EXPERIMENT 06. Helium Neon Laser. γ ε. Littrow Prism. Prism. Mirror Coating β. Arrangement within the Laser Resonator. Collision He->Ne 3 2 S nm - PDF

-POWER γ HVPS-06 Helium Neon 0 S 0 Collision He- Ne 3 S 63 nm 3s Laser transition Energy ev 9 8 Electron Impact p spontaneous Emission 7 0 S 0 s recombination impact F A B C

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-POWER γ HVPS-06 Helium Neon 0 S 0 Collision He- Ne 3 S 63 nm 3s Laser transition Energy ev 9 8 Electron Impact p spontaneous Emission 7 0 S 0 s recombination impact F A B C D E EXPERIMENT 06 H G TC-0 P Helium Neon Laser Prism Littrow Prism Mirror Coating β α ε γ ε β α Arrangement within the Laser Resonator INTRODUCTI 3 FUNDAMENTALS 3. He-Ne energy- level diagram 3. Amplification of the Neon atoms.3 Resonators 8.4 Laser tubes and Brewster windows 9. Wavelength selection 9.. Littrow prism 9.. Birefringent crystal 9..3 Jones Matrix Formalism 0.6 Mode selection 3.7 Bibliography 3 3 EXPERIMENT 3 3. Optical stability 3 3. Gaussian beams Measurements 3.3 Output power 3.4 Mode structure 3. Wavelength selection 3.. Dispersive elements (prisms) Diffractive elements Interfering elements Elements sensitive to polarisation Littrow prism Birefringent crystal Single mode operation with Etalon Operation with infrared lines 7 4 UNPACKING 7 SET-UP AND COMPENTS USED 8. Basic alignment 0. Alignment of the birefringent Tuner.3 Alignment of the Littrow Prism Tuner 4.4 Alignment of the Fabry-Perot Etalon. The tube controller TC 0 6 He-Ne energy- level diagram Introduction The Helium-Neon laser was the first continuous laser. It was invented by Javan et. al. in 96. Nowadays lasers are usually pre-adjusted using a He-Ne laser. But how did Javan manage to do this? This shows that it is no coincidence that Javan's first He-Ne laser oscillated at a wavelength of.µm, since the amplification at this wavelength is considerably higher than the 63 nm line which is reached at what is now commonly known as the red line, which was made to oscillate only one year later by White and Ridgen. The similarity between the manufacturing techniques of He- Ne lasers and electron valves helped in the mass production and distribution of He-Ne lasers. The replacement of tubes by transistors in the sixties left a sufficiently redundant production capacity. In Germany for example, the Siemens tube factory took over this production and has produced over one million He-Ne lasers to date. It is now clear that He-Ne lasers will have to increasingly compete with laser diodes in the future. But He-Ne lasers are still unequalled as far as beam geometry and the purity of the modes are concerned. Laser diodes will have to be improved to a great extent before they pose a serious threat to He-Ne lasers. Fundamentals. He-Ne energy- level diagram The fascination for inert gases and their clear atomistic structure formed the basis for many spectroscopic investigations. The knowledge obtained through spectroscopic data was extremely helpful in deciding to choose helium and neon for the first lasers, using Schawlow Towne's discovery of lasing conditions in 98 to estimate whether an inversion was feasible in laser operation. The lifetime of the s- and p-states were well known. Those of the s-states were longer than those of the p-states by a factor of about 0. The inversion condition was therefore fulfilled. the excitation and laser processes at a wavelength of 63 nm are indicated. The left side of the representation shows the lower levels of the helium atoms. Observe how the energy scale is interrupted and that there is a larger difference in energy in the recombination process than is evident in the diagram. Paschen's names for the neon energy levels are used (Racah's term descriptions are often found as well). The terms are simply numbered consecutively, from bottom to top. A characteristic of helium is that its first states to be excited, S and S 0 are metastable, i.e. optical transitions to the ground state S 0 are not allowed, because this would violate the selection rules for optical transitions. As a result of gas discharge, these states are populated by electron collisions (collision of the second type, Fig. ). A collision is called a collision of the second type if one of the colliding bodies transfers energy to the other so that a transition from the previous energy state to the next higher or lower takes place. Apart from the electron collision of the second type there is also the atomic collision of the second type. In the latter, an excited helium atom reaches the initial state because its energy has been used in the excitation of a Ne atom. Both these processes form the basis for the production of a population inversion in the Ne system. befor collision after collision S 0 S 0 S 0 Energy ev S 0 Helium 3s 3 S 63 nm Electron Impact S 0 Collision He- Ne s Neon Laser transition p spontaneous Emission recombination impact Fig. : Excitation and Laser process for the visible Laser emission Fig. shows the reduced energy-level diagram for helium and neon. Only those levels important in the discussion of Electron Helium Atom S 0 Fig. : Electron collision of the second kind If we look at Fig. we can see that the S 0 is slightly below the 3s level of the neon. However, the additional thermal energy kt is sufficient to overcome this gap. As already mentioned, the lifetime of the s-states of the neon are approximately 0 times longer as those of the p- states. An immediate population inversion between the 3s and the p levels will therefore be generated. The s level is emptied due to spontaneous emission into the s level. After this the neon atoms reaching their ground state again, primarily through collisions with the tube wall (capillary), since an optical transition is not allowed. This calming down process is the bottle neck in the laser cycle. It is therefore advisable to choose a capillary diameter that is as small as possible. However, the laser will then suffer more losses. Modern He-Ne lasers work at an optimum of these contradictory conditions. This is the main reason for the comparatively low output of He-Ne lasers. Page - 3 - He-Ne energy- level diagram We have discussed the laser cycle of the commonly known red line at 63 nm up to this point. However the neon has several other transitions, used to produce about 00 laser lines in the laboratories. The following explanation describes the energy-level diagram for further visible lines. After that infrared laser transitions will be discussed. 3s s p nm 3. nm.6 nm Red Green Fig. 3: The most important laser transitions in the neon system The 3s state is populated by Helium atoms of the S 0, state as a result of an atomic collision. The 3s state consists of 4 sub-states out of which it is primarily the 3s state which has been populated through the collision process. The population density of the other 3s sub-states is app. 400 times less than that of the 3s state. The s state is populated by the Helium atoms of the 3 S, as a result of an atomic collision. The four sub-states of the s group are all populated in a similar way. Visible (VIS) optical transitions and laser processes are taking place between the 3s pi and infrared (IR) between the si pi energy levels. The following table shows the most important laser transitions. The Einstein coefficients A ik are given for the visible lines and amplification is indicated as a percentage per meter. Further laser transitions are known, which start at the 3s level and terminating at the 3p level of the neon. However, these laser transitions lie even further within the infrared spectral range and cannot be detected with the silicon detector used in the experiment. They are not particularly suitable for experiments. Notice that these lines are originating from the same level as the visible lines and are therefore competing with them. Since the cross-section of the stimulated emission is increasing with λ 3 as well, the amplification of these lines is therefore very strong. This applies to the 3.39 µm line in particular, which, due to a sufficiently long capillary, shows laser activity (so called super fluorescence) even without an optical resonator. Transition Wavelength A ik Gain [nm] [0 8 s - ] [%/m] 3s p ,00, 3s p ,039 4,3 3s p ,0034,0 3s p ,0339 0,0 3s p ,00639,9 3s p ,006,7 3s p ,0000 0,6 3s p ,00 0, 3s p9 3s p ,0083 0, s p 3. s p 77.0 s p3 60. s p4.6 s p 4. s p s p s p s p9 s p s3 p 98.8 s3 p 6.7 s3 p Table : Transitions and Laser lines Laser transitions are demonstrated in the experiment if laser tube is supplied with perpendicular or Brewster windows Laser transition is demonstrated if laser tube is supplied with Brewster windows and special set of mirrors Laser transitions are demonstrated in the experiment if laser tube is supplied with Brewster windows and IR mirror set Transition not allowed Appropriate measures must be taken to suppress the super fluorescence to avoid a negative influence on the visible laser lines. Mirror Capillary Cathode Quartz glass Metal He Ne Gas Reservoir Fig. 4: Modern He-Ne laser with glass-to-metal soldering of the anode, cathode and laser mirror Fig. 4 shows a modern laser tube made with highly perfected manufacturing techniques and optimised to suit the physical aspects of the laser. This applies to the resonator in particular, which is designed for a best possible Page - 4 - Amplification of the Neon atoms output in the fundamental mode with a purely Gaussian beam and spectral purity in single mode operation (e.g. for interferometric length measurement). The fulfilment of this demand depends, amongst other aspects, on the optimal adaptation of the resonator to the amplification profile of the Neon. The behaviour of Neon during amplification will therefore be discussed first.. Amplification of the Neon atoms The Neon atoms move more or less freely in the laser tube but at different speeds. The number N of neon atoms with the mass m, within a speed interval of v to v+dv is described according to the Maxwell-Boltzmann distribution (Fig. ). n(v) 4 v = e N 3 π (kt / m) mv kt T is the absolute temperature and k Boltzman s constant The above equation is applicable for all directions in space. However, we are only interested in the distribution of speed in the direction of the capillary. Using v = v x + v y + v z we obtain for the direction x: mv kt n(v x ) = kt / m e dv Eq.. x N A resting observer will now see the absorption or emission frequency shifted, due to Doppler's effect (Ch.Doppler: Abh. d. K. Boehmischen Ges.d.Wiss. (). Vol.II (84) P.46), and the value of the shift will be: v v = 0 assuming v c Eq.. ± v/c ν 0 is the absorption or emission frequency of the resting neon atom and c the speed of light. If the Doppler equation (Eq..)is used to substitute the velocity v in the Maxwell- Boltzmann s velocity distribution (Eq..) the line broadening produced by the movement of Neon atoms can be found. Since the intensity is proportional to the number of absorbing or emitting Neon atoms, the intensity distribution will be: I(v) = I(v ) e 0 v v0 c v 0 v w dv Eq..3 kt v w is the most likely speed according to: vw = m Propability K 373 K 473 K Fig. : Probability Distribution for the velocity v of the neon atoms at an interval v to v + dv. The full width at half maximum is calculated by setting I(ν)=/ I(ν 0 ) and the result is: vw vdoppler = 4 ln v0 Eq..4 c We can conclude from Eq..4 that the line broadening caused by Doppler's effect is larger in the case of: higher resonance frequencies ν 0 or smaller wavelengths (ν 0 =c/λ 0, UV-lines) higher most likely velocity v w that means higher temperature T and smaller in the case of: a larger particle mass. The line profile also corresponds to a Gaussian distribution curve (Eq..3). Fig. 6 shows this kind of profile. The histogram only approaches the distribution curve when the speed intervals dv are small. rel. Intensity dv v=0 FWHM Velocity v Fig. 6: Inhomogeneous line profile, speed intervals dv Why these speed intervals dv or frequency intervals dν you may ask. Actually there are formal reasons for this. Not having any intervals at all would be like wanting to make a statement on fishing out a particle with an exact speed or frequency from the ensemble. It is almost impossible to do. So, we define finite probabilities of ensembles by using intervals. If we succeed in this, we can make the intervals smaller and work with smooth curves . On closer observation we can see that a line broadened by the Doppler effect actually does not have a pure Gaussian distribution curve. To understand this, we pick out an ensemble of Ne atoms whose speed components have the value v in the direction we are looking at. We expect that all these atoms emit light with the same frequency ν or wavelength λ. But we have to consider an additional effect which is responsible for the natural linewidth of a transition. We know that each energy level poses a so called life time. The population n of a state decays into a state with lower energy with a time constant τ s following the equation : v w Velocity of Ne atoms in m/s A n(t) n(t 0)e t = = with τ s = /A Page - - Amplification of the Neon atoms A is the famous Einstein coefficient for the spontaneous emission. The emission which takes place is termed as spontaneous emission..0 Fig. 8: Natural linewidth (FWHM) caused by spontaneous emission.0 rel. Population Density 0. n/n 0 =/e rel. Intensity t=/a Time t Fig. 7: Decay of the population of state into a state with lower energy This shows us, that the ensemble of Ne atoms does not emit light at a single frequency. It emits a frequency spectra represented by an Lorentz profile (Fig. 8). δ (v) =, ν 0 ν 4 π (v v ) + (/ τ ) s The exact profile formation can be determined from the convolution of the Gaussian profile with the individual Lorentz profiles. The result obtained in this manner is called as the Voigt profile. Since one group of particles in an ensemble can be assigned to a given speed v, these groups have characteristics that differentiate them. Every group has its own frequency of resonance. Which group a photon interacts with depends on the energy (frequency) of the photon. This does not affect the other groups which are not resonant on this interaction. Therefore such kind of a gain profile is termed inhomogeneous. 0.0 v=0 Fig. 9: Natural broadened line profiles (homogeneous) for groups of speed v within the inhomogeneous Doppler broadened gain profile As we already know gain occurs in a medium when it shows inversion. This means that the population density of the upper level n (3s in the Ne-system) is larger than the population density of the lower state n (p). In Fig. 0 the population profiles are rotated by 90 to draw them in the well known energy level diagram. Transition can only take place between sub-ensembles which have the same velocity v because the optical transition does not change the speed of the particular Ne atom. Energy 3s Transistion n rel. Amplitude ρ(ν) FWHM δν p n Population density ν 0 Frequency ν Fig. 0: Population inversion and transition between sub-ensembles with same velocity v The situation of Fig. 0 shows a population inversion n n. Besides some specific other constants the gain is Page - 6 - Resonators proportional to the difference n - n. Now we will place the inverted ensemble of Ne atoms into an optical cavity, which is formed by two mirrors having the distance of L. Due to the spontaneous emission photons are generated which will be amplified by the inverted medium and reflected back from the mirrors undergoing a large number of passes through the amplifying medium. If the gain compensates for the losses, a standing laser wave will be built up inside the optical resonator. Such a standing wave is also termed as oscillating mode of the resonator also eigenmode or simply mode. Every mode must fulfil the following condition: λ c L= n or L= n v L represents the length of the resonator, λ the wavelength, c the speed of light, ν the frequency of the generated light and n is an integer number. Thus every mode has its frequency of c v(n) = n L A λ/ n λ/ n+3 speaking, a resonator has an indefinite amount of modes, whereas the active material only emits in an area of frequency determined by the emission line width. Fig. shows the situation in the case of material that is inhomogeneously broadened. Inhomogeneous Gain Profile n-6 n- n-4 n-3 n- n- n n+ n+ n+3 n+4 n+ n+6 ν Resonator Modes Fig. : Inhomogeneous gain profile (Gaussian profile) interacting with an optical resonator If the laser is operating in a stationary state, we can see that it is emitting several longitudinal modes. These are exactly the same modes that will be found in the emission profile. Since the modes are fed by an inhomogeneous emission profile they can also exist independently. The He-Ne-Laser is a classic example of this. B L Fig. : Standing longitudinal waves in an optical resonator. A with n nodes and B with n+3 nodes e.g. A He-Ne-Laser with a resonator length of 30 cm at an emission wavelength λ of 63.8 nm will have the following value for n: v L 0,3 n = L = = = c λ 63,8 0 The difference in frequency of two neighboured modes is: c c c v = v(n + ) v(n) = (n + ) n = L L L In the above example the distance between modes would be 8 30 v = = 0,3 8 0 Hz=00 MHz If the active laser material is now brought into the resonator standing waves will be formed due to the continuous emission of the active material in the resonator and energy will be extracted from the material. However, the resonator can only extract energy for which it is resonant. Strictly Page - 7 - Resonators.3 Resonators In the following section some fundamentals used in the description and calculation of optical resonators will be introduced. Stability diagrams, the beam radius and beam sizes for the resonator types used in later experiments will be calculated and discussed. The investigations and calculations will be carried out for an empty resonator since the characteristics of the resonator will be particularly influenced (e.g. thermal lenses, abnormal refractive index etc.). The ABCD law will be introduced and used in this context. Just like the Jones matrix formalism this type of optical calculation is an elegant method of following the beam (ray tracing) in a complex optical system. Fig. 3 shows that an identical lens system can be constructed for every optical resonator. The beam path of the resonator can be traced using the ABCD law, aided by an equivalent lens system. So, how does the ABCD law work? First we must presume that the following calculations are correct for the limits of geometric optics, that is if the beam angle is to the optical axis, close to sinα α. This has been fulfilled in most systems, especially for laser resonators. A light beam is clearly defined by its height x to the optical axis and the slope at this f R L=R L= f Fig. 3: Spherical resonator with equivalent lens guide point (Fig. 4). A B X α α X f Y α α X Fig. 4: (A) light beam with the characteristic parameters, (B) Trace through a lens. f R X The matrix to be introduced is called the beam transfer matrix or ABCD matrix. When this matrix is applied to the input quantities x and α the resulting output quantities will be x and α : x A B x = α C D α Example A in Fig. 0 shows the free propagation of a beam, from which we can deduce that α = α and x = x +α y. So, the ABCD matrix in this case is: y A = 0 In example B which shows a thin lens the matrix is: 0 B = /f It is easy to understand that the combination of example A and B is a result of free beam propagation with subsequent focusing with a thin lens X = A B X A series of ABCD matrices for different optical elements can be drawn out with this method. They have been compiled by Kogelnik and Li [3]. The above examples are sufficient for the calculation of a resonator. Beams in an optical resonator have to pass through the same optical structure several times. After passing through it n times the ABCD law for a particular place Z of the lens guide (Fig. 3) would be: n n xf A B xi = αf C D αi In this case the ABCD matrix is the identical lens guide given to the resonator. The n-th power of a x matrix is calculated as follows: A B n a b = C D sin( θ) c d a = A sin(n θ) sin(
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