Measurements of Intermodal Dispersion In Graded Index Optical Fiber

The aim of this research is to examine experimentally the laser pulse transmittance in graded index optical fiber. However attention is paid on the evaluation of intermodal dispersion. Four signals ( λ =680nm and power= 0.1mW) of different frequencies (138.889, 277.778, 645.16, and 1369.863 Hz), of pulse widths (7.2, 3.6, 1.55, and 0.73 ms) respectively are sent through a 400m multimode graded index fiber. A p-i-n detector is used to receive output signals. Intermodal dispersion has been noticed and the pulse width broadening for each frequency is recorded. They are (7.22, 3.61, 1.555, and 0.732 ms) that lead to frequencies of (138.504, 277.008, 643.08, 1366.120 Hz) respectively. That change in frequency has to be taken into account whenever fiber optic dependence communication, guidance, or control systems are considered.

, proposed a provably optimal technique for minimizing intersymbol interference (ISI) in multimode fiber (MMF) systems using adaptive optics via convex optimization [4].I. Kamitsos and N. K. Uzunoglu, (2007), showed that multimode fibers can be characterized by multipath propagation of optical signals and this leads to severe intersymbol interference at the output of the fiber [5].
This research aims to study the intermodal dispersion introduced when laser signals of different frequencies are lunched into multimode graded index fiber.Results are beneficial in designing and building optical fiber guiding systems.

Theoretical background
The width (duration) of the pulse propagating in an optical fiber increases with distance of propagation.The pulse of light is composed of wavelengths; the propagation velocity is not the same for all wavelengths.This phenomenon is called intermodal dispersion [6].
Intermodal dispersion in practical results from the propagation delay differences between modes within a multimode fiber (MMF).As the different modes which constitute a pulse in multimode fiber travel along the channel at different group velocities, the pulse width at the output is dependent upon the transmission times of slowest and fastest modes [7].On the contrary of multimode the refractive index of the core in gradedindex fibers is not constant but decreases gradually from its maximum value n1 at the core center to its minimum value n2 at the core-cladding interface.Intermodal dispersion in multimode fibers is minimized with the used graded index fiber [8].

Experimental setup
The optical fiber arrangement shown in Figure (1) is exploited here to carry out the experiment.It consist of three parts mainly the transmitter, optical fiber and receiver.A. Figure (2) shows the diagram of the transmitter circuit.It consists of laser of wavelength ( λ) of 680nm.This circuit works at pulsed laser mode operating at four different frequencies that can be changed from frequency to another by a selector.The transmitter circuit is divided into two parts, the first part is a frequency modulator and the second part is a laser diode drive.Frequency is implemented by using astable IC 555 timer circuit operates as an astable multivibrator as in Figure (2).In the present application four frequencies are required; therefore four capacitors at the values 1 μF, 2.2 μF, 4.7 μF, and 10 μF are used instead of C2 to get different frequencies.
PDF created with pdfFactory Pro trial version www.pdffactory.comB. A duplex optical fiber of length 200m with core / cladding diameter 62.5 /125μm, numerical aperture 0.275, and Sc connector is utilized here in order to obtain a single fiber of 400m length.This is done simply by connecting two adjacent ends of the duplex fiber together using Sc adapter.The design goal for any transmitter is to couple as much light as possible into the optical fiber.In practice, the coupling efficiency depends on the type of optical source as well as on the type of fiber: LD and multimode graded fiber are used here.C. Figure (3) shows the diagram of the receiver circuit that uses p-i-n photodiode as the detector, which is connected to a current to voltage converter.The current from the p-i-n detector is usually converted to a voltage before the signal is amplified.The current to voltage converter is perhaps the most important section of any optical receiver circuit.In this circuit IC 741 comparator is used with feedback resistance as shown in Figure (3).

Measurements and Results
The intermodal dispersion introduced by launching four laser signals of different frequencies is examined.
The pulse width of the first signal (of frequency 138.889Hz) is measured to be 7.2ms before launching.The pulse width of the signal is altered to 7.22ms (138.504Hz) after being transmitted into fiber, Figure (4).Thus intermodal dispersion is introduced and can be evaluated as follows: where To is the output pulse width, Ti is the input pulse width, and L is the fiber length.
The second unlaunched signal pulse width is 3.6ms (277.778Hz) and the transmitted signal pulse width is 3.61.ms(277.008Hz), Figure (5).Hence the pulse width difference between To and Ti and the introduced intermodal dispersion are 10μs and 25 ns/m respectively.
The pulse width of the third unlaunched signal (645.1613Hz) is 1.55ms and the transmitted signal pulse width (643.0868Hz) is 1.555ms, Figure (6).In this case δTg is found to be 5μs and the intermodal dispersion is equal to 12.5ns/m.
The pulse width of the fourth unlaunched signal (1369.86Hz) is 0.73ms and the pulse width of the transmitter signal is 0.732ms (1366.120Hz).The difference between the pulse width of the unlaunched signal and the pulse width of the transmitted signal is found to be 2 μs and the intermodal dispersion is equal to 5ns/m.

Conclusions
The facts derived from the practical results at this work are agreed with the theoretical aspectation and can assure the practicability of adopting these results in designing and building fiber optics guided system.