The
minimum time-bandwidth product (TBWP) for a Gaussian pulse
is 0.44 (i.e. pulse duration in seconds X pulse bandwidth
in Hertz > 0.44).
The minimum time-bandwidth product (TBWP) for a Sech2pulse
is 0.32.
For example:
A transform-limited Gaussian pulse with a duration of 2
picoseconds (2x10-12 sec) would have a bandwidth
of: 0.44/2x10-12=0.22x10+12sec-1(Hz)=2.2x10+11Hz
|
|
Most
people do not work with Hertz but prefer (A) nanometers
or (B) cm-1.
A. To obtain the bandwidth in nanometers
first calculate the bandwidth in Hertz (as shown above)
then use the following formula:
Bandwidth (nm)=Bandwidth (Hz) * central_wavelength2
(m) / speed of light (m/sec)
For example:
Assuming bandwidth=2.2x10+11Hz and central wavelength=800nm,
the corresponding bandwidth in meters will be:
2.2x10+11 * (800x10-9)2
/ 3x10+8=2.2x10+11 * 64x10-14
/ 3x10+8=4.69x10-10 m=0.469 nm
B. To obtain the bandwidth in cm-1
first calculate the bandwidth in Hertz (as shown above)
then use the following formula:
Bandwidth (cm-1)=Bandwidth
(Hz) / speed of light (cm/sec)
For example:
Assuming bandwidth=2.2x10+11Hz
the corresponding bandwidth in cm-1 will be:
2.2x10+11 / 3x10+10=7.33
cm-1 |
|
Here
are two tables to help you get a quick idea of the
bandwidth in cm-1 (the nice thing about cm-1
is that
the bandwidth is independent of the central wavelength)
Pulse
Duration |
Gaussian
Bandwidth
(Hz) |
Gaussian
Bandwidth
(cm-1) |
| 25 fs |
1.76E+13
|
586.67 |
| 50 fs |
8.80E+12
|
293.33 |
| 70 fs |
6.29E+12
|
209.52 |
| 100
fs |
4.40E+12
|
146.67 |
| 300
fs |
1.47E+12
|
48.89 |
| 500
fs |
8.80E+11
|
29.33 |
| 1 ps |
4.40E+11
|
14.67 |
| 2 ps |
2.20E+11
|
7.33 |
| 5 ps |
8.80E+10
|
2.93 |
| 10 ps |
4.40E+10
|
1.47 |
| 20 ps |
2.20E+10
|
0.73 |
Pulse
Duration |
Sech2
Bandwidth
(Hz) |
Sech2
Bandwidth
(cm-1) |
| 25 fs |
1.28E+13
|
426.67 |
| 50 fs |
6.40E+12
|
213.33 |
| 70 fs |
4.57E+12
|
152.38 |
| 100
fs |
3.20E+12
|
106.67 |
| 300
fs |
1.07E+12
|
35.56 |
| 500
fs |
6.40E+11
|
21.33 |
| 1 ps |
3.20E+11
|
10.67 |
| 2 ps |
1.60E+11
|
5.33 |
| 5 ps |
6.40E+10
|
2.13 |
| 10 ps |
3.20E+10
|
1.07 |
| 20 ps |
1.60E+10
|
0.53 |
|
| |
Here are two
tables to help you get a quick idea of the bandwidth in
nm (the bandwidth expressed as a function of the central
wavelength)
| Pulse Duration |
Gaussian Bandwidth (nm) |
| c=3.00E+08 |
@450
nm |
@800
nm |
@1300
nm |
@3000
nm |
@10 micron |
| 4.50E-07 |
8.00W-07 |
1.30E-06 |
3.00E-06 |
1.00E-05 |
| 25
fs= |
2.5E-14 |
11.88 |
37.55 |
99.15 |
528.00 |
5866.67 |
| 50
fs= |
5E-14 |
5.94 |
18.77 |
49.57 |
264.00 |
2933.33 |
| 70
fs= |
7E-14 |
4.24 |
13.41 |
35.41 |
188.57 |
2095.24 |
| 100
fs= |
1E-13 |
2.97 |
9.39 |
24.79 |
132.00 |
1466.67 |
| 300
fs= |
3E-13 |
0.99 |
3.13 |
8.26 |
44.00 |
488.89 |
| 500
fs= |
5E-13 |
0.59 |
1.88 |
4.96 |
26.40 |
293.33 |
| 1
ps= |
1E-12 |
0.30 |
0.94 |
2.48 |
13.20 |
146.67 |
| 2
ps= |
2E-12 |
0.15 |
0.47 |
1.24 |
6.60 |
73.33 |
| 5
ps= |
5E-12 |
0.06 |
0.19 |
0.50 |
2.64 |
29.33 |
| 10
ps= |
1E-11 |
0.03 |
0.09 |
0.25 |
1.32 |
14.67 |
| 20
ps= |
2E-11 |
0.01 |
0.05 |
0.12 |
0.66 |
7.33 |
| Pulse Duration |
Sech2 Bandwidth (nm) |
| c=3.00E+08 |
@450
nm |
@800
nm |
@1300
nm |
@3000
nm |
@10
micron |
| 4.50E-07 |
8.00W-07 |
1.30E-06 |
3.00E-06 |
1.00E-05 |
| 25 fs= |
2.5E-14 |
8.64 |
27.31 |
72.11 |
384.00 |
4266.67 |
| 50 fs= |
5E-14 |
4.32 |
13.65 |
36.05 |
192.00 |
2133.33 |
| 70 fs= |
7E-14 |
3.09 |
9.75 |
25.75 |
137.14 |
1523.81 |
| 100
fs= |
1E-13 |
2.16 |
6.83 |
18.03 |
96.00 |
1066.67 |
| 300
fs= |
3E-13 |
0.72 |
2.28 |
6.01 |
32.00 |
355.56 |
| 500
fs= |
5E-13 |
0.43 |
1.37 |
3.61 |
19.20 |
213.33 |
| 1 ps= |
1E-12 |
0.22 |
0.68 |
1.80 |
9.60 |
106.67 |
| 2 ps= |
2E-12 |
0.11 |
0.34 |
0.90 |
4.80 |
53.33 |
| 5 ps= |
5E-12 |
0.04 |
0.14 |
0.36 |
1.92 |
21.33 |
| 10 ps= |
1E-11 |
0.02 |
0.07 |
0.18 |
0.96 |
10.67 |
| 20 ps= |
2E-11 |
0.01 |
0.03 |
0.09 |
0.48 |
5.33 |
|
