In laser science, laser beam quality defines aspects of the beam illumination pattern and the merits of a particular laser beam's propagation and transformation properties (space-bandwidth criterion). By observing and recording the beam pattern, for example, one can infer the spatial mode properties of the beam and whether or not the beam is being clipped by an obstruction; By focusing the laser beam with a lens and measuring the minimum spot size, the number of times diffraction limit or focusing quality can be computed.
Anthony E. Siegman was the first to propose the formalism for a laser beam quality factor that could be measured and used to compare different beams, independent of wavelength. [1] The factor is called beam propagation ratio (M2), and it is closely related to the beam parameter product. While the M2 factor does not give detail on the spatial characteristics of the beam, it does indicate how close it is to being a fundamental-mode Gaussian beam. It also determines the smallest spot size for the beam, as well as the beam divergence. M2 can also give an indication of beam distortions due to, for example, power-induced thermal lensing in the laser gain medium, since it will increase.
There are some limitations to the M2 parameter as a simple quality metric. It can be difficult to measure accurately, and factors such as background noise can create large errors in M2. [2] Beams with power well out in the "tails" of the distribution have M2 much larger than one would expect. In theory, an idealized tophat laser beam has infinite M2, although this is not true of any physically realizable tophat beam. For a pure Bessel beam, one cannot even compute M2. [3]
The definition of "quality" also depends on the application. While a high-quality single-mode Gaussian beam (M2 close to unity) is optimum for many applications, for other applications a uniform multimode tophat beam intensity distribution is required. An example is laser surgery. [4]
Power-in-the-bucket and Strehl ratio are two other attempts to define beam quality. Both these methods use a laser beam profiler to measure how much power is delivered to a given area. There is also no simple conversion between M2, power-in-the-bucket, and Strehl ratio.
The equation for the divergence of a pure Gaussian TEM00 unfocused beam propagating through space is given by
where D00 is the diameter of the beam waist, and λ is the wavelength. Higher mode beams often start with a larger beam waist, D0, and/or have a faster divergence Θ0. In this case Equation (1) becomes
where Θ0 and D0 are the divergence and waist of a higher mode beam and M2 is greater than 1 and is named the "Beam Propagation Ratio" per the ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot diameter is defined by
where d00 is the ideal focused spot diameter, f is the focal length of the focusing lens, and D00 is the input beam waist and is placed one focal length from the lens as shown in the figure. However, when a multimode beam is focused, Equation (3) becomes
M2 cannot be determined from a single beam profile measurement. The ISO/DIS 11146 define that M2 should be calculated from a series of measurements as shown in the figure below. [5] M2 is measured on real beams by focusing the beam with a fixed position lens of known focal length, and then measuring the characteristics of the beam waist and divergence. These measurements can be taken with a laser beam profiler. [6]
The multiple measurements ensure that the minimum beam diameter is found and enable a "curve fit" that improves the accuracy of the calculation by minimizing measurement error.
Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in common use: D4σ, 10/90 or 20/80 knife-edge, 1/e2, FWHM, and D86. The beam width can be measured in units of length at a particular plane perpendicular to the beam axis, but it can also refer to the angular width, which is the angle subtended by the beam at the source. The angular width is also called the beam divergence.
In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Practically speaking, however, the far field can commence physically close to the radiating aperture, depending on aperture diameter and the operating wavelength.
In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM00) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse phase dependence is altered; this results in a different Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam (for a given wavelength and polarization) are determined by a single parameter: the so-called waist w0. At any position z relative to the waist (focus) along a beam having a specified w0, the field amplitudes and phases are thereby determined as detailed below.
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element is described by a 2×2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.
Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.
The resolution of an optical imaging system – a microscope, telescope, or camera – can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to the physics of diffraction. An optical system with resolution performance at the instrument's theoretical limit is said to be diffraction-limited.
In optics, the Airy disk and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance from the object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and is given by the Fresnel diffraction equation.
In optics, the complex beam parameter is a complex number that specifies the properties of a Gaussian beam at a particular point z along the axis of the beam. It is usually denoted by q. It can be calculated from the beam's vacuum wavelength λ0, the radius of curvature R of the phase front, the index of refraction n (n=1 for air), and the beam radius w (defined at 1/e2 intensity), according to:
In nonlinear optics, filament propagation is propagation of a beam of light through a medium without diffraction. This is possible because the Kerr effect causes an index of refraction change in the medium, resulting in self-focusing of the beam.
In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point. The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot.
In laser science, the parameter M2, also known as the beam propagation ratio or beam quality factor is a measure of laser beam quality. It represents the degree of variation of a beam from an ideal Gaussian beam. It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same wavelength. It relates the beam divergence of a laser beam to the minimum focussed spot size that can be achieved. For a single mode TEM00 (Gaussian) laser beam, M2 is exactly one. Unlike the beam parameter product, M2 is unitless and does not vary with wavelength.
Ring lasers are composed of two beams of light of the same polarization traveling in opposite directions ("counter-rotating") in a closed loop.
In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. A related parameter is the confocal parameter, b, which is twice the Rayleigh length. The Rayleigh length is particularly important when beams are modeled as Gaussian beams.
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers — ultraviolet, visible, infrared, continuous wave, pulsed, high-power, low-power — there is an assortment of instrumentation for measuring laser beam profiles. No single laser beam profiler can handle every power level, pulse duration, repetition rate, wavelength, and beam size.
Time-domain thermoreflectance is a method by which the thermal properties of a material can be measured, most importantly thermal conductivity. This method can be applied most notably to thin film materials, which have properties that vary greatly when compared to the same materials in bulk. The idea behind this technique is that once a material is heated up, the change in the reflectance of the surface can be utilized to derive the thermal properties. The reflectivity is measured with respect to time, and the data received can be matched to a model with coefficients that correspond to thermal properties.
Laser linewidth is the spectral linewidth of a laser beam.