Lasers are very commonly used in everyday life, e.g. in laser pointers, CD-Players or the lasers used in cash registers. But what makes lasers special and distinguishes them from other light sources? Which advantages do they have and what are their applications in physics?
In the experiment "Laser" in the Advanced Physical Practicum the task is to find out which mathematic coherences there are between parameters of the laser and to test how good they match the experimental observation.
Table of Contents
1. Introduction/Motivation
2. Laser medium
2.1 Requirements for lasing
2.2 Possibilities for energy levels
3. Laser resonator
4. He-Ne laser
5. Fabry-Perot interferometer
6. Dielectric mirrors
7. Basic optical formulas
7.1 Snell's law
7.2 Fresnel equations
7.3 Brewster angle
8. Propagation using ray transfer matrix analysis
9. Properties of M²
10. Coherence
11. Parameters of the practicum
12. Autocollimation of the laser beam
13. Transversal modes
14. Gain factor and Brewster angle
15. Axial modes
16. Holography
17. Gaussian laser profile
18. Identification of the transversal modes
19. Calculation of gain factor and Brewster angle
20. Fabry-Perot-Interferometer
21. Gaussian laser profile
22. More questions
23. Conclusion
Objectives & Topics
This report details the experimental investigation into laser physics, specifically focusing on the characterization of Helium-Neon lasers, resonator properties, and beam quality metrics. The primary objective is to evaluate the mathematical coherences between various laser parameters and compare them with empirical experimental observations.
- Operating principles of laser media and energy level systems.
- Resonator stability conditions and mode analysis (longitudinal and transversal).
- Measurement and calculation of the Brewster angle and gain factor.
- Analysis of laser beam profiles, including Gaussian beam characteristics and the M² factor.
- Practical experimental techniques, including holography and interferometer applications.
Excerpt from the book
13. Transversal modes
By putting a thin wire inside the cavity and by making little adjustments to the mirrors, different transversal modes can be seen. Astonishing to see is the extremely high sensitivity of the adjusted mirrors. Even if someone walks on the ground, the pattern on the wall moves. We also put a lens into the beam to enlarge the patterns of the transversal modes. It's important to notice that the TEMa,b mode means a+1 maxima in the x-direction and b+1 maxima in the y-direction, since the TEM0,0 mode is circular shaped, which has already one maxima in both directions.
Summary of Chapters
1. Introduction/Motivation: This chapter introduces the common applications of lasers and defines the motivation for exploring the mathematical relationships between various laser parameters through experimental observation.
2. Laser medium: Explains the fundamental requirements for lasing, including gain media and the necessity of three- or four-level energy systems to achieve population inversion.
3. Laser resonator: Details the confocal construction of resonators, interference conditions, and the distinction between longitudinal and transversal modes.
4. He-Ne laser: Describes the specific operation of Helium-Neon lasers, including gas mixing, excitation mechanisms, and bandwidth influences.
5. Fabry-Perot interferometer: Discusses the construction and quality factor (finesse) of Fabry-Perot etalons used for wavelength separation.
6. Dielectric mirrors: Explains the use of Bragg mirrors to achieve high reflectivity compared to metallic alternatives.
7. Basic optical formulas: Outlines the mathematical foundation covering Snell's law, Fresnel equations, and the Brewster angle.
8. Propagation using ray transfer matrix analysis: Introduces matrix multiplication as a method to simplify light transfer calculations through various optical components.
9. Properties of M²: Defines the beam quality factor M² and its importance in determining how easily a laser beam can be focused.
10. Coherence: Defines the concepts of coherence length and time, which are critical for interference phenomena.
11. Parameters of the practicum: Lists the specific laboratory environment, tools, and setup parameters used during the experiments.
12. Autocollimation of the laser beam: Describes the practical procedure for adjusting dielectric mirrors to ignite the laser.
13. Transversal modes: Explains the observation of different TEM modes and the high sensitivity of the mirror adjustments.
14. Gain factor and Brewster angle: Describes the experimental setup for measuring the Brewster angle and evaluating gain through photo diode intensity readings.
15. Axial modes: Details the use of an oscilloscope to analyze the distance between longitudinal modes and the width of a single mode.
16. Holography: Examines the calculation of coherence length in the context of creating a three-dimensional holographic image.
17. Gaussian laser profile: Explains the use of CCD cameras and filters to analyze beam intensity and find the waist of the beam.
18. Identification of the transversal modes: Provides a deeper analysis of hybrid modes and the influence of mirror alignment on high-order mode excitation.
19. Calculation of gain factor and Brewster angle: Presents the data analysis and calculations for the gain factor and the Brewster angle derived from intensity measurements.
20. Fabry-Perot-Interferometer: Briefly notes that the modal characteristics were determined earlier in the experiment.
21. Gaussian laser profile: Re-examines the Gaussian profile fit and the calculation of standard derivation in the context of FWHM.
22. More questions: Addresses further calculations, including effective focal length, theoretical waist, and laser intensity.
23. Conclusion: Summarizes the experimental findings and acknowledges the practical insights gained regarding laser setup and beam characterization.
Keywords
Laser, He-Ne laser, Resonator, Transversal modes, Longitudinal modes, Brewster angle, Gain factor, M² factor, Coherence, Fabry-Perot interferometer, Gaussian beam, Population inversion, Finesse, Ray transfer matrix, Holography
Frequently Asked Questions
What is the primary focus of this work?
The work focuses on the experimental characterization of a Helium-Neon laser, specifically analyzing its physical properties like modes, intensity, and beam profile.
What are the central thematic fields?
The core themes include resonator theory, laser beam optics, interferometry, and the mathematical modeling of laser gain and beam quality.
What is the primary research goal?
The goal is to determine the mathematical relationships between various physical parameters of the laser and test how well these theoretical models match empirical experimental observations.
Which scientific methods are applied?
The study utilizes ray transfer matrix analysis, Gaussian beam fitting, interference measurements via Fabry-Perot interferometry, and data analysis via oscilloscope and CCD camera measurements.
What is treated in the main part of the report?
The main part covers the theoretical principles of laser construction, practical experimental procedures (such as mirror alignment and mode identification), and quantitative calculations for gain, Brewster angles, and beam quality.
Which keywords characterize this document?
Key terms include Laser, Resonator, TEM modes, Brewster angle, M² factor, Coherence, and Interferometry.
How is the Brewster angle determined in the experiment?
The Brewster angle is determined by rotating a glass plate and measuring the intensity of the reflected light using a photo diode to find the point of minimal reflection, subsequently analyzing the data for asymmetry.
What challenges did the authors encounter with the axial mode measurements?
The authors initially encountered a discrepancy between the calculated frequency and the expected value, which required repeating the experiment after technical improvements to the setup.
How does the Gaussian profile fit help in determining beam quality?
By fitting a Gaussian profile to the measured intensity distribution, the authors calculate the standard deviation and FWHM at different distances from the focus, which is then used to compute the beam quality factor M².
Why are dielectric mirrors used instead of metallic ones?
Dielectric mirrors are used to achieve extremely high reflectivity through interference in multiple layers with varying refractive indices, which is essential for maintaining the high finesse required for the laser resonator.
- Arbeit zitieren
- Moritz Lehmann (Autor:in), Niklas Stenger (Autor:in), 2017, Laser. Advanced Physical Practicum, München, GRIN Verlag, https://www.grin.com/document/378240
