Creating a visible and infrared light source for testing bendable fibres a laser based system. Designing and characterising the beam size and beam propagation.

Student: Quan Minh Nguyen (21006611)Supervisor: Professor Adrian Keating

Table of Contents1. Introduction:31.1Objective and Background:31.2Overview:32. Literature review:62.1 Geometrical Optics:62.2 Gaussian Beam:72.3 ABCD Matrix:113. Research method:124. Projects progress:125. Reference13

1. Introduction:1.1 Objective and Background:The projects purpose is to explore the science behind Fibre Optics by investigate the image output from a bendable optical fibre bundles. The objective of this project is to design a system that capable of testing the performance of fibre bundles under a variety of light sources or under different wavelengths to be more specific. Fibre Optics is a crucial contribution to telecommunication and medical application nowadays [6]. For example, a bundle of many fibres that smaller than the hair of a human is capable of transmitting telecommunication signal with lighting fast speed. It can reach up to 2.4 terabits per second, which is equivalent to hundred hours of digital video or 30 million phone calls across the Atlantic [1]. From a medical point of view, Endoscopes that doctors used to see inside patients bodies with minimal entryway is constructed from optical fibres [3]. 1.2 Overview:The method used to find the performance of the optical fibre is to get an output image when a light beam fired through a single fibre in the bundle. The image is used to determine whether there was any energy loses to the surrounding fibres. Figure 1-1 represent the intended setup of the system for the experiment.Fibre-coupled laser module with FC/PC connectorBeam collimatorBeam splitterLensCameraFocusing lensFibre bundlesLensCameraOptical benchXYZ stage

Figure 1-1: Layout of the desired systemThere is a light source and two cameras at each ends to produce an input as well as to capture outputs. The laser beam first goes through a collimator to be shaped into a collimated beam. The collimated beam after went through a 50:50 beam splitter, will have half of its power goes through the focusing lens. The focusing lens focuses the collimated beam into a less than 5m spot to go to the single fibre in the bundles. The output from the fibre then passes through another lens which magnifies the output before it is captured by a camera. Back to when the beam first hit the fibre bundle, some of the light will be reflected back to the beam splitter which guides the light to the second camera (represented by red arrow). The second camera will produce the image of the input to the fibre bundles while the first camera will produce the output from the bundles.Figure 1-2 illustrate the intended alignment of collimator, splitter and focusing lens using SolidWorks. These parts can be called a beam shaping unit. This unit, along with a XYZ stage are the most important parts of the system.

Figure 1-2: Exploded view of collimator, splitter and focusing lens unit.Figure 1-3 and 1-4 shows the assembly of the beam shaping unit on to the XYZ stage

Figure 1-3: Assembly of collimator, splitter and focusing lens on XYZ stage, exploded view.

Figure 1-4: Assembly of collimator, splitter and focusing lens on XYZ stage, collapsed view.(Figures produced mainly by assembling SolidWorks parts taken from Thorlabs website)[9-16]

2. Literature review:For the proposal design of such system showed in the Overview section, an extensive study of Optical science must be conducted. The study includes, but not limited to Paraxial Geometrical Optics, Gaussian Beam Theory for Laser, and Matrix Methods in Paraxial Optics2.1 Geometrical Optics:Lens is the extensively used device when constructing an optical system as so the human eyes themselves are lenses [4]. Therefore, Geometrical Optics and Paraxial Rays is an important study for the design of any optical system. The use of Paraxial rays assume rays which make small angle with the optical axis is allowed to form good image [6]. It is said to be complete enough to describe essentially all laser amplification and laser propagation problem [8]. Most importantly, this assumption allows small angle approximation, [6], which simplifies the calculation.Snells Law or Law of Refraction is one of the most fundamental knowledge of any lens design. When light goes from one medium to another, its direction will change [6]. That change in direction follows Snells Law, which is give as:

Where: i is the angle between incident ray and an axis perpendicular to medium interface t is the angle between refracted ray and an axis perpendicular to medium interface nt, ni is the refractive index of the medium defined as:

[4]In geometrical optics, it is necessary to approximate the lens as a thin lens to make the calculation simple. This assumes that if the lens thickness is small compare to the focal length, the lens can be approximate as a thin lens [6]. The thin lens equation is given as:

Where: s is the distance to the object s is the distance to the image f is the focal length. It is defined as image distance for an object at infinity, or the object distance for an image at infinity[6]Numerical aperture and f-number are also important definitions as they required when selecting lens for this particular project. F-number is defined as the ratio of focal length f over the diameter of the entrance opening of the lens or clear aperture D [4]. The term Numerical Aperture, which is adapted from microscopy defines the capability of the system to gather light [4].

Where: n is the refractive index of the medium (equals 1 for air) is half the angle of the cone of light that can enter the lensIt related to f-number by the equation:

2.2 Gaussian Beam:Because this project deals with laser-base system, it is essential to know how laser beam propagate. In order to achieve those, a study of Gaussian Beam is required.Laser has many unique properties. First is that in its fundamental transverse mode, it has its wavefront first planar then nearly spherical. Also its irradiance (intensity) and electric field follows Gaussian profile as shown in figure 2-1 [6]. Therefore, for simplicity, it is assume that the simplest mode or TEM00 is applied as it is the ideal mode [8]. Second, the Gaussian beam profile will remain Gaussian throughout the propagation [5].

Figure 2-1: Propagation of Gaussian beam(Figure taken from [2])It is important to note that because Gaussian beam has irradiance follows Gaussian profile as shown in figure 2-2, its intensity decrease significantly with the increase in the radius of the spot [8]. Therefore, it is necessary to define a radius at which the decrease in intensity becomes insignificant [8]. It is conventional to apply the 1/e2 criterion to define that radius. The 1/e2 definition defines the spot size radius (or beam waist radius) to be the radius at which the intensity is decreased to 1/e2 or 13.5% of its peak value and the focused energy is contained in that radius is 86.5%. The beam waist radius of 1/e2 contour is denoted as w0 [2][8]. 0W-w-2w2w00.865100Contour radius (r/)Relative intensityRelative Power100201/e2500

Figure 2-2: Relative intensity and power of Gaussian beam with Gaussian profile(Figure adapted from [2][5][8])When a Gaussian beam propagates in free space as in figure 2-1, the change in the spot size radius and wavefront radius of curvature relative to propagation distance z is given as:

Where: w0 is the beam waist radius is the lights wave length z is the distance propagatedNote: wavefront radius of curvature is infinite (planar wavefront at z = 0)[2][8]With regard to the peak intensity and peak power, relative the intensity and power of TEM00 Gaussian beam with beam waist radius w is given as:

Where: I0 is the peak relative intensity (=1) P() is the peak relative power (=1) r is the contour radius w is the radius of the 1/e2 irradiance after the beam propagated distance z[2][5][8]It is worth pointing out that Figure 2-2 and above equations showed the intensity is truncated as the growth in contour radius while more power is contained within the contour radius and vice versa. Also, if r is substituted by w those equations becomes:

And the 1/e2 criterion is satisfied.Figure 2-3 below shows another unique properties of Gaussian beam is that the smaller the beam waist, the bigger the divergence. This can be prove by using equation (6) with a fixed propagation distance z and wavelength [6].W01W02

Figure 2-3: Relationship between beam waist and beam divergence.(Figure adapted from [6]) For the propagation of Gaussian beam, it is also important to know the Rayleigh range. It is defined as:

[7]The Rayleigh range as shown in figure 2-4 defines a range over which, the spot size expands with factor of square root of two. The importance of this definition is due to the fact that when Gaussian beam propagates from the waist, the diffraction causes the beam radius to increase rapidly [8]. The part of the Gaussian beam within the Rayleigh range is said to be a collimated beam [6][8].W0

Collimated range 2zRzR

Figure 2-4: Rayleigh range and far-field divergence angle(Figure adapted from [2][5][6]) Another important definition is the far-field divergence angle as shown in figure 2-4

[2][6]It is important because when related to numerical aperture in equation (4) and f-number (5), it yields:

[2][5][6][8]Therefore, when combine (12) and (13), it gives:

[2][5][6][8]Equation (14) is the governing equation of the design of Gaussian beam. It allows calculation of desired spot size w0 with respect to diameter of the collimated beam D and focal length f of the lens. Figure 2-5 illustrate the relationship between collimated beam diameter, far-field divergence angle, aimed focused spot and focal length. Solving for D and f in equation (14) for w0 less than 2.5m will give the required focusing lens.

fD0 = 2.5m

Figure 2-4: Relationship between collimated beam diameter, far-field divergence angle, aimed focused spot and focal length.2.3 ABCD Matrix:The Geometric ray tracing represented above is a good way to approach ray transfer through a simple lens. However, when facing with complex system of lenses consist of several elements a systematic approach that facilitates analysis [6] is required. This is where the Matrix Method comes. The matrix method however needs the analysis to be constrained to paraxial rays [6].The definition of the matrix method is such that: when incident ray goes through an optical system, the ray coming out from that system is related to the incident ray by an ABCD system matrix [6] as in equation (15) and figure 2-5.

Where: y1, y2 are the heights of the images 1, 2 are the slope angle related to the optical axis[6]12y1y2

Figure 2-5: Ray transfer through optical system(Figure adapted from [6])A simple thin lens matrix can be described by: 3. Research method:So far, the method applied to approach the problems in the project is as follow:1. The note taken during the meeting was carefully analysed to define the priority study that required.2. The reputable optics manufacturers website such as CVI Melles Griot and Newport were the first places that I went to as in the initial instruction. They have almost all the information required to design the system. They have fundamentals of Geometric Optics as well as Gaussian Beam theory and many more summarised and neatly typed on their website or printed in PDF form. It is good to have a general idea but because the notes is summarised, the derivation is missing.3. More in-depth study was acquired by using reputable literatures such as books and peer-reviewed journals. These books and journals although not easy to find, but are all available in University of Western Australia online library catalogue or through the connected databases. The search for those literatures was conducted by finding the reference at the end of the technical notes from the manufacturer as well as by suggestion from Professor Keating. Moreover, random online search is also used to find those literatures.4. The knowledge from the literatures was carefully studied. It begins with reading and note taking. After that, some of the important derivations were reproduced to understand the mechanism.5. During the study of from the books and journals, the information is always compared to the manufacturers technical notes to see if there was any deviation.6. The components were designed and parts were chosen from Thorlabs website to produce a concept of the desired system. The concept model was produced by assembling SolidWorks parts available on Thorlabs website with some parts such as screws taken from SolidWorks tools box. The assembly in SolidWorks was done based on the knowledge previously acquired from some courses in UWA as well as the information from SolidWorks manual and forum.4. Projects progress:Please refer to Appendix 1

5. Reference1.Allen, TB, The Future Is Calling, National Geographic Society. Available from: . [13/10/2013].2.CVI Laser Optics and Melles Griot, Gaussian Beam Optics, CVI Laser Optics and Melles Griot and Auburn SeeWolf, LLC. Available from: . [12/08/2013].3.Discovery, How are optical fibers used in medicine?, Discovery Communications, LLC. Available from: . [13/10/2013].4.Hecht, E & Zajac, A 1987, Optics, 2nd edn, Addison-Wesley Pub. Co., Reading, Mass.5.Newport, Gaussian Beam Optics, Newport Corporation. Available from: . [15/10/2013].6.Pedrotti, FL & Pedrotti, LS 1993, Introduction to optics, 2nd edn, Prentice Hall, Englewood Cliffs, N.J.7.Self, SA 1983, 'Focusing of spherical Gaussian beams', Appl Opt, vol. 22, no. 5, pp. 658-61.8.Siegman, AE 1986, Lasers, University Science Books, Mill Valley, Calif.9.Thorlabs, BA1 - Mounting Base, 1" x 3" x 3/8" Available from: . [8/10/2013].10.Thorlabs, CM1-BS015 - Cube-Mounted Non-Polarizing Beamsplitter, 1100 - 1600 nm. Available from: . [8/10/2013].11.Thorlabs, F810FC-1550 - 1550nm FC/PC Collimation Package, NA = 0.24, f = 37.13 mm Available from: . [8/10/2013].12.Thorlabs, LA1576-C - N-BK7 Plano-Convex Lens, 9.0 mm, f = 12.0 mm, ARC: 1050-1620 nm. Available from: . [8/10/2013].13.Thorlabs, PT3 - 1" XYZ Translation Stage with Standard Micrometers, 1/4"-20 Taps Available from: . [8/10/2013].14.Thorlabs, SM1AD9 - Externally SM1-Threaded Adapter for 9 mm Optic, 0.40" Thick Available from: . [8/10/2013].15.Thorlabs, SM1L20 - SM1 Lens Tube, 2" Thread Depth, One Retaining Ring Included Available from: . [8/10/2013].16.Thorlabs, TR075 - 1/2" x 3/4" Stainless Steel Optical Post, 8-32 Stud, 1/4"-20 Tapped Hole Available from: . [8/10/2013].