{"id":10125,"date":"2022-09-10T02:34:31","date_gmt":"2022-09-10T02:34:31","guid":{"rendered":"https:\/\/www.szlaser.com\/?page_id=10125"},"modified":"2022-09-12T12:02:27","modified_gmt":"2022-09-12T12:02:27","slug":"beam-reduction","status":"publish","type":"page","link":"https:\/\/www.szlaser.com\/index.php\/wiki\/beam-reduction\/","title":{"rendered":"Beam Collimation, Divergence, Beam Expansion, and Beam Reduction"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1331.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-1 fusion-sep-none fusion-title-text fusion-title-size-one\"><h1 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:32;line-height:1.3;\"><h1>Beam Collimation, Divergence, Beam Expansion, and Beam Reduction<\/h1><\/h1><\/div><div class=\"fusion-text fusion-text-1\"><p>Another characteristic of all lasers is the divergence of the output beam. As a laser beam leaves the output coupler it will spread as it propagates. In other words, the spot diameter will get larger as the beam travels farther from the laser as shown in Figure 6.20. The full-angle beam divergence is calculated by<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-full wp-image-10127\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-of-full-angle-beam-divergence.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-of-full-angle-beam-divergence.png\" alt=\"\" width=\"202\" height=\"74\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27202%27%20height%3D%2774%27%20viewBox%3D%270%200%20202%2074%27%3E%3Crect%20width%3D%27202%27%20height%3D%2774%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-of-full-angle-beam-divergence-200x73.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-of-full-angle-beam-divergence.png 202w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 202px) 100vw, 202px\" \/><\/p>\n<p>where<br \/>\nDf is the final spot diameter,<br \/>\nDi is the initial spot diameter, and<br \/>\n\u0394d the distance between the final and initial spots.<br \/>\nTypical divergences for HeNe lasers, for example, are usually measured in the milliradians.<\/p>\n<p>All laser beams diverge naturally as a consequence of propagation and diffraction. Optical elements can be used to focus beams but there are limits to the control of beam divergence simply due to the physics of propagation.<\/p>\n<p>A common practice for laser scientists and engineers is to collimate a laser beam using a telescope or other dispersive optical element system. It is often misunderstood by the novice laser operator that a collimated laser beam will not remain collimated forever because of diffraction.<\/p>\n<p>Figure 6.21 shows a typical configuration for expanding and collimating a laser beam using two lenses and a spatial filter (a pinhole). The two lenses are placed apart from each other such that their focal spots coincide and in the near field within a meter or two from the lenses the beam appears to be perfectly collimated with no divergence. While this may be true (no divergence) diffraction due to propagation is still happening and in the far-field<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-full wp-image-10130\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam.png\" alt=\"\" width=\"511\" height=\"125\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27511%27%20height%3D%27125%27%20viewBox%3D%270%200%20511%20125%27%3E%3Crect%20width%3D%27511%27%20height%3D%27125%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam-200x49.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam-300x73.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam-400x98.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam-500x122.png 500w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-expanding-a-laser-beam.png 511w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-full wp-image-10131\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam.png\" alt=\"\" width=\"532\" height=\"223\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27532%27%20height%3D%27223%27%20viewBox%3D%270%200%20532%20223%27%3E%3Crect%20width%3D%27532%27%20height%3D%27223%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam-200x84.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam-300x126.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam-400x168.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam-500x210.png 500w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/a-typical-configuration-for-collimating-a-laser-beam.png 532w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>distances (greater than a thousand meters or so) the beam size is limited by the output lens aperture diameter, D aperture, and the distance propagated, z, as<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-full wp-image-10132\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27169%27%20height%3D%2762%27%20viewBox%3D%270%200%20169%2062%27%3E%3Crect%20width%3D%27169%27%20height%3D%2762%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-D.png\" alt=\"\" width=\"169\" height=\"62\" \/><\/p>\n<p>which is the increase in beam diameter from input to output of the optical system. Many laser beams exit the laser aperture in a very tiny beam only a few millimeters in diameter and for many applications this beam needs to be expanded many times. The expansion of the beam expander shown in Figure above is calculated as<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-full wp-image-10133\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27146%27%20height%3D%2757%27%20viewBox%3D%270%200%20146%2057%27%3E%3Crect%20width%3D%27146%27%20height%3D%2757%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/09\/equation-of-MP.png\" alt=\"\" width=\"146\" height=\"57\" \/><\/p>\n<p>where f1 and f2 are the focal lengths of lenses 1 and 2, respectively, and MP is the magnification power of the beam expander. We also should realize that the beam expander can be used in reverse as a beam reducer.<\/p>\n<\/div><div style=\"text-align:right;\"><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-1 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.szlaser.com\/index.php\/wiki\/spherical-lense\/\"><span class=\"fusion-button-text awb-button__text awb-button__text--default\">What is spherical lense &gt;<\/span><\/a><\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":7,"featured_media":0,"parent":8230,"menu_order":73,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-10125","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v18.7 (Yoast SEO v25.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Beam Collimation, Divergence, Beam Expansion, and Beam Reduction - SZLASER<\/title>\n<meta name=\"description\" content=\"Another characteristic of all lasers is the divergence of the output beam. 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