THE TRANSMISSION CURVE OF A FABRY PEROT SYSTEM BASED ON PLANE AND SPHERICAL MIRROR SEPARATION FAHMIRUDIN BIN ESA

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1 THE TRANSMISSION CURVE OF A FABRY PEROT SYSTEM BASED ON PLANE AND SPHERICAL MIRROR SEPARATION FAHMIRUDIN BIN ESA THIS PROJECT IS CARRIED OUT TO FULFIL THE PREREQUISITE TO BE HONOURED MASTER OF SCIENCE (PHYSICS) FACULTY OF SCIENCE UNIVERSITI TEKNOLOGI MALAYSIA OCTOBER 2009

2 V ABSTRACT The purpose of this study is to investigate the transmission curve of multiple reflections, which is known as Fabry Perot interferometer based on spherical and plane mirror separation. This multiple reflections of light should occur between two high reflectance coefficients of parallel mirrors that are named as cavity before they get to be transmitted. The transmitted rays along the edge of secondary mirror were observed. The highest interference peak occurs when they experienced same phase. These transmitted rays then were scanned by periodic linear change in the Piezo voltage that had been set at 128 V and its frequency was tuned up to 100 Hz. Proper alignment on setup arrangement and some modification of the system had been done and the captured data effectively clarified by theoretical approach. The cavity was fixed set as the radius of curvature for confocal measurement; there were 75 mm and 100 mm whereas for plane parallel distance was set from 250 mm of separation until 400 mm improved by 50 mm every increment. Free spectral range parameters for confocal separations were MHz per division for 75 mm and MHz per division for 100 mm separation. Based on the waist of the Gaussian beam, the slimmer of full wave half maximum was owned by the separation of 75 mm. Based on high reflectance coefficient, the calculated value of finesse was More difficult adjustment had been encountered while testing the plane parallel mirror. The more sensitive, probably in micro meter changed, opto-mechanical system on the piezo electric scanning should be required.

3 V ABSTRACT The purpose of this study is to investigate the transmission curve of multiple reflections, which is known as Fabry Perot interferometer based on spherical and plane mirror separation. This multiple reflections of light should occur between two high reflectance coefficients of parallel mirrors that are named as cavity before they get to be transmitted. The transmitted rays along the edge of secondary mirror were observed. The highest interference peak occurs when they experienced same phase. These transmitted rays then were scanned by periodic linear change in the Piezo voltage that had been set at 128 V and its frequency was tuned up to 100 Hz. Proper alignment on setup arrangement and some modification of the system had been done and the captured data effectively clarified by theoretical approach. The cavity was fixed set as the radius of curvature for confocal measurement; there were 75 mm and 100 mm whereas for plane parallel distance was set from 250 mm of separation until 400 mm improved by 50 mm every increment. Free spectral range parameters for confocal separations were MHz per division for 75 mm and MHz per division for 100 mm separation. Based on the waist of the Gaussian beam, the slimmer of full wave half maximum was owned by the separation of 75 mm. Based on high reflectance coefficient, the calculated value of finesse was More difficult adjustment had been encountered while testing the plane parallel mirror. The more sensitive, probably in micro meter changed, opto-mechanical system on the piezo electric scanning should be required.

4 vii TABLE OF CONTENTS CHAPTER SUBJECT PAGE TITLE STUDENT'S DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS i ii iii iv v vi vii xi xii xv CHAPTER 1 INTRODUCTION General Introduction Two beams interferometer (Michelson Interferometer) 3

5 viii 1.3 Multi beam interferometer (Fabry Perot Interferometer) Statement of Problem Hypothesis Objectives of the study 9 ' 1.7 Scope/limitation of work Dissertation plan 10 CHAPTER 2 LITERATURE REVIEW Introduction Spherical and plane mirror Fabry Perot interferometer High resolution confocal interferometer and its free spectral range Transmission of Gaussian beam Piezoelectric actuators Ideal Fabry Perot Free Spectral Range (FSR) Full Wave Half Maximum and Finesse Helium Neon (HeNe) Laser Stimulated emission Population inversion 30

6 IX 2.10 Si PIN Photodiode 32 CHAPTER 3 RESEARCH METHODOLOGY Experiment setup and adjustment Helium Neon (HeNe) Laser Beam Enlarging System, Lens Mirrors Scanning Piezo Element and Amplifier Si PIN Photodiode 43 CHAPTER 4 RESULTS AND DISCUSSIONS Basic Adjustment Measurement of Spherical Interferometer Curvature radius of 75 mm on spherical mirrors Curvature radius of 100 mm on spherical mirrors 52

7 4.3 Measurement of Plane Interferometer 56 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations 60 REFERENCES 63

8 xii LIST OF FIGURES FIGURE TITLE PAGE 1.1 Modern technical Michelson interferometer for interferometrical measurement of length by laser Light reflects in even number of times before passing second mirror (a) Light goes straight through (b) Light reflects twice (c) Light reflects four times Half and quarter wavelength show constructive and destructive interference Mode matching arrangement Geometry of symmetric nonconfocal cavity Confocal cavity showing the trajectory of a ray Confocal Fabry Perot Incidence of Gaussian beam on a plane Fabry Perot interferometer Transverse field distribution of fundamental mode Beam contour of Gaussian beam 19

9 xiii 2.8 Fabry and Perot's multi-beam interferometer Diagram of the derivation of the individual amplitudes Relative intensity (I/Io) versus change of mirror spacing in units Pi Definition of finesse Helium Neon laser energy level (for 632.8nm) Helium atom collides with Neon atom Illustration of Si pin photodiode Experimental setup The significant of module C in spherical measurement Piezo-crystal controller Scanning Fabry Perot interferometer, principle. The space d between two reflecting surfaces is varied by moving on of the plates The maximum tuned in piezo voltage Second adjustment with set of 100 mm mirror Second adjustment with set of 75 mm mirror Peak interference for 75mm separation Zoomed peak interference for 75mm separation Zoomed peak interference for 100mm separation Confocal cavity with voltage amplitude is 10 V; scanning frequency is about 30 Hz Peak transmission for 250mm separation 56

10 xiv 4.9 Peak transmission for 300mm separation Transmission fringes recorded at various separations. The figure shows a single series of measurements, and the device was returned to the confocal configuration to check reproducibility 61'

11 XV LIST OF SYMBOLS D, d - Separation between two mirrors or cavity m, n - Integer number or order of interference A - Wavelength di - Focal distance between laser and bioconvex lens d2 - Focal distance between bioconvex lens and first mirror wj - Minimum waist of output laser beam m>2 - Minimum waist of laser beam before entering first mirror c - Speed of light = x 10 8 ms" 1 C/, C2 - Center point for spherical mirror 1 and mirror 2 Mi, Mi - Mirror 1 and mirror 2 R 0, r - Radius of mirror's curvature H,n - Refractive index of the medium between the plates / - Perpendicular distance between the reflecting surfaces E, - Cosine of the angle 0 that the incidence wave normal makes with the normal between

12 the plates Phase change suffered on reflection at an etalon surface Incidence's angle Transmittance coefficient Reflectance coefficient Transmission's amplitude Ik Wave number = A Variable frequency free spectral range Full wave half maximum Finesse

13 CHAPTER 1 INTRODUCTION 1.1 General Introduction An instrument designed to exploit the interference of light and the fringe pattern that result from optical-path differences, in any of a variety of ways, is called an optical interferometer. In this study, the Fabry Perot interferometer was essentially investigated and Michelson interferometer also introduced as the basis of interferometer study. To achieve interference between two coherent beams of light, an interferometer divides an initial beam into two or more parts that travel diverse optical paths and then reunite to produce an interference pattern. One principle for broadly classifying interferometers distinguishes the manner in which the initial beam is separated. Wavefront division interferometers

16 4 (measuring beam). This is an important characteristic of this type of interferometer. They are therefore called two-beam interferometers, whereas in the interferometers or resonators developed later by Fabry Perot, not just two, but many beams were made to interfere. 1.3 Multi beam interferometer (Fabry Perot Interferometer) In 1899, Fabry and Perot [3] two young French physicists at the University of Marseilles introduced a new interferometric device, which was named the Fabry-Perot interferometer. The design of the interferometer is, in principle, light is passed through a pair of parallel, highly reflecting mirrors. Interference between components of the light undergoing multiple reflections result in extremely well-defined interference fringes emerging from the device, from which spectral properties of light can be deduced. The highly reflective surfaces divide the wave into multiple parts; each contribution reflects an even number of times in the interferometer before exiting, they can be illustrated schematically in Figure 1.4 below:

19 7 will cause destructive interference. Therefore, the Fabry Perot interferometer only transmits light under circumstances which closely match the constructive interference condition, provided the reflectivity of the mirrors is high. In this study two sets of Fabry Perot interferometer will be investigated. These are plane and spherical sets of mirror. The study is made to obtain experience in handling the correct alignment and adjustment system include mode matching arrangement for producing as high as constructive interference occurred at the transmission edge. For different sets of mirror, it has been required different types of arrangement. The separations between two parallel mirrors have been changed and they have been resulted for different value of frequency between two higher peak transmissions in half scanning system [2, 4], Theoretically, a Gaussian beam produced by laser source after experienced in beam enlarging system, both type of mirrors serve both type of propagation wave. Those are plane wave and spherical wave [4], The measured transmission curves are represented as Gaussian curve, which showed minimum waist of beam as full wave half maximum at the middle of peak intensity. Even the finesse is dependent on the free spectral range and the full wave half maximum; however it has been derived in chapter 2, which is proved that it is much more dependent on the reflectance coefficient of the dielectric coated mirror. Further description about the study will be discussed in the rest of following chapter.

20 8 1.4 Statement of Problem A key issue with Fabry Perot system is it needs a high resolution device for the detection of light intensity that depends on the transmission" curve of the system. To fully understand the system, there must be optimum parameters that affect the transmission curve of the system. The transmission curve of a Fabry Perot based on plane and spherical mirror separation will be studied by using same reflection coefficients. Proper alignment and some modification of the system hopefully will clarify the captured data with the theoretical approach. 1.5 Hypothesis The hypotheses made are as follows; 1. The transmission curves of a Fabry Perot change with mirror spacing of the reflection coefficients are kept remain. 2. An improvement of Fabry Perot system is expected by using proper lens collimator for plane and spherical mirror separation 3. Captured data from oscilloscope will determine the theoretical approach. 4. There will be weaknesses that need improvement in the construction system.

21 9 1.6 Objectives of the study The objectives of this study are; 1. To construct a high-resolution Fabry Perot system based on plane and spherical mirror separation. 2. To understand the working principle of Fabry Perot system based on the transmission curve of a Fabry Perot with change of mirror spacing by using same reflection coefficients. 3. To determine the optimum parameter of Fabry Perot system in terms of length of resonator, free spectral range, frequency wave half maximum and finesse. 4. To observe the captured data from oscilloscope and theoretical approach and also identify the weakness of the construction system. 1.7 Scope and limitation of work The highlight of the work was the construction of Fabry Perot system with high-resolution transmission curve. The work flow of this research includes:

22 10 i. Construct Fabry Perot system based on spherical mirror separation; the separation will be limited at 10 cm while for the plane mirror will be kept at any several distance. ii. iii. iv. Calibration the piezo movement of the mirror at certain frequency of 100 Hz. Using a 0.96 reflection coefficients for both mirror; spherical and plane. Evaluate the system performance. 1.8 Dissertation plan This thesis comprises five chapters. The important of basic light interference in general overview has been discussed in introduction section followed by Michelson interferometer and Fabry Perot interferometer. This chapter also gives an inside problem to the Fabry Perot system that shows the important of this study to produce high transmission curve and recognize their parameters that could be involved. The second chapter deals with the background study or literature review on the previous studies done by previous research in Fabry Perot interferometer field. It highlights the most important system from such as the arrangement of instrument, the reflection coefficient of mirrors, selected cavity spacing and their technique of measurement. All those things will be essentially described in this chapter. Other considered parameters like free spectral range, resolving power, finesse and so on will be also mentioned. All

23 11 the parameters that will be considered in this experiment will be theoretically discussed in details. The third chapter states the experimental and measurement techniques which includes the construction and the apparatus used. The parameters and physical measurements are defined by the every element of the setup. In attendance of variety component in the complete instrument, it should be enough for the experiment to be held. The fourth chapter deals with results and analysis of the system performance. The characteristics of Fabry Perot system is clarified experimentally. The final chapter summarizes the findings and comments on the Fabry Perot system based on plane and spherical mirror separation. Recommendations for further work are also mentioned.

24 CHAPTER 2 BACKGROUND OF STUDY 2.1 Introduction In this chapter, previous works are simultaneously described in order to keep in view and observe in details about the related parameter in this experiment. Such thing of mechanism must be done by the researchers who are interested in continuing or developing earlier findings in any field generally. Specifically, for this experiment, several journals have been reviewed in order to enhance and support understanding correlated to scanning Fabry Perot interferometer. From the observation, several important elements have been pointed out to describe which are very similar to what in objectives stated.

25 Spherical and plane mirror Fabry Perot interferometer The foremost element is the mirror itself because in Fabry Perot interferometer device, it can be classified into two types of mirrors; plane'and spherical mirror that so significant in producing multiple reflection. There gives much interest in application of Fabry Perot interferometer by using spherical mirror rather than plane mirror because it serves several advantages. This was proven by Fork, Herriott and Kogelnik [4] who determined that the spherical mirror interferometers have extraordinarily high resolutions. They recognized that confocal resonators offer high peak transmission than nonconfocal arrangements. However, nonconfocal setups are more lenient in terms of the relatively loose tolerance on the mirror separation and own capability to select various free spectral ranges with a given pair of mirrors but low light gathering intensity of the resonator. In their paper also mentioned about mode matching method which is the method to allow beam to get its path in the system properly by using geometrical optics approach [4], In other hand, it can be described as to match beam parameters between the laser source optical element or beam enlarging system and the interferometer. The whole of the explanation can be illustrated as Figure 2.1 [4] below. Bioconvex lens or matching lens takes part in important role so that an adequate radius of beam after laser source as well as collected beam by interferometer device can be achieved.

37 REFERENCES 1. Frank L. P., S. J., Leno S. P. and Leno M. P. Introduction to Optics. 3 rd ed. Sansome St., S. F.: Addison -Wesley Luhs, W. Fabry Perot Resonator. MEOS GmbH Eschbach Fabry, C. and Perot, A. On the Application of Interference Phenomena to the Solution of Various Problems of Spectroscopy and Metrology. Astrophysics Journal : Fork, R. L., Herriott, D. R. and Kogelnik, H. A Scanning Spherical Mirror Interferometer for Spectral Analysis of Laser Radiation. Applied Optics (12): Johnson, J. R. A High Resolution Scanning Confocal Interferometer. Applied Optics (6): Abu-Safia, H., Al-Tahtamouni, R., Abu-Aljarayesh, I. and Yusuf, N. A. Transmission of a Gaussian Beam through a Fabry Perot Interferometer. Applied Optics (18): Hercher, M. The Spherical Mirror Fabry Perot Interferometer. Applied Optics (5):

38 64 8. Wilksch, P. A. Instrument function of the Fabry-Perot spectrometer. Applied Optics (10): Davis, G. R., Furniss, I., Towlson, W. A., Ade, P. A. R., Emery, R. J., Glencross, W. M., Naylor, D. A., Patrick, T. J., Sidey, R. C. and Swinyard, B. M. Design and Performance of Cryogenic, Scanning Fabry Perot Interferometers for the Long Wavelength Spectrometer on the Infrared Space Observatory. Applied Optics (1): Allen, L. and Jones, D. G. C. The Helium Neon laser. Advances in Physics (56): Allen, L. and Jones, D. G. C. Principles of Gas Lasers. American journal of Physics (7): Kasap, S. O. Optoelectronics and Photonics: Principle and Practices. Upper Saddle River, N. J.: Prentice-Hall Britun, N., Gaillard, M., Oh, S. G. and Han, J. G. Fabry-Perot Interferometer for Magnetron Plasma Temperature Diagnostics. Journal Physics D: Applied Physics : Kerner, K., Rochester, S. M Yashchuk, V. V. and Budker, D. Variable Free Spectral Range Spherical Mirror Fabry-Perot Interferometer. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley

Some Topics in Optics

Some Topics in Optics The HeNe LASER The index of refraction and dispersion Interference The Michelson Interferometer Diffraction Wavemeter Fabry-Pérot Etalon and Interferometer The Helium Neon LASER A