In general, \(\sigma_x \ne \sigma_y\). For example, in semiconductor lasers the height and width of the emitting aperture differ. Such beams are called astigmatic.

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The 1064 nm ORION’s higher output power, low noise and narrow linewidth ideally position this semiconductor optical solution for multiple applications where absolute accuracy, lifetime reliability over demanding field conditions, and high resolution are vital, such as seeding of fiber and solid state lasers, Second Harmonic Generation (SHG), Optical Parametric Oscillators (OPO), laser spectroscopy, LIDAR and other precision metrology applications.

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The \(D4\sigma\) beam diameter is a simple rearrangement of the above equation in which it is noted that twice the radius or the beam diameter is equal to \(4\sigma\)

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A useful parameter characterizing a general two-dimensional distribution \(E(x,y)\) is the variance in the \(x\) and \(y\) directions

The 1064 nm ORION™ laser module builds upon the proven performance of RIO’s game-changing PLANEX™ product series. In addition to unrivaled reliability (Telcordia GR-486 qualified technology platform) and robustness, the ORION laser modules provide superior value with up to 20 mW output power, very low RIN, low phase noise and narrow linewidth, exceptional wavelength stability.

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The ORION’s packaging was designed with the customer’s need in mind: highly integrated, small form factor and self-contained module. This optical solution is positioned for reducing the development cycle time and allow for simple integration into advanced fiber optic systems. External monitoring and control can be achieved via SPI, RS-232 or RS-485 standard interfaces.

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A laser beam will usually consist of a superposition of several modes. A single mode beam radius is easily described by \(1/e^2\) points. This, of course, fails for any beam shape other than Gaussian. ISO 11146 is intended to provide a simple, consistent way of describing the width of a beam.

Sometimes it is the full width at half maximum (FWHM) value that is desired or known. In general, there is no direct relationship between the \(1/e^2\) radius \(w\) and the FWHM. However, in the special case of a Gaussian beam, there is.

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Now, the quantities \(\sigma_x^2\) and \(\sigma_y^2\) will always be positive, but \(\sigma_{xy}^2\) can be negative, zero, or positive.