{"id":511,"date":"2011-01-07T13:21:50","date_gmt":"2011-01-07T13:21:50","guid":{"rendered":"http:\/\/niziev.com\/?p=511"},"modified":"2011-01-07T13:22:52","modified_gmt":"2011-01-07T13:22:52","slug":"dynamics-of-mode-formation-in-an-open-resonator","status":"publish","type":"post","link":"https:\/\/niziev.com\/?p=511","title":{"rendered":"Dynamics of mode formation in an open resonator"},"content":{"rendered":"<p><a href=\"http:\/\/niziev.com\/wp-content\/uploads\/2011\/01\/Dynamics-published.pdf\">Download pd<\/a>f<\/p>\n<p>We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamics\u00a0of mode formation. Simulations of an axially symmetrical empty resonator rely on an analytical\u00a0description of radiation diffraction from a narrow ring. Reflection of an incident wave with a specified\u00a0amplitude-phase distribution from the mirror is calculated by the Green function method. The process of\u00a0mode formation is characterized by relaxation oscillations of various frequencies depending on the resonator\u00a0parameters. The evolution of the relaxation oscillation amplitude can be aperiodic in nature, or it\u00a0can occur as beats of a different frequency. It has been shown that there is a consistency between the\u00a0known conditions of paraxial resonance obtained in the approximation of geometric optics and the aperiodic\u00a0processes of evolution of relaxation oscillation amplitude in mode forming. An investigation has\u00a0been performed on the factors affecting the time of mode formation. The possibility has been shown\u00a0for multipass mode suppression and TEM10 mode generation by the use of an absorber mask on the\u00a0resonator mirror.\u00a0We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamicsof mode formation. Simulations of an axially symmetrical empty resonator rely on an analyticaldescription of radiation diffraction from a narrow ring. Reflection of an incident wave with a specifiedamplitude-phase distribution from the mirror is calculated by the Green function method. The process ofmode formation is characterized by relaxation oscillations of various frequencies depending on the resonatorparameters. The evolution of the relaxation oscillation amplitude can be aperiodic in nature, or itcan occur as beats of a different frequency. It has been shown that there is a consistency between theknown conditions of paraxial resonance obtained in the approximation of geometric optics and the aperiodicprocesses of evolution of relaxation oscillation amplitude in mode forming. An investigation hasbeen performed on the factors affecting the time of mode formation. The possibility has been shownfor multipass mode suppression and TEM10 mode generation by the use of an absorber mask on the resonator mirror.<\/p>\n<p><strong>1. Introduction<\/strong><\/p>\n<p><strong>2. Mathematical Model<\/strong><\/p>\n<p><strong>3. Calculation Results<br \/>\nA. Oscillation Amplitude and Time of Mode Formation<br \/>\nB. Oscillation Period and the Character of Field Amplitude\u00a0Evolution<br \/>\nC. Laguerre\u2013Gaussian Nonzero Modes<\/strong><\/p>\n<p><strong>4. Conclusion<\/strong><\/p>\n<p><strong>Appendix: Wave Reflection from the Round Mirror ofFinite Dimensions<\/strong><\/p>\n<p><strong>References<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download pdf We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamics\u00a0of mode formation. Simulations of an axially symmetrical empty resonator rely on an analytical\u00a0description of radiation diffraction from a narrow ring. Reflection of (&hellip;)<\/p>\n<p><a href=\"https:\/\/niziev.com\/?p=511\">Read the rest of this entry &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[],"_links":{"self":[{"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/posts\/511"}],"collection":[{"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/niziev.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=511"}],"version-history":[{"count":2,"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/posts\/511\/revisions"}],"predecessor-version":[{"id":514,"href":"https:\/\/niziev.com\/index.php?rest_route=\/wp\/v2\/posts\/511\/revisions\/514"}],"wp:attachment":[{"href":"https:\/\/niziev.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/niziev.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/niziev.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}