Class ProjectIn

OPTICAL COMMUNICATION NETWORKSFabry Perot Filter Analysis and Simulation

using MATLABTamir Suliman

Professor: Suresh Subramaniam

ABSTRACT

n this project a program is written in MATLAB used to analyze and simulate Fabry- Parot and Mach Zehnder Interferometers. The program model of the interferometer is determined using the proposed transfer function model of the Fabry -Parot filter Transmission intensity, Finesse and the contrast

Factor. Analysis was carried out in MATLAB environment of the developed model to explain the behavior of the interferometers and the parameters that affect the performance and the design.

I1. INTRODUCTION

Fabry Parot:

A Fabry-Parot Filter consist of the cavity formed by two highly reflective mirrors placed parallel to each other , as shown in the figure 1.The input light beam to the filter enters the first mirror at right angles to its surface. The output of the filter is the light beam leaving the second mirror. This filter is called Fabry-Parot or etalon. This is a classical device that has been used widely in interferometric applications. Fabry-Parot filters have been used for WDM in several optical network test beds. There are better filters today, such as thin film resonant multi cavity filter and they can still be viewed as Fabry-Perot filter. This type of filter transmits a narrow band of wavelengths and rejects wavelengths outside of that band. An interesting feature of this type of filter is its ability to "select" a different peak wavelength as the filter is tilted.

Theory:

The basic concept of an FP filter is shown in fig. 1.1.It was described first by Fabry Charles and Albert Perot in 1899.Two highly reflective planner plates are accurately positioned in parallel and thus from cavity. A light beam entering the cavity is reflected multiple times between the plates. Each time when the beam hits a plate, a small part of its power escapes. When the two plates are align perfectly in parallel, the multiple beams escaping at each side of the FP cavity are exactly parallel. Each beam has a fixed phase difference with respect to the preceding one; this phase difference corresponds to the extra path length travelled in the cavity.

Fig.1.1 Fabry-Perot Interferometer

If the transmitted beams are out-of-phase, destructive interference occurs and this corresponds to a transmission minimum. Whether the multiply-reflected beams are in-phase or not depends on the wavelength (λ) of the light (in vacuum), the angle the light travels through the etalon (θ), the thickness of the etalon (l) and the refractive index of the material between the reflecting surfaces (n).The phase difference between each succeeding reflection is given by δ

Fig 1.2 Fabry-Pérot etalon

2. MODELLING METHODOLOGY

If both surfaces have a reflectance R, the transmittance function of the etalon is given by:

Maximum transmission (Te = 1) occurs when the optical length difference (2nlCos θ) between each transmitted beam is an integer multiple of the wavelength. In the absence of absorption, the reflectance of the etalon Reis the complement of the transmittance, such that Te + Re = 1. The maximum reflectivity is given by:

The wavelength separation between adjacent transmission peaks is called the free spectral range (FSR) of the etalon, Δλ, and is given by:

Where λ0 is the central wavelength of the nearest transmission peak, and the FSR is related to the full-width half-maximum, δλ , of any one transmission band by a quantity known as the finesse:

The power transfer function of the filter is the fraction of the input light power that is transmitted by the filter as a function of optical frequency f, or wavelength. For the Fabry-Perot filter, this function is given by

This is also can be expressed in terms of the optical free space wave length as

Here A denotes the absorption loss of each mirror, which is the fraction of incident light that Etalons with high finesse show sharper transmission peaks with lower minimum transmission coefficients. A Fabry-Pérot interferometer differs from a Fabry-Pérot etalon in the fact that the distance l between the plates can be tuned in order to change the wavelengths at which transmission peaks occur in the interferometer. Due to the angle dependence of the transmission, the peaks can also be shifted by rotating the etalon with respect to the beam.

3. SIMULATION OF THE MODEL AND RESULTS

Theoretical simulation is employed to determine the factors that control the Fabry-Perot filter using MATLAB. A written code for event simulation model using MATLAB has been done to plot three important parameters that determine the performance and the efficiency when it comes to design the Fabry-Perot filter. The first plot is about the transmitted intensity versus the mirror reflectivity of the filter. The second plot is about the finesse and the mirror reflectivity. The finesse is an important parameter that determines the performance of a Fabry-Perot filter. Conceptually, finesse can be thought of as the number of beams interfering within the Fabry-Perot cavity to form the standing wave.The primary factor that affects finesse is the reflectance R of the Fabry-Perot mirrors, which directly affects the number of beams circulating inside the cavity. The finesse as a function of the reflectance is defined in equation (4) above.Another important factor in the design of the filter is the contrast factor which is defined primarily as the ratio of the maximum to minimum transmission (i.e. the ratio in the intensity transmission values of the peaks and the troughs shown in Figure (3.1).

Fig 3.1The Transmitted Intensity of Fabry-Perot Filter

Fig 3.2The Reflectivity Finesse and the Mirror Reflectivity

Fig 3.3The Contrast Factor and the Mirror Reflectivity

4. CONCLUSIONS

Simple analysis of Fabry-Perot interferometers assumes a perfectly parallel plate cavity with two mirrors. Low cost practical cavity will always have deviation from the standard analytical model. An attempt is made to analyze the factors that control and affect the performance and the design of the Fabry-Perot filter versus the parameter that control those factors.A higher finesse value indicates a greater number of interfering beams within the cavity, and hence a more complete interference process.The equation and the plots also show that a linear increase in finesse, translates into a quadratic increase in the value of the contrast factor. Since the contrast factor and the finesse are directly proportional to each other. The plots also shows that A higher finesse value indicates a greater number of interfering beams within the cavity, and hence a more complete interference process.MATLAB is a great and easy tool to use to simulate optical electronics.

REFERENCES

[1]. Rajiv Ramasawi and Kumar N. Sivarajan, “Optical Networks”, (2002), Morgan Kaufmann., California, page- 130-134.[2]. B.E.A. Saleh and M.C. Teich, “Fundamentals of Photonics”, (1991), John Wiley & Sons, Inc., New York, page-314.[3]. M Born and E Wolf, “Principles of Optics”, (1980), Pergamon Press., Oxford, Chap 7.6.[4] Keiser G., “Optical Fiber Communications”, 3rd Edition, McGRAW-HILL, Boston (USA), 2000, page - 166 – 171[5]. Wikipedia http://en.wikipedia.org/wiki/Fabry-Perot [6]. Micron Optics http://micronoptics.com [7]. Math works Website for MATLAB http://mathworks.com