Module Labworks Optics Abbe School of Photonics Contact person Supervisors
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1 Module Labworks Optics Abbe School of Photonics, Friedrich-Schiller-Universität, Physikalisch-Astronomische-Fakultät, Max-Wien-Platz 1, Jena, Germany Phone: Fax: Web : Contact person: Dr. Roland Ackermann Phone : roland.ackermann@uni-jena.de Supervisors: Joachim Buldt (joachim.buldt@uni-jena.de), Thorsten Goebel (thorsten.goebel@uni-jena.de) Maximilian Heck (maximilian.heck@uni-jena.de) Helium Neon Laser [ version of February 16, 2018]
2 Contents 1 Safety issues Eye hazard Chemical hazard Theoretical basics Helium Neon Laser Basics of resonator modes Transversal modes in a laser resonator Longitudinal modes in a laser resonator Optical elements for wavelength selection Brewster s angle Transmission grating Beam parameter product Measurement of the beam quality factor M 2 (Task 8) Setup and equipment Setup alignment procedure Goals of the experimental work 15 A Preliminary questions 16 B Final questions (to be answered in the introduction/discussion section of the report (indirect, not explicit)!) 17
3 1 Safety issues 1.1 Eye hazard The laser system used is classified according to DIN IEC as a Class 3B Laser. This means the visible, continuous wave laser radiation emitted during laser operation has an average power of less than 5 mw. Therefore the laser radiation itself and also the stray light is potentially dangerous to the eye. It is recommended to use an appropriate laser safety goggles in addition with protective sides against laser stray light caused by additional optics during the measurements. Since some measurements and the alignment procedure may require to take off the protective goggles temporarily, it is very important to remove all reflecting objects attached to your hands/wrist (e.g. rings, watches etc.). Therefore, DO NOT look straight into the laser beam and avoid to look into reflections of the beam. 1.2 Chemical hazard Acetone and its vapors are toxic. Use the minimal required quantity of acetone while cleaning the optical elements. Do not sniff the vapors of the acetone for prolonged periods. Avoid contact with skin or eyes. If accidental contact happens, wash the interested area with abundant cold water. Do not hesitate to ask for assistance if pain persists. Figure 1: Laser Safety: λ = 633 nm, Class 3B Laser 2 Theoretical basics 2.1 Helium Neon Laser A helium-neon laser is a gas laser, consisting of a mixture of helium and neon gas in a ratio between 5:1 and 20:1 bound in a glass tube. The pump energy of the laser is provided by an electrical discharge of several hundred Volts between an anode and cathode at each end of the glass tube. A current of 5 to 100 ma is typical for cw operation. The used HeNe tube has Brewster s angle windows at both ends. The HeNe Laser can work at different wavelengths. There are infrared emissions at 3.39 µm and 1.15 µm and different emissions in the visible spectrum. Normally a HeNe Laser is working at the red nm wavelength with a very narrow gain bandwidth of a few GHz, which is dominated by Doppler broadening. The laser process in a HeNe laser starts with collision of electrons from the electrical discharge with the helium atoms in the gas, which excites helium from the ground state to the 2 3 S 1 and 2 1 S 0 metastable excited states. Collision of the excited helium atoms with the ground-state neon 3
4 Figure 2: Energy level diagram of a He Ne system (origin: File:Hene-2.png). atoms results in transfer of energy to the neon atoms, exciting neon electrons into the 3S 2 level. The difference between the energy states of the two atoms is in the order of 0.05 ev, which is supplied by kinetic energy. The number of neon atoms in the excited states builds up as further collisions between helium and neon atoms occur, causing a population inversion. Spontaneous and stimulated emission between the 3s 2 and 2p 4 states results in emission of nm wavelength light. After this, fast radiative decay occurs from the 2p to the 1s ground state. For more details we recommend to read [6]. Also more basics about laser principles may be found in [7], specially about rate equations. 2.2 Basics of resonator modes Laser light usually is assumed to have a Gaussian intensity distribution in the transverse plane. Details of the theory of Gaussian beams can be found in [2]. Here only results are presented. The intensity distribution of the laser spot in the beam waist plane for the fundamental TEM 00 mode is described by a Gaussian profile in the following way I(r, z) = I 0 exp 2r2 w(z) 2, (1) with r being the distance from the beam center. Higher modes are characterized by so called Hermit or Laguerre polynomials. The laser mode stays in the Gaussian distribution along the resonator but the beam width (the distance from the beam axis to the point where the intensity drops to 1/e 2, see Fig. 3) increases 4
5 w(z) w 0 θ 0 2 w0 z z R Figure 3: Gaussian beam width w(z) as a function of the axial distance z. w 0 : beam waist; z R : Rayleigh range; θ: total angular spread (origin: with increasing distance from the beam waist. In a certain distance z the beam width w(z) is given by w(z) = w λz πw (2) The radiation converges towards the beam waist and diverges with increasing distance from the center of the resonator, having a plane wavefront in the waist. In distance z from the waist the radius of the wavefront curvature R(z) is R(z) = z 1 + πw λz. (3) In a confocal resonator (the focal points of both mirrors are at the same point, see Fig. 4) the beam waist is inside of the resonators with the distance d between the mirrors and the beam waist is given by λd w 0 = 2π. (4) In a non-confocal resonator the stability parameters g 1 and g 2 have to be defined g 1 = 1 (d/r 1 ) g 2 = 1 (d/r 2 ), (5) whereas d is the resonator length and R 1 and R 2 are the curvatures of the mirrors. To reach a stable resonator mode the wavefront curvature has to be equal to the curvature of the used resonators. By this request it is possible to evaluate the position and size of the beam waist, and the spot size on the the mirrors can be estimated. Hence, we know the curvature of the 5
6 beam front in two planes, which we name z 1 (distance of the beam waist to mirror 1) and z 2 (distance of the beam waist to mirror 2). If one claims R(z 1 ) = R 1 and R(z 2 ) = R 2 the position of the beam waist can be evaluated z 1 = and the radius of the beam waist is given by w 0 = The so called stability area is defined by g 2 (1 g 1 ) g 1 + g 2 2g 1 g 2 d, (6) ( ) 1/2 ( ) 1/4 λd g 1 g 2 (1 g 1 g 2 ) π (g 1 + g 2 2g 1 g 2 ) 2. (7) 0 < g 1 g 2 < 1. (8) Within this region of resonator parameters stable mode structure is guaranteed. If g 1 g 2 is >1 the spot size is imaginary or infinity. If g 1 g 2 1 the spot size may be greater than the resonators, resulting in significant losses, what means mode instability. Figure 4: Stability diagram for a two-mirror cavity. Blue-shaded areas correspond to stable configurations. (origin: 6
7 2.3 Transversal modes in a laser resonator In a laser with cylindrical symmetry, the transverse mode patterns are described by a combination of Gaussian beam profile and Laguerre polynomials. The modes are denoted TEM pl where p and l are integers labeling the radial and angular mode orders, respectively. The intensity at a point (r, ϕ) (in polar coordinates) from the center of the mode is given by I pl (ρ, ϕ) = I 0 ρ l [L l p(ρ)] 2 cos 2 (lϕ)e ρ, (9) where ρ = 2r 2 /w 2, and L l p is the associate Laguerre polynomial of order p and index l, w is the spot size of the mode corresponding to the Gaussian beam radius. With p = l = 0, the TEM 00 mode is the lowest order, or fundamental transverse mode of the laser resonator and has a form of a Gaussian beam. The pattern has a single maximum and a constant phase across the mode. Modes with increasing p show concentric rings of intensity, and modes with increasing l show angularly distributed maxima. In general there are 2l(p + 1) spots in the mode pattern (except for l = 0). The overall size of the mode is determined by the Gaussian beam radius w. This size increases or decreases for different distances form the beam waist, however, the modes preserve their general shape. Higher order modes are relatively larger compared to the TEM 00 mode, and thus, the fundamental Gaussian mode of a laser may be selected by placing an appropriately sized aperture in the laser cavity. Figure 5: Rectangular transverse mode patterns TEM mn (origin: wiki/transverse_mode). 7
8 In many lasers, the symmetry of the optical resonator is restricted by polarizing elements such as Brewster s angle windows. In these lasers, transverse modes with rectangular symmetry are formed (Fig. 5). These modes are designated TEM mn with m and n being the horizontal and vertical orders of the pattern. The intensity at point (x, y) is given by ( 2x x 2 2 ( 2y y 2 ) 2 I mn (x, y) = I 0 H m exp ) H n exp, (10) w w w 2 where H m (x) is the m-th order Hermite polynomial. The TEM 00 mode corresponds to exactly the same fundamental mode as in the cylindrical geometry. Modes with increasing m and n show maxima appearing in the horizontal and vertical directions, with in general (m+1)(n+1) maxima present in the pattern. As before, higher-order modes have a larger spatial extent than the 00 mode. The overall intensity profile of the laser output is a superposition of all transverse modes allowed in the laser cavity, though often it is desirable to operate only on fundamental mode. 2.4 Longitudinal modes in a laser resonator For a stable laser operation in a laser cavity a standing wave is necessary. As this wave arises in propagation direction it is called longitudinal mode. Examples of standing waves are shown in Fig. 6 which can only form if the condition w 2 L = q λ 2 (11) is fulfilled. Here, L is the length of the cavity, λ is the laser wavelength, and q is an integer (q = 1, 2, 3,... ). In case of a realistic resonator, the length L is much larger than the wavelength λ and therefore one can define the frequency separation between two modes [3]: ν = c 2nL. (12) The refractive index n equals 1 in case of propagation in air. The number of longitudinal modes that can exist in a resonator depends on the gain profile of the active medium. Only at frequencies where amplification takes place, modes can start to oscillate. See also Fig. 7 for the potentially oscillating modes. For more information to the gain profile and gain bandwidth see 8
9 Figure 6: Depicted are the first six longitudinal modes in a cavity (origin: org/wiki/longitudinal_mode). In the frequency domain: gain of the amplifying medium losses c 2L potential oscillating modes n Figure 7: The combination of the gain profile and the longitudinal modes yield to possible longitudinal modes existing in a resonator. 9
10 2.5 Optical elements for wavelength selection Brewster s angle Let us consider an electromagnetic wave with its polarization oriented parallel to the plane of incidence. There exists an incidence angle, called Brewster s angle, for which no reflection occurs, considering this particular polarization state. (a) (b) Figure 8: (a) Illustration of the polarization states of light which incidence on an interface at Brewster s angle. (origin: (b) Reflection coefficient for different angles of incidence (origin: equation). If the incident angle is equal to Brewster s angle the reflected and transmitted beams are perpendicular to each other (Fig. 8). Hence, by using the law of refraction n 1 sin θ B = n 2 sin θ one may easily calculate the Brewster s angle by Transmission grating θ B = arctan n 2 n 1. (13) When a wave propagates, each point on the wavefront can be considered to act as a point source, and the wavefront at any subsequent point can be found by adding up the contributions from each of these individual point sources. Here, an idealized grating is considered, which is made up of a set of long and infinitely narrow slits with the spacing g. When a plane wave with a wavelength λ incidence normally on the grating, each slit acts as a line of point sources. The light in a particular direction, ϕ, is made up of the interfering components from 10
11 each slit (Fig. 9). Due to the difference in phase the waves from different slits mainly cancel one another partially or completely. However, when the path difference between the light from adjacent slits is equal to the wavelength, λ, the waves are all in phase. Thus, the diffracted light will have maxima at angles ϕ m given by the grating equation g sin ϕ m = mλ, (14) with m as an integer and g being the separation of the slits. The light that corresponds to direct transmission is called the zero order, and is denoted m = 0. The other maxima occur at angles which are represented by non-zero integers m. Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam. Figure 9: Diffraction of light by a transmission grating, with g being the slit separation and ϕ the diffraction angle. (origin: Beam parameter product The beam parameter product (BPP) is the product of the beam radius w at its narrowest position times the divergence angle θ (half-angle). The BPP can be used to quantify the beam quality. It also determines how good the beam can be focused to a small spot size. Because the BPP (BPP = θ w = M 2 λ π ) is dependent on the wavelength, a pre-factor M2 is inserted, called beam quality factor. The beam quality factor ranges from 1 to infinity where M 2 = 1 represents the optimum beam quality (perfect Gaussian) and higher M 2 correlates to worse beam quality (mostly due to higher mode content). 11
12 2.7 Measurement of the beam quality factor M 2 (Task 8) Determine the quality parameter M 2 with the help of a convex lens with a focal length f = 125 mm and a camera. Basic equations: 1) I(r, z) = I 0 ( w0 w(z) 2) w(z) = w ( z z R ) 2 3) z R = πw 2 0 λ ) 2 exp ( 2 r 2 w(z) 2 ) w 0 1 e 2 beam radius z R Rayleigh length, z axial position λ wavelength 4) θ 0 = w(z) z = w 0 z R θ 0 divergence angle (half angle) in far field 5) BPP fund = θ 0 w 0 = λ π Beam parameter product for fundamental mode 6) BPP = M 2 λ π = θ measuredw measured General beam parameter product M 2 unitless value concerning the second moment width of the beam Procedure of evaluation: a) Focus laser beam with 125 mm lens! b) Capture images with CMOS-camera (pixel pitch distance 5.2 µm) at 35 different positions (Avoid overexposure by using gray filters!): i. 20 points with increment of 5 mm ii. 10 points with increment of 10 mm iii. 5 points with increment of 50 mm c) Find center of gravity concerning gray values in captured images. d) Make line scan in x-direction crossing the center of gravity. e) Fit a Gaussian ( distribution ) with regards to formula 1) with parameters A, B, and C: A exp 2 (x B)2 to estimate 1 spot radius (C) for every single image. C 2 e 2 f) Reconstruct the caustic (see figure below) of the beam by means of formula 2) to obtain the waist radius (w 0 ) and the beam quality factor M 2 : w 2 (z) = w (M2 ) 2 ( λ πw 0 ) (z z0 ) 2. g) Estimate M 2 and compare it with other laser sources! What is influencing the beam quality? 12
13 Figure 10: Gaussian beam and its fundamental parameters (origin: wiki/gaussian_beam) 3 Setup and equipment The setup consists of the following components shown in Fig. 11: Profile Rail (1) HeNe Laser Tube with power supply (2) Laser mirror adjustment (3 + 4) Photo detector in holder (5) Alignment laser with power supply (6) Birefringent tuner (7) (not used) Littrow prism tuner (8) (not used) Single mode etalon (9) (not used) Set of laser mirrors in holder (10) PLAN - plane mirror R = mirror curvature 1000 mm R = mirror curvature 700 mm OC24 - plane mirror output 2.4 % Grating (600 lines / mm) Mount with thin filament Camera Set of gray filters For the whole setup it is very important that all optic elements are well cleaned and that there is no staining on the optics. DO NOT touch optical surfaces! 13
14 Figure 11: Setup of the used elements (origin: micos He-Ne Laser manual) 3.1 Setup alignment procedure The first task in this lab work is the definition of the optical axis for the laser system. For this purpose an alignment laser should be used. The next step is to adjust the laser mirrors perpendicular to the optical axis so that the back reflected beam hits itself exactly at the beam output aperture. The perfect alignment to the optical axis can be recognized by observing a flickering laser beam caused by interference effects with the plane mirror in the holder. Afterwards, the main laser tube has to be centered in the adjustment beam. Be sure that the Brewster s angle windows of the main laser (2) are well cleaned and its power supply is switched off. The goal is to adjust the main lasers capillary around the optical axis of the adjustment laser. The actual position can be observed at a reflective screen like a piece of white paper. Finally, to get the laser to work arrange the pre-adjusted components 2, 3 and 4 like in Fig. 11. Switch off the adjustment laser 6 and switch on the main laser tube 2. If no laser light can be observed, a gentle twisting of max. ±45 of one of the adjustment screws shown in the draft above cause the oscillation flicker up. If you get the laser oscillation the output power can be optimized with the position of the laser mirrors and supplementary with the x/y-adjustments of the main tube. Afterwards the laser output power has to be optimized. Now you can start with the measurement of the laser output power depending on different laser geometries (task number 4 to 7) For measuring the wavelength the grating and a screen should be used. 14
15 4 Goals of the experimental work In this lab different combinations of mirrors (M1 and M2) are used as resonator. These are: a) M1: plan, M2: R = 1000 mm b) M1: plan, M2: R = 700 mm c) M1: plan, M2: plan d) M1: R = 700 mm, M2: R = 1000 mm Combination c) is only used if enough time is left. 1. (at home, before the lab!) Evaluate the beam width inside the resonator for a resonator length of d = 50 cm. Use all four mirror combinations. 2. (at home, before the lab!) Evaluate the optical stability area with respect to the resonator length d for all given mirror combinations. Therefore, plot the corresponding stability area (g 1 g 2 ) over the distance d for all four mirror combinations. 3. Build up and align a stable running HeNe-Laser out of the given components. For tasks 4, 5, and 6 you can decide to change the order to: 4a), 5a), 6a) followed by 4b) and 5b) so you do not need to realign the laser several times (there is no 6b)!). 4. Measure the dependence of the laser output power on the tube current for d = 50 cm for the mirror combination a) and b). Repeat each measurement twice: once increase the current until upper limit reached afterwards decrease the current to lower limit. Discuss potential deviations between first and second measurement. 5. Measure the dependence of the laser output power on the resonator length for I = 6, 5 ma and the mirror combination a) and b). Start with the setup as in task 4 (d = 50 cm) and only move the left mirror to increase resonator length. For combination a) start with 2 cm steps until rapid changes in output power occur then switch to 1 cm steps. For b) do 1 cm steps. 6. Measure the output power dependence on the laser tube position while using the mirror combination a) and a resonator length of d = 50 cm. 7. Measure the laser wavelength by using the grating. 8. Measure the laser beam quality factor M 2 by using a convex lens (focal length f = 125 mm) and a camera. Reduce the output power with gray filters to avoid overexposure of the camera. See also section 2.7 for detailed description of this task. 9. Additional: Change the setup by using a thin filament in order to achieve higher TEM modes. 15
16 A Preliminary questions You should be able to answer these questions but be also prepared to answer additional questions, mainly related to the keywords below. What kind of Laser is used for this experiment? What are the main conditions for stable laser operation? Is the used laser radiation polarized and if so in which direction? Why? Determine Brewster s angle for air - fused silica transition? What is the meaning of the stability area of two mirrors? Can you use one mirror with negative curvature? Which parameters are important to achieve high laser output? How can you achieve different output wavelengths of the laser? How can you measure this? What kind of resonator modes exist in a stable laser setup? How can you influence the output mode of a laser? Keywords resonator, polarization, wavelength, frequency, laser, gauss beam, resonator modes, beam parameter product 16
17 B Final questions (to be answered in the introduction/discussion section of the report (indirect, not explicit)!) These questions are intended to help you to check if your report includes the most important information beside the tasks. Do not copy these questions to your report! What is the used setup? How does a HeNe-Laser works? How can you achieve a stable running HeNe-Laser? What can you say about the polarization? Which parameters of the laser geometry can you change? What consequences have these changes? What can you say about the laser wavelength? What is the content of gaussian optics? Which optical elements have you used and how did they work? What is the beam parameter product (BPP)? What is described by beam quality factor M 2? 17
18 References [1] Young, M.: Optics and lasers: including and optical waveguides. 4th edition. Springer, Berlin, 1993 [2] Saleh, B. E. A. ; Teich, M. C.: Fundamentals of Photonics (Wiley Series in Pure and Applied Optics). 2nd edition. JohnWiley & Sons, Hoboken, New Jersey, 2007 [3] Homepage of wikipedia URL=< [4] Träger, F.: Springer handbook of lasers and optics, (Springer). 1st Edition [5] Homepage and encyclopedia of the RP Photonic Consulting GmbH URL=< [6] Svelto, O.: Principles of Lasers [7] Siegman, E.: Lasers, University Science Books (January 1986) 18
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