INTERFEROMETRIC TECHNIQUE FOR CHROMATIC DISPERSION MEASUREMENTS

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Linda Parsons
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1 007 Poznańskie Warsztaty Telekomunikayne Poznań 6-7 grudnia 007 POZNAN POZNAN UNIVERSITY UNIVERSITYOF OF TECHNOLOGY ACADEMIC ACADEMIC JOURNALS JOURNALS No 54 Eletrial Engineering 007 Jan LAMPERSKI* INTERFEROMETRIC TECHNIQUE FOR CHROMATIC DISPERSION MEASUREMENTS An original interferometri method of hromati dispersion measurement is presented. Measurement setup makes use of the Mah-Zender interferometer onfiguration. It was shown that the desribed tehnique an be implemented for a haraterization of short optial fibers. The method is appliable to all kinds of fibers. Keywords: Chromati dispersion, Mah-Zender interferometer. INTRODUCTION The hromati dispersion is a variation in propagation time of light for different wavelengths. In transmission systems, different spetral signal omponent veloities result in pulse broadening and system degradation. There are two most important tehniques of measuring hromati dispersion: the pulse delay method and the phase shift or differential phase shift methods [-3]. The first method based on a differential time delay between the pulses of different wavelengths. The aquired points are fitted to an appropriate model equation. The seond method differential phase shift method allows to determine the hromati dispersion at an arbitrary wavelength diretly from measurements. In the presented work, we fous on a theoretial analysis of operation of the Mah-Zender interferometer (MZI) base onfiguration for hromati dispersion measurements. It is assumed that referene arm of interferometer has a known dispersion and an adustable delay line. In the seond arm, the test fiber is installed. A MZI input is ouplet to the tunable laser soure and the output interferene signal is measured. The measurement setup allows to obtain a refrative index n and a group refrative index n g [4] with the wavelength: n g n = n * Poznan University of Tehnology. PWT POZNAŃ 6-7 GRUDNIA 007 /5

2 Jan Lamperski Finally a dispersion oeffiient an be alulated: D m = ν n. MATHEMATICAL MODEL OF MACH-ZENDER BASED MEASUREMENT CONFIGURATION The transfer funtion of the Mah-Zender interferometer an be obtained by the multiplying matrix of input and output diretional ouplers and the matrix of interferometer arms. The 3-dB oupler matrix an be expressed by: [ T ] = The sattering matrix of interferometer arms, with the time delay differene of τ is given by: [ T ( ν )] = 0 exp 0 ( πντ ) The overall M-Z transfer funtion is: exp( πντ ) [ + exp( πντ )] [ ( )] [ ( )] + exp πντ exp πντ T ( ν ) = [ T ][ T ( ν )][ T ] = MZ The power transfer matrix is given by: os sin ( πντ ) sin ( πντ ) ( πντ ) os ( πντ ) PWT POZNAŃ 6-7 GRUDNIA 007 /5

3 Interferometri Tehnique for Chromati Dispersion Measurements 3 In the proposed measurement setup the delay time differene between referene l 0 +x and measured l fib optial arms is expressed by: n τ = ( ν ) * l fib n ( l + x n ) fib 0 * 0 0 where x additional adustable delay of referene arm. Finally, the optial power funtion at a photodiode input of hromati dispersion measurement onfiguration beomes: os ( Φ) = os ( ν )* l fib n ( l x n ) n πν fib * 0. MEASUREMENT PROCEDURE AND SIMULATION RESULTS The interferene measurements are performed aross the wavelength range for different delays x i of interest identifying optial frequeny ν 0 and amplitude for a lowest frequeny of interferene pattern whih orresponds to extreme values of Φ (Fig. and ): Φ ν ( ν ) = 0 ν 0 PWT POZNAŃ 6-7 GRUDNIA 007 3/5

4 4 Jan Lamperski Fig.. Variation of faze Φ upon wavelength for x=0.000 µm Fig.. Illustration of deteted interferene pattern, x=0.000 µm The deteted power allows to alulate the refrative index and group refrative index at frequeny ν 0 : Φ Φ ( ν x ) n ( ) ( ν x ) 0, ν i fib 0, ν 0 i n = 0 n g PWT POZNAŃ 6-7 GRUDNIA 007 4/5

5 Interferometri Tehnique for Chromati Dispersion Measurements 5 The proess is repeated for different delays adustments x i, Fig.3. Fig. 3. Illustration interferene patterns for different delay line settings 4. CONCLUSIONS The main advantage of the proposed method is its effetiveness for short fiber measurements, whih is ruial for the haraterization of highly attenuating speiality fibers. The method an be implemented to all kinds of fibers. The main drawbak of this tehnique is that the results for short samples measurements are not adequate for the long ones. REFERENCES [] K. Perliki, Pomiary w optyznyh systemah telekomunikaynyh, WKŁ, 00. [] EXFO Appliation Note 3. [3] EXFO Appliation Note 77. [4] A. Maewski, Podstawy tehniki światłowodowe, Ofiyna Wyd. Politehniki Warszawskie, 000. PWT POZNAŃ 6-7 GRUDNIA 007 5/5

9 Geophysics and Radio-Astronomy: VLBI VeryLongBaseInterferometry

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