P O Z NA N UN I V E R S ITY O F TE C H N O LO GY A C A D E M IC J O U R N AL S
No 54 Electrical Engineering 2007
__________________________________________
Jan LAMPERSKI*
INTERFEROMETRIC TECHNIQUE FOR CHROMATIC
DISPERSION MEASUREMENTS
An original interferometric method of chromatic dispersion measurement is presented. Measurement setup makes use of the Mach-Zender interferometer configuration. It was shown that the described technique can be implemented for a characterization of short optical fibers. The method is applicable to all kinds of fibers.
Keywords: Chromatic dispersion, Mach-Zender interferometer
1. INTRODUCTION
The chromatic dispersion is a variation in propagation time of light for different wavelengths. In transmission systems, different spectral signal component velocities result in pulse broadening and system degradation.
There are two most important techniques of measuring chromatic dispersion: the pulse delay method and the phase shift or differential phase shift methods [1-3]. The first method based on a differential time delay between the pulses of different wavelengths. The acquired points are fitted to an appropriate model equation. The second method – differential phase shift method – allows to determine the chromatic dispersion at an arbitrary wavelength directly from measurements.
In the presented work, we focus on a theoretical analysis of operation of the Mach-Zender interferometer (MZI) base configuration for chromatic dispersion measurements. It is assumed that reference arm of interferometer has a known dispersion and an adjustable delay line. In the second arm, the test fiber is installed. A MZI input is couplet to the tunable laser source and the output interference signal is measured.
The measurement setup allows to obtain a refractive index n and a group refractive index ng [4] with the wavelength:
λ ∂ ∂ − =n n ng
2007
Poznańskie Warsztaty TelekomunikacyjnePoznań 6 - 7 grudnia 2007
Finally a dispersion coefficient can be calculated: 2 2 1 λ ν ∂ ∂ − = − n Dm
2. MATHEMATICAL MODEL OF MACH-ZENDER BASED
MEASUREMENT CONFIGURATION
The transfer function of the Mach-Zender interferometer can be obtained by the multiplying matrix of input and output directional couplers and the matrix of interferometer arms.
The 3-dB coupler matrix can be expressed by:
[ ]
⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − = 1 1 2 1 1 j j TThe scattering matrix of interferometer arms, with the time delay difference of τ is given by:
( )
[
]
(
)
⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = ντ π ν j T 2 exp 0 0 1 2The overall M-Z transfer function is:
( )
[ ] ( )
[
][ ]
[
(
(
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[
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⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − − + − − + − − − = = ντ π ντ π ντ π ντ π ν ν j j j j j j T T T TMZ 2 exp 1 2 exp 1 2 exp 1 2 exp 1 2 1 1 2 1The power transfer matrix is given by:
( )
( )
( )
( )
⎥⎦⎤ ⎢ ⎣ ⎡ πντ πντ πντ πντ 2 2 2 2 cos sin sin cosIn the proposed measurement setup the delay time difference between reference
l0+x and measured lfib optical arms is expressed by:
( )
(
)
c n x l n c l nfib * fib 0 * 0 + 0 − = ν τwhere x – additional adjustable delay of reference arm.
Finally, the optical power function at a photodiode input of chromatic dispersion measurement configuration becomes:
( )
( )
(
)
⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + − = Φ c n x l n c l nfib fib 0 0 0 2 2 cos * * cos πν ν2. MEASUREMENT PROCEDURE AND SIMULATION RESULTS
The interference measurements are performed across the wavelength range for different delays xi of interest identifying optical frequency ν0 and amplitude for alowest frequency of interference pattern which corresponds to extreme values of
Φ (Fig. 1 and 2):
( )
0 0 ν ν ν → = ∂ Φ ∂Fig. 1. Variation of faze Φ upon wavelength for x=10.000 µm
Fig. 2. Illustration of detected interference pattern, x=10.000 µm
The detected power allows to calculate the refractive index and group refractive index at frequency ν0:
(
ν0,xi)
→nfib( )
ν0 Φ(
)
g i n n x → ∂ ∂ → = ∂ Φ ∂ λ ν ν 0 , 0The process is repeated for different delays adjustments xi, Fig.3.
Fig. 3. Illustration interference patterns for different delay line settings
4. CONCLUSIONS
The main advantage of the proposed method is its effectiveness for short fiber measurements, which is crucial for the characterization of highly attenuating speciality fibers. The method can be implemented to all kinds of fibers. The main drawback of this technique is that the results for short samples measurements are not adequate for the long ones.
REFERENCES
[1] K. Perlicki, Pomiary w optycznych systemach telekomunikacyjnych, WKŁ, 2002. [2] EXFO Application Note 123.
[3] EXFO Application Note 77.
[4] A. Majewski, Podstawy techniki światłowodowej, Oficyna Wyd. Politechniki Warszawskiej, 2000.
