IACS Institutional Repository

Tiwari, R S

Mehta, N

Agarwal, P

Indian J. Phys. 80 (1), 49-53 (2006)
Investigation o f antimony addition on the glass transition kinetics o f 
SegoTe2o.xSbj: using calorimetric measurements
R S Tiwari, N Mehla, P AgarwaP and A Kumar*
Deparlmem o f Physics. Harcouri Buller Technological liisiiiute. Kanpur«2()8 (X)2. UlUir Pradesh. India 
‘Department o f Physics, D B S  College^ Kanpur-2<)8 (K)2, Uttar Pradesh, India
It-mail : dr_ashok_,kumarC?^yahoo.com 
Received 6 June 2005, accepted 22 November 2(X>5
Abstract : Calorimetnc measurements have been performed m glassy alloys ScgoTe2oand Sew)Tc2o «Sb,(jr = 0.5 and 1) to study the effect of the 
lower concentration of antimony additive on the kinetics of glass transition in gla.ssy ScKoTejo alloy. The variation of 1\ with heating rate and 
composition has also been studied The he.ating rate dependence of ks used to evaluate the activation eneigy of glass transition.
The thermal stability of these glasses has also been discussed. It has been found that thermal stability increa.ses on addition of Sb in 
glassy SegoTe2o-system. This increase is explained in terms ofdecrea.se in activation energy of glass transition.
Keyword.s : Chalcogenide glasses, differential scanning calorimetry, glass transition kinetics, thermal relaxation.
PACS Nos. i 61.43.Dq, 71.23.Cq. 65.60.+a
1. Introduction
Studies o f the chalcogenide glasses in Se-Te-Sb system 
have received great attention because o f their important 
applications as photoreceptor in xerography and in 
switching devices [1], The addition o f Sb in Se-Tc 
system modifies considerably the structure o f the system. 
Se-Te-Sb shows memory type switching [2].
One o f the most important problems in the area o f 
chalcogenide glasses is the understanding o f glass 
transition kinetics, which can he studied in terms o f glass 
transition temperature and activation energy o f thermal 
relaxation {Eg), In some o f the chalcogenide glassy 
systems, glass transition temperature Tg is found to vary 
with the average coordination number. Physical quantities 
such as, the melting temperature, the magnitude o f photo- 
darkening and width o f  the band tails in chalcogenide 
glasses is found to be related with Tg , Therefore, a study 
o f the kinetics o f glass transition is one o f the most 
important problems in the area o f chalcogenide glasses.
The glass transition is exhibited as an endothermic 
peak or a shift in the base line in Differential Scanning 
Calorimetry (DSC) due to change in sjjecific heal. 
However, in chalcogenide glasses, such an endothermic 
peak can also be observed due to a fast change in 
enthalpy when the glassy system relaxes quickly due to 
a decrease in viscosity at the glass transition temperature. 
DSC technique can, therefore, be quite useful in the 
study o f thermal relaxation in these glasses.
It has been found by various workers that the structure 
o f glassy wSe-Te system is considerably modified by 
addition o f Sb. The effect o f Sb on glass transition 
kinetics in Se-Te system at higher concentration (>  1.5) 
o f Sb keeping the Te concentration constant, has been 
studied by various workers [3—8], However, no attempt 
has been made to see the effect o f Sb addition on the 
glass transition kinetics in Se-Te system at lower 
concentration o f Sb (<  1.5), Hence, studies on glass 
transition kinetics and related parameters for Se-Te-Sb
Corresponding Author
© 2006 lACS
50 R S I'iw a ri, N  M vhta. P A f*ar\va! and A K um ar
system are reporled here for lower concciUralion o f Sb. 
Beside this, we have added the Sb in glassy Seso'le^o 
alloy at the cost o f Te.
2. Material preparation
Glassy alloys o f Se8(»Te2o-,vSb, ( a  = O, 0.5, 1) were
prepared by quenching technique. The exact proportions 
o f high purity (99.999%) wSe, Te and Sb elements, in 
accordance with their atomic percentages, were weighed 
using an electronic balance (LIBROR, AFXi>l20) with 
the least count o f 10 gm. The material was then sealed 
in evacuated ( - - 1 0 rorr) quartz ampoules (length -5 cm 
and internal diameter ~8 mm). The ampoules containing 
material were heated to 800'T' and were held at that 
temperature for 12 hours. The temperature o f the furnace 
was raised slowly at a rate o f 3-4 ‘^ C/minutc. During 
heating, the ampoules were ci>nstantly rocked, by rotating 
a ceramic rod to which the ampoules were tucked away 
in the furnace. This was done to obtain homogeneous 
glassy alloys.
After rocking for about 12 hours, the obtained melts 
were cooled rapidly by removing the ampoules from the 
furnace and dropping to ice-cooled water rapidly. The 
quenched samples were then taken out by breaking the 
quartz ampoules.
3. Experimental techniques
The glassy nature o f the alloys was ascertained by X-ray 
diffraction. The XRD pattern o f glassy Ses(iTe:o is shown 
in Figure 1. Ab.sence o f any sharp peak in XRD pattern 
in Figure 1 confirms the glassy nature o f SesoT^^o alloy. 
Similar XRD patterns were obtained for the other two 
glassy alloys.
The glasses thus prepared, were ground to make fine 
powder for DSC studies. The thermal hchaviour was 
investigated using differential scanning calorimeter. 10 to
20 mg o f each sample was heated at a constant heating 
rate and the change.s in heat flow with respect to an 
empty pan were mcasuied. Five heating rates (5, 10, 15, 
20 and 25'"C/min) were chosen in the present study 
Measurements were made under almost identical conditions
4. Results and discussion
Figure 2 shows typical DSC thermograms at different 
heating rates for Scs(>Ten)Sbi alloy. Similar thermograms 
were obtained for other glassy alloys. It is clear trom 
Figure 1 that well-defined endothermic and exothermic 
peaks arc observed at glass transition temperature 1), and 
crystallization temperature f\. The values o f at different 
healing rates lor various glassy alloys are given in 
Table 1.
Figure 2. DSC scans of glassy SeHoTC|*iSb| alloy for different heating rates.
4.L Composition dependence o f  :
The composition dependence o f T^ r is shown in Figure 3. 
From Figure 3, it is clear that increases on addition of 
Sb in glassy Sc«oTe2o alloy. The structure o f Se-Te system 
prepared by melt quenching is regarded as a mixture of
Table 1. Glass transition temperatures of glassy ScK(,Te20 tSb, alloys at 
djnercnl heating rates.
Investigatiim of antimony addition on the i^lass transition kinetics of SeHoTe20rSb  ^ etc. 51
Sample
Soso 1^20 
St\oTc|.> «iSbo 5
Scho
/,(K)
5 K/min 10 K/min 15 K/min 20 K/min 25 K/imn
335 338
337 340
338 342
341
342 
345
342 
344 ' 
347
343
346
350
Se
5 K / min 
IV K / mill 
I  ^ K / ni III 
iU  K / lulii
X (at % >
3. C'oniposition depcmlence of I^
Scs rings, Se6rc2 mixed ring and the Se-l'e chains. A 
strong covalent bond [91 exists between the atoms in the 
ring, whereas in between the chains, only the Van dcr 
VVaals forces are dominant. The addition o f a small 
amount o f Sb (<  1.5) to the Se-l'e system leads to its 
entry into the crosslink chains and hence increasing
Ibl.
IT e  increase in 7]^  due to addition o f Sb in glassy 
SeK()Te2o alloy can also be explained in terms o f average 
coordination number (<z>) o f glassy ScsoTe2o-,Sb« ( a  = 0, 
0-5, 1.0) alloys.
The glass transition temperature o f chalcogcnide 
glasses shows dependence on average coordination number 
<2> [lOJ, which in turn, depends on the percentage o f 
substituent atoms. The variation o f with < e >  can be
expressed as
InT^ = a <z> b. ( I )
Above relation is similar to the empirical relation proposed 
by Tanaka [ l l j .  The plots o f In 7]^  vs. <z> is shown in 
Figure 4 for the different alloys. The constant ‘c/’ is 
positive showing the increase o f Tf^  with <z>.
4.2. Thermal stability o f  glassy SesoTe2 o-x^ f^ x alloys :
The glass transition temperature Tg represents the strength 
or rigidity o f the glass structure in chalcogcnide glasses. 
Hence, Tg affords valuable information on the thermal
Fimire 4. Plots of In \>\. <z> for glassy Sc8oTe2o rSbv alloys.
Stability o f glassy stale 112,13] but 7^  alone does not 
give any information on the thermal stability [14]. 
However, it has been found that the difference o f peak 
Crystallization temperature 7, and glass transition 
temperature 7^ . is a strong indication o f the thermal 
stability [15]. The higher the values o f (7, — the 
greater is the thermal stability. The values o f 7^  and (7^ . 
-  Tg) at all heating rales are given in Table 2 for 
different healing rates. It is interesting to note that the 
value o f (7^  -  7\.) is increased on addition o f Sb in 
binary SeKoTe2o alloy (.see Figure 5)
Table 2 Values of l\ and (7  7^) (m K) for tei nary alloys at diflerent heating 
rales
/f(K/mm) Se^oTejo Se^ olcivsSbos SejjolcpjSbi
7; 7. /; 7.-7, 7. -  7’,
5
10
15
20
25
377
384
388
392
395
42
46
47 
.50 
52
380
387
392
395
399
43
47
50
51
53
399
405
412
417
422
61
63
67
70
72
5 K  / m m  
10 K / mlu 
15 K /min
Figure 5. Composition dependence of (TV -  T,).
4.3. Heating rate dependence o f  Tg :
The glass transition temperature Tg represents the strength
52 R S Tiwari, N  Mehta, P  Agarwal and A Kumar
or rigidity o f the glassy structure o f the alloys. It is well 
known that o f glassy alloys varies with the heating 
rate P  [16-20]. The empirical relation used to analyze 
the dependence o f on ^  is o f the form :
A ■¥ B\og, (2)
where A and R are constants.
The value o f A indicates the glass transition 
temperature for the heating rate o f 1 K/min. It has been 
found by various workers that the slope B in the cq. (2) 
is related to the cooling rate o f the melt : the lower the 
cooling rate o f melt» the lower the value o f B. The 
physical significance o f B seems to be related with the 
response o f the configurational changes within the glass 
transformation region. The plot o f vs. log P  for the 
present glassy alloys is shown in Figure 6. The values o f 
A and B for different alloys are given in Table 3. The 
values o f B for all the glassy alloys have been found to 
be different, indicating that these glassy alloys undergo 
different structural changes. The results shown in Table 3 
indicate the validity o f this relationship for the present 
glassy alloys.
JS2
350
Figure 6. Plots of vs, log f i foe glassy ScBuTe2«.*Sb:* alloys.
Table 3. Values of A and 8 of glassy SegoTc2o ,Sb, alloys.
Sample Eg (kJ/mol) A { K ) 8 (min)
Eq. (3) Eq. (4)
Se«)Tc2o 178.8 184.5 326.7 11.8
ScgoTcivsSbos 168.8 174.5 327.8 12.5
SctioTctvSb) 146.9 152-6 325.9 16.5
4.4. Evaluation o f  activation energy o f  glass transition 
(^s) •
The activation energy o f glass transition {Eg) can be 
evaluated using the use o f the Kissinger’s linear 
dependence [21] in the form :
In (T ^ )IP  = Eg/RTg + constant. (3)
In addition, when the variation o f ln(l/T; .^“) with In p  is 
much slower than that o f MTg then eq. (3) converts in to 
the form (22] :
In /? = -  Eg/RTg + constant. (4)
The plots o f In {Tg-)/p and In P  against’ 10VT^ . are shown 
in Figure 7. Using the slopes o f these plots, the activation 
energy o f the glass transition process is calculated for the 
various alloys and is given in Table 3. It is clear from 
this table that the E  ^ values are in good agreement with 
each other. This shows that one can use any o f the eqs. 
(3) and (4) for the evaluation o f Eg.
12
10
8
Y 6 
4 
2
Y = In O / (K-mlnV‘
Y = ln p (K/mint
2.91 2.92 2.93 2.94 2.95 2.9<i 2.97 2.98 2.99
1000/ T, (K) ‘
SciM»Tei*jiSbo 5
12
10
8
Y 6 
4 
2 
O
Y = ln(p/ T^(K-miii) ‘
y g  In p (K /  m ill)
2.88 2.9 2.92 2.94
1000/T,(K)‘‘
SrHoTciySb,
2.96 2.98
12
10
8
Y 6 
4 
2 
0
Y In (p/’^ *)<K-niin)'
Y  B In p (K  / min)
2.84 2.86 2.88 2.9 2.92 2.94 2.96 2.98
1000/T.{K )* ‘
Figure 7. Plots of In and In vs. l(KX)/r, for glassy Se«,Tc2o..Sb,
alloy.s.
‘'From Table 3, it is clear thaf£ ’^  decreases on addition 
o f Sb in binary Se8«Te2o alloy. The glass transition 
activation energy is that amount o f energy, which is 
absorbed by a group o f atoms in the glassy region so
Investif^ation o f antimony addition on the glass transition kinetics o f SefioTe2o-,xSb^  etc. 53
that a jump from one metasiable state to another is 
possible. This means that is involved in the molecular 
motions and rearrangements o f atoms in the glass 
transition region. When the sample is heated in DSC 
furnace, the atoms undergo infrequent transitions between 
the local potential minima separated by different energy 
harriers in the configuration space, where each local 
minimum represents a different structure. The most stable 
local minimum in the glassy region has lower internal 
energy. Accordingly, the atoms in the glass having 
minimum activation energy have higher probability to 
jump to the metasiable state (or local minimum) state o f 
lower internal energy and hence, are the most stable. In 
the glassy Sc8oTe2o-v^b, {x = 0, 0.5, 1) system, increases 
in the sequence < (£'^ 0 i:^ o5 < which indicates
that thermal stability o f glassy Se8oTc2o alloy is increased 
on addition o f Sb. This is also confirmed from the value 
of {T^  -  Tf.) for the present alloys, which increases in the 
sequence T^ .)i-=o < (T, -  ~ Hence,
one can ccmclude that the activation energy o f glass 
transition process is related to thermal .stability in the 
pic.sent glasses. Higher thermal stability may require less 
activation energy for glass transition process as found in 
the present study. This is confirmed from the plots o f E  ^
vs. n\ -  7),) at all the five heating rates [see Figure 8]. 
Similar relation between E  ^ and C f -  T^) have been 
repented by Mehta ct al 1231 in case o f SctoTc.^oM io (M  
-  Ag, Cd, Sb) alloys.
5. Conclusions
Calorimetric measurements have been performed in glassy 
Se8oTe2a-.^ Sb^  alloys (jc = 0, 0.5, 1.0). DSC scans o f these 
alloys show the well-defined endothermic peak at glass 
transition temperature (Tg). It has been found that the
glass transition temperature increases with increase in the 
concentration o f Sb. This increase in Ty o f ternary alloys 
is explained in terms o f cross-linking o f Sb in Sc-Te 
chains in these alloys.
In the present work, the significant variation has been 
found in the activation energy o f glass transition and 
thermal stability even at low concentration o f the Sb 
additive. The activation energy o f glass transition process 
iEy) is found to be related with (T, -  Ty) in reverse 
sequence. Hence, one can conclude that the activation 
Energy o f glass transition process is related to thermal 
istabilily in the present glasses. The glasses having higher 
activation energy for glass transition process shows less 
thermal stability.
References
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(1996)
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(1978)
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Grosso Berlin : Springer) 178 (1979)
(191 M E Kolkaia and M K EUMously Acta Phys. flungarica 54 303 
(1983)
1201 K Weiser, R J Gambino and J A Reinhold Appl. Phys. l.ett. 22 48
(1973)
(211 H E  Kissinger Artu/. Chem. 29 1702 (1957)
(221 S Mahadevan, A Giradhar and A K Singh 7. Non-Cryst. Solids 88 
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(231 N Mehta. R K Shukla and A Kumar 7. Optoelecron. Adv. Mater. 6 
1185(2004)



Investigation of Antimony Addition on the Glass Transition Kinetics of Se80Te20-xSbx Using Calorimetric Measurements

Sawhney, Neeru

Dua, Amita

Chandan, Anil

Spectroscopy of Lower Spin States in Tellurium Isotopes with the Inclusion of Hexadecapole Interaction

Varghese, Thomas

Balakrishna, K M

Siddappa, K

Indian J. Phys. 80 (3). 289-292 (2006)
Gamma ray Compton profiles of dysprosium and holmium
Thomas Varghesc*, K M )Balakrishna‘ and K Siddappa’
Department of Physics, Nirmala College. Miivattupuzha-686 661. Kerala. India 
'Department of Studies in Physics, Mangalore Uiniversiiy, Mangalagangoln-574 199, Mangalore. India
E-mail : surajtl|Dmas@sancharnct.in
Received 7 March 2005^  accepted 23 December 2005
Abstract ; The electron momentum distribution and Compton profiles of rare earth elements dysprosium (Dy) and holmium (Ho) were measured 
using HPGe detector. The measurements were carried out on a high purity thin elemental foil using 59.54 keV gumma rays from Am-241. TTie data 
was recorded and analyzed using a 4 K multichannel analyzer. The experimental data was corrected for instrumental resolution effects, sample 
absorption, energy dependence of the differential Compton cross section and double scattering. The results arc presented along with theoretical free 
atom values. The present experimental Compton profiles of Dy consiiiuie the first measurement.
Keywords : Compton scattering. Compton profile, electron momentum density, impulse approximation.
PACSNos. : 29.30.Kv, 32.80.Cy
1. Introduction
Compton scattering is one o f the interactions between an 
incident radiation and electron in the target atom. It is 
predominant in the incident energy range from 0.1 to 1 
MeV. When photon is Compton-scattered, the wavelength 
of ihe emerging beam is increased depending upon the 
angle o f scattering but independent o f the material. The 
emerging beam is Doppler-broadened due to the motion 
of the target electrons. The momentum distribution o f 
electrons is investigated by measuring the energy spectrum 
of Compton-scattered photons. The Compton profile can 
be considered as the Doppler broadening o f the Compton- 
shifted line. The spectral analysis o f  the scattered radiation 
reveals the line shape. The interpretation o f Compton 
line shape, the Compton profile, are based upon impulse 
approximation. In this approximation, the double 
differential cross section, with respect to both scattering 
^ngle and the energy o f  the scattered photon, is 
proportional to the Compton profile which is the projection 
of the electron momentum density along the direction o f 
the scattering vector. The implication o f  this approximation
is that the bound electron can be treated as free with the 
same momentum distribution [1—4],
When the impulse approximation is valid, the relativistic 
Compton cross section is given by (5J :
[d^cr/d£2da}\ = — coJmc^)B)/
-f C02)\\ + OJ/mc^)]y{q\ (1) 
where = classical electron radius, /?i = 1, c =  137.036 
(atomic unit a.u.), fy, = energy o f the incident photon in 
a.u., = energy o f the photon after scattering in a.u.
B =  + [£U2A2/£y,i4|] -  [4M,A2]
+ l4MfA|], (2)
A, = 1 + qfme. (3)
A j = 1 ~ qfmc. (4)
O) — C02- (5)
k kx — 2^* (6)
J iq ) = i!n (Po )dp^p^ CD
e relationship between the energy o f  the scattered
photon and q (in atomic units) is given by :
’Corresponding Author
<D 2006 lACS
290 Thomas Varghese, K M Balakrishna and K Siddappa
q = -137{a^, -  ~ cos0 )/mc^]/
[cOi + col -  2co^ co2CosO]^^". (8)
In this paper, a systematic study o f the Compton profiles 
o f rare earth elements dysprosium and holniium has been 
reported.
2. Geometry and experimental setup
Compton profiles o f Dy and Ho were measured using 
59.54 keV gamma rays from 300 mCi Am-241 point 
source capsule obtained from M/s. Amersham Inc., U.K. 
Although the resolutitm o f experiment with Am-241 is 
lower than for synchrotron radiation, the reporting o f a 
measurement with this source is still important where no 
experimental data are available in the literature. The 
reflection geometry setup is employed in the present 
work to reduce the angular spread over a wide range f6|. 
Using sufficiently thick lead as shielding material with 
graded shielding arrangement, compact geometry is 
obtained by properly optimizing the source to target and 
target to detector distance.
The geometry and shielding arrangement o f the 
experimental setup employed for the present study has 
been described elsewhere i?). A  well-collimated beam o f 
photons from the source is made to fall on the target 
scatterer mounted on a target holder. The optimum distance 
between the source and the target is chosen to be 20 cm 
and that between the target to the detector 25 cm. I'hcsc 
scattered photons are made to fall on the detector, which 
is shielded properly with lead and graded shielding to 
minimize the background radiation. The gamma rays 
scattered at a mean angle 165°(±2°), were detected by 
the HPGc detector. The momentum resolution o f the 
detector which depends on detector properties and beam 
divergence (±2®), was about 0.51 a.u. o f momentum [8]. 
The source S is kept in a lead source holder H having 
a cylindrical hole 1 cm in length and 0.5 cm in diameter. 
A  collimator C made from lead in the form o f a di.se 
having cylindrical hole o f diameters 1.0 cm is placed 
suitably in front o f the source. The source is properly 
shielded with lead so that the detector sees only the 
scattered gamma rays from the scatterer. The alignment 
o f source, target and detector is done with the help o f 
laser beam. The entire setup constitutes a low background 
and high-resolution gamma ray spectrometer.
The HPGe photon detector used in this study, has 
dimensions o f 5.05 cm o f active diameter and an active 
volume o f 90 cc. The operating bias voltage o f the
detector is +2500 V. The detector was maintained at 
liquid nitrogen temperature with a cryo.stat of M) [ 
capacity. Thin elemental foils o f Dy and Ho, havirio 
dimensions o f 2.5 x 2.5 cm and thickness o f 0.02.5X g,iv 
cm‘ and 0.0735 gm/cm^, respectively, were used as targets 
The purity o f the foils was greater than 99.9%.
The linearity o f the spectrometer was studied bv 
using standard gamma ray sources and was found that \ 
possesses very good linearity. The stability was also 
tested and it was ob.served that the shift in the peak 
channel was less than a channel over a period o f 3 days 
The data were collected and analyzed using a PC based 
4 K MCA. A separate measurement was made without 
the sample to obtain background contribution that was 
scaled to the measurement time o f the foil and then 
subtracted point by point from the measured data. The 
signal to noise ratio was found to be 50 : 1. About 11)^  
counts were collected at the Compton peak. The spectrum 
recorded for 59.54 keV gamma rays scattered at 165' is 
presented in Figure 1. The raw data were corrected foi 
background, absorption in the sample, instrumental 
resolution and differential scattering cross section (9,101 
The clastic and inelastic-double scattering (DS» 
contribution was removed by using Monte Carlo 
simulation technique 111). The data were then converted 
to momentum scale to obtain the Compton profile.
The conventional system o f atomic units (a.u.) is used 
for the evaluation o f Compton profiles. In this system.
25n()() -
2(KKK) -
15(KK) -
KKKK) -
5(KX) -
COMPTON PEAK
COHERENT PEAK
450
------- 1-----------r "
550 600
Channel Number —
-T—
650
Figure I. The spectrum recorded for 59.54 keV gamma rays scattered at 
165^
Gamma ray Compton profiles o f dysprosium and holmium 291
=  I ,  //I =  1 und C  = 137 .036 . Also, 1 a.u. o f  Tabic l.  Comparison o f Complon profiles o f Dy and Ho with theory.
momentum 1.9929 X kg m s *, 1 a.u. o f energy
- 2 7  -12 eV  and 1 a.u. o f  length = 5.2918 x 10 ‘ m. 
The uncertainty in setting the target foil angle was 
about 2 %, which contributes a negligible error in the 
measured Compton profile. The statistical error due to 
count rate were reduced and kept within 2%  by counting 
the data for a long time. The counts under the peak were 
determined accurately after subtracting the background 
counts and applying Guassian fitting. The error due to . 
the uncertainty in evaluating the solid angles was less  ^
than !%• The estimated error in the determination o f. 
photopeak efficiency o f the detector using the standard 
weak sources, was about 2%. The errors associated in 
evaluating the source strength was estimated to be about 
y/c. All the errors were compounded according to the 
well-known rules o f propagation o f errors and the resultant 
error was quoted on the measured Compton profiles. The 
binding energy o f K-shell is greater than the recoil 
energy. Hence, the experimental Compton profiles (high 
energy side) are normalized to the area o f corresponding 
tree-atom profile in the momentum range o f  O to 7.0 a.u. 
excluding the contribution o f  1s electrons. The 
normalizations used for Dy and Ho are 24.93 and 25.22, 
respectively.
3. Results and discussion
The present experimental results for Dy and Ho are 
compared in Table 1 with the theoretical values calculated 
from the relativistic Hartree-Fock (H F ) wave functions 
II2J and renorm alized free atom (R F A ) profiles, 
respectively [13]. It can be seen that at cy =  0 a.u., the 
measured values are smaller (-24%  for D y) than profiles 
calculated from HF wave function. This deviation is due 
to the fact that the contribution o f  inner-core electrons is 
small in this region [14J. Also, this deviation indicates 
the neglect o f electron correlation beyond the HF parallel 
spin exchange. A  proper inclusion o f electron coiTclation 
produces an isotropic correction, which reduces the 
difference between experiment and theory. However, 
between 0.3 and 4.0 a.u., the present results o f Dy are 
slightly broader than the theory. This broadening may be 
due to electron correlation which pushes a part o f the 
^cupied states below the Fermi momentum to momentum 
'^ alucs above the Fermi momentum. In the high 
•Momentum transfer region (q  >  4,0 a.u.), experimental 
values are very close to the corresponding theoretical 
It is interesting to note that in the high momentum
<!
u.u Dy Dy
)*■»»>•
Ho Ho
0.0 9.535 ± 0.286 11.9 9.498 ±  0.284 9.63
0.1 9.497 ± 0.284 11.3 9.445 ± 0.283 9.55
0,2 9.431 ±0.282 9.97 9.389 10.281 9.46
0.3 9.215 ±0.276 8.77 9.207 ± 0.276 9.14
0.4 8.799 ± 0.263 8.03 8.750 ± 0.262 8.82
0 5 8 434 ± 0.253 7 62 8.416 10.252 8.28
0.6 8.121 ±0.243 7.35 8.099 1 0.243 7.79
0.7 7.689 ± 0.230 7.10 7.680 ± 0.230 7.30
0.8 7.305 ±0.219 6.83 7.32410.219 6.97
0.‘> 7.018 ± 0.210 - 7.042 ± 0.211 -
1.0 6.727 ±0.201 6.23 6.751 ±0.202 6.36
1.2 6.113 ±0.183 5.65 6.165 ±0.184 5.77
1.4 5.625 ±0.168 5.16 5.673 ±0,170 5.27
1.6 5.195 10.155 4.77 5.23010.156 4.85
1.8 4 788 ±0.143 4 46 4.807 ±0.144 4.52
2.0 4.43010.132 4.23 4.413 ±0.132 4.28
3.0 3.423 ±0.102 3.33 3.436 10.103 3.39
4.0 2.502 ± 0.075 2.49 2-594 ± 0.077 2.56
5.0 1 86f> ±  0.055 1.83 1.905 ±0.057 1.89
6.0 1.417 ± 0.042 1.39 1.468 ±  0.044 1.43
7.0 1.08010.032 1.10 1.14010.034 1.13
range o f 3.0 to 7.0 a.u., the experimental results o f Ho are 
also in good agreement with the theoretical values based 
on RFA model. This is so becau.se the contribution in the 
high momentum region, comes mainly from the inner-core 
electrons and these electrons are reasonably described by 
the free-atom values [15,161.
It can be seen that in the low momentum transfer 
region (0 < q < 0.2 a.u.), the theoretical profiles o f  Ho 
arc slightly greater than the experiment. However, in the 
region (0.3 < q <  2.0 a.u,), the present results for Ho are 
slightly broader than RFA values. The present exp>erimental 
results for Ho compare well with the recent 662 keV 
results o f Ahuja and Sharma [13], indicating reliability o f 
the pre.scnl data.
4. Conclu.sion
In this paper, we have reported experimental data on 
Compton profile o f the rare earth elements Dy and Ho. 
The results are in relatively good agreement with 
theoretical free atom profiles, particularly in the high 
momentum transfer region. In order to throw more light 
on the electron momentum distribution o f  rare earth 
elements, improvements in the calculations based on
292 Thomas Varghese, K M Balakrishna and K Siddappa
proper models and more extensive and systematic 
measurements, particularly with synchrotron radiation 
sources, arc needed.
Acknowledgments
The authors wish to thank Mangalore University for 
providing the opportunity to undertake this study. The 
financial support of the University Grants Commission is 
gratefully acknowledged.
References
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[2] B G Williams Compton Scattering (London : McGraw-Hill) pll 
(1977)
[3] M Cooper Adv. Phys. 20 453 (1971)
|4) M J Cooper Rep. Prog. Phys. 48 415 (1985)
[5] J M Jauch and F Rohrlich The Theory of Photons and Electrons 
(Cambridge : Addison Wesley) p231 (1955)
[6] P P Kane, L Kissel, R H Pratt and S C Roy Phys. Rep^  140
(1986)
17] 'Fhomas Vaighese, K M Balakrishna and K Siddapa indian J 
Appl. Phys. 60 569 a m )
f8) S Manninen and T Paakkari Nucl. instrum. Meth. 155 115 (197({|
[9] R Benedek. R Prasad, S Manninen, B K Sharma, A Bansil and p h 
Mijnarends Phys. Rev. B32 7650 (1985)
110] S Manninen, T Paakkari and K Kajantle Phil. Mag. 29 167 (1974)
[11) V Haloncn, B G Williams and T Paakkari Phys. Fenn. 10107 (1975^
(121 F Biggs, L B Mendelsohn and J B Mann At. Data Nucl. Data Tables 
16 201 (1975)
113| B L Ahuja and M Sharma Rad. Phys. Client. 73 131 (2(X)5)
114 1 Thomas Varghese, K M Balakrishna and K Siddappa Indian J. 1%^ 
76B 657(2002)
115 i B K Sharma. B L Ahuja, H Singh and F M Mohammad Pranuwa j 
P/i.V5.40 399(1993)
(16] C N Chang. S B Lee and C C Chen J. Phys. Soc. Jpn, 60 452^  
(1991)


Gamma Ray Compton Profiles of Dysprosium and Holmium

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Front Title.................................................................^........................................................................................................ 427
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Advisory Board and Editors................ ................................................................................................................  429-430
From Editors Desk .........................................................................................................................................................431
Front Contents.....................................................................................................................................................  433-434
Proceedings o f  the National conference on ^*Laser and their Applications in Basic and Applied Sciences** 
(NCLBAS -2005 ) held at Department o f  Physics, Visva^Bhartui, Santiniketan~731 235, India, during January 10*13,
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S N  S a h u ............................................................................................................................................................435
Foreword
SWAPAN Mandal......................................................................................................................................... 437
Photon-number distributions in the steady states of traditional and random lasers
V  PeRinovA and a  L u k S ................................................................................................................................439-447
Mixedness and entanglement of an analytically solvable time-dependent ion-field interaction
M R B W ahiddin, M Abdel-Aty, H F A bdel-Hameed and A-S F Obada...................................................449-462
Dynamic reactivity profiles of helium and neon atoms interacting with an intense laser field
Utpal Sarkar and Pratim Kumar Chattaraj............................................................................................463-470
Confocal laser scanning microscopy and laser light scattering : applications in soft matter and 
technological materials
BaldevRaj andB V R T ata............................................................................................. *.................... 471-486
Velocity selective resonances and electromagnetically induced transparency in atomic rubidium 
Shrabana Chakrabarti, Amitkiran Pradhan, Amitava Bandyopadhyay, A yan Ray *
BiswAJiT Ray, D ipankar Bhattacharya and Pradip N Ghosh...................................................................... 487-489
Optical vortices produced by forked holographic grating and sign of their topological charge
Ravindra P Singh, Sanjoy Roychowdhury and V irendra K Jaiswal.......................................................... 491-494
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A mathematical criterion for single photon sources used in quantum cryptography
A nirban Pa t h a k ......................................................................................................................................................495-499
Inverse variational problem for nonlinear equation in optics
B I alukdar .......................................................................................................................................... 501-504
Laser guide artificial star for high resolution imaging
Swapan K Sa h a .........................................................................................................................................................505-509
Vibrational spectral studies on 2,5-dichloroaniline
H C R ai, a  B Sharan and Surfndra Ra i ............................................................................................................... 511-515
Development of ultraviolet laser for disinfection of potable water
G C B hAR and U CHAfTEIUEE.................................................................................................................................... 517-521
Damping effect on power loss in optical fibers due to higher order nonlinear term
SuNiTA Sharma, S K G hoshal and D evendra M o h a n ............................................................................................523-526
A study on the propagation of a Gaussian soliton pulse through an optical fibre when dispersion 
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pRASANTA M an d au  H arihar B howmik, D ebduti D e AND SouRANGSHU M likhopadhyay .................................... 527-530
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T ulika T amuly and G  D  B aku a h ...........................................................................................................................531-535
Control of molecular dynamics in intense laser fields
M  M ohan, A  M aan and P Jh a ................................................................................................................................537-543
Nonclassical photon statistics in spontaneous Raman and in stimulated Raman
B iswajit Sen and Swapan M a n d a l ..........................................................................................................................545-549
List o f Participants o f NCLBAS-2005 ................................................................................................................ 551-554
Forthcoming Publications...............................................................................................................................  555-556
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434 Contents


Front Contents

Bhar, G C

Chatterjee, U

Indian
X /’/iys.80(5).517-521 (2006)
Development of ultraviolet laser for disinfection of potable water
G C Bhar* an4 U Chattcrjee
Laser Laboratory, Physics Department, Burdwan finiversity. Burdwan-713 104. West Begnal. India
i
E-mail : dgp_buphj^cb(g>sanchcrnet.in
Abstract : The ultraviolet (U V ) radiation is an effective means against bacteria and protozoan pathogens for disinfection of drinking water 
killing micro-organisms by causing irrcpairablc damage to their DNA. SSomc protozoan cysts like giardiu require a high doze of UV  intensity of 
16000 |iW.s/cm^ for total destruction. Low level of UV  radiation a.s that available from commercial source for insecticides and viriside is 
incapable of elimination of such resistive cysts. So U V radiation is of demand for this. But except excimer lasers that are of limited life and hard 
to operate, there is practically no UV laser as such. The easy way is to generate through nonlinear frequency mixing of laser radiations from Nd : 
YAG and Dye lasers in a suitable nonlinear crystal. Except borates, few nonlinear crystals can be used in the UV region down to 200 nm or 
below. The borate group includes BBO, LBO, CLBO, LB 4 etc. while the most recent addition is KABO. Although the generation of UV  
radiation of 240-280 nm that is important for DNA ab.sorption is of no problem, but tuning below 2(K) nm is not quite easy. The shortest 
wavelength wc have generated is 187.9 nm in BBO through sum frequency mixing. Wc have shown that it can be tuned to still lower wavelength 
if impurity-frcc BBO is used and the crystal be cooled. Crystal LB4 is better in this respect as it transmits down to 170 nm. But since nonlinearity 
of LB4 IS very low, available intensity of UV  radiation may not be sufficient for such disinfecting applications. So some ingenious technique of 
multipass has been proposed and demonstrated to realize high conversion in such cry.stals.
Keywords : UV  radiation, nonlinear optical devices, frequency mixing, multipass configuration.
PACS Nos. : 42.65.Ky, 42.72.Bj
1. Introduction
The ultraviolet (U V ) radiation is an effective means 
against bacteria and protozoan pathogen for disinfection 
of drinking water. And in fact it is better than other 
disinfectants like ozone, chlorine, chlorine dioxide and 
chloramine as it does not leave harmful residue. The UV 
radiation kills microorganism by causing irreparable 
damage to their D NA .
There are four principal factors that need discussion 
determining effectiveness o f  U V  light inactivation o f 
microorganism :
(i) Wavelength o f  U V  radiation,
(ii) Intensity o f  U V  radiation,
(iii) Exposure time o f U V  radiation,
(iv) Resistance o f  target microorganism.
The wavelength o f  interest for disinfection is 250-270 
nm. The commercial sources include some incandescent
light bulbs, halogen bulbs, high efficiency light bulbs 
and also computer screen which also emit U V  radiation 
that are too weak for this purpose. However, special U V  
emitting lamps are used to disinfect water. Commercially 
available low-pressure mercury vapour lamps emit 
principal U V  wavelength at 254 nm. Maximum dose o f 
many commercially available U V  units is 25—35 mW/cm^. 
Typical U V  intensity requirements for disinfection studied 
in advanced countries [ 1 ] are the following :
(a) Bacteria : E coli — 3mJ/cm ,^
Vibro Cholerae -  3.4 mJ/cm .^
(b) Viruses : Hepatitis A  virus -  20 mJ/cm .^
(c) Protozoan cysts : Giardia muris — 82 mJ/cm^.
As a result, one o f the world’s largest potable 
disinfection plants in London uses U V  as the primary 
disinfectant and adds free chlorine for the residua] 
infectanls prior to storage. Since using commercial
Corresponding Author ©  2006 lAC S
518 G C Bhar and U Chatterjee
nonlaser UV source, famous M/S WaterHeallh International 
o f U SA clarifies that “ it does not treat parasites or 
microorganism cysts with protective coverings such as 
Cryptosporidium and Giardia.”
The U V radiation after absorption alters nitrogenous 
heterocyclic components within D N A  and R N A  and 
causes molecules to form new bonds. This effect renders 
microorganism unable to replicate. The U V  dosage 
measured in mW.sec per sq. centimeter must either 
eliminate D NA  replication or partially damage the genetic 
materia] [2]. Under certain conditions, cells damaged by 
UV may repair and reactivate themselves through enzyme 
activity. Photoreactivation i.e. the revival o f  organism in 
visible light shortly after U V  light exposure, may be a 
function o f  the light intensity. Permanent inactivation 
requires damage to nucleic acids for which key parameter 
is an appropriate U V  dose. So high intensity UV light as 
that generated by laser is the answer to this problem.
But there is practically no UV laser as such, excepting 
the excimer ones which are o f limited life and hard to 
operate. The easy way is to generate through harmonic 
generation or sum frequency mixing o f laser radiation 
from commercially available Nd : YA G  and Dye lasers 
in a suitable nonlinear crystal. There are not many such 
nonlinear crystals transmitting in the U V  region o f  200 
nm or below except borates. These include BBO, LBO, 
CLBO, LB4 and the most recent addition is KABO . The 
U V  generation in the region 240-280 nm, important for 
D N A  absorption, is o f no problem. The generation o f 
fourth harmonic at 266 nm o f common Nd : YAG  laser 
line has been realized in CLBO  crystal. Tuning below 
20 0  nm is difficult and the shortest wavelength we have 
generated is 187.9 nm in BBO through sum frequency 
mixing (SFM ). Crystal LB4 is better in this respect but 
since its nonlinearity is very low, available intensity o f 
Tkble 1. Linear and nonlinear optical parameters of some borate group crystals.
UV radiation may not be sufficient for the application. So 
some ingenious technique o f multipass has been proposed 
and demonstrated to realize high conversion in such 
crystals.
2. U V  generation through frequency-mixing in Nonlinear 
Crystals
We have been engaged in characterization o f various UV 
and IR crystals meant for different applications. The UV 
radiations are generated through third harmonic generation 
(TH G ) o f Nd : YAG  laser and Dye laser and also 
through sum frequency mixing o f  these two input laser 
radiations. The techniques are described in crystals of 
BBO, LBO, CLBO  and LB4 and means are demonstrated 
for efficient conversion into UV since high U V  intensity 
is necessary for removal o f resistant microorganism. Out 
o f these, the crystal o f most interest is BBO having 
highest nonlinearity o f the lot and its U V  transmission is 
as low as 187 nm. It can still be shifted to shorter 
wavelength i f  the impurity content causing onset of 
band-edge-absorption can be reduced by after-growth 
quality improvement technique. With the availability of 
various samples o f crystals from BARC, it had been 
possible to verify the concept 13,4]. Linear and nonlinear 
characterizations o f UV  transmitting crystals are illustrated 
in Table 1.
3. Experiments and results
Our basic pump laser is Spectra Physics model DCR-11 
which is a Q-switched Nd : YA G  laser having pulse 
repetition rate o f 10 pps while the Dye laser is o f the 
same make (model PD L-2) pumped by the second 
harmonic o f the Nd : YA G  laser. The dye laser is 
capable o f operating through the entire visible and very 
near infrared. The follow ing two types o f  nonlinear
Crystal BBO LBO CBO CLBO LB«
Symmetry 3 c 3 m 222 42 m 4 mm
Transparency (//m) 0.19-3.4 0.16-2.6 0.17-3.0 0.18-2,75 0.16-3.5
Absorption coefficient (cm"*) at 200 nm 0.96 1.10 0.50 0.0042 0.004
Birefringence 0.11 0.039 0.057 0.0496 0.0546
Effective nonlinear coefficient (pm/V> 2.20 1.20 3.67 0.47 0.16
Efamage thxeshold (1 ns. 10 (GW/cmf<) 13 27 20-26 26 40
Walk-off (degree) 4 0.37 1.76 1.78 2.1
SHG cut-off (nm) 411 554 4S0 470 487
Chemical property Hygroscopic Non-hygroscopic Hygroscopic Hygroscopic Non-hygroscopic
Development o f ultraviolet laser fo r  disinfection o f  potable water 519
interactions have been studied for generation o f U V
radiS'tion i
(i) Harmonic generation o f 2nd and 3rd o f Nd : YAG  
laser and Dye laser in CLBO  and LB4  crystals.
(ii) Sum frequency mixing in BBO. CLBO and LBO 
crystals.
The experimental arrangements along with tuning range 
for second harmonic generation (SHG) and third harmonic 
generation (TH G ) o f  Dye laser radiation.s in CLBO are 
illustrated in Figures 1 and 2 respectivly. In the SHG
90
Figure 1. Phase-mutching characteristic for coliinear SHG (236.8- 
265 nm) in a CLBO  crystal. The experimental points (• )  arc shown 
over the theoretical curve (solid line). The inset shows the experimental 
setup for noncollincar configuration. BD is beam dumper for Nd : 
YAG laser radiation. M  and M ' are dichoric mirrors, M  being a partially 
transmitting dichoric mirror.
experiment, frequency doubling o f dye laser (74ATFM C) 
the generated harm onic is 236.8-265 nm. 
A long focal length (110 cm) lens is used to loosely 
focus the fundamental dye laser radiatiem in the CLBO 
crystal, A  dichoric filter is used to separate the residual 
fundamental beam from the generated UV. The crystal 
being non-centrosymmetric, the three wave mixing for 
THG requires a second stage where the residual 
fundamental beam after SHG is sum-frequency mixed 
with the SHG in a second nonlinear crystal. Thus for the 
THG experiment in CLBO, dye (LDS-698) laser radiation 
producing fundamental 678.9-713 nm beam is mixed 
with its second harmonic radiation 339.5-356.6 nm made 
*n a Type-I, 6  =  30® cut, 7.3 mm long BBO crystal [5]. 
Hgure 2 shows the phase-matched tuning range 226.3- 
237.5 nm for different noncollinear angle between the 
fundamental and harmonic beam. The short wavelength 
cut-off arises due to noncritical phase-matching while in
^  80
<  75 
S
6 5
0.225 0 .2 .1 0  0 .2 3 5
THG Wavelength (pm)
0 .2 4 0
Figure 2. Phase-matching churacteristic;^ of CLBO  crystal for THG  
of LDS-698 nm dye laser radiation (678.9-713 nm) by noncollinear 
configuration for internal noncollinear angle a  = 0.5® (lower curve) and 
5.7® (upper curve).
our experiment, the long wavelength limit is set by the 
crystal cut. Hence, the latter can be extended further 
using another suitably cut CLBO crystal. The region 
below 230 nm and down to 200 nm is covered by THG 
in a Type-I, 0  =  60® cut BBO crystal using dye laser 
radiations, the dyes used being LDS-698 and DCM.
Shorter wavelength region is accessed through sum- 
frequency mixing in crystals having deep UV transmission. 
The region below 200 nm has been covered in BBO and 
CLB O  crystals. The experimental arrangements are 
illustrated in Figure 3. First the second harmonic o f a 
dye (Coumarine) laser covering a tuning range o f 456-530 
nm is generated in a Type-I, O = 60® cut BBO crystal. 
This is then sum-frequency mixed in a CLBO crystal 
with fundamental Nd : YAG  laser radiation (1064 nm). 
The interaction is made noncollinear to avoid use o f 
filter for separation o f the generated 195.3-210 nm from 
the input parent beams. The limiting generated wavelength 
is 195.3 nm employing a noncollinear angle o f 8®. In 
BBO crystal, still shorter wavelength can be accessed by 
sum-frequency mixing due to its available UV transmission 
and phase-maichability thereof. To cover the longer 
wavelength U V  generation o f 240—280 nm, we have 
used LBO  cryital and noncollinear sum-frequency mixing 
o f Nd : YAG  and dye laser radiation.
Apart from the tuning range, other facts o f  importance 
is the intensity o f the generated radiation that is necessary
520 G  C  B h ar and U  Chatterjee
axis in other direction as shown in Figure 4 . Such a 
crystal pair o f  BBO is employed for TH G  o f dye laser 
radiation 200—230 nm [6 ]. W e demonstrate 
conversion efficiency for U V  at 210 nm. In LB 4 crystal 
pair, we have generated 288 nm UV radiation at power 
level o f 21 M W  by the same technique.
F ig u re  3 . P hase-m atching c h a racteristics o f CLBO crystal for 
generation of 1 9 5 .3 -2 1 0  nm by noncollinear SFM of Nd : YAG (1 06 4  
nm) and dye SHG (2 3 9 .2 —2 6 2 nm) radiations for internal noncollinear 
angle a  = 0 .8 °  (lower dashed curve) and 8° (upper dashed curve). 
Lower and upper solid curves are theoretically predicted ones for a  = 
0 .8 °  and 8° respectively. The inset show s the schem atic o f the 
experim ental setup. M | is a dichuric mirror transm itting only the 
generated SHG (2 3 9 .2 —2 6 2  nm). M z  and M y  are also dichortc mirrors 
for 1064 nm. B  and E  are respectively beam dumper and extra dense 
flint glass prism. /? is a 90° polarization rotator for dye laser radiation. 
The BBO crystal is rotated in a vertical plane while the CLBO in 
horizontal plane to satisfy proper phase-matching conditions.
to deactivate the microorganism. This is tied up with the 
frequency conversion efficiency in the nonlinear process. 
While the tuning wavelength is dictated by the crystal 
phase-matching properties, for the efficiency o f conversion, 
we have to look for ingenious techniques other than 
crystal properties. Two such techniques for increasing 
efficiency have been demonstrated in the laboratory with 
success :
( i ) W alk-off compensation (W O C ) configuration,
(ii) Multipass configuration (M FC ).
Birefringently phase-matched frequency conversion process 
occurs in presence o f  both ordinary and extraordinary 
polarized radiations. The later while propagating through 
the crystal, suffers birefringent walk-off whereas the 
former is not. As a result o f  separation o f the -beams, the 
effective crystal interaction length is limited which reduces 
conversion efficiency. To overcome this limitation, it is 
suggested that the walk-off produced in one crystal is to 
be compensated by using another crystal with its optic
F L
F igure 4 . The experim ental setup for WOC SHG scheme in I lu  
crystals. L  is CaF2 lens, F  is dichoric mirror transmitting >70';> (,i 
2 8 8 .5  nm only.
Still more advantageous technique is multipass 
configuration illustrated in Figure 5 where twin crystal of 
W O C set up is ingeniously used for more than one pass 
through the pair and hence the nonlinear conversion is 
further improved [7]. With this it has been possible to 
realize 21% conversion efficiency in LB4 crystal in SlKi 
o f Nd : YA G  laser radiation, even though the nonlincani) 
o f LB4 is 1/6-th that o f KDP.
N<l:YACi
l.ASliR
Figure 5. Generation of 532 nm by SHG of Nd : YAG laser radiation 
using multipass configuration in LB4 crystals. L\ and L 2 are lense.s. f  
is prism and is u beam dumper for Nd : YAG laser radiation. DichoiK 
mirror M  reflects >98% at 532 nm and transmits about 100% of I0f>4 
nm radiation.
4. Conclusion
In conclusion, we have demonstrated high intensity, widely 
tunable UV source capable o f deactivation/removal o1 
even highly resistant protozoan cysts using commercially 
available Nd : Y A G  and Dye laser and common nonlinear 
crystals.
Acknowledgments
The authors acknowledge the partial financial support 
from the DRDO, Ministry o f  Defence, Government of 
India. They are also grateful to the authorities o f  V E C C  
Kolkata, Government o f  India for input laser power 
supply control and stability.
Development o f ultraviolet laser fo r disinfection o f potable water 521
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and G C Bhar Jpn. J. Appl. Phys. 43 4190 (2004)
(7] U Chattetjee, S Gangopadhyay. C Ghosh and G C Bhar Appl. 
Opt. 44 817 (2005)


Development of Ultraviolet Laser for Disinfection of Potable Water

Sunita, Sharma

Ghoshal, S K

Mohan, Devendra

Indian J, Phys. 80 (5), 523-526 (2006)
I J P
Damping effect on power loss in optical fibers due to higher order
nonlinear term
Sunita Sharma*. S K  Gho|hal and Devcndra Mohan 
Guru Jambhcshwar Univcrsily|Hisar-I25 001, Haryana, India
E-mu)] : Sun_ph3l2003@yahoo.com
Abstract : The nonlinear response of optical fiber based on aiihannonic oscillator model is investigated analytically and numerically. The 
response of the fifth order nonlinear rcfraciive index with the frequency of LASER at 1.33y/m is examined. The present work is motivated from 
a number of theoretical and experimental studies on power loss in optical fiber. The power loss due to imaginary part of fifth order nonlinear 
refractive index for Pure Silica Core Fiber, Dispersion Shifted Fiber and Dispersion Compensating Fiber is calculated. The variation of power 
loss with damping constant is also calculated at 2 mW . Wc find a finite contribution due to fifth order anhurmonic term. Controlling such 
nonlinearity is very important for technological applications.
Keyword.s : Anharmonic oscillator model, susceptibility, refractive index, damping factor.
PACSNos. : 42.6.5.-k. 42.81.-i
1. Introduction
The response o f any dielectric with electromagnetic wave 
becomes nonlinear for intense electromagnetic fields, and 
optical fibers are no exception. On a fundamental level, 
the origin o f nonlinear response is related to anharmonic 
motion o f bound electrons under the influence o f the 
applied field, i f  the external field is strong enough to 
distort the internal dipole field . So, the induced 
polarization P  from the electric dipoles is not linear in 
the electric field but satisfies the relation;
P =  ( • )
where is the vacuum permittivity and iJ  =  1 > 2 ,- 
“) is the 7-th order susceptibility. The linear susceptibility 
represents the dominant contribution to P. Since 
S1O2 is a symmetric molecule, vanishes for silica 
glasses. As a result optical fibers do not normally exhibit 
second-order nonlinear effects. Nonetheless, the electric- 
quadrupole and magnetic-dipole moments can generate 
weak second-order nonlinear effects. Defect or color 
centers inside the fiber core can also contribute to second 
harmonic generation under certain conditions [1]. Materials
that exhibit strong nonlinearity o f refractive index are 
suitable conditions for applications in optical switching 
devices [2]. The imaginary part o f refractive index (n) is 
a convenient way o f expressing the loss term. This loss 
is due to y (damping factor) which originates due to 
complex interaction o f Si and O atom with external 
electromagnetic field. The Kerr nonlinearity originates 
from third order non-resonant electronic susceptibility 
and Raman susceptibility. Electrostriction is the process 
in which the material density increases in response to the 
intensity o f an applied electromagnetic field creating a 
proportional change in the refractive index o f the material 
[31. The power loss in optical fibers due to Kerr and 
Electrostrictive nonlinear effects at 1.55 //m is studied 
extensively in recent years [4].
2. Model calculation
The origin o f  nonlinearity is the non-resonant electronic 
response. In anharmonic oscillator model, the equation o f 
motion o f the displaced electron as a forced harmonic 
oscillator is represented by :
*Corresponding Author
Q 2006 lACS
524 Sunita Sharma, S K Ghoshal and Devendra Mohan
Y  X +  cOqX 4* Dx^ + -f Fx^
= {eE^2m).{ 4- e (2)
where y is the damping factor, e is electronic charge, m 
is mass o f the electron, (o is the frequency o f laser, oJq 
is oscillating frequency o f the atom, D, G and F  are 
second, third and fifth order anharmonic terms.
= I + Z
. r N e ''D ‘'[e \ ia d + b c ) + f { a c - b d ) }
4m^eoA\ .A 2X A 3 f .AA
G N e^ 'D ^ jad+bc)
-A l . iA i f .A A
3GNe^(.ah +  gb )
l6m^eQA\.A2.A5
c =  (<ab^  -  Aa?) (Q^ -  9 a f ) -  6cu^r^ , 
d  =  -3 e o r (a ^  -  A(o^) -  2a>Y{o^ -  9o)^), 
c, =  (.oio -  A a i\
f  =  - 2 to r,
g = { 0 )0 -  Aco^f -  Aw^r^, 
h =  -A  corCo)^ -  A o )\  
k =  (a)o^-9aj‘),
I = -3 o )r ,
m =  {OJ^  -  Aq>^\
Ai = [{cuo -  a i^ f + *,
/I2 =  {fOo -  2 5 o )^ f + 25ce)^r\
A j = {0 )1— Ao^y^ + Ao)^T^,
A^ =  {0)o -  9o)^y' + 9a^ 7■^
As = l { 0 )^ -  o )^ f  +
3 N e ^ G D ^ m {a l  4- k b ) +  f { a k  -  b l )
Am^eoA\.A2.A3.AA
3 N e ^ G ^ {a l  +  k b )
16m*e„Al.A2.A4
F N e %
where
a = (GJb* -  2 5 o ) ‘ )  Kfflg -  o / )^  -  l O o f r ^  { o j ^  -  o f f  
+ 9 o ) '^ r \ o 3 ^ -  0/ V +  3 o) * T * { q) ^ - q)'^)-\ + 5 o )Y  
{o )^  {co^ -  o ) f f  -  3 o )T { o )^  -  o f ) *  -  cof Y ^
-  2 o ) Y  { o ^ - o ) ^ ) %
b  =  { o j ^ -  2 5 0 )^ ) [ o ) ^ Y ^  { 0 ) S -  o f f  -  3 o ) Y { o ) ^ -  o f f  
-  o f  Y ^  -  2 o ) Y { a ^ f -  o f f  ] -  5 c o Y [ { o ) o ^ -  o f f  
- \ O o f Y \ o ) ^ -  o f f - ¥  9 o f Y \ o j ^ ~  o ) ^ f +  S o ) * Y *  
{O J ^ -  o f ) ] ,
3. Results
Table 1. Power loss while considering second order nonlinearity.
-NEG.3TP
-NEG.5TP
-POS.3TP
-POS.5TP
2 3 4
TYPE OF FIBEn
Figure 1, Power loss due to 3rd and 5th order nonlinearity versus type of 
fiber.
— NEG.3* — POS.30
—A— NEG.5e ■ M POS.Sa
Figure 2. Electrostrictive power loss due to 3rd and 5th order nonlinearity 
versus type of fiber.
Type of fiber Nonlinear Power loss Dumping factor Im[n2^’>(£y)l Power loss due
refractive index (in A.U.) (j^ (in A.U.) (in A.U.) to y(in A.U.)
(in A.U.)
Pure silica core fiber ( 1) 2.79 73.31 r u * ± i % h *  (~l% )y 1.45 38.10
y2«(-»-l%)y 1.68 44.15
Dispersion shifted fiber (2) 3.35 8S.03 Xu* ±2% ri*(-2% )y 1.4 36.79
2^*  (+2%)^' 1.8 47.30
Dispersion compensating fiber (3) 4.44 116.67 y ,» (~59b)y 1.1 28.90
X2 « (+5%)y 2.23 58.60
Power loss due to Kerr and Electrostrictive effects while considering third order nonlinearity.
Damping effect on power loss in optical fibers due to higher order nonlinear term 525
Type of fiber Damping factor ()^ Nonlinear refractive Power loss
(in A.U.) Index (in A.U.) (in A.U.)
Pure silica core fiber (I ) Y, = (-1% ))' ^2k 1.74
p(3)
^2k 45.72
0.40 p(3)^2e 10.51
(4-l%)y , *hk 1.62
p(3)
^2k 42.57
(3)
4 0.38
p(3)
^2e 9.98
Dispersion shifted fiber (2) r^  = {-2 % )r J ./•''>1 ^2k 1.78 p(3)^2k 46.77
1 „(3) 0.41 p O ) ^Ic 10.77
(+2%)y 1 „ 0 ) 1.54 p(3)*2k 40.47f 0.36 p(3) 9.46
Dispersion compensating fiber y, =. (-5%)y tf "2k 1.97
p(3)
^2k 51.77
: «2e 0.45
p<3)
*2e 11.82
Y^ = (+5%)y „(3)"ik 1.47
p(3)
^2k 38.63
H2e 0.34
p(3)
^2e 8.93
Ibble 3. Comparison of Kerr and Electrostrictive power loss due to 2nd and 5th order nonlinearity.
Type of fiber Nonlinear refractive Power loss Im [w2 '^(^ t^ )l (in A.U.) Power loss (5th order)
index (in A.U.) (2nd order) (in A.U.) (in A.U.)
Pure Silica ^2k 1.175 30.87
Core fiber (1) fhk 2.26 />3i 59.39 ^2e 0.275 ^2^  ^ 7.22
^2k 1.361 2^^ ^^  35.76
fhe 0.53 Pjt 13.92 y2=(+l% )y
x/(5)
^2e 0.319 2^^ 1^  8.38
Dispersion ^2k 1.134 29.80
Shifted fiber (2) 2.72 P.5 71.48 (-2%)y 0.266 2^^ ^^  6.99
^2k 1.458 38.31
• 0.63 P:j 16.55 X2 == (^-2%)^ ^2e 0.342 Pj^ ^^  8.98
Dispersion ^2k 0.891 23.41
Compensating fiber <3) 3.60 Pj( 94.60 Yx = (-5% )y ^2e 0.209 5.49
^2k 1.807 P^ t^ ) 47.4g
^he 0.84 Pj, S22.07 Y2  ^(+5%)Y ^2e 0.423 P2^ ^^  11.11
■ ♦■■'NEG.Sk '■ ■ ■ P08.3k
lU- - neq.sk —M— POS.Sk
PL CONC. '■ NEG.3TP
— ^ P O S .3 T P
Tvp« rmmn
Figure 3. Power loss (Kerr) due to 3rd and 5th order nonlinearity versus Figure 4. Power loss due to 2nd and 3rd order nonlinearity versus type of 
type of fiber. fiber.
526 Sunita Sharma, S K Ghoshal and Devendra Mohan
-PL CONC. 
-POS.5TP
-NEQ.5TP
TYPE OF FIBER
Figure S. Power loss due to 2nd and 5th order nonlinearity versus Type of 
fiber.
4. Conclusions
The power loss due to Dispersion Compensating Fiber 
(DCF) is more than in Dispersion Shifted Fibers (DSF) 
which in turn has more loss in power than Pure Silica 
Core Fiber (PSCF). It shows that the power loss depends 
on refractive index of the optical material. With the 
increase in refractive index the coupling power also 
increases. Figure 1 shows that Kerr and Electrostrictive 
contribution to power loss due to 5th order nonlinearity 
is less than in case of 3rd order nonlinearity. Comparison 
of Figures 2 and 3 shows that the power loss due to 
Kerr effect is more than that due to Electrostrictive 
effects in higher order nonlinearity i.e, 3rd and 5th orders 
both. Kerr nonlinearity can be enhanced with increasing 
the coupling power [5]. We have calculated that the 
power loss due to Kerr effect increases with increase in 
refractive index (Figure 3) and hence with coupling 
power which is in confirmation with [4]. The contribution 
of power loss due to imaginary part of refractive index 
is significant and hence absorption, scattering and 
dispersion phenomena also play an important role in 
power loss in materials of optical fibers. A closer look at 
Figures 4 and 5 reveals the fact that with increase in
order of nonlinearity, the power loss decreases. The loss 
tangent shows that the power loss due to 5th order is 
10% of due to 3rd order. So the power loss due to the 
7th order nonlinearity will be less than 5th order and 
hence the contribution of higher order nonlinearities is 
neglected.
A h r e v a t i o n s :
A.U. Arbitrary unit.
PL CONC. : Power loss while considering 2nd order 
nonlinearity and the effect of concentration of impurities on 
it.
NEG.3TP and NEG.5TP : Total power loss due to 3rd and 
5ih order nonlinearity using y; = (~x%)y
(where jc= 1,2,5).
POS.3TP and POS.5TP: Total [xjwer loss due to 3rd and 5th 
order nonlinearity using
2^ = (+ x%) r  
(where x  = 1,2,5).
POS.3k and NEG.5k : Power loss due to 3rd and 5th order 
nonlinearity due to Kerr effect using
y2 = (+;c%) y and y, = (-jc%) y respectively (where x: =1,2,5).
POS.3e and NEG.3e : Power loss due to 3rd and 5lh order 
nonlinearity due to electrostriction using
2^= ( + x % )  Y  and y, = ( - x % )  y respectively (where jc=1,2,5). 
References
(1) G P Agarwal Nonlinear Fiber Optics (San Diego, Calif ■ 
Academic) Ch 1. Sec 3, pl6 (1989)
[2J Jan Jasny. Bernhard Nickel and Pawel Borowicz J. OpL Soc. Am. 
B21 729 (2004)
[3] Eric L Buckland and W Boyd Opt. Lett. 22 676 (1997)
[4] Sunita Sharma. S K Ghoshal and Devendra Mohan in Microwaves 
€tnd Optoelectronics (eds) M D Shirsat et al (New Delhi: Anamaya 
Publishers) p411 (2004)
[5] Hai Wang David Goorskey and Min Xiao Opt. Lett. 27 258 (2002)


Damping Effect on Power Loss in Optical Fibers Due to Higher Order Nonlinear Term

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