Beam Waist Measurement II-Advanced Physics-Lab Report, Exercises of Advanced Physics

Download Beam Waist Measurement II-Advanced Physics-Lab Report and more Exercises Advanced Physics in PDF only on Docsity! INTRODUCTION Gaussian Beam: In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions. Many lasers emit beams with a Gaussian profile, in which case the laser is said to be operating on the fundamental transverse mode, or "TEM00 mode" of the laser's optical resonator. When refracted by a lens, a Gaussian beam is transformed into another Gaussian beam (characterized by a different set of parameters), which explains why it is a convenient, widespread model in laser optics. The mathematical function that describes the Gaussian beam is a solution to the paraxial form of the Helmholtz equation. The solution, in the form of a Gaussian function, represents the complex amplitude of the electric field, which propagates along with the corresponding magnetic field as an electromagnetic wave in the beam. In most laser applications it is necessary to focus, modify, or shape the laser beam by using lenses and other optical elements. In general, laser-beam propagation can be approximated by assuming that the laser beam has an ideal Gaussian intensity profile, corresponding to the theoretical TEM00 mode. Coherent Gaussian beams have peculiar transformation properties that require special consideration. In order to select the best optics for a particular laser application, it is important to understand the basic properties of Gussian beams. Figure:2 Gaussian beam intensity profile Unfortunately, the output from real-life lasers is not truly Gaussian (although helium neon lasers and argon-ion lasers are a very close approximation). To accommodate this variance, a quality factor, M 2 (called the "M-square" factor), has been defined to describe the deviation of the laser beam from a theoretical Gaussian. For a theoretical Gaussian, M 2 =1; for a real laser beam, M 2 >1. Helium neon lasers typically have an M 2 factor that is less than 1.1. For ion lasers, the M 2 factor is typically between 1.1 and 1.3. Collimated TEM00 diode laser beams usually have an M 2 ranging from 1.1 to 1.7. For high-energy multimode lasers, the M 2 factor can be as high as 25 or 30. In all cases, the M 2 factor, affects the characteristics of a laser beam and cannot be neglected in optical designs. docsity.com In the following section, Gaussian Beam Propagation, we will treat the characteristics of a theoretical Gaussian beam (M 2 = 1); then, in the section Real Beam Propagation we will show how these characteristics change as the beam deviates from the theoretical. In all cases, a circularly symmetric wavefront is assumed, as would be the case for a helium neon laser or an argon-ion laser. Diode laser beams are asymmetric and often astigmatic, which causes their transformation to be more complex. Although in some respects component design and tolerancing for lasers are more critical than they are for conventional optical components, the designs often tend to be simpler since many of the constants associated with imaging systems are not present. For instance, laser beams are nearly always used on axis, which eliminates the need to correct asymmetric aberration. Chromatic aberrations are of no concern in single-wavelength lasers, although they are critical for some tunable and multiline laser applications. In fact, the only significant aberration in most single-wavelength applications is primary (third- Order) spherical aberration. Scatter from surface defects, inclusions, dust, or damaged coatings is of greater concern in laser-based systems than in incoherent systems. Speckle content arising from surface Texture and beam coherence can limit the system performance.Because laser light is generated coherently, it is not subject to some of the limitations normally associated with incoherent sources. All parts of the wavefront act as if they originate from the same point, and consequently the emergent wavefront can be precisely defined. Starting out with a well-defined wavefront permits more precise focusing and control of the beam than would otherwise be possible. In the real world, truly Gaussian laser, beams are very hard to find. Low-power beams from helium neon lasers can be a close approximation, but the higher the power of the laser, the more complex the excitation mechanism (e.g., transverse discharges, the order of the mode, the more the beam deviates from the ideal.To address the issue of non-gaussian beams, a beam quality factor, M 2 , has come into general use. For a typical helium neon laser operating in TEM00 mode, M 2 <1.1. Ion lasers typically have an M 2 factor ranging from 1.1 to 1.7. For high-energy multimode lasers, the M 2 factor can be as high as 10 or more. In all cases, the M 2 factor affects the characteristics of a laser beam and cannot be neglected in optical designs, and truncation, in general, increases the M 2 factor of the beam. In Laser Modes, we will illustrate the higher-order Eigen solutions to the propagation equation, and in The Propagation Constant, M 2 will be defined. The section Incorporating M 2 into the Propagation Equations defines how non-Gaussian beams propagate in free space and through optical systems. BEAM WAIST: The location with minimum beam radius, the beam waist of a laser beam is the location along the propagation direction where the beam radius has a minimum. A small beam waist (more precisely, a beam waist with small waist radius) can be obtained by focusing a laser beam with large diameter with a lens which has a short focal length and high aperture. Note that the position or beam radius of the beam waist can be at different locations for different transverse directions. This phenomenon is called astigmatism. docsity.com