Using this formula for your example yields a beam radius of 31.5 mm at z = 1000 m.  Another way to check your results is to use the Paraxial Gaussian Beam Data analysis function:

Lowdivergencelaser

When we talk about highly monochromatic lasers, we consider that the beam linewidth is very narrow. You can use these lasers especially for applications such as laser spectroscopy or coupling with optical fibers in fiber communications.

Do not provide any information or data that is restricted by applicable law, including by the People’s Republic of China’s Cybersecurity and Data Security Laws ( e.g., Important Data, National Core Data, etc.).

Laser beamdivergenceand spot size

You can be surprised by the fact that measured linewidths of real solid-state lasers, such as diode-pumped YAG lasers, are <1 kHz. This is not the bottom line. In fact, linewidths less than 1Hz are also achievable by suppression of external noise influence. Narrow-linewidth lasers are used in holography, frequency metrology and light detection and ranging (LIDAR).

Gaussian beamdivergence

Simply using the far-field divergence angle to estimate beam radius, when measured from the waist location, is an over-simplification.  The actual dependence is slightly more involved (see the Wikipedia page on the properties of a Gaussian Beam, or any reference on Gaussian beams):

Take a look at other types of light sources: incoherent light sources (light bulbs, LED, stars). These sources produce radiation by spontaneous emission in all directions, with a spread of wavelengths and no interrelationships among individual photons. Spontaneous emission is a random process. On the other hand, lasers use stimulated emission, producing photons with identical properties (all photons move at the same wavelength and direction).

in order to get an exact understanding of POP, I have stripped down a simulation to purely a POP simulation, i.e. without any optical element but a free-space propagation (Gaussian beam diffraction) over 1000m:

Laser (Light Amplification by Stimulated Emission of Radiation) is an artificial source of light radiation that emits a coherent beam of photons, as the source is stable in frequency, wavelength, and power. Unlike the light emitted by common sources, such as light bulbs, laser light is mostly monochromatic, i.e. only one specific wavelength (color).

Divergence angleof beam

Specific properties of artificial light obtained by lasers are advantageous for transmitting data for hundreds of miles, up to terabits per second, by a convenient, single wavelength coherent source. Nowadays, you can transmit data with laser beams through free-space optics technology over moderate distances with many Gbit/s data rates.

According to Teich/Saleh a 21mm 1/e² radius Gaussian beam should result in a divergence theta of (omega_0 is the 1/e² radius)

The laser beam is highly coherent, which means that the electromagnetic waves are in the same phase with each other and propagate in the same direction. You can get a laser beam of high intensity and directivity by superposition of electromagnetic waves that are in phase. Such a highly directional beam can be focused on a very sharp point, which is not possible with ordinary light.

Laser power detector for measurement up to 50 000 W that traps > 97 % of the incident light and handles high intensities of small beams.

Gentec-EO's high-accuracy laser beam measurement instruments help engineers, scientists and technicians in all sorts of laser applications from the factory to the hospital, laboratory and research center. Learn about our solutions for these measurement types:

Reading from the cross section in the image plane, I get around 31mm at 1/e², so a difference of 7.5mm to the expected 23.5mm.

My beam waist is 21mm. Exploring that with the Beam File Viewer, this is a 21mm radius at 1/e². However, in the help file I find

Portable laser power meter for up to 250 W with flexible calibration options so the customers only pay for what they use. Includes 3 measurement modes : SSP, CWP and SSE.

Divergence anglecalculator

where w_0y (omega) should be the same as Waist X?! According to these formulas this would be a 1/e radius (not squared), if I do the math right. Maybe w_0y is not equal to Waist X?

It would be great to get a hint, if my modelling of such a minimal system, i.e. only the Gaussian beam diffraction, is correctly done in Zemax. I attach my file.

What is beamdivergence

However, real laser light is not purely directional because some propagation effects can distort the laser beam, especially if it is interacting with nonlinear media. When you propagate laser beam it gets broadened with distance. In order to achieve an adequate beam size and directivity you need to additionally precisely control, measure and direct laser beam with lenses and mirrors.

Gaussian beamdivergencecalculator

Ordinary light sources mainly emit polychromatic light and their emission is spatial. The source of ordinary light emits many rays in all directions, randomly. Ordinary light consists of a mixture of rays with different wavelengths, where each wavelength corresponds to one color that your eyes register.

Since the discovery of the laser, more than 30 Nobel Prizes have been awarded in the field of natural sciences for scientific discoveries directly related to lasers. In 2018, Donna Strickland became the second woman to receive a Nobel Prize in physics, which she was awarded for her work on ultra-short and high-intensity laser pulses. Measuring the laser's properties with precision and accuracy is key to such research, which is why Gentec-EO develops and manufactures high-accuracy laser power meters and laser energy meters.

Jeff, thank you so much for your support! I gained some good insight into POP and improved my understanding of Gaussian beams :)

Divergence angleformula

Laser specifications change over time for many reasons and it causes problems accross all industries. Learn about how laser output measurement solves numerous problems in YOUR industry. Download the guide below.

The laser has also become an important research instrument and has found its application in many fields, such as the correction of vision, the sharpening of the astronomical image from space, testing the DNA molecule and in obtaining pure energy by laser fusion of atoms.

The sun, stars and fire are natural sources of ordinary light. We recognize the light received by the human eye as white, whether it is the light of a lamp or the sun. However, we do not notice the spectrum of colors that make white, except through a prism by which light can be decomposed into different components.

Laser specifications change over time for many reasons and it causes problems accross all industries. Learn about how laser output measurement solves numerous problems in YOUR industry. Download the guide below.   Gentec-EO's high-accuracy laser beam measurement instruments help engineers, scientists and technicians in all sorts of laser applications from the factory to the hospital, laboratory and research center. Learn about our solutions for these measurement types: Laser power meters Laser energy meters Laser beam profilers Terahertz power meters