1
00:00:18,850 --> 00:00:24,950
In this lecture we would look into another
important characteristic of a single mode
2
00:00:24,950 --> 00:00:29,590
optical fiber and that is Waveguide Dispersion.
3
00:00:29,590 --> 00:00:36,760
We have seen that in a multimode fiber if
it is a step index multimode fiber, then the
4
00:00:36,760 --> 00:00:44,879
data rate is limited by what is known as inter
modal dispersion, which is due to different
5
00:00:44,879 --> 00:00:51,960
modes carrying light into the fiber and these
different modes to have a with different velocities,
6
00:00:51,960 --> 00:00:58,540
they have different propagation constants
that gives raise to what we call as inter
7
00:00:58,540 --> 00:01:00,090
modal dispersion.
8
00:01:00,090 --> 00:01:07,270
We can minimize inter modal dispersion in
a multimode fiber by having a graded index
9
00:01:07,270 --> 00:01:17,990
profile, and then in such a fiber we have
inter modal dispersion which is very small.
10
00:01:17,990 --> 00:01:23,890
And then another kind of dispersion comes
into picture which is known as material dispersion,
11
00:01:23,890 --> 00:01:29,130
which is nothing, but the wavelength dependence
of the refractive index of the material of
12
00:01:29,130 --> 00:01:30,130
the fiber.
13
00:01:30,130 --> 00:01:35,530
So, in a graded index multimode fiber we have
seen that the material dispersion and inter
14
00:01:35,530 --> 00:01:37,690
modal dispersion can become comparable.
15
00:01:37,690 --> 00:01:43,280
So, we will have to take into account material
dispersion as well as inter modal dispersion,
16
00:01:43,280 --> 00:01:51,899
while in a multimode step index fiber, inter
modal dispersion is so, large that we ignore
17
00:01:51,899 --> 00:01:55,770
material dispersion.
18
00:01:55,770 --> 00:02:02,979
Although by using a graded index fiber, we
can minimize inter modal dispersion, but we
19
00:02:02,979 --> 00:02:05,859
cannot completely get rid of it.
20
00:02:05,859 --> 00:02:15,860
So, the obvious way to get rid of inter modal
dispersion is to use a single mode fiber.
21
00:02:15,860 --> 00:02:22,410
Then in a single mode fiber material dispersion
would always be there because the refractive
22
00:02:22,410 --> 00:02:28,750
index of the material would always depend
upon the wavelength of light and we are using
23
00:02:28,750 --> 00:02:32,920
light source which has which always has finite
spectral width.
24
00:02:32,920 --> 00:02:39,800
So, all the wavelength and components will
contribute; then apart from this material
25
00:02:39,800 --> 00:02:45,550
dispersion a single mode fiber also exhibits
another kind of dispersion which is known
26
00:02:45,550 --> 00:02:49,670
as wave guide dispersion what is this wave
guide dispersion?
27
00:02:49,670 --> 00:02:56,440
Because we have finite line width of the source,
so, different wavelength components of the
28
00:02:56,440 --> 00:03:02,360
source have different propagation constants
of modes.
29
00:03:02,360 --> 00:03:09,510
So, in a way each wavelength component has
its own mode, and that mode propagates with
30
00:03:09,510 --> 00:03:14,370
different velocity, it has different propagation
constant, and that give raise to what is known
31
00:03:14,370 --> 00:03:15,780
as wave guide dispersion.
32
00:03:15,780 --> 00:03:22,480
We call it wave guide dispersion because it
is purely due to purely due to the wave guidance
33
00:03:22,480 --> 00:03:29,130
in a fiber, because wave guidance in a fiber
is different for different wavelengths.
34
00:03:29,130 --> 00:03:39,790
So, if I look at single mode fiber then it
supports LP01 mode and if I plot its b-V curve
35
00:03:39,790 --> 00:03:47,200
b-V diagram, then it goes like this and I
know b is related to propagation constant
36
00:03:47,200 --> 00:03:54,970
like this, and V is related to the wavelength
like this.
37
00:03:54,970 --> 00:04:03,680
So, propagation constant depends upon lambda
and this relationship between the propagation
38
00:04:03,680 --> 00:04:10,831
constant and lambda can be obtained from the
relation between b and V.
39
00:04:10,831 --> 00:04:20,289
So, for a given fiber the propagation constant
beta of the mode depends upon lambda naught,
40
00:04:20,289 --> 00:04:25,310
and this gives raise to what is known as wave
guide dispersion.
41
00:04:25,310 --> 00:04:30,310
So, what I can do now?
42
00:04:30,310 --> 00:04:41,870
I can obtain the propagation constant of the
mode in terms of fiber parameter and the normalized
43
00:04:41,870 --> 00:04:49,970
prorogation constant B. How to find out the
broadening of pulse due to this?
44
00:04:49,970 --> 00:04:58,010
So, the idea is exactly the same the procedure
is exactly the same as we had done in the
45
00:04:58,010 --> 00:05:07,180
case of material dispersion, in case of material
dispersion we consider optical waves propagating
46
00:05:07,180 --> 00:05:10,970
in infinitely extended medium that is in bulk
medium.
47
00:05:10,970 --> 00:05:21,900
So, we considered plane waves, and what we
had done if you remember that in a bulk medium
48
00:05:21,900 --> 00:05:34,190
the plane waves go like this E is equal to
E0 which is a constant, e to the power i omega
49
00:05:34,190 --> 00:05:36,880
t minus kz.
50
00:05:36,880 --> 00:05:48,030
Where k is the propagation constant E0 is
constant this is a plane wave and k can be
51
00:05:48,030 --> 00:06:01,930
written as omega by c times n, and since n
is since n depends on frequency or wavelength
52
00:06:01,930 --> 00:06:03,680
k also depend upon frequency.
53
00:06:03,680 --> 00:06:12,710
So, this is a function of omega and so, this
is a function of omega and I know that if
54
00:06:12,710 --> 00:06:21,900
there is a group of waves if there is a pulse,
then the group velocity can be given by one
55
00:06:21,900 --> 00:06:32,700
over vg is equal to dk over d omega, and that
is how we obtain the group velocity and then
56
00:06:32,700 --> 00:06:38,220
transient time and subsequently the material
dispersion.
57
00:06:38,220 --> 00:06:48,800
In case of optical fiber what I do not have
plane waves, but I have modes, and these modes
58
00:06:48,800 --> 00:07:14,500
propagate as psi r phi is equal to let me
put psi 0 e to the power i omega t minus beta
59
00:07:14,500 --> 00:07:22,960
z, and this is a function of r and phi both
this is this is not a constant this is a function
60
00:07:22,960 --> 00:07:27,760
of r and phi.
61
00:07:27,760 --> 00:07:37,070
Then instead of having k have beta which is
a propagation constant and if I want to now
62
00:07:37,070 --> 00:07:42,690
find out the pulse broadening then again I
will have to find out the group velocity and
63
00:07:42,690 --> 00:07:50,961
in this case the group velocity will be given
by d beta over d omega, and this beta is a
64
00:07:50,961 --> 00:07:56,470
function of lambda naught or the frequency
omega.
65
00:07:56,470 --> 00:08:00,450
So, the procedure would exactly be the same.
66
00:08:00,450 --> 00:08:14,550
So, that is why I have written beta in terms
of this and since b depends upon v which subsequently
67
00:08:14,550 --> 00:08:17,370
is a function of lambda or omega.
68
00:08:17,370 --> 00:08:23,169
So, that is how can now find out d beta over
d omega.
69
00:08:23,169 --> 00:08:33,289
So, if I look at this, this I have obtained
for a weekly guiding fiber because if you
70
00:08:33,289 --> 00:08:38,950
look into it b is equal to beta square over
k naught square minus n2 square divided by
71
00:08:38,950 --> 00:08:41,120
n1 square minus n2 square.
72
00:08:41,120 --> 00:08:48,140
So, this I can approximate by beta over k
naught minus n2 over n1 minus n2 for a weekly
73
00:08:48,140 --> 00:08:52,040
guiding fiber, where n1 is very close to n2.
74
00:08:52,040 --> 00:09:00,720
So, if I look at this expression then eve
if the refractive indices of the materials
75
00:09:00,720 --> 00:09:07,839
of the core and cladding do not depend upon
lambda, we would still have dispersion due
76
00:09:07,839 --> 00:09:15,339
to dependence of beta over lambda or dependence
of any effective over lambda.
77
00:09:15,339 --> 00:09:24,029
So, to calculate the dispersion we will follow
exactly the same procedure as we had done
78
00:09:24,029 --> 00:09:32,399
for material dispersion and then in this way
I will find out the group velocity by d beta
79
00:09:32,399 --> 00:09:41,660
over d omega and subsequently the pulse broadening
and wave guide dispersion coefficient.
80
00:09:41,660 --> 00:09:48,939
So, I again write down the expression for
beta which is 2 pi over lambda naught which
81
00:09:48,939 --> 00:09:55,170
is nothing, but k naught, n2 plus b times
n1 minus n2 and this I can write as omega
82
00:09:55,170 --> 00:10:04,119
by c times n2 plus b times n1 minus n2, and
if vg is the group velocity then 1 over vg
83
00:10:04,119 --> 00:10:07,230
is equal to d beta over d omega.
84
00:10:07,230 --> 00:10:11,019
So, I do d beta over d omega from here.
85
00:10:11,019 --> 00:10:21,569
So, I will get 1 over c n2 plus b n1 minus
n2 plus omega by c then the differential of
86
00:10:21,569 --> 00:10:27,899
this would be 0, and if I take the differential
of this then it would be omega by c n1 minus
87
00:10:27,899 --> 00:10:31,589
n2 dB over bV times dV over d omega.
88
00:10:31,589 --> 00:10:40,300
So, please pay attention here that I have
ignored here the material dispersion, I have
89
00:10:40,300 --> 00:10:49,199
assumed that n1 and n2 do not depend upon
omega in order to isolate the effect of wave
90
00:10:49,199 --> 00:10:50,199
guide dispersion.
91
00:10:50,199 --> 00:10:57,350
So, in order to purely find out the effect
of wave guide dispersion or to purely find
92
00:10:57,350 --> 00:11:06,779
out the wave guide dispersion, I have assumed
n1 and n2 to be constant with respect to omega.
93
00:11:06,779 --> 00:11:10,980
So, what is dV over d omega?
94
00:11:10,980 --> 00:11:17,369
I have V is equal to 2 pi over lambda naught
times a times n1 square minus n2 square which
95
00:11:17,369 --> 00:11:23,269
is nothing, but omega by c times a times square
root of n1 square minus n2 square.
96
00:11:23,269 --> 00:11:27,190
So, dV over d omega would simply be V over
omega.
97
00:11:27,190 --> 00:11:38,619
So, I put it there then will get 1 over vg
is equal to 1 over c n2 plus n1 minus n2 times
98
00:11:38,619 --> 00:11:47,689
b plus 1 over c n1 minus n2 times V times
db over dV.
99
00:11:47,689 --> 00:11:54,019
So, now I simply rearrange the terms here.
100
00:11:54,019 --> 00:12:02,949
So, I take this n2 by c here and n1 minus
n2 by c here which I take common from this
101
00:12:02,949 --> 00:12:04,000
term also.
102
00:12:04,000 --> 00:12:11,610
So, here I have in the square brackets b which
is coming from here as V times db over dV.
103
00:12:11,610 --> 00:12:19,639
So, this I can simply write as n2 by c plus
n1 minus n2 by c, and this I can write as
104
00:12:19,639 --> 00:12:26,249
d of bV over dV right.
105
00:12:26,249 --> 00:12:34,309
Now I take n2 by c common and then I can write
it as n2 by c times one plus n1 minus n2 over
106
00:12:34,309 --> 00:12:42,860
n2, d(bV) over dV and this I can approximate
by delta for a weekly guiding fiber delta
107
00:12:42,860 --> 00:12:50,050
is n1 minus n2 over n1 or n1 minus n2 over
n2 because it is weekly guiding fiber.
108
00:12:50,050 --> 00:12:52,279
So, I can approximate it by this.
109
00:12:52,279 --> 00:13:02,269
So, 1 over vg becomes this much once I have
vg then I can find out what would be the time
110
00:13:02,269 --> 00:13:13,170
taken by pulse to traverse length L of the
fiber, and that would be given by L by vg
111
00:13:13,170 --> 00:13:23,880
which is equal to L n2 by c, 1 plus delta
d(bV) over dV now if I have a source of spectral
112
00:13:23,880 --> 00:13:28,250
width delta lambda naught.
113
00:13:28,250 --> 00:13:36,610
Then the broadening would be given by due
to wave guide dispersion delta tau w is equal
114
00:13:36,610 --> 00:13:43,040
to d tau over d lambda naught, times delta
lambda naught and tau is this much from the
115
00:13:43,040 --> 00:13:44,389
previous slide.
116
00:13:44,389 --> 00:13:48,670
So, if I just take d tau over d lambda naught
from here.
117
00:13:48,670 --> 00:13:57,300
So, what I will get L n2 by c, times delta
times d2(bV) over dV square, times dV over
118
00:13:57,300 --> 00:14:02,920
d lambda naught times delta lambda naught
which comes from here.
119
00:14:02,920 --> 00:14:05,870
What is dV over d lambda naught?
120
00:14:05,870 --> 00:14:15,589
We know V is equal to if you write back the
expression for V, then V is equal to 2 pi
121
00:14:15,589 --> 00:14:22,730
over lambda naught times a times square root
of n1 square minus n2 square.
122
00:14:22,730 --> 00:14:29,819
So, if you do dV over d lambda naught from
here you will get it as minus V over lambda
123
00:14:29,819 --> 00:14:30,819
naught.
124
00:14:30,819 --> 00:14:37,869
So, if I substitute it there then I get the
pulse broadening delta tau w as minus delta
125
00:14:37,869 --> 00:14:45,059
L n2 over c lambda naught times V d2(bV) over
dV square times delta lambda naught.
126
00:14:45,059 --> 00:14:54,790
As usual I define the dispersion coefficient
as broadening per kilometer length of the
127
00:14:54,790 --> 00:14:59,230
fiber per nanometer spectral width of the
source.
128
00:14:59,230 --> 00:15:05,040
So, dw is delta tau w over l delta lambda
naught.
129
00:15:05,040 --> 00:15:13,929
So, it would be minus delta n2 by c lambda
naught times V d2 to bV over dV square.
130
00:15:13,929 --> 00:15:23,709
So, I have got this wave guide dispersion
coefficient now.
131
00:15:23,709 --> 00:15:31,519
I can convert it into or express it into picoseconds
per kilometer nanometers.
132
00:15:31,519 --> 00:15:37,339
So, what I do I put c the value of c here,
which is 3 into 10 to the power 8 meters per
133
00:15:37,339 --> 00:15:40,010
second and.
134
00:15:40,010 --> 00:15:51,240
So, if now I put lambda naught in nanometers
then the dimensions of this would be seconds
135
00:15:51,240 --> 00:15:59,621
per meter nano meter, and this would be 10
to the power 12 picoseconds this meter I can
136
00:15:59,621 --> 00:16:03,269
convert into kilo meters and I retain this
nanometers.
137
00:16:03,269 --> 00:16:12,589
So, it will become minus delta times n2 by
3 lambda naught, times 10 to the power 7 times
138
00:16:12,589 --> 00:16:21,540
V d2(bV) over dV square in picoseconds per
kilometer nanometer, where lambda naught should
139
00:16:21,540 --> 00:16:26,749
be put in nanometers.
140
00:16:26,749 --> 00:16:39,059
So, what I see clearly that is I want to if
I want to find out the wave guide dispersion
141
00:16:39,059 --> 00:16:48,889
of a given fiber then I need to calculate
this term V times d2(bV) over dV square and
142
00:16:48,889 --> 00:16:56,519
then multiply it by fiber parameters n2 and
delta and of course, divided by the wavelength
143
00:16:56,519 --> 00:16:59,720
central wavelength of the pulse.
144
00:16:59,720 --> 00:17:08,020
So, I know how b varies with V for a single
mode fiber.
145
00:17:08,020 --> 00:17:18,510
So, if I draw that then the variation of b
with V goes something like this, then what
146
00:17:18,510 --> 00:17:25,799
I can do can find out first because I need
to find out this second derivative of bV.
147
00:17:25,799 --> 00:17:31,799
So, first I find out the first derivative
of bV which is d(bV) over dV which goes like
148
00:17:31,799 --> 00:17:40,210
this, and then I find out d2(bV) over dV square
times V which comes out like this.
149
00:17:40,210 --> 00:17:48,990
So, what I have done for different values
of V, I have solved the transcendental equation
150
00:17:48,990 --> 00:17:53,460
corresponding to LP01 mode and obtained the
values of b.
151
00:17:53,460 --> 00:18:02,450
After having obtained the value of b for different
values of V, then I have plotted this and
152
00:18:02,450 --> 00:18:11,100
then numerically differentiate it this bV
with V and then by numerical differentiation
153
00:18:11,100 --> 00:18:13,059
I have obtained this.
154
00:18:13,059 --> 00:18:21,540
So, this I refer to as exact variations that
are by exactly solving the transcendental
155
00:18:21,540 --> 00:18:23,870
equations.
156
00:18:23,870 --> 00:18:32,780
Now I also know that there is an empirical
relationship between b and V and that empirical
157
00:18:32,780 --> 00:18:39,840
relationship is given by this formula b is
equal to a minus b over V square where a is
158
00:18:39,840 --> 00:18:49,060
this b is this and this relationship is valid
in the range of V going from 1.5 to 2.5.
159
00:18:49,060 --> 00:18:56,690
From here it is not difficult to obtain d(bV)
over dV, which will come out to be A square
160
00:18:56,690 --> 00:19:05,149
minus B square over V square and then V times
d2(bV) over dV square, which comes out to
161
00:19:05,149 --> 00:19:09,440
be 2 B square over V square.
162
00:19:09,440 --> 00:19:17,169
So, from here I can if I want to calculate
the wave guide dispersion then I can simply
163
00:19:17,169 --> 00:19:25,080
put 2 B square over V square in place of this
and I can immediately get the wave guide dispersion,
164
00:19:25,080 --> 00:19:33,960
but how accurate it is how accurate this empirical
relationship is for obtaining wave guide dispersion.
165
00:19:33,960 --> 00:19:42,679
So, for that what we have done here I have
plotted the variation of B as a function of
166
00:19:42,679 --> 00:19:49,450
V from empirical relationship, and then this
and this obtained from empirical relationship
167
00:19:49,450 --> 00:19:50,980
also.
168
00:19:50,980 --> 00:19:55,370
So, I have plotted it here as red circles.
169
00:19:55,370 --> 00:20:03,870
So, these red circles show the variations
of various terms with respect to V as obtained
170
00:20:03,870 --> 00:20:06,130
from empirical relationship.
171
00:20:06,130 --> 00:20:17,360
So, what I see that variation of V fits well,
variations of db over dV also fits quite well,
172
00:20:17,360 --> 00:20:27,580
but this term deviates a quite a lot except
at a particular values of V which is close
173
00:20:27,580 --> 00:20:28,580
to 1.9.
174
00:20:28,580 --> 00:20:35,230
So, at around V is equal to 1.9 the agreement
between the empirical relationship and the
175
00:20:35,230 --> 00:20:44,110
exact values is good, but when you deviate
from this value then they are the agreement
176
00:20:44,110 --> 00:20:46,279
is not good.
177
00:20:46,279 --> 00:20:57,419
So, what should I do well then I cannot use
this for the entire range of V, then mark
178
00:20:57,419 --> 00:21:07,240
use in 1979 gave another empirical formula
which is much accurate more accurate, it is
179
00:21:07,240 --> 00:21:15,440
again empirical relationship between V times
d2(bV) over dV square and V and a relationship
180
00:21:15,440 --> 00:21:17,620
is given by this.
181
00:21:17,620 --> 00:21:24,010
When I plot this which has (Refer Time: 21:21)
shown here in green circles, then I find that
182
00:21:24,010 --> 00:21:32,409
this relationship fits very well in the entire
range of V from 1.5 to 2.5.
183
00:21:32,409 --> 00:21:40,200
So, I can safely use this relationship for
calculating wave guide dispersion in a single
184
00:21:40,200 --> 00:21:44,610
mode fiber.
185
00:21:44,610 --> 00:21:52,889
Now let us look at an example take a typical
conventional single mode fiber whose parameters
186
00:21:52,889 --> 00:22:01,529
are given by this and this I have adopted
from the text book introduction to fiber optics.
187
00:22:01,529 --> 00:22:08,039
So, for these values of fiber parameters.
188
00:22:08,039 --> 00:22:17,220
If I calculate the value of V then the value
of V comes out to be 2746.3 nanometer divided
189
00:22:17,220 --> 00:22:18,639
by lambda naught ok.
190
00:22:18,639 --> 00:22:24,701
So, when I put lambda naught in nanometers
then for that value of lambda naught I can
191
00:22:24,701 --> 00:22:33,230
find out the value of V, and these 2 values
of n1 and n2 correspond to delta which is
192
00:22:33,230 --> 00:22:35,429
about 0.27 percent.
193
00:22:35,429 --> 00:22:42,140
Now let me analyze this and calculate all
the dispersions and analyze this fiber a.
194
00:22:42,140 --> 00:22:52,010
So, I analyze and this fiber at three different
wavelengths by calculating various parameters.
195
00:22:52,010 --> 00:22:59,070
So, when I put lambda naught is equal to 1100
nanometer then V is 2.497.
196
00:22:59,070 --> 00:23:08,390
So, it is close to single mode, but it is
not exactly single mode and the wave guide
197
00:23:08,390 --> 00:23:15,519
dispersion if I calculate comes out to be
minus 1.78 picoseconds per kilometer nanometer,
198
00:23:15,519 --> 00:23:22,440
material dispersion is minus 23 picoseconds
per kilometer nanometer, and total dispersion
199
00:23:22,440 --> 00:23:26,409
is about minus 25 picoseconds per kilometer
nanometer.
200
00:23:26,409 --> 00:23:34,750
So, these are the values at 1100 nanometer
wavelength, at 1300 nanometer wavelength wave
201
00:23:34,750 --> 00:23:46,299
guide dispersion is minus 3.7, material dispersion
is very low plus 1.5 weight, as we can expect
202
00:23:46,299 --> 00:23:54,639
because this is few silica glass fiber and
for fused silica glass fiber the 0 dispersion
203
00:23:54,639 --> 00:23:57,799
wavelength is around 1270 nanometers.
204
00:23:57,799 --> 00:24:06,909
So, the total dispersion is minus 2.14 picoseconds
per kilo meter nanometers.
205
00:24:06,909 --> 00:24:13,919
Near to communication window at 1516 nanometer,
wave guide dispersion is about minus 6 picoseconds
206
00:24:13,919 --> 00:24:20,860
per kilometer nanometer, while material dispersion
is plus 22 picoseconds per kilometer nanometers.
207
00:24:20,860 --> 00:24:27,350
So, the total dispersion comes out to be about
16 picoseconds per kilometer nanometer.
208
00:24:27,350 --> 00:24:38,450
So, what I see in this fiber that this fiber
has very low dispersion of about minus 2 picosecond
209
00:24:38,450 --> 00:24:49,190
per kilometer nanometers at 1300 nanometer
wavelength, while it has plus16 picoseconds
210
00:24:49,190 --> 00:24:58,279
per kilometer nanometer dispersion near the
lowest loss wavelength.
211
00:24:58,279 --> 00:25:09,840
So, to have a much better picture and wider
picture, I have plotted here dispersion as
212
00:25:09,840 --> 00:25:16,750
a function of wavelength in the range 1.1
micron to 1.7 micron.
213
00:25:16,750 --> 00:25:25,710
So, this green curve shows that this is wave
guide dispersion which is always negative,
214
00:25:25,710 --> 00:25:34,230
this red curve shows the material dispersion,
and this blue curve shows the total dispersion.
215
00:25:34,230 --> 00:25:41,049
Here we have calculated the total dispersion
by adding the material dispersion and wave
216
00:25:41,049 --> 00:25:51,750
guide dispersion which is not rigorously correct,
but it is quite accurate when the dispersions
217
00:25:51,750 --> 00:25:54,070
are not very high.
218
00:25:54,070 --> 00:26:01,279
If the values of dispersions are very high,
then I should not just add the material dispersion
219
00:26:01,279 --> 00:26:02,419
and wave guide dispersion.
220
00:26:02,419 --> 00:26:09,740
In fact, what I should do while calculating
wave guide dispersion I should also take into
221
00:26:09,740 --> 00:26:15,150
account the variation of n1 and n2 with respect
to lambda.
222
00:26:15,150 --> 00:26:21,919
So, I should automatically include material
dispersion while calculating wave guide dispersion,
223
00:26:21,919 --> 00:26:31,380
that would be much more rigorous analysis,
but for small values of dispersion like this,
224
00:26:31,380 --> 00:26:35,559
if I just add them up then it is sufficient.
225
00:26:35,559 --> 00:26:42,389
So, this is what I have.
226
00:26:42,389 --> 00:26:48,700
What is the meaning of negative dispersion
and positive dispersion?
227
00:26:48,700 --> 00:27:00,980
We have seen that in material dispersion also
that for the wavelengths which are less than
228
00:27:00,980 --> 00:27:08,190
1.27 micrometer, the dispersion is negative
material dispersion is negative for the wavelengths
229
00:27:08,190 --> 00:27:17,500
longer than 1.27 micrometer the material dispersion
is positive, and wave guide dispersion is
230
00:27:17,500 --> 00:27:19,169
always negative.
231
00:27:19,169 --> 00:27:29,190
So, the total dispersion what I see is now
shifted from 1.27 which is 0 material dispersion
232
00:27:29,190 --> 00:27:34,740
wavelength from 1.27 micro meter to about
1.3 micro meter.
233
00:27:34,740 --> 00:27:41,549
So, I have 1.3 micrometer near 0 total dispersion
wavelength.
234
00:27:41,549 --> 00:27:51,790
So, in the next lecture we would see what
is the meaning of negative and positive dispersion,
235
00:27:51,790 --> 00:27:59,710
how various fiber parameters effect wave guide
dispersion, how we can tailor the dispersion
236
00:27:59,710 --> 00:28:02,909
in a fiber by having different profiles.
237
00:28:02,909 --> 00:28:04,119
Thank you.