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diff --git a/chapters/HeNelaser.tex b/chapters/HeNelaser.tex new file mode 100644 index 0000000..9918f80 --- /dev/null +++ b/chapters/HeNelaser.tex @@ -0,0 +1,291 @@ +%\chapter*{Helium-Neon Laser} +%\addcontentsline{toc}{chapter}{Helium-Neon Laser} + +\documentclass{article} +\usepackage{tabularx,amsmath,boxedminipage,epsfig} + \oddsidemargin 0.0in + \evensidemargin 0.0in + \textwidth 6.5in + \headheight 0.0in + \topmargin 0.0in + \textheight=9.0in + +\begin{document} +\title{Helium-Neon Laser} +\date {} +\maketitle \noindent + \textbf{Experiment objectives}: assemble and align a 3-mW HeNe laser from +readily available optical components, record photographically the transverse mode structure of the +laser output beam, and determine the linear polarization of the light produced by the HeNe laser. + +\subsection*{Basic operation of the laser} + + The bright, highly collimated, red light beam ($\lambda = 6328 {\AA}$) from a helium-neon (HeNe) +laser is a familiar sight in the scientific laboratory, in the industrial workplace, and even at the +checkout counter in most supermarkets. HeNe lasers are manufactured in large quantities at low cost +and can provide thousands of hours of useful service. Even though solid-state diode lasers can now +provide red laser beams with intensities comparable to those obtained from HeNe lasers, the HeNe +laser will likely remain a common component in scientific and technical instrumentation for the +foreseeable future. +% +%In this experiment you will (a) assemble a 3-mW HeNe laser from readily available optical components, +%(b) align a HeNe laser cavity using two different cavity mirror configurations, (c) record +%photographically the transverse mode structure of the laser output beam, and (d) determine the linear +%polarization of the light produced by the HeNe laser. The principal goal of this experiment is for +%you to get hands-on experience with the various optical components of a working laser; however, to +%help you appreciate fully the role played by each of the components, a brief overview of the +%principles of HeNe laser operation is given here. + +\begin{figure}[h] +\centerline{\epsfig{width=\textwidth, file=HeNesetup.eps}} \caption{\label{HeNesetup.fig}Diagram of +optical and electrical components used in the HeNe laser experiment.} +\end{figure} + +The principal goal of this experiment is for +you to get hands-on experience with the various optical components of a working laser; however, to +help you appreciate fully the role played by each of the components, a brief overview of the +principles of HeNe laser operation is given here. The three principal elements of a laser are: +(1) an energy pump, (2) an optical gain medium, and (3) +an optical resonator. These three elements are described in detail below for the case of the HeNe +laser used in this experiment. +\begin{enumerate} +\item \textbf{Energy pump}. A 1400-V DC power supply +maintains a glow discharge or plasma in a glass tube containing an optimal mixture (typically 5:1 to +7:1) of helium and neon gas, as shown in Fig.~\ref{HeNesetup.fig}. The discharge current is limited +to about 5 mA by a 91-k$\Omega$ ballast resistor. Energetic electrons accelerating from the cathode +to the anode collide with He and Ne atoms in the laser tube, producing a large number of neutral He +and Ne atoms in excited states. He and Ne atoms in excited states can deexcite and return to their +ground states by emitting light spontaneously. This light makes up the bright and diffuse pink-red +glow of the plasma that is seen at even in the absence of laser action. + +The process of producing He and Ne in specific excited states is known as pumping, and in the HeNe +laser this pumping process occurs through electron-atom collisions in the discharge. In other types +of lasers, pumping is achieved by using light from a bright flashlamp or by using chemical reactions. +Common to all lasers is a process for preparing large numbers of atoms, ions, or molecules in +appropriate excited states so that a desired type of light emission can occur. + +\item \textbf{Optical gain medium}. +To achieve laser action it is necessary to have more atoms in excited states than in ground states, +and to establish what is called a \emph{population inversion}. To understand the significance of a +population inversion to HeNe laser action, it is useful to consider the processes leading to +excitation of He and Ne atoms in the discharge, using the simplified diagram of atomic He and Ne +energy levels given in Fig.~\ref{HeNelevels.fig}. The rather complex excitation process necessary for +lasing occurs +in four steps. \\ +\emph{(a)} An energetic electron collisionally excites a He atom to the state labeled $2_1S^0$ in +Fig.~\ref{HeNelevels.fig}. A He atom in this excited state is often written He*($2_1S^0$), where the +asterisk is used +to indicate that the He atom is in an excited state. \\ + +\emph{(b)} The excited He*($2_1S^0$) atom collides with an unexcited Ne atom and the two atoms +exchange internal energy, with an unexcited He atom and excited Ne atom, written Ne*(3$s_2$), +resulting. This energy exchange process occurs with high probability because of the accidental near +equality of the excitation energies of the two levels in these atoms.\\ + +\emph{(c)} The 3$s_2$ level of Ne is an example of a metastable atomic state, meaning that it is only +after a relatively long time -- on atomic that is -- that the Ne*(3$s_2$) atom deexcites to the +2$p_4$ level by emitting a photon of wavelength 6328 $\AA$. It is this emission of 6328 $\AA$ light +by Ne atoms that, in the presence of a suitable optical suitable optical configuration, +leads to lasing action. \\ + +\emph{(d)} The excited Ne*(2$p_4$) atom rapidly deexcites to the Ne ground state by emitting +additional photons or by collisions with the plasma tube deexcitation process occurs rapidly, there +are more Ne atoms in the 3$s_2$ state than there are in the 2$p_4$ state at any given moment in the +HeNe plasma, and a population inversion is said to be established between these two levels. When a +population inversion is established between the 3$s_2$ and 2$p_4$ levels of the excited Ne atoms, the +discharge can act as an optical gain medium (a light light amplifier) for light of wavelength 6328 +$\AA$. This is because a photon incident on the gas will have a greater probability of being +replicated in a 3$s_2\rightarrow 2p_4$ stimulated emission process (discussed below) than of being +destroyed in the complementary $2p_4\rightarrow 3s_2$ absorption process. + + +\begin{figure}[h] +\centerline{\epsfig{width=0.8\textwidth, file=HeNelevels.eps}} +\caption{\label{HeNelevels.fig}Simplified atomic energy level diagram showing excited states of +atomic He and Ne that are relevant to the operation of the HeNe laser at 6328~$\AA$.} +\end{figure} + +\item \textbf{Optical resonator}. As mentioned in 2(c) above, Ne atoms in the 3$s_2$ metastable +state decay spontaneously to the 2$p_4$ level after a relatively long period of time under normal +circumstances; however, a novel circumstance arises if, as shown in Fig.~\ref{HeNesetup.fig}, a HeNe +discharge is placed between two highly reflecting mirrors that form an \emph{optical cavity} or +\emph{resonator} along the axis of the discharge. When a resonator structure is in place, photons +from the Ne* 3$s_2\rightarrow 2p_4$ transition that are emitted along the axis of the cavity can be +reflected hundreds of times between the two high-reflectance end mirrors of the cavity. These +reflecting photons can interact with other excited Ne*(3$s_2$) atoms and cause them to emit 6328 +$\AA$ light in a process known as \emph{stimulated} emission. The new photon produced in stimulated +emission has the same wavelength and polarization as the stimulating photon, and it is emitted in the +same direction. It is sometimes useful for purposes of analogy to think of the stimulated emission +process as a "cloning" process for photons. The stimulated emission process should be contrasted with +spontaneous emission processes that, because they are not caused by any preceding event, produce +photons that are emitted isotropically, with random polarization, and over a broader range of +wavelengths. As stimulated emission processes occur along the axis of the resonator, a situation +develops in which essentially all Ne* 3$s_2\rightarrow 2p_4$ decays contribute deexcitation photons +to the photon stream reflecting between the two mirrors. This photon multiplication (light +amplification) process produces a very large number of photons of the same wavelength and +polarization that travel back and forth between the two cavity mirrors. To extract a light beam from +the resonator, it is only necessary that one of the two resonator mirrors, usually called \emph{the +output coupler}, has a reflectivity of only 99\% so that 1\% of the photons incident on it travel out +of the resonator to produce an external laser beam. The other mirror, called the high reflector, +should be as reflective as possible. The diameter, bandwidth, and polarization of the HeNe laser beam +are determined by the properties of the resonator mirrors and other optical components that lie along +the axis of the optical resonator. + +\end{enumerate} + + +\section*{Experimental Procedure} + +\textbf{Equipment needed}: Commercial HeNe laser, HeNe discharge tube connected to the power supply, +two highly reflective mirrors, digital camera, polarizer, photodetector, digital multimeter. + +\subsection*{Safety} +A few words of caution are important before you begin setting up your HeNe laser. \\ +First, \textbf{never} look directly into a laser beam, as severe eye damage could result. During alignment, you +should observe the laser beam by placing a small, white index card at the appropriate point in the optical path. +Resist the temptation to lower your head to the level of the laser beam in order to see where it is going. \\ +Second, \textbf{high voltage} ($\approx 1200$~V) is present at the HeNe discharge tube and you should avoid any +possibility of contact with the bare electrodes of the HeNe plasma tube. \\ Finally, the optical cavity mirrors +and the Brewster windows of the laser tube have \textbf{very delicate optical surfaces} that can be easily +scratched or damaged with a single fingerprint. If these surfaces need cleaning, ask the instructor to +demonstrate the proper method for cleaning them. + + + +\subsection*{Alignment of the laser} + +To assemble the HeNe laser and investigate its properties, proceed with the following steps. + +\begin{itemize} + +\item The discharge lamp has very small and angled windows, so first practice to align the beam of +the commercial HeNe laser through the discharge tube. To do that turn on the commercial laser, place a white +screen or a sheet of paper at some distance and mark the position of the laser spot. Now without turning the +power, carefully place the discharge tube such that the laser beam passes through both angled windows without +distortion, and hit the screen almost in the same point as without the tube. Repeat this step a few times until +you are able to insert the tube inside the cavity without loosing the alignment. Then carefully slide the tube +out of the beam and clamp it down. + +\item Set up a hemispherical resonator configuration using a flat, high reflectivity (R = 99.7\%) +mirror, and a spherical mirror with a radius of curvature of r = 0.500 m and reflectivity R = 99\%. +The focal length f of the spherical mirror is given by f = r/2 = 0.250 m. In the diagram of +Fig.~\ref{HeNesetup.fig}, the flat, highly-reflective mirror will be serving as the right end of the +cavity, and the spherical, less-reflective mirror will be serving as the left end of the cavity and +is known as the output coupler. The high reflectivity of each mirror is due to a multilayer +dielectric coating that is located on only one side of each mirror. Be sure to have the reflecting +surfaces of both mirrors facing the interior of the optical cavity. Set the distance between the two +mirrors to approximately d = 47 cm. + +\item To align the optical resonator of your HeNe laser it is easiest to use a beam of a working, +commercial HeNe laser as a guide. Direct this alignment laser beam to the center of the high reflector mirror, +with the output coupler and the HeNe discharge tube removed. With the room lights turned off, adjust the high +reflector mirror so that its reflected beam returns directly into the output aperture of the alignment laser. +Now insert and center the output coupler mirror, and also adjust it such that the reflected beam (from the back +of the mirror) returns to the alignment laser. Now insert a small white card near the front of the output +couplers very close to the laser beam but without blocking it, and locate the reflected beam from the high +reflector mirror - it should be fairly close to the input beam. Using fine adjustment screws in the high +reflector mirror overlap these two beams as good as you can. In case of success you most likely will see some +light passing through a high reflection mirror - fine-tune the position of the mirror some more to make this +light as bright as possible. +%and +%aAdjust the output coupler mirror until you observe concentric interference rings on its intracavity +%surface. It is likely that the interference rings will be converging or diverging slowly. It may be +%necessary to adjust the spacing, d, between the two mirrors to achieve perfectly circular rings. + +\item Now reinsert the HeNe plasma tube between the two mirrors of the optical cavity and adjust the +plasma tube position so that the alignment beam passes through the center of the Brewster windows of the plasma +tube. Be careful not to touch the Brewster windows or mirror surfaces during this process. With the HeNe plasma +tube in place, it should be possible to see a spot at the center of the high reflector mirror that brightens and +dims slowly. %at approximately the same rate as the diverging and converging circular interference rings +%observed earlier. + +\item Turn on the high voltage power supply to the HeNe plasma tube and (with luck) you will observe +the HeNe lasing. If lasing does not occur, make small adjustments to the plasma tube and the two +mirrors. If lasing still does not occur, turn off the high voltage supply, remove the HeNe plasma +tube, and readjust the resonator mirrors for optimal interference rings. If after several attempts +you do not achieve proper lasing action, ask the instructor for help in cleaning the Brewster windows +and resonator mirrors. + +\item Once lasing is achieved, record your alignment procedure in your laboratory notebook. %Describe +%with a well-labeled sketch the nature of the concentric rings that you observed when aligning the +%optical cavity. Determine the range of distances between the two mirrors for which lasing action can +%be maintained in the confocal resonator configuration. Do this in small steps, by increasing or +%decreasing the mirror separation distance d in small increments, and making small adjustments to the +%two mirrors to maintain laser output. +Turn off the alignment laser - you do not need it anymore. + +\end{itemize} + +\subsection*{Study of the mode structure of the laser output} + +Place a white screen at the output of your laser at some distance and inspect the shape of your beam. +Although it is possible that your beam is one circular spot, most likely you will notice some +structure as if the laser output consists of several beams. If you now slightly adjust the alignment +of either mirror you will see that the mode structure changes as well. + +As you remember, the main purpose of the laser cavity is to make the light bounce back and forth +repeating its path to enhance the lasing action of the gain medium. However, depending on the precise +alignment of the mirrors it may take the light more than two bounces to close the loop: it is often +possible for the beam to follow a rather complicated trajectory inside the resonator, resulting in +complex transverse mode structure at the output. +\begin{itemize} + +\item +Take photographs of the transverse mode structure of the HeNe laser output beam. By making small +adjustments to the mirrors and the position of the HeNe plasma tube it should be possible to obtain +transverse mode patterns. Mount your photographs in your laboratory notebook. + +\item +Adjust the mirrors such that the output mode has several maxima and minima in one direction. To +double-check that this mode is due to complicated trajectory of a light inside the resonator, very +carefully insert an edge of a white index card into the cavity, and move it slowly until the laser +generation stops. Now mover the card back and force around this point while watching the generation +appear and disappear, and pay close attention to the mode structure of the laser output. You may +notice that the complicated transverse mode pattern collapses to simpler mode when the card blocks +part of the original mode volume, forcing the generation in a different mode. Describe your +observation in the lab journal. + + +\end{itemize} + +\subsection*{Measure the polarization of the laser light} + +When a linearly polarized light beam of intensity $I_0$ passes through a linear polarizer that has +its axis rotated by angle $\theta$ from the incident light beam polarization, the transmitted +intensity $I$ is given by Malus's law: +\begin{equation} +I = I_0 cos^2\theta. +\end{equation} + +In our experiment the laser generates linearly polarized light field. This is insured by the Brewster +windows of the HeNe plasma tube: the angle of the windows is such that one light polarization +propagates almost without reflection. This polarization direction is in the same plane as the +incident beam and the surface normal (i.e. the plane of incidence). The light of the orthogonal +polarization experiences reflection at every window, that makes the optical losses too high for such +light. + +\begin{itemize} + +\item Visually inspect the discharge tube, note its orientation in the lab book. Make a rough prediction of +the expected polarization of the generated beam. + +\item Determine the linear polarization of the HeNe laser output beam using the rotatable polarizer +and photodiode detector. Make detector readings at several values of angle $\theta$ (every +$20^\circ$ or so) while rotating the polarizer in one full circle, and record them in a neat table in +your laboratory notebook. Graph your data to demonstrate, fit with the expected $cos^2\theta$ +dependence, and from this graph determine the orientation of the laser polarization. Compare it with +your predictions based on the Brewster windows orientation, and discuss the results in your lab +report. + +\end{itemize} + + +\section*{Acknowledgements} + +This lab would be impossible without help of Dr. Jeff Dunham from the Physics Department of the +Middlebury College, who shared important information about experimental arrangements and supplies, as +well as the lab procedure. This manual is based on the one used in Physics 321 course in Middlebury +College. + +\end{document} +\newpage |