Effect of fiber length on laser linewidth measurement using self heterodyne detection
Abstract — The spectrum of laser source radiation forms a
qualitative criterion of the laser source applicability in a fiber optic
communication source. Hence there is a need to estimate its spectral
linewidth. The self-heterodyne detection technique has been
commonly used in the determination of the optical linewidth of
lasers. The fiber length to be used in the system and its effect on
overall measurement of linewidth have been researched extensively.
As modern day lasers are capable of generating very narrow
linewidths, fiber length to be used in the self heterodyne system to
measure the linewidth becomes very long. When very long optical
fibers are used to provide the sufficient delay necessary for the
measurement, factors associated with fibers such as fiber non
linearity will make an impact on the overall performance of the self
heterodyne system. This paper is concerned with studying the effect
of fiber length on laser linewidth measurement using self heterodyne
detection with OPTSIM simulation software. Software simulation
provides more freedom and accurate results to study the impact of a
parameter on a system compared to real time experiments. The
results obtained follows largely to what is presented in the literature
with real time experiments but shows certain limitations of the
system and precautions to be taken if the system is to be used for
measuring laser sources with narrow linewidth.
Index Terms — Self heterodyne, coherent length, linewidth,
laser characteristics.
I.BACKGROUND
In this method, the laser beam is split to travel two different
path lengths so that one is delayed and the other is frequency
shifted compared to the other. The linewidth measurement is
performed by recording the rf beating signal from the laser
beam and its time delayed version as shown in Figure 1. In
the limit of large delay time, the spectrum becomes exactly
Lorentzian with a width equal to twice of the laser optical
spectral width. A time delay of at least 6 times longer than the
coherence time was suggested for a direct laser linewidth
measurement from the system.
Related to the linewidth ∆v and group index of refraction of
the propagation medium ng, the formula for coherence length
lc is given by
lc 
Table 1: Required Delay Length for DSHI Linewidth
Measurement
Linewidth
Coherence Length
DSHI Length
∆v (Hz)
Lc (km)
Ld (km)
1
65,000
390,000
10
6,500
39,000
100
650
3900
1000
65
390
10000
6.5
39
The acoustic optic modulator used in the upper arm is to shift
the Lorentzian linewidth away from DC for easier
measurement. For the case of a Lorentzian-shaped laser field
spectrum, the line shapes retain their form during conversion
from the optical spectrum to the electrical spectrum through
the self heterodyne process, except that the electrical line
shape has linewidth twice the actual optical linewidth. Let the
laser line shape be expressed as:
SE ( f ) 
1
 f 
1 

 v / 2 
2
---------------------- (2)
Its autocorrelation is given by
S( f ) 
1
 f 
1  
 v 
2
---------------------------- (3)
The FWHM linewidth of S(f) is twice as that of SE(f)
c
--------------------------- (1)
n g v
Table 1 lists the coherence length and required delay length
for measurement of several linewidth.
Figure 1: Setup for optical self-heterodyne detection
II.EXPERIMENT SETUP
The experimental setup used to study the effect of fiber length
in a self heterodyne experiment is shown in Figure 1.
Simulation was run for various values of the fiber length
using the parametric scan feature available in Optsim.
III.RESULTS AND DISCUSSION
Linewidth (kHz)
Figure 2 shows the result obtained for measured linewidth by
varying the fiber length used in the system. The graph shows
that the measured laser linewidth stabilizes once the fiber
length is about 6 times the coherent length of the laser source.
When the fiber length is less than the coherent length of the
laser source, the two signals that produce the beat note are not
mutually incoherent and as a result, the linewidth measured
by the system is smaller than the actual lineidth.Even if the
fiber length is equal to the coherent length, ripples still appear
in the spectrum because of the interference of two waves.
Figure 3b
12
10
8
6
4
2
0
0
20
40
60
Fibre Length (km)
Figure 2: Linewidth variation with fiber length
Figure 3c
Figure 3a
Figure 3d
Figure 3 Displayed spectrum for different fiber length. (a: 50
km, b: 300 km, c: 350 km, d: 400 km)
For Lorentzian line shape, the 3 dB linewidth can be inferred
from the displayed line shape by using the relation shown in
Table 2.
devices can be used to get the necessary frequency shift. One
of which is the phase modulator as shown in the configuration
below.
Table 2: Self Heterodyne Linewidth Relation
Measured Full-Width Point
Displayed Width
-3 dB
2Δv
-10 dB
2 sqrt (9) Δv
-30 dB
2 sqrt (99) Δv
Table 2 shows that the laser linewidth can be inferred from
any of the listed measured full-width point. But the 20 dB
measurement will give better results since the broadening
effect of the 1/f noise is more pronounced at the center of the
spectral lineshape.If we need to make a 20 Db measurement,
the signal and noise levels should permit. As the length of the
fiber used in the measurement is increased, the signal level
decreases and the noise level increases as shown in the Figure
3. If the fiber length is to be increased beyond certain limit,
the displayed spectrum does not allow 20 dB measurement
because of the signal and noise levels. If the fiber length is to
be further increased, even 3 dB measurement is also not
possible. The reduction in signal level and increase in noise
level are due to fiber non linearity and fiber losses. The fiber
length used in the self heterodyne detection system should be
about 6 times the coherent length but if the length is very
long, losses and fiber non linearity will affect the
measurement.
IV.CONCLUSION AND RECOMMENDATION
This paper studied the effect of fiber length on laser linewidth
measurement using self heterodyne detection with OPTSIM
simulation software. Software simulation provides more
freedom and accurate results to study the impact of a
parameter on a system compared to real time experiments.
The results obtained follows largely to what is presented in
the literature with real time experiments but shows certain
limitations of the system and precautions to be taken if the
system is to be used for measuring laser sources with narrow
linewidth.If the fiber length to be used in the self heterodyne
system is beyond certain limit, fiber losses and fiber
nonlinearity affects the measurement. It can be shown that the
linewidth broadens with increase in time delay and hence the
fiber length. One solution to reduce the fiber length used in
the self heterodyne measurement will be to broaden the laser
linewidth before measuring and calibrate the system to obtain
the original bandwidth.
V METHOD TO IMPROVE 20 DB MEASUREMENT
The previous experiment results shows that the 20 dB
measurement has advantages in determining the linewidth of
the laser. If the fiber length is long, it is difficult to get 20 dB
above noise floor. The frequency shifter can be effectively
used to obtain an improved 20 dB measurement. A number of
With this arrangement the photo detector output can be given
as:
The strength of the distribution depends on the magnitude of
the Bessel function coefficient. Figure below shows the
Bessel function coefficients. Our interest will be in the order
1 and 2.
The chart below shows that the spectrum above the noise
floor is maximum at certain values of the phase modulator
input amplitude and inturn the modulation index. This follows
the Bessel function coefficients of order 1 as expected from
the equation.
80
70
60
50
50 km
100 km
150 km
200 km
250 km
300 km
3
3.
6
4.
2
4.
8
40
30
20
10
0
0.
1
0.
6
1.
2
1.
8
2.
4
Spectrum peak (dB)
Spectrum peak value Vs modulating
signal value for different values of
fiber length
Modulating signal amplitude
This shows that an optimum value of the modulation index of
the phase modulator can improve the linewidth measurement.
Figure below shows the spectrum peaks at fundamental
frequency and its harmonics for various values of modulating
signal voltage.
V.REFERENCES