry K arnalaka U nivt'isily iJhaivsad-'iKO (UH liulia
and
N C Shivapiakaslv*^
InpailiiKMil ol Inslium eiita lm n  Indian Iiislilulc ol S cu n cc  H an^aloit “iriO 0 1 K ainataka liuli.i 
h -m ail sluvC")|sii use cinel in 
K c i v t v v f l  2 4  J a n i t a i y  200h < tn c p l< t l  2 1  A i i i ’ i i u  2 0 0 6
lliL uiNsi.il si i i iLl iirc  ol N-mLMhyl -2 lp -o U y l p licnoxv) bc n/ im id a/ o lL '  has heen dclLimi iiLt l hy X-iay m ethods The com pound 
mnnoLliiiu s>s lcm  sp a ic  gm up P 2 / l w ith u l l  paiam clcis ri = 1 I (i47‘)(2)A h  -  H  4202M )A r = 12 V;‘)4(‘))A and /I =<)H 144(S)*^ 
'(iIl 1 1 1 1‘j is plaiiai and m akes a d ihedial anylc o f  127 4K(1)" wilh Ihe aiyloxy iiiig and is coplanai wnh N t 'H , “roup Tin two molcLulLs 
iliu In Van del Waals and vseak intei m olecular C'-lI N iniciailions
Mils ( issial sliiiLliiic, he 
S.is (.1 10 N / 1 1 1  fiO II
icytlic iiri^
inid.i/i)!(.', a heieiocyclic ring .sysieni, is picscnl in many 
oLCLiiiing cyanocobalam m e D erivatives o f 
'1 icla/ok-s provide a laige numbei of biologically active 
''uiKlsll] and substitution pattern on the benzimidazole 
ill' alicis the biological activity Intioduciion of the long 
I gioup and additional methyl groups in the phenoxy 
LMhantes ariii-mnammatory activity[2] 4-ammopij)eridme 
aikichcd to benzimidazole leads to potent antihistamine.
1 ), antibacterial and antifungal aclivities(4J, gastic 
nhibitoLs .such as omeprazole and langprazole as pitent 
diiigs|5| I'hc crystal structure analysis of the title 
 ^ hjs been undertaken to establish the solid .stale 
■''imation
- I'uliow benzimidazole prepared by refluxing equimolar 
id o- phenylenedi-amine and urea in boiling amyl 
' ^^■'"’ '‘Onveited to 2 -ch!oro-l- methyl benzimidazole by 
ot Hai ri.sonl 6 ] The title compound was synthesized 
^^idensaiion ol n-octyi phenyl m the dry DMF with 2- 
''■liiit; Aiilhnr
chloro-l- methyl ben7 imidazole|2 | and rcciystallised liom 
ethanol The intensity data wcie collecled using a CAD-4 
diffractomeler|7 j The data have been coirei. led toi Loienlz and 
polarization factors|8 ] The ciyslallogiapliic data aic given in 
Table 1 The structure has been solved by diiecl mcthods|9| 
and refincdl 10] to K (Residue factor) value 0 055 All hydrogen 
atoms placed in geometrically calculated positions have been 
kept fixed
Table 2 gives selected bond lengths and bond angles Table 
3 gives hydrogen bonding geometiy The chemical diagram ol 
the molecule is shown in Figure 1 An ORTHPlll] plot of the 
molecule i.s shown in Figure 2
CHj CH3
I C H , C H 3
CH3
FiRure 1. rhem ical diiigrnm uf ihc molecule
© 20 0 C ilA C S
Tibli! 1. Crystal duu and itfined paramclers lot the cnmpniind
1026 V N NaniMnilw Mm thy ct al
Crystal morphology 
Ciyslal si/c 
("hcmical formula 
MolcLular wcighr 
Crystal sysltin 
Spate gioiip 
( \ l l  tonsiaiils
VolllIIlL
Radiation used
Niimbei ol loimula iiiiiis ( /)
l)cnsily(cjkulaicd)
Unique data measuied 
Obseived data with l>2fT(l) 
F((K)0)
FlleUion density M a \ ( ) 
Lleetion dtiisitv Min (
K lactoi (H)
Woiylited K (Kw)
colorless needle like
0 2 s 0 I X 0 1 min 
C ,, 11,^  N, ()
n t i  4f)
M onoelinie
P 2 |/e
(I-I 1 (i470(2)A 
h ~ \-\  4 2 ‘) 2 ( l  )A  
r -1 2  5y‘)4(‘))A 
/J 144(H )"
1050 0 (4 )A '
( 'likCX 
4
1 I4() gm/ee 
151*)
1 15S 
72X
0 122 e/ A '
-0  101 e/ A ’
0 0 ‘i ‘i 
0 161
'I " I :
N N
\  /  > -
Table 2 Selected bond lengths (A) and Ixmd angles 
atoms with e s d ’s are m paieiitheses
(Jl-C I I .142(2)
N l- ( 'l  1 162(2)
Nl ( 14 1 454(2)
N2-C’2 I 10(,(2)
CI-OI-('M  
C’ I-N U ('7  
(1 -N U C I4  
( '7 -N I-C I4  
( l-N 2-('2  
N2-C'I-NI 
N2-t'2-C 7 
N l-('7  C2
(Jl-C'H
N1-C7
N 2-('l
I 41(,i2i 
I V)|(j 
I 2‘))|i
I 16 54(1) 
105 ()H(I) 
127 56(2) 
127 21(2) 
10.1 11(1) 
I 16 20(2) 
I 10 61(1) 
104 06(1)
uii(J imidazole ling ts I 4.1(5)“^ The atyloxy groupai 
angle ol 127 48( I )“ with the benztmida/olc t ing aiuh^  ^h, 
cc|ua(orially The observed bond length C’ 1-0 ! - 1  I42n 
nttrmal Csp^-O bond sht>wing expected residual bond lmiym. 
ol 0  09 A  due looxygenf 16] However, the C 8-C)l = l4l(.i_ 
comparatively larger and has been obseived m ili f  
benzimidazole molcculej 14 1
The bond lengths and angles of the imidazole ring aic in 
agreement with those in 2-chloio bcnzimidazt)le| 12| Bond 
lengths N l- r i|  I .V)2 (2 )A| and N2 -C 1 1 1 29.1(2)A|aie in good 
agreement with the values lepoiied for benzimidazolel I 364(3)A
J'ahle ,1 llydiogeii bonding ge'ometiv(A ' )
1) II A D H II
u A l)-H A
('(.-HO N2"' 1 00(2) 2 68(2) 1 21(2
r i4 - in 4 A N2'" 0 98(4) 2 82(4) 171(1
( 10 HIO 
Symnu'iiy
N2"" 1 01(2) 2 88(2) 1 66(2
(I)
(II)
X, -y+l/2  / 1/2 
-x+ I, -y+1, -/+2
Figure 2 ORTKP I’UDl ol the innieeule with 10% piobability theimal 
t llipsouls
and 1.308(3)A lf  131 and 2 -(0 -methoxy phenoxy)-!-methyl 
benzimidazole [ 1 36()(2)Aand 1 295(2)AH 14] ThcN2-Cl bond 
length corresponds to a typical double bond character, while 
the NI - C 1 4 1 1  4.S4(2)A i bond distance shows Csp^-N 
hybridization and agrees with the literature! 1 5 1 values The 
extK’yclic angles around atom NI show considerable asymmetry, 
although the sum of the valence angles around Nl [359 87(2)°] 
indicates no significant pyramidalization
The benzimidazole img is coplanar with N-CH^ group The 
displacement ot all atoms in the ring are less than 0  0 1 A from the 
least squares planes. The dihedral angle between the phenyl
Furthermoie, the confoimalions of the mdividiitil .ir'' 
group relative to the aromatic ring have been ot vital impi '- 
in the study ot the hallucinogenic potency of pnlMiuiii 
phenyl amines The conformation ol the molecule abnui lie 
OI bond IS gauche The C 8 -0 1 - f  1 -N2 torsion angle is ' i 
which indicates theayr? periplanar arrangement Thenii'iiv 
are held together in cry.stal lattice by van der Waals Imef' 
weak mtermolecular C-H .N interactions
R e fe re n c e s
[1] K H ottm ann Uetero < \( n C(fmpound\,
l}criv(m\'c\. Pan I, p247 (New York Inlcrseiniui I* ’ 
12J M V Kulkarni. and V D Paul A n h  Pharm (WL'inliunv ' 
(19HI)
[31 P H L Awouters. C' I h Niemegeeis and P A J Jjii'"''"  ^
Fm sih  (Drug Res ) 1.1 181 (1981)
[4 1 C Kus, H fiokcr. G Ayhan and R Ertan Farmn^' 
(1996)
Cryual structure of N-methyl-I-lp-ocyl pkeuory) bcnc,uudu:ole
Nisliirii K Mikjwa, N M aekuwj , Y Tj.kai), M Shigj ,md H 
^ntilK «2 812 ( l ‘)% )
[) iKiiii'-i''' I T Ralph and A C' 0 Smiih J (h e tHI Srn , 2030
\,nm,s { AD4 n  vtTsion 1 2 Delfl, The NethorlamK
,,i,il \oimis ) (1091)
( K l>iii Ueltl, The Nethcilandi (Emal Nonius) (1990)
, \: sluldiitk SlihL X S-^7  rro fim nun fot Sohuum  of ( ivsfal 
,,, , (lniivt’isily of Ciollingen. Germany) (1997)
M slKMiisk SHUXL~f)7 r n ti ’iani foi Rt'fiiif'tntnl uf ( iw u il  
(UnivLTsiiy ()l Gouingen. Geiinanv) (1997)
1027
i^anoijtory IcnriessLe) (1905)
< n u  C52 1799
I n i  Engm Kendi SuhevU O.bey Mcral Tuncb.lek and Hakan Goku 
A im  f ,vsr ( '54  8^4 (I99K)
......OVW C5U
A U I),n e ........
/ t h e m  S,„ |IVrl,m Tuns, :  S| SI') ,|(,S7 )
....... . ... .....(Niw DlIIii hiMilKe Hall) p 141 (1909)


English

Crystal Structure of N-methyl-2-(p-octyl phenoxy)Benzimidazole

From Editor's Desk

Front Title

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Rao, Madhusudhana  D D

Devi, Indra M

Arunamani, T

Indian J. Phys. 80 (2). 201-204 (2006) g >A ^ote
Earth-ionosphere wave guide model for Rugby — Visakhapatnam path consistent
w i t h  V L F  p h a s e  v a r i a t i o n  m e a s u r e m e n t s
D N  Mudhusudhana Rao‘ , Mjndira Devi'*, T  Arunamani* and Ibrahim Khan’ 
'Department of Physics. Andhra University, Visakhapatnam -530 003. Andhra l>radcsh, India 
^Department of Instrumentation T|ichnology, Andhra University C'oJIege of Rngineermg, 
Visakhapatnar| - 530 003, Andhra Pradesh, India
E mull: indtramalludi^>yahoo com
Ret'eived 12 May 2005, art eptcd 28 November 2005
Abstract : The phase variation measurements of 16 kHz VLF transmissions from Rugby (England) made at Visakhapatnam (India) tor over one 
year have been used as the basis to find the model for the Barth — ionosphere wave guide for the transmission path that reconciles with experimental 
mcasurenicnis The computations have been earned out assuming a perfectly conducting Earth and three different lower ionospheric conductivity 
mcKkIs. namely, .sharply bounded with infinite conductivity, sharply bounded with finite conductivity and a diffuse boundary with exponentially varying 
.oniiuctivity It IS found that the exponential model gives a diurnal phase shift or day U> night shift in the height of reflection much less than what is 
obiiunecl from measurements. But a sharply bounded ionosphere with finite conductivity is found to reproduce not only the diurnal height change but 
iilsu the seasonal variation in it, seen in experimental data
Keywords Radio wave propagation, ionosphere. D-rcgion. VLF phase variations
PAf.S Nos. . 94 20.Vv, 94 30 Va, 95 85.Bh, 96.35.Kx
It IS not very long ago that almost all long distance 
communications were by means o f sky wave. However, in recent 
times, there has been an increase in use o f  satellites for 
communication and navigation. These systems operate at 
Irequencies on which the ionsopheric effects are minimal and 
lienee, the interest in ionosphere as a communication channel 
(especially for HF) has lessened. This, however, does not mean 
that ionospheric propagation is no longer important since other 
services like broadcasting, ship and aircraft communication etc. 
rely on ionospheric propagation. Further, the vulnerability 
the hardware o f satellite systems to hazards in space and 
degrading influence o f vagaries in space weather in satellite 
f*ignals emphasize that ground-based systems are reliable 
-alternatives and bring back the interest to ionosphere. The D- 
tegion of the ionosphere lying at its base has profound influence 
[f>n the character o f radio waves passing through it particularly 
|in the very low, low, medium, and high frequency (VLF, LF, MF 
HF) bands which are still the principal bands used in 
nimunication and broadcasting. Because o f the complexities
Corresponding Author
in its chemistry and dynamical behavior, the D-region continues 
to be an area o f intense investigation. In this context, it may be 
noted that one o f the goals o f recent TIMED (Thermosphere, 
Ionosphere Mesosphere Energetics satellite) Project o f NASA  
is D-region investigations [IJ. In the study o f the D-region, 
ground-based propagation experiments are still considered 
invaluable, since they provide reliable information on long term 
basis. Among the many ground-based techniques, the recording 
o f phase and amplitude o f long distance VLF (3-30 kHz) signals 
still proves to be best suited, since the reflection point for these 
waves lies entirely in the D-region bc:»th during day and night 
and uncertainties involved in separating D- and E-region 
contributions inherent in medium and high frequency 
observations, do not arise.
Many aspects o f VLF wave propagation to great distances 
are generally explained in terms o f the wave guide theory [2]. 
The lower ionosphere, namely, the D-region and the surface o f 
the Earth, assumed to be perfectly conducting, act as the walls 
o f the wave guide through which the signal travels from the 
transmitter to the receiver. Although a number o f modes are
(D2(X)6IACS
202 D N  Madhusudhana Rao, M  Indira Devi. T  Arunamani and Ibrahim Khan
excited when a VLF wiive propagates in the Earth-ionosphere 
wave guide, at long distances, only the first order mode remains 
significant since higher order modes get attenuated (31. In this 
Earth -  ionosphere wave guide, the lower ionosphere (D-region) 
acting as a reflecting layer o f VLF waves is described by different 
models, viz., sharply bounded with finite conductivity, sharply 
bounded with infinite conductivity or a diffuse boundary with 
exponentially varying conductivity. D ifferent workers 
considered one or more o f these models o f the ionosphere to 
explain their experimental measurements o f diurnal phase / 
amplitude variations. For example, Crombie |4J and Scarabucci 
and Mendonca [5) employed a homogeneous model while Wait 
and Spies (6|, Kikuchi |7) and Joshi and Iyer [8| considered 
exponentially-varying ionosphere to explain their experimental 
results. It is the purpose o f the present work to reconcile the 
experimental measurements o f diurnal phase shift or shift in 
reflection height o f 16 kHz Rugby transmissions received at 
Visakhapatnam with computed values using the models 
described above. The model that gives the values consistent 
with the experimentally measured ones is considered appropriate 
for the propagation path.
The phase variation measurements o f 16 kHz transmissions 
from Rugby (52.3‘*N, 1.2“W ), England made at Visakhapatnam 
(17.7®N, 83.3°E) during November, 1984 — October, 1985 have 
been considered in this study. The locations o f transmitting 
and receiving stations and the propagation path are shown in 
Figure 1.
BO®
■f.
rm m m
S R W  SRR  SSW  SSR
♦ ♦ 4 t
SS8n
mmmmn
mmmmm
1 5 ^ 1 2 ^ 9 ^ 6 ^ 3 ^  & 3& 60P 90“ 120“150“ 180®
Figure 1. Propagation path beiwcen Rugby (R ) and Visakhapatnam (V).
The technique o f measurement is coherent phase detection 
technique in which the incoming 16 kHz signal is received by a 
Tracor 900A V LF  receiver and the signal phase is compared 
with that o f a signal obtained from a highly stable standard 
frequency generator type H P (5 0 6 5 A ) Rubidium Vapor 
Frequency Standard by which an accuracy o f 1 part in 10** is 
normally exhibited by the receiver.
In Figure 2, the monthly mean diurnal phase variations arc 
shown. The sunrise and sunset times at the transmitter and 
receiver are indicated by arrows. The diurnal phase curves 
exhibit typical characteristics with the propagation time fairly
00  04  0 8  12 16 20  24
TIME (1ST)
SSR S R W  SRR SSW
1
MAY 19R.'-.
UN 198f)
Q.UJ>
JUL 198^
AUG 1985
SEP 1985
:T1985
08 12 16 
TIME (1ST)
Figure 2. Monthly mean diumal phase variations (SRW. SSW. SRR- 
refer to sunrise and sunset times at Visakhapatnam and Rugby
Earth-ionosphere wave guide model for Rugby—Visakhapatnam path consistent etc 203
steady and greater when both the tranvsmitter and receiver are in 
darkness, than when both are in day light. This typical 
traperoidal phase variation implies that the first order mode is 
predominant. These monthly mean phase change data are u.sed 
to derive one of the important quantities, namely, the 
transmission delay or diurnal change in transmission time, which 
IS. the phase difference of the signal between day and night. 
This diurnal change in transmission time is found to valry from 
7.2 /is/Mm in April to 11.7 fts/Mm in December with an annual 
mean of 8.5 ps/Mm which value compares well wit^ those 
obtained by Kikuchi [9] and Joshi and Iyer [8] for VLFiignals
propagating over similar path lengths.
This diurnal change in the phase of VLF waves isf due to 
change in phase velocity brought about by a changej in the 
height of reflection between night and day. Hence, the diurnal 
shift in height of reflection; Ah , can be calculated from the 
diurnal phase shift using the relation 13]
A h  = -
cAt
16/id 2a
km, (1)
where c is the velocity of light, h^  - the height of the day time 
reflecting layer, a - the radius of the earth, - the distance of the 
receiver from the transmitter, A - the wavelength of the VLF 
signal and At - the phase change in seconds (all distances / 
(lengths given in kilometers). Taking the daytime height of 
reflection to be 70 km, the day to night change in reflection 
‘height has been computed for each month. The monthly mean 
values are grouped season wise and the average value in each 
Reason IS presented in Table 1.
T^able 1. Seasonal vanation day-to-night shift in reflection height ( Ah ) 
m^m VLF phase measurements.
Season A/i (km)
Winter 20.5
Hquinox 17.6
Summer 15.7
Annual 18.0
It is evident that the diurnal shift in reflection height shows 
seasonal variation with maximum in winter. A similar seasonal 
Nnd in Ah has been reported by Olga et al [ 10] in the phase 
jariation data of 12.9 kHz signal. As the daytime D-region is 
stable, the rise in day to night shift in reflection height in 
i^nter suggests a variation in the night time electron density 
S^ht about by changes in minor neutral constituents [11].
In the waveguide mode theory for VLF waves, if Vj^  and v^  ^
I phase velocities of the VLF waves for the all night and all
paths respectively, the diurnal phase shift (0dn) givenV[2]
— |lOVs/Mm.
31 (2)
where c is the velocity of light. The first order mode phase 
velocity is given by
.^^=l + Re (3)
C] is given by
cr =
I tt
(4)
in which h is the height of reflection of the VLF wave in the 
ionosphere, a is the radius of the earth, A is the wavelength,
k - ln f A  and a = (\ -ia )J o )) where (O is
the angular frequency of the VLF wave and co^  , the ionospheric 
conductivity parameter given by (o^  = o)^ , /v , and v being
the angular frequency and the effective collision frequency, 
respectively.
Using the wave guide mode equations for a perfectly 
conducting ground and infinitely conducting or sharply 
bounded ionosphere with a finite conductivity, it is possible to 
obtain the diurnal phase shift theoretically and thereby estimate 
the night time reflection levels assuming its day time value. For 
a given ionospheric model, the conductivity parameter is 
specified and using the above theory, phase velocities and the 
diurnal phase shift can be computed.
In the present investigation, the phase variation is calculated 
using a wave guide model consisting of a perfectly conducting 
Earth and an ionosphere which is (i) infinitely conducting, (ii) 
sharply bounded with finite conductivity { o)^  -  2x  10^ ) and
(iii) with exponentially varying conductivity. In the case of 
exponential model, the conductivity parameter assumed is
identical to that suggested by Wait [12] viz., co^  -  2.5 x lO^ ' 
exp[^(z-/i)], where p  is the height gradient and h is the 
reference height.
Assuming the height gradient to be 0.3 km'^  for day time and 
0.5 km * for night time and taking the day time reference height 
{h^ to be 70 km, the diurnal phase shift has been calculated as 
a function of h^ , the night time reference height. The night time 
reference height where the computed agrees with the 
measured value for each of the three ionospheric models, gives
204 D N Madhusudhana Rao, M Indira Devi, TArunamani and Ibrahim Khan
the night time reflection height (//^) and the difference (h^-hj) 
gives the diurnal shift in reflection height ( /l/i). The results of 
the computation of Ah for the three models in three seasons 
are shown in Table 2.
Tabic 2. Computed values of M  (km) in different ionospheric models.
Season Sharply bounded 
Infinite conductivity
Sharply bounded*f 
finite conductivity
Diffuse layer 
with Exponential 
conductivity
W inter 23 4 2 0  4 1 0 .4
Bquinox 1 8 .9 16 3 9 .6 5
Summer 19 9 17 .5 9 75
Annual 2 1 .0 1 8 .0 10 0
It may be pointed out here that the (=  10 km ) obtained 
in the case of an exponentially varying ionospheric conductivity, 
agrees very well with 11.5 km obtained by Joshi and Iyer [8 ]. 
However, the exponential model is not able to reproduce the 
seasonal variation in Ah seen in the experimental data. But the 
model with a sharply bounded ionosphere with finite
conductivity not only gives Ah value in agreement with that 
obtained from measured phase deviations but also reproduces 
seasonal variation in it.
Wave guide model analysis for Earth ~ ionosphere wave 
guide for VLF propagation has been carried out to compute the 
diurnal phase shift of 16 kHz signals assuming perfectly 
conducting Earth and three different lower ionospheric
conductivity models. It is found that a wave guide model 
a perfectly conducting Earth and sharply bounded ionosphfie 
with finite conductivity as the two walls of the guide, 
results consistent with the experimentally measured diuin,! 
phase variation of 16 kHz Rugby (England) transmlsslon^  
recorded at Visakhapatnam (India).
Acknowledgment
The authors wish to express their gratitude to Prof. K V V Ramara 
for his interest and valuable suggestions while carrying oui ih,, 
work.
References
[ 1 j S Gonzalez R e p o r t  on  S pace  and  A tm osp h e r ic  Scieiues m 
U t t e r  No. 36 p3 (National Astronomy and Ionospheric (\niu 
Arecibo Observatory) June, (2 0 0 3 )
(21 J R  Wail E le c tro m a g n e tic  W a ves  in S tra tified  M e d ia  (I*ei”jnion 
Press, Oxford) (1 9 6 2 )
[3 ] J R  Wait Pro c . IR E .  47 , 998  (1 95 9)
[4 ] D D Crombie R a d io  Sci 68D. 27 (1 96 4)
[5 ] R R Scarabucci and F Dt* Mendonca R a d io  Si i 2 37^ (10() i
[6 ] J R  Wait and K P Spies N B S  le c h n ic a ! N o t e ,  Nn 300 (\B', 
Boulder. Colorado) (1 9 6 4 )
[7J T Kikuchi 7. A tm os . T e rr  Phys  48  15 (1 98 6)
[ 8 1 H P  Joshi and K N Iyer J A tm os. Terr Ph ys  50 507 i l ‘)SS) 
[9 ] T Kikuchi ./. A tm o s  Terr Phys. 45  743 (1 98 3) 
flO] I P  Olga, S N Radicella and P M Fernandez ./ Atnim  len l'h\ 
4 9  129 (1 9 8 7 )
[111 Ibrahim Khan, Y V P K Raghava and D N MadhusiuJhan.i K.i 
P ro c . A P  A k a d em v  o f  S c ien ces  5 215 (2 0 0 1 )
[1 2 ] J R Wait ./ R e s  N B S  671) 375 (1 96 3)


Earth-Ionosphere Wave Guide Model for Rugby - Visakhapatnam Path Consistent with VLF Phase Variation Measurements

Gopalakrishn, G S

Mahesh, M J

Ashamanjari, K G

Indian J. Phys. 80 (3), 293-296 (2006) o A ^ t e
Magnetic and thermal characterization of Na2NiP207 crystals
G S Gopalakrishna*, M J Mahesh and K G Ashaman jari 
Dcparlmcni of Studies in Geology, University Of Mysoie, Maiiasagangotri. Mysore’370 006. India
E-mail . gopalaVirish2004Ca5yahoo.com 
Received 5 September 2005. an epted 28 November 2005
Abstract : Na2Nip20v crystals were synthesized by hydrothermal technique and characterized by D'rA/lX’JA, XRD, FTIR and measured 
m agnetic properly. Na2NiP207 crystals arc crystallized in monoclinic system. DTA/TGA results revealed a phase transition at 524‘’C and 
magnetically, it is a frequency-dependent paramagnetic material and the thermal treatment to the material has resulted in change of 
magnetic properties from paramagnetic to fern magnetic.
Keywords : Hydrothermal synthesis, pyrophosphates, DTA/TGA, XRD, magnetism.
PACS Nos. : 8 LIOD11, 61.10.Nz,.81.70.Pg, 78.30.Hv.
Ihe Study of alkali transitional metal phosphates has 
drawn significant attention owing to their wide synergetic 
properties and applications as prospective materials in 
technology, v iz ., in electronic device and as solid 
electrolyte with high thermal resistance, a potential device 
m space application, sensors, la.ser materials, piezoelectric, 
luminescence, ceramics and magnetic materials, e tc . [1 - 
h). fhe magnetic susceptibility measurement of phosphates 
has attracted great attention since last few decades because 
of its potential applications in field sensing and magnetic 
recording heads and its improved performance for opto> 
electronic devices 17—9J. Recently, the authors have 
reported a scries of phosphates, which exhibited tunnel 
lype of framework structures with open cavities and have 
shown good electrical and magnetic properties [10-12]. 
Here, we report a new group of phosphates, which seems
he prospective magnetic materials with relatively high 
thermal stability.
The synthesis experiments were carried out by earlier 
reported hydrothermal route at moderate temperature and 
pressure conditions 111,12]. The reagents used are of 
analar grade of NaOH (99.99%), H 3 PO 4  (98%) and NiCb  
W % ) from Glaxo chemicals without further purification. 
Ij^ally, NaOH and H 3 PO 4  were taken in a teflon-lincd 
Corresponding Author
Morey type autoclave with capacity o f 50 ml. Later, a 
known quantity o f nickel chloride o f known molar 
concentration was added to it and thoroughly stirred till 
homogeneity was attained. The pH o f starting reactant 
was 4.18. The crystallization was carried out by 
spontaneous nucleation and the rate o f nucleation was 
controlled through programmed slow rate o f heating 
(5—lO '^C/h). The experiments were carried out for 10 days 
continuously at temperature range o f 250-260"C and 
pressure o f 60-100 bars followed by sudden quenching 
to the ambient conditions. The resultant product was 
thoroughly washed with distilled water using ultrasonic 
cleaner and pH o f the resultant product was 3.29. 
Na2NiP207 crystals are obtained under the follow ing 
molar ratios :
Na20 : N iO  : P2O5 :: 2-4 ; 1.5-2.5 : 10-12. 
Successful growth o f technologically important phosphate 
crystals in the fonn o f  single crystals will depend on 
several growth parameters. In the case o f hydrothermal 
synthesis, the most important growth parameters are 
selection o f starting reactants, suitable solvent, percent 
fill, temperature, pressure, e tc . Among them, the selection 
o f the reactant materials and the solvent is the most 
important aspect. In the present experiment, H 3P O 4 and
© 2006 lACS
294 G S Gopalakrishna, M  J Mahesh and K G Ashamanjari
NaOH solutions have been used as the solvents and 
nickel chloride as solute. The linkage between the solvent 
and solute is essentially o f coordination type and hence, 
various acid-base complexes have been observed in 
solution. It is easy to understand the acid-base complex 
formation in simple systems. But it is difficult in a multi- 
component system like the one discus.sed in the present 
work, consisting o f more than four components. Therefore, 
understanding o f the formation o f such a coordination 
compound is extremely difficult. However, on the basis 
o f pH conditions o f chemical reactions prevailed in the 
initial (4.18) and resultant products (3.29), it has changed 
from acidic to relatively stronger acidic conditions. Ba.sed 
on these results, the following reactions have been 
proposed :
N iCb + H3PO4 N iHP0 4  + 2HC1 1 ,
2NaOH -f H3PO4 HNU2P04  + 2 H2O 2,
NiHP04 + HNa2P04 Na2NiP207 -h H 2O 3. 
The crystals obtained by this method were o f good 
quality with well-developed faces : (100), (210) and 
{CK)1 ). On the whole, the crystals exhibited smooth 
surface morphology, sub-vitreous luster, green colour and 
having a size o f 2.0-2.5 mm (Figure 1).
X-ray diffraction (XRD)  :
X-ray studies have been carried out by Rigaka Miniflex
817/384, 670 /288  X -176 Y-148  
Scale Mjcron/Pixel
Figure 1. CCD photograph and schematic diagram of Na2Nip2 0 7  crystal.
Tftble 1. Powder XRD data of Na^ NiP^ O,. 
Number of lines
diffractometer with graphite monochromatized CuK<2 
radiation (A =  1.5405 A )  in steps o f 0.02° at roo,., 
temperature (Figure 2) The cell parameters and tlu
uirinnnHnnjirulnjuifuijinjiniinjinnHnjirinjlnxmnjinjinivljinnju^
8 10  15 20 25 30 35  40 45 50 55
20  (degree)
Figure 2. Powder XRD pattern of Nu2NiP207 crystal.
volumes were calculated by using the software programme, 
‘The Crysfire 2002 system for automatic powder indexing 
and user’s manual’ [13] and the results are given m 
Table 1.
DTATTGA :
The thermogravimetric analysis (T G A ) and differential 
thermal analysis (D TA ) o f Na2N iP207 have been rccoidcd 
by using TG A  7 Perkin Elmer, US analy/.cr in the 
temperature range o f  55-8 ()()°C  under the oxygen 
atmosphere. The heating rale used for the analysi.s was 
10°C/minute. The diagram clearly exhibited large weight 
loss at 524°C (Figure 3). The weight loss at 524"T is 
due to the endothermic irreversible phase transition. Tins 
compound exhibited relatively high thermal stability.
FTIR-spectrum :
FT’IR-Spectrum was recorded using a high resolution 
Perkin Elmer Infrared Si>eciropholometer. in the range of 
4000—400 cm~‘ (Figure 4). The compound exhibits 
prominent multiple absorption bands especially in three 
frequency regions i.e. at Fj (2312.3 cm~*)» ^ 2  (12112 - 
952.8 cm-«) and p, (723.3-461 em'O. The vibrations at 
F| is due to the Ni-O-Ni bonding, and are due to 
the presence o f  P -O -P  bonding. The degree ol 
multiplication and fineness in the spectrum o f phosphates 
increases as the degree o f polymerization increases in the 
[PO4] tetrahedral [10-12], It is clearly noticed that the
Input data «  1 g
Standard deviations 
Cell parameters
Calculated *=190
Mean Absolute discrepancies 
Q = 1429£‘-03 A(2<9) = 1736it~()l,
0.0053
« =  10.1543 
96.684°
Max. Error accepted 
(Dcg.2t9) = 4500£^1
0.0082
a 9.9819 
Fa 997.17 A*
Figures of mcni
Af(18) = 5.3
0.0042
C-9.9053A 
Monoclinic system
F(18) = 5.5. 
(0.0174. 1*^0) 
0.038
Magnetic and thermal characterization afNa2NiP20y crystals 295
Figure 4 f-TIR spectrum of Na2NiP2 0 7  compound.
compound has exhibited more number o f splittings and 
higit degree o f sharpness especially in the low frequency 
regions indicating condensation o f [P 0 4 l “^ tetrahedral to 
This result is supported by the X-ray results. 
No vibrations are noticed at 3600-30(X) cm~  ^ indicating 
absences o f hydrate molecules.
l^iignetic susceptibility :
Magnetic susceptibility measurements were made using 
Cjouy balance method by applying field .strengths o f 0.5- 
^^ 0 K Gauss at 300 K  (Figure 5). Magnetic moments o f 
compound show paramagnetic behavior. In general, 
nickel derivatives fall into two broad classes; N ickel(II) 
derivatives have two unpaired electrons either high spin 
octahedral with in the range o f  2.81—3.93 BM or low 
spin octahedral with lesser (<2.83 B M ) [14,15]. In 
present work, Na^NiP^O.^ materials have shown 
‘Magnetic moments in the range o f  1.54-2.34 BM. These 
'values are much lower than those reported for nickel 
derivatives with low spin octahedral. It could be attributed
Figure 5. Magnetic moment magnetic field strength of NajNiPjOy 
comp<’»und at various temperature.
to the bonding o f diamagnetic phosphorus ion with the 
paramagnetic nickel ion through the common oxygen ion 
(P-O -N i) in the structure. Here, nickel derivatives o f 
sodium-bearing phosphates have positive correlation with 
magnetic moment, l b  unravel the thermal effect on the 
magnetic properties, the material has been subjected to 
heat treatments for an hour at 100, 200, 300, 400, 500 
and 55(FC followed by DTA/TGA studies. After the 
thermal treatment, magnetic susceptibility measurements 
were made and the corresponding values were 
calculated. The results o f the thermally-treated
materials have shown negative correlation with the 
magnetic field strength. It has been attributed to the fact 
that the heat treatment could have changed the behavior 
o f the materials from paramagnetic to ferrimagnetic and 
resulted in a negative correlation with the magnetic field 
strength.
Na^NiP.O., crystals were synthesized by hydrothermal 
method in the form o f single crystals with well-developed 
moiphology. DTA/TGA studies revealed that the material 
has relatively high thermal stability. The XRD  studies 
have shown, that it is crystallized in monoclinic system. 
It is also a frequency-dependent paramagnetic material 
and has a positive correlation with the magnetic field 
strength. However, the thermal treatment to the material 
has resulted in a change in the magnetic properties from 
paramagnetic to ferrimagnetic and has exhibited
negative correlation with the magnetic field strength.
Acknowledgement
The authors would like to express thanks to DST, New 
Delhi, for financial assistance under the project SP/S2/M- 
44/96.
296 G S Gopalakrishna, M  J Mahcsh and K G  Ashamanjari
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Sci. 2121 {2mA)
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112] M J Mahesh. G S Gopalakrishna, K G Ashamanjan and J Shaslmllutf 
Prasad Indian J. Phys. 79 37 (2005)
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U.ser\s Manual (England : The Lattice Press) (2(X)2)
(141 R S Beach and A E Bcrkowiiz Appl. Phys. Lett. 64 3652 ( 1 9 9 4 ;
[151 Rnj Ranian Jha. D K Jha and J P Mishra Asian J. Clwm 1 1  
(1999)


Magnetic and Thermal Characterization of Na2NiP2O7 Crystals

hulHtn7. phys. 80 (4 ), 415-416 (2 0 06 )
(;;^«RTHCOMING PUBLICATIONS
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mallei and t e c h n o lo g ic a l  m a te r ia ls  I
Bai nr:v Raj ano BVR  T aia t
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S nKAH AN A  C lIA K K A liA K T !,  A m ITKIKAN PkaOIIAN, A m I IAVA B AN O Y O t'A O I 1 YAY,
A y\n R ay, B iswaiii R ay , D ipankar B hatiac'harya ano Praoip N G hosh
\  ibiaiional s p e c tr a l  s tu d ie s  o n  2 ,  5  d i c h l o r o a n i l in e  
II Rai, a  B Sharan ano Suri.nora R ai
A co m p a rativ e  s tu d y  b e tw e e n  A u t l e r - T o w n e s  s p l i t t in g  a n d  q u e n c h in g  o f  
spontaneous e m i s s io n
Tulika Tamui y ano G  D B aruah
fh o io n -n iim b er d i s t r ib u t i o n s  in  th e  s t e a d y  s ta te s  o f  t r a d it io n a l  a n d  r a n d o m  la s e r s  
V Plrinova ano a  L uks
Laser g u id e  a r ti f ic ia l  s ta r  f o r  h ig h  r e s o l u t i o n  im a g in g  
Swapan K Saha
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M ukesh K umar
L^cvelopmenl o f  u l tr a v i o le t  la s e r  f o r  d i s i n f e c t io n  o f  p o ta b le  w a te r  
O C B har and  U  C hatterjee
^ ‘^ nclassical p h o to n  s t a t i s t i c s  in  s p o n t a n e o u s  R a m a n  a n d  in  s t im u la te d  
^ ‘Unan p r o c e s s e s
B iswajit Sen a n d  S waran M a n u a l
C n ii t 'd .  o n  n e x t  p a s t* J
4 1 6 Forthcom ing Publications
Damping etYect on power loss in optical fibers due to higher order nonlinear term 
S U N IT A  S h A R M A ,  S  K  O n O S I l A L  A N O  D l .V I .N O R A  M o H A N
A  study on the propagali<m o f a Ciaussian soliton pulse through an t>ptical fibre 
when dispersion is compensated accommodating the nonlincctrity o f the fibre media 
P k a s a n t a  M a n u a l , I I a u i m a r  B i i o w m i k , D n a o i r n  D l  a n i 3
S oUR ANC iSH l i  M l’KI IOPAOMYAY
Optical vortices pix^duced by ft^rked holographic grating and sign o f their 
U^pological charge
R a v i n o k a  P  S i N c a t ,  S a n j c ^y  R o y c h o w o h i i r y  a n o  V i r i  n o r a  K  J a i s w a l
Dynamic reactivity profiles o f helium and neon atoms interacting with an 
intense laser field
U i L A L  S a k k a k  a n u  P r a h m  K u m a r  C i i a t t a r a j
Inverse variational problem for nonlinear equatit>n in optics 
B  T a l u k d a r
A  mathematical criterion ft>r single photon sources used in quantum cryptography 
A n i r b a n  P a t h a k
Control o f molecular dynamics in intense laser fields 
M  M o h a n , A  M a a n  a n u  P J i i a


Forthcoming Publications

Mandal, Prasanta

Bhowmik, Harihar

De, Debduti

Indian J. P h ys . 80 (S). 527-530 (2006)
I J P
A study on the propagation of a Gbussian soliton pulse through an optical 
nber when dispersion is compens^ited accommodating the nonlinearity of
the ^ber media
I
Prasanta Mandal’", Harihar BhowmijL, Debduti De and Sourangshu Mukhopadhyay
Deportment of Physics &  Technophysics, Vid]jiasagar University, Midnapore-721 102, West Bengal, India 
E-mail: prasantft_mandal2004@yahoo.co.in
Abstract : It is well known that the propagation of soliton pulse through an optical fiber depends on the compensation of Group Velocity 
Disp>ersion (G V D ) and Self-Phase Modulation (SPM). This balance is to be maintained exactly where in dispersion compensated fiber, the 
dispersion are balanced mutually that is waveguide dispersion cancels material dispersion.
In this context, if we consider the nonlinearity in fiber media, then how these dispersions are compensated mutually, is analytically 
observed by us in this paper. At the same time, how the soliton pulse will be affected by the media of the optical fiber where the dispersion 
compensation is done accommodating the nonlinearity of the optical fiber.
Keywords : Gaussian soliton pulse, optical fiber, material dispersion, waveguide dispersion, nonlinearity 
PACSNos. : 42.65.Tg, 42.65,Wi, 42.81.Dp
1. Introduction
Optical fibers have created a revolution in the field of 
telecominunication and have become the back bone of 
today’s global communication networks. Optical fiber 
communication is considered to be more advantageous 
because, it has large channel handling capacity, high 
signal to noise ratio due to presence of low noise, no 
electromagnetic interference e tc . In communication 
engineering, optical fiber and free space communications 
is being more and more important. Apart from these 
remarkable advantages, the major disadvantages are 
information loss and cross talk because of optical loss 
and dispersion [1], The problem of dispersion can be 
overcome with the help of Gaussian soliton pulse [2], In 
soliton communication the pulse broadens neither in the 
time domain nor in frequency domain. In addition to 
optical communication optical soliton also finds 
application in pulse compression, photonic switching and 
soliton laser. It is expected that in future almost all 
conmiunication will be done by optical soliton. Optical 
fibers are based on silica glass materials. This material is 
^Corresponding Author
non crystalline and nonlinear in nature. Control of 
dispersion effect in optical fiber is a primary requirement. 
For an ideal communication dispersion compensation fiber 
is essential. In this paper, we see how dispersion are 
compensated mutually, if nonlinearity is considered [3— 
5]. At the same time, how Gaussian soliton pulse will be 
affected by the media of the optical fiber where the 
dispersion compensation is done accommodating the 
nonlinearity of the optical fibre, has also been investigated.
2. Dispersion in optical fiber
Pulse dispersion represents one of the most important 
characteristics of an optical fiber. It determines the 
information-carrying capacity of a fiber optic commu­
nication system. In digital communication systems, 
information to be sent is first coded in the form of 
pulses and decoded at the receiver after transmission. A 
pulse of light broadens in time as it propagates through 
the fiber, this phenomenon is known as pulse dispersion 
and occurs for three reasons :
(i) Multi-path dispersion, (ii) Material dispersion,
(iii) Waveguide dispersion.
®  2006 lA C S
528 Prnsanta MandaU Harihar Bhowmik, Debduti De and Sourangshu Mukhopadhyay
2,L  Multi-path dispersion :
When rays making large angles with the axis have to 
traverse a longer optical path length they take a longer 
time to reach the output end. So the pulse broadens as 
it propagates through the fiber. Hence, even though 
many pulses may be well resolved at the input end, 
because o f broadening o f the pulses they may not be so 
at the out put end. When the out put pulses are not 
resolvable, no information can be restored. In case o f 
step index fiber, a ray making an angle O with the axis 
would occupy a tim e interval o f  duration
AT = !h L {  ^ - 1 1
c [n 2 j when it traverses a distance L  in time /.
Here, (c/n\) represents the speed o f light in the medium 
o f refractive index nr, c is the speed o f light in free 
space.
2.2. Material dispersion :
Material dispersion is due to the explicit dependence o f 
the refractive index o f the core cladding on the wavelength 
(>^)). It is a characteristic o f the material only. Material 
dispersion plays a very important role in design o f a 
fiber optics communication system. When a temporal 
pulse passes through a homogeneous medium, it 
propagates with a group velocity (v^) given by
1/v^ ^dkjdw
_  d [n  
dw\^c n(w) j.
where ^ (w )a “ n(vv), n (w ) a  frequency-dependent 
c
refractive index.
In terms o f wavelength, the group velocity becomes
1 1 dn
dXQ]■
Thus, the time taken by a pulse to traverse length L  o f 
fiber is given by
Hence, temporal broadening o f the pulse is
d r
dAo
The above broadening is referred to as material dispersion. 
Material dispersion in terms o f ps/km-nm is
= -
1 1 ps/km-nm.
where Aq is measured in micro meters and c 
km/s.
3 X 10^
For pure s ilica . at Aq =  1550 nm.
d^n
d ^
= -4 .2x10 fxm ^ , so that D „  “  22 ps/km-nm.
2,3. Waveguide dispersion :
Wave guide dispersion is due to the explicit dependence 
o f the refractive index o f the core and cladding on the 
frequency (w). In case o f wave guide dispersion, wave 
propagation vector
p  =  —  [;i2 + (/J, -  tl2  ) *(v )],
where ^ -n orm a lized  propagation  constant, 
w 2
v = — ayjni -W 2 . the waveguide parameter, a is the
c
radius o f the core, n\ and «2 are the core and cladding 
refractive index.
Hence, group velocity is given by
Vg dw c c ]^dv J *
Thus, the time taken by a pulse to traverse length L  o f 
the fiber is given by
2nt "2
For a source having a spectral width idAo* the 
corresponding waveguide dispersion is given by
d t d } (/>v)
dv^
In terms o f ps/km-nm, the waveguide dispersion is given 
by
cAq dv^ ps/km.nm.
A study on the propagation of a Gaussian soliton pulse etc. 529
where is measured in nanometer. For step index fiber,
d'^ibv) _
 ^ dv  ^ '
In case of pure silica, at >?o =  1550 nm, B  = 0.996, 
£/ = 2 >um, n i = 1.46, n j = 1.45, so that D„. «  22 ps/km-
nm.
3. Dispersion compensation fiber
Dispersion compensating fiber is a fiber that balancesf 
the pulse broadening mutually. Total dispersion of a| 
signal mode fiber is given by f
^  ^  ^  2;rc d ^ f i
How this dispersion is compensated mutually? Let us 
consider a pulse propagating through an optical fiber. 
We know group velocity attains a maximum value at the 
zero dispersion wavelengths and on either side it is 
monotonically decreases with wavelength. Then the red 
components of the pulse will travel slower than the blue 
components of the pulse. Because of this fact, the pulse 
will get broadened. The leading edge of the output pulse 
is blue shifted and the trailing edge is red shifted. Then 
after propagating through such a fiber for a certain 
length L \. We allow the pulse to propagate through 
another fiber, where the red components will now travel 
faster than the blue components and the pulse will tends 
to reshape itself into its original form. This is the basic 
principle behind dispersion compensation. That is, if 
(D ,)i and ( A > 2  be the dispersion coefficients of the first 
and second fibers and if the length of the two fibers (L i 
and L 2 ) are such that
(D ,h  U  + (A )2  L 2 = 0,
then the pulse emanating from the second fiber will be 
same to the pulse entering the first fiber.
4. Effect of nonlinearity in dispersion compensation 
fiber
Here, we treated the optical fiber as a nonlinear medium, 
that is intensity dependent refractive index. Consider the 
propagation o f an optical pulse in a lossy fiber 
characterized by the refractive index
n (iv )«n o (w ) + n2o/ *
where /lo(iv) is the linear part of the refracting index, 
'*2 0 / is the intensity-dependent nonlinear part.
In case o f material dispersion, if we use nonlinear
effect, the group velocity is given by
1 _  d k  _  d  [ w  
Vg dw  dw  L c
where ^ = — n(uO .
c
Now, group velocity in terms of the free space wavelength 
X ^{ —2 n c / w ) is given by
d^Q
Hence, the time taken by the pulse to traverse length L  
of the fiber is given by
T =T(Ao) = ”7 ^  d/iQ dA^
If the spectral width of the source is the temporal
broadening of the pulse is given by
d/iQ c
^^^"0 . n^o
We know ^ 2 0  =
4c€o «o
d^n^o ^ ^X^ d^np ^ 6n^
2c 6 q riQ nl
Thus, V t  ^
.9f10
XqC
dXS
d  rtp
dAi
6n>I , — 1
2  ps/km-nm. (i)
In case of waveguide dispersion, we consider that v 
(waveguide parameter) is approximately constant. Then
530 Prasanta Mandal, Harihar Bhowmik, Debduti De and Sourangshu Mukhopadhyay
(n o + « 20^ - « 2 ) r r
1 ( d \b v )
D^¥/n 1
j 2d^[bv)
dv^
10' 1 +
dv^
” 20^ ps/km-nm, (ii)
where A = .
H2
5. Conclussion
Here, we conclude that when nonlinearity is absent, 
material dispersion and waveguide dispersion are mutually 
cancelled at >^o = 1550 nm. This wavelength is called 
zero dispersion wavelength. Hence, we can infer that due 
to nonlinearity material dispersion increases by a
factor
6/120^
and waveguide dispersion increases by
a factor I
" 20^'
To compensate large material
dispersion, waveguide dispersion should be equally 
increased. We can control wave-guide dispersion by 
changing A and the radius of the core. Again, if the 
intensity term within the expression (i) and (ii) is 
controlled, we can change the broadening of the soliton 
pulse. This is the most important finding in the above 
treatment.
References
[1] Cristiani Opt. Commun. 146 241 (1998)
[2] S K Turislyn and E G Shapiro Opt. Lett. 23 682 (1998)
[3] K Prozean Proc. Indian Nat. Set. Acad. 67A (November) 609 
(2001)
[4] D Andedson Prox. Inst. Electr. Engg. 123 122 (1985)
[5] A Kumar« S N Sarkar and A K Ghatak Opt. Lett. 11 321 (1986)


A Study on the Propagation of a Gaussian Soliton Pulse Through an Optical Fibre When Dispersion is Compensated Accommodating the Nonlinearity of the Fibre Media

Tamuly, Tulika

Baruah, G D

Indian J. Phys. 80 (S). 531 -535 (2(K)6)
A comparative study between Autlpr-Townes splitting and quenching of
spontaneous emission
Tulika Tamuljj and G D Baruah*
Department of Physics. Dibrugarh Ui|versiiy, Dibrugarh-786 004, Assam. India 
E-mail : gdbar|tah<^rcdiffmail.com
Abstract : Modification of spontaneous emission is an active research topic in quantum optics. The three-peak spectrum of 
resonance fluorescence was one of the first development in this area. Cavity electrodynamics has made possible the enhancement and 
suppression of spontaneous emission from an atom via a tailoring of the mode density. Eliminations of resonance fluorescence from a 
driven thrcc-lcvel atom was proposed in. Dynamical suppression has also been achieved from a driven, cavity-confined, two-level 
atom. Furthermore, it has been predicted and experimentally demonstrated that three level atoms can exhibit a narrowing of spectral 
imewidth on one transition controlled by coherent driving another transition. The coherent preparation of atomic state essential for 
this can be realized via Autlcr-Townes splitting. In the present work, wc have worked out a correlation between Autler-Townes splitting 
and quenching of spontaneous emission via quantum interference. It is believed that the present correlation will be helpful in understanding 
the process of lasing without inversion.
Keywords ; Autlcr-Townes splitting, quantum interference, lasing without inversion.
PACS Nos. : 42.55.Px. 42.50.-p, 42.50.Gy
1. Introduction
A number of discussions of various aspects about the 
theory of three-level lasers have appeared in the literature 
since Bloembergen [1] and others employed a semi classical 
approach to derive most of the theoretical properties of 
three-level systems. Of particular reference may be made 
about the statistical matrix method of Vuylsteke [2] who 
worked out the general equation of motion of the statistical 
matrix for a three-level system. In a three-level gas maser, 
Vuylesteke showed how splitting of emission line or the 
so-called Autler-Townes splitting occurs under certain 
conditions {31. To understand how the splitting occurs, it 
is essential to consider a three-level system as was 
visualized by Bloembergen [1] where it is assumed that a 
strong radiation field is incident on the system which 
saturates the ground and the uppermost level. There is 
also a signal frequency which is reiatively weak and this 
is incident on the upper two-Icvels. If the intensity of the 
radiation field coupling the satu’^ ated pair is increased
beyond the minimum required to equalize the populations 
of the two levels, the perturbation of the levels becomes 
more and more effective until it becomes inappropriate to 
treat the radiation field as a perturbation. The field then 
has the effect of causing appreciable mixing of the two 
unperturbed stales in times short relative to the transverse 
relaxation time T2. Under this conditions, transitions of 
the systems from or to a third-level arc conditioned by 
the mixing of the states coupled by the pump field. The 
general effect of this is a splitting of the level at the 
signal-field frequency. Autler-Townes [3] splitting, and 
similar other phenomena like three-peak spectrum of 
resonance fluorescence [4—7], are considered as significant 
from the point of view of quenching of spontaneous 
emission via quantum interference. Modification of 
spontaneous emission is an active research topic in 
quantum optics [8]. It has been shown [9] that the 
emission spectrum can be substantially modified via atomic 
coherence and interference even for an atom in an^ofdinary
Corresponding Author 02006IAC S
532 Tulika Tamuly and G D  Baruah
vacuum. The coherent preparation of atomic states 
essentional for this effect can be realized via Autler- 
Townes splitting [10], In a recent paper [11] it was shown 
that spectral line elimination and cancellation of 
spontaneous emission is possible under certain conditions, 
and experiment has also been performed to observe this 
phenomenon [12]. It was also shown [13] that the spectrum 
of resonance fluorescence under certain conditions can 
have spectral lines which are very narrow compared to 
the natural width of individual levels.
All spontaneous emission suppression effects 
mentioned above have one common origin the quantum 
interference of spontaneous transitions from two closely 
lying atomic levels to a third-level. The splitting of emission 
lines by mixing of the states coupled by the pumped field 
and quenching of spontaneous emission via quantum 
interference are presumably two different issues but still 
it is reasonable to believe that one effect influences the 
other. One of the interesting developments in quantum 
optics in recent years has to do with an idea involving 
atomic coherence and interference mediated by a strong 
electromagnetic field coupling two levels of an atom 
[1.3,14,15]. The phenomenon of electromagnetically induced 
suppression of absorption and lasing without inversion 
that has been much studied [16—20] and observed [21-23]. 
The fundamental physical principle here is quantum 
interference between the two routes by which an atom 
reaches the upper laser level through absorption of a 
photon. When the interference is destructive, the rate of 
absorption may be vanishingly small, whereas no such 
interference exists to make the rate of emission vanish. 
The semi classical theory of Scully and co-workers explain 
successfully all the basic physics of quantum interference 
and lasing without inversion. Its success stems from the 
fact that quantum interference originates from atomic 
coherence which is fully accounted for as long as the 
atom is treated quantum mechanically. In the sections to 
follow, are first considered the splitting of emission line 
under condition of strong E.M. field and also the cases 
of resonance modulation where under some circumstances, 
system becomes totally emissive or can be both emissive 
and dissipative.
2. System
The three-level system considered, is a A-type ihree-Ievel 
atom with two closely lying lower level \a> and |^> and 
a single upper level \ o  interacting with a strong field
driving the lower two levels and with a weak probe field 
coupling each of the two levels to the upper level as 
shown in Figure 1. The frequency co of the driving field 
is assumed to be in exact resonance with the atomic 
frequency and the frequency Q of the
probe field is considered to be sufficiently close to both 
the atomic frequencies area = E^)/ti and = ( e  ^
that either of the upward transition \a> —> | o  and 
\b> —> |c> can occur with absorption of a probe photon 
The driving field is assumed to be sufficiently strong and 
the probe field sufficiently weak that the lower doublet 
population are determined mainly by the driving field and 
that absorption of a probe photon can be treated by the 
1st order perturbation theory.
a
|c>
|a>
|b>
Figure 1. Three-level atom with levels of c. «. b in the presence o t a 
strong field of frequency cu driving the lower two levels a and b and u 
weak probe field of frequency £2 coupling the two levels a and b to  the  
upper level c.
It must be noted that this system is analogous to 
Bloembergen’s original three-level systems where a strong 
field is incident between lower-two level and a weak field 
is incident between upper and lower level. However in a 
Bloembergens systems, the topic of quantum interference 
is not discussed but we shall see in the following sections 
that a system may behave as quantum system the system, 
may be emissive and as well as absorptive or dissipative 
under some circumstances. This is analogous to quantum 
interference.
3. Splitting of emission line and the equation of motion 
of statistical matrix
We consider a //-system with an unperturbed energy level 
scheme consisting of three non-degenerate levels two of 
these form a closely spaced doubbt far removed from the 
third-level and it is assumed that the transition matrix 
element exist in zero order between the two components 
of doublet as well as between the third level and one of 
the doublet level.
A comparative study between Autler-Townes splitting and quenching o f  spontaneous emission 533
Suppose the Stark electric field which is applied to the 
^.system to be constant in lime. Then since we have 
a s s u m e d  a vanishing 1 st order effect and since the second 
order perturbation o f any level depends inversely on the 
energy separation between that level and the other levels 
in the level diagram, we may expect that for field strengths 
w h ich  result in appreciable perturbation o f the doublet the 
third relatively isolated, level w ill not be changed 
appreciably by the field. This result is illustrated in 
Figure 2 .  Depending upon the particular situation, and the 
stren g th  o f the perturbing field, a number o f changes in 
the absorption spectrum may be expected. In general, in 
the unperturbed spectrum, the two absorption lines have 
control frequencies 1 ^ 2  ^nd 0 2 ^ , the.se lines will appear at 
slig h tly  different frequencies < v ^ 2  y l,>  i/j” In 
addition, because o f  the mixing o f  the doublet levels by 
the Stark field, a third line, at frequencies v^ \ coiTcsponding 
to a  forbidden transition in the unperturbed spectrum may 
b e co m e  apparent in the perturbed spectrum.
The splitting o f the spectral line is manifested by the 
fo rm ula  ( 2 4 ]  :
1 1
Qms Qmo
[ l - ( 3 G - l ) S 2 ] ( l  +  5 ^ - F ^ )  +  2 f ^ [ l - 2 ( e  - 1 ) 5 ^ ]
Qms ^ Qms
l ~ 2 (e  -1)5^ ___
( l - f  ’ 3^2
( 1)
(2)
The general behaviour o f 1/Qms displayed in Figure 2 (a) 
in which the quantity ( -Q mc/Qms) € = 0 , 3 has been 
plotted as a function o f  F  for several values o f parameter
S^. The material can be both emissive and dissipative 
within the same line as indicated by the curve for
=  1.
Finally, the feature o f major interest is the resonance 
modulation splitting which is displayed both for a totally 
dissipative line (5^ = 1/8 ) and for the emissive lines (5^ 
= 3, = 1 ) and both dissipative and emissive lines (5^
= 1/9).
The material can be both emissive and dissipative 
within the same line as indicated by the curve for 5^=1, 
and the resonance modulation splitting which is displayed 
both for a totally dissipative line (5^ = 1 /8 ) and for the 
emissive line (5^ = 3, =  5).
For » 1 ,  eq. ( I )  reduces to
(3e  -1 )
Q m s ( 5 ^ - F ^ )  +  4F^
(3)
From eq. (3 ) when we put e  = 0, we get expression 
1/Qms as
1 1
Q m s  Q m o  ( . S ^ + 4 F ^
Qmo _________ __________ _
QM S iS'^ -  + 4F^
On plotting L.H.S. vs. F, we get the graphs as shown in 
Figures 2 (a,b,c). Here. HQ ms has the. maximum value at 
= 0 i.e. = O.
4. Quenching of spontaneous emission and spectral line 
elimination :
We consider a three-level model atom as shown in
5 3 4 Tulika Tamuly and  G  D  Baruah
Figure 3. It has two upper levels |a|> and \o2> which are 
coupled by the same vacuum modes to the lower level |o. 
The two upper levels are coupled by strong coherent field 
with frequency Dq to another upper lying level \b>. The 
interaction picture Hamiltonian can be written as
laser pulse
Figure 3. Scheme of emission cancellation into a single mode.
V = e^ '‘ \a^xb\ + \aixb\ + H C.
X C | **
+H.C. (4)
Now, in steady state, the probability amplitude of
the atom being in the lower level with one photon emitted, 
is given by [25-27]
-X j  + i [ v t  - + u „ ) ]
(5)
Since the spontaneous emission spectrum is proportional 
to lC (^f = o)p one might expect that there would be three 
peaks in the spectrum corresponding to the three resonant 
denominators in eq. (5).
5. Comparison of the results of Aulter-lbwnes splitting 
and quenching of spontaneous emission
It is appropriate now to summarize the results as indicated 
in the earlier sections and make a comparison between the 
two schemes which have been our main aim in the 
present work. The salient points of the quenching of the 
spontaneous emission was in the following facts and it is 
essential to discuss the points for our convinience. It is 
clear that the nature of the quenching including the 
spectral narrowing and splitting should also determines 
their curve. This situation is definely connected with the 
historical development of the three-ievel maser idea given 
originally by Bloembergen. As indicated in Figure 3, if 
microwave radiaticm appropriately mixes two upper states, 
then emission (both spontaneous and stimulated) of photon 
with frequency Kis cancelled. As shown in eq. (1), there 
would be splitting of emission lines and three peaks
would be observed corresponding to three resonant 
denominators for /? =  0. However fo r  p -  1, we can have 
only two peaks. A  simple explanation of peak elimination 
can also be given the dressed stale picture as shown by 
eq. (5). In all the cases, we observe that the principle of 
superposition and mixing of states is applicable; under 
these circumstances, q u e n c h in g  o f  e lim in a tio n  does occur. 
But we have observed that though in Aulter-Towne’s 
splitting, superposition of states is not considered, splitting 
and quenching do occur. In a recent work [28], it was 
shown that Aulter-Towne’s spectrum quenching and 
splitting of spectral line occur simultaneously and maximum 
quantum interference achieved is a V-type atoms coupled 
to a single mode. If this is so, Aulter-Towne’s splitting 
plays a significant role in quenching of spontaneous 
emission.
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A Comparative Study Between Autler-Townes Splitting and Quenching of Spontaneous Emission

Ghosh, Dipan Kumar

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