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Module Labworks Optics Abbe School of Photonics, Friedrich-Schiller-Universität, Physikalisch-Astronomische-Fakultät, Max-Wien-Platz 1, 07743 Jena, Germany Phone: +49 3641 947 960 Fax: +49 3641 947 962 E-mail: [email protected] Web : www.asp.uni-jena.de Contact person: Dr. Roland Ackermann Phone : +49 3641 947 821 E-mail : [email protected] Supervisor: Christoph Stihler ([email protected]), Thorsten Goebel ([email protected]) Helium Neon Laser [ version of February 22, 2017] Contents 1 Safety issues 1.1 Eye hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Chemical hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theoretical basics 2.1 Helium Neon Laser . . . . . . . . . . . . . . . . . . 2.2 Basics of resonator modes . . . . . . . . . . . . . . 2.3 Transversal modes in a laser resonator . . . . . . . . 2.4 Optical elements for wavelength selection . . . . . . 2.4.1 Brewster’s angle . . . . . . . . . . . . . . . 2.4.2 Fabry Perot Etalon . . . . . . . . . . . . . . 2.4.3 Littrow prism . . . . . . . . . . . . . . . . . 2.4.4 Birefringent filter . . . . . . . . . . . . . . . 2.4.5 Transmission grating . . . . . . . . . . . . . 2.5 Measurement of the beam quality factor M 2 (Task 8) . . . . . . . . . . 3 3 4 6 8 8 9 9 9 10 12 3 Setup and equipment 3.1 Setup alignment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Further adjustment of the optical elements . . . . . . . . . . . . . . . 13 14 14 15 4 Goals of the experimental work 17 A Preliminary questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 18 B Final questions (to be answered in the introduction/discussion section of the report!) 18 He Ne Laser 1 Safety issues 1.1 Eye hazard The laser system used is classified according to DIN IEC 60825-1 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.). 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. 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 632.816 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 23 S1 and 21 S0 metastable excited states. Collision of the excited helium atoms with the ground-state neon atoms results in transfer of energy to the neon atoms, exciting neon electrons into the 3S2 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 3s2 and 2p4 states results in emission of 632.82 nm wavelength light. After this, fast radiative decay occurs from the 2p to the 1s 3 He Ne Laser Figure 1: Energy level diagram of a He Ne system (origin: http://en.wikipedia.org/wiki/ File:Hene-2.png) 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 TEM00 mode is described by a gaussian profile in the following way I(r, z) = I0 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/e2 , see Fig. 2) increases with increasing distance from the beam waist. In a certain distance z the beam width w(z) is given by v t λz 2 (2) w(z) = w0 1 + 2 . πw0 4 Abbildung A.1 zeigt den Längsschnitt eines solchen Strahl mit Ta Abbildung A.1: Längsschnitt eines Gaussschen Strahls. Strahls. Abbildung A.1: Längsschnitt eines Gaussschen verdeutlicht die Bedeutung oben eingeführten Größen.Strahls. Zusätzlich Abbildung A.1:der Längsschnitt eines Gaussschen Abbildung A.1: Längsschnitt eines Gaussschen kel θ0 eingezeichnet, welcher die lineare Aufweitung des Strahl im Abbildung A.1 zeigtA.1 denzeigt Längsschnitt eines solchen Strahl mit Taille bei z0w0=bei 0u Abbildung den den Längsschnitt eineseines solchen Strahl mitw0Taille Abbildung zeigt Längsschnitt solchen Strahl mit Taille w0 schreibt.A.1 Abbildung A.1 zeigt den Längsschnitt eines m verdeutlicht die Bedeutung der obender eingeführten Größen. Zusätzlich istsolchen der Divergenzw verdeutlicht die Bedeutung oben eingeführten Größen. Zusätzlich istStrahl der He Ne Laser verdeutlicht die Bedeutung der oben eingeführten Größen. Zusätzlich ist Div der verdeutlicht diedie Bedeutung der oben eingeführten Größen. kel θ0 eingezeichnet, welcher die lineare Aufweitung des Strahl Fernfeld z Zusä zR z kel θkel welcher lineare Aufweitung desim Strahl im Fernfeld 0 eingezeichnet, θ0 eingezeichnet, welcher die lineare Aufweitung des Strahl im Fernf √ kel θ0 eingezeichnet, welcher die lineare Aufweitung des Stra schreibt.schreibt. w(z) w0 θ0 z zr 2 w0 schreibt. schreibt. w(z) w(z) √ A Gausssche √ √ Anhang Strahlen und Strahlqualitä w θ z z 2r w0 (A 0 00 rz w(z) w θ z 2 w √ 0 0 w(z) w0 θ0 z zr 2 w0 w(z) w0 θ0 z zr 2 w0 w0 θ0 z zR √ 2 w0 (A.9 Figure 2: Gaussian beam width w(z) as a function of the axial distance z. w0 : beam waist; zR : Rayleigh range; θ: total angular spread (origin: http://en.wikipedia.org/wiki/Gaussian_beam) 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 2 2 πw R(z) = z 1 + 0 . (3) λz In a confocal resonator (the focal points of both mirrors are at the same point, see Fig. 3) the beam waist is in the middle of the resonators with the distance d between the mirrors and the beam waist is given by r λd w0 = . (4) 2π In a non-confocal resonator the stability parameters g1 and g2 have to be defined g1 = 1 − (d/R1 ) g2 = 1 − (d/R2 ), (5) whereas d is the resonator length and R1 and R2 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 beam front in two planes, which we name z1 (distance of the beam waist to mirror 1) and z2 (distance of the beam waist to mirror 2). If one claims R(z1 ) = R1 and R(z2 ) = R2 the position of the beam waist can be evaluated z1 = g2 (1 − g1 ) d, g1 + g2 − 2g1 g2 (6) 5 He Ne Laser and the radius of the beam waist is given by λd w0 = π !1/2 g1 g2 (1 − g1 g2 ) (g1 + g2 − 2g1 g2 )2 !1/4 . (7) The so called stability area is defined by 0 < g1 · g2 < 1. (8) Within this region of resonator parameters stable mode structure is guaranteed. If g1 · g2 is >1 the spot size is imaginary or infinity. If g1 · g2 '1 the spot size may be greater than the resonators, resulting in significant losses, what means mode instability. Figure 3: Stability diagram for a two-mirror cavity. Blue-shaded areas correspond to stable configurations. (origin: http://en.wikipedia.org/wiki/Optical_cavity) 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 centre of the mode is given by I pl (ρϕ) = I0 ρl [Llp (ρ)]2 cos2 (lϕ)e−ρ , (9) 6 He Ne Laser where ρ = 2r2 /w2 , and Llp 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 TEM00 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 TEM00 mode, and thus, the fundamental Gaussian mode of a laser may be selected by placing an appropriately sized aperture in the laser cavity. Figure 4: Rectangular transverse mode patterns TEMmn (origin: http://en.wikipedia.org/ wiki/Transverse_mode) 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. 4). These modes are designated TEMmn with m and n being the horizontal and vertical orders of the pattern. The intensity at point (x, y) is given by √ !2 √ !2 2x −x2 2y −y2 , Imn (x, y) = I0 Hm Hn exp exp w w w2 w2 (10) 7 He Ne Laser where Hm (x) is the m-th order Hermite polynomial. The TEM00 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 Optical elements for wavelength selection 2.4.1 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 5: (a) Illustration of the polarization states of light which incides on an interface at Brewster’s angle. (origin: http://en.wikipedia.org/wiki/Brewster_angle) (b) Reflection coefficient for different angles of incidence (origin: http://en.wikipedia.org/wiki/Fresnel_ equation) If the incident angle is equal to Brewster’s angle the reflected and transmitted beams are perpendicular to each other (Fig. 5). Hence, by using the law of refraction n1 ·sin θB = n2 ·sin θ one may easily calculate the Brewster’s angle by θB = arctan n2 . n1 (11) 8 He Ne Laser 2.4.2 Fabry Perot Etalon A Fabry Perot Etalon consists of two exactly parallel high reflective mirrors. Transmission of light by a given wavelength λ occurs only if mλ = 2nl cos θ, (12) with l being the distance between the two mirrors and θ being the angle between the optical axis and the surface normal of the mirrors (Fig. 6). Hence an Etalon is capable to separate different wavelengths by either tilting the etalon or increasing the distance of the mirrors. The etalon used in this lab has a aperture of 12.7 mm and a thickness of l = 10 mm. Figure 6: Light enters the etalon and undergoes multiple internal reflections. (origin: http://en. wikipedia.org/wiki/Fabry_Perot) 2.4.3 Littrow prism A Littrow prism is a prism with a mirror at one surface. Due to the wavelength depending refraction of the prism each laser wavelength will propagate at a certain direction trough the prism and hit the mirror at a different angle. So only one wavelength will be back reflected into the incidence beam. Therefore one may separate wavelengths by tilting the Littrow prism in the light path (Fig. 7). 2.4.4 Birefringent filter Here another effect is used to select different wavelengths. In a birefringent crystal the optical properties, as the index of refraction, vary with the direction of the incoming beam. In the simplest case an anisotropic crystal has one axis of symmetry, called the optic axis. For propagation parallel to the optic axis the index of refraction is independent of the oscillation 9 He Ne Laser Figure 7: If a shaft of light entering a prism is sufficiently narrow, a spectrum results. (origin: http: //en.wikipedia.org/wiki/Prism_(optics)) direction of the E-field vector. If the propagation has another direction the incident light is split into the ordinary and extraordinary beam. Each of them experiences another index of refraction (no and ne ) depending on the angle of incidence. Also the two beams propagate in different directions, according to their index of refraction and the direction of the optic axis. In this lab, the optic axis is parallel to the surface of the quartz crystal in use. Hence, the ordinary and extraordinary beam have a different index of refraction but no walk off occur. Thus the quartz crystal may be used as phase plate. Here we may separate the incident E-field vector into one component parallel and one perpendicular polarized to the optic axis. The component Ee , which is parallel to the optic axis, will propagate as extraordinary wave with the index of refraction ne and the other one as ordinary wave Eo with no . If no > ne the two beams will have, after a certain propagation distance d, a phase difference of (no − ne ) · d. If this phase difference is equal π/2 and the amplitude of the ordinary and extraordinary beam are equal the phase plate converts linear polarized light into circular polarized light. Such a phase plate is called λ/4-plate. After another transition the light is again linear polarized. Since each wavelength has a different index of refraction only a certain wavelength will be linear polarized after two transitions through a λ/4-plate. 2.4.5 Transmission grating 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 incides 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 each slit (Fig. 8). Due to the difference in phase the waves from different slits mainly cancel one 10 He Ne Laser 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 ϕm given by the grating equation g sin ϕm = mλ , (13) 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 8: Diffraction of light by a transmission grating, with g being the slit separation and ϕ the diffraction angle. (origin: http://de.wikipedia.org/wiki/Optisches_Gitter) 11 He Ne Laser 2.5 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: w0 2 r2 exp −2 2 w(z) w(z) 1) I(r, z) = I0 2) q 2 w(z) = w0 1 + zzR 3) zR = 4) θ0 = 5) BPPfund = θ0 w0 = 6) BPP = M 2 λπ = θmeasured wmeasured πw02 λ w(z) z w0 → 1 e2 beam radius zR → Rayleigh length, z → axial position λ → wavelength = w0 zR θ0 → divergence angle (half angle) in far field λ π Beam parameter product for fundamental mode 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: (x−B)2 A · exp −2 C 2 to estimate e12 spot radius (C) for every single image. f) Reconstruct the caustic (see figure below) of the beam by means of formula 2) to obtain the waist radius (w0 ) and the beam quality factor M 2 : w2 (z) = w02 + (M 2 )2 πwλ 0 (z − z0 )2 . g) Estimate M 2 and compare it with other laser sources! What is influencing the beam quality? 12 He Ne Laser Figure 9: Gaussian beam and its fundamental parameters (origin: https://en.wikipedia.org/ wiki/Gaussian_beam) 3 Setup and equipment The setup consists of the following components shown in Fig. 10: • 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) • Littrow prism tuner (8) • Single mode etalon (9) • Set of laser mirrors in holder (10) – PLAN - plane mirror – R = 1000 - mirror curvature 1000 mm – R = 700 - mirror curvature 700 mm – OC24 - plane mirror output 2.4 % • Grating (600 lines / mm) • Translation stage with thin filament For the whole setup it is very important that all optic elements are well cleaned and that there is no staining on the optics. 13 He Ne Laser Figure 10: Setup of the used elements (origin: micos He-Ne Laser manual) 3.1 Setup alignment procedure 3.1.1 Basics 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. 10. 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 He Ne Laser 3.1.2 Further adjustment of the optical elements Littrow prism The adjustment of the Littrow prism can be done with the same procedure like the laser mirrors were adjusted. Afterwards, the parts 2 and 3 can be assembled again and the main laser can be switched on. The cleaning of the optics is tremendously important. If the laser starts oscillating, optimize it for best intensity. The laser line tuning can be done with the adjustment screws of the Littrow prism mount. Birefringent filter (BFP) Rotate the birefringent filter (8) in its mount to Brewster’s angle. Insert the birefringent filter (8) between the adjustment laser (6) and one plane mirror (4). Repeat the alignment of the laser mirror to eliminate the beam displacement caused by the inserted optics. After that the set-up can be completed again. Another way would be to directly place the BFP in the adjusted laser. With a gentle twist of one of the adjustment screws, the laser may start again. However, this procedure is very sensitive and only possible, when the laser runs at the highest output power. If the BFP is rotated around it optical axis you can see the main line several times. If the birefringent filter is rotated in small angles around one main line you can get additional wavelengths with different gains as well. Etalon The Etalon (9) will be placed on the rail instead of the BFP (8). If put into the resonator the laser normally keeps its oscillation more or less strong. By observing the back reflections at the mirror surface (3) you can identify a non perpendicular adjustment when several spots are visible. The zero order adjustment is achieved if all reflections fall into the beam of the main laser. Other orders can be adjusted by tilting the etalon holder (9). The realization of another laser wavelength than the main wavelength is very difficult and sensitive. At first try to maximize the output power. By using the 700 mm curvature mirror and the 2.4 % transmission mirror, an output of 3.5 mW is possible. Also by using the BFP an output power of 3 mW is possible. At such a high output power it is easy to get laser oscillation at different wavelengths. At an output power which is lower than 3 mW the gain of a wavelength different from the main wavelength may be to low to compensate the losses within the resonator. The birefringent filter should be used at first. After the BFP is build into the resonator and the laser is running, one may see the main line up to four times. The strongest one should be chosen and the laser should be optimized again. If the birefringent filter is rotated in small angles around the chosen main line one can get additional wavelength with different gains. One may switch between different laser wavelengths by using the grating, as the position of the diffracted beam depends on the wavelength used. With the Littrow prism one can see the change of wavelength easily because the color changes from red to orange. Here the Littrow prism should be used instead of the output coupler to- 15 He Ne Laser gether with the 700 mm curvature mirror. Keep the distance between the prism and the laser tube as short as possible and minimize the resonator length. Afterwards you can place the grating behind the curved mirror and use this faint laser output for the wavelength selection. The Etalon will be places on the rail instead of the BFP. When inserted into the resonator the laser normally keeps its oscillation more or less strong. By using the Etalon one may find another wavelength only if the Etalon is placed exactly perpendicular into the beam. That is the case if no back-reflection occurs. The zero order adjustment is achieved when all reflections fall into the beam of the main laser. Afterwards one may switch to different wavelengths by slightly tilting the etalon. 16 He Ne Laser 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 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 (g1 · g2 ) over the distance d for all four mirror combination. 3. Build up and align a stable running HeNe-Laser out of the given components. 4. Measure the dependence of the laser output power on the tube current for d = 50 cm for the mirror combination a) and b). 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). 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. 9. Additional: Change the setup by using a thin filament in order to achieve higher TEM modes. 17 He Ne Laser A Preliminary questions • 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? • Which parameters are important to achieve high laser output? • How can you achieve different output wavelengths of the laser? How can you measure this? Keywords resonator, polarization, wavelength, frequency, laser, gauss beam B Final questions (to be answered in the introduction/discussion section of the 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? 18 He Ne Laser 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=<http://www.wikipedia.org/>, 2007-10-06 [4] Träger, F.: Springer handbook of lasers and optics, (Springer). 1st Edition 2007. [5] Homepage and encyclopedia of the RP Photonic Consulting GmbH URL=<http://www.rp-photonics.com/encyclopedia.html> [6] Svelto, O.: Principles of Lasers [7] Siegman, E.: Lasers, University Science Books (January 1986) 19