{"id":233,"date":"2023-06-07T15:17:31","date_gmt":"2023-06-07T13:17:31","guid":{"rendered":"https:\/\/logbooks.ifosim.org\/finesse\/?p=233"},"modified":"2023-06-07T15:20:19","modified_gmt":"2023-06-07T13:20:19","slug":"gouy-phase-in-a-recycling-cavity-with-one-focussing-element","status":"publish","type":"post","link":"https:\/\/logbooks.ifosim.org\/finesse\/2023\/06\/07\/gouy-phase-in-a-recycling-cavity-with-one-focussing-element\/","title":{"rendered":"Gouy phase in a recycling cavity with one focussing element"},"content":{"rendered":"\n<p>Investigating here whether the &#8220;simple&#8221; external solution with just one focussing element can work at all. Idea is that after BS, one would have a 45deg plane mirror to direct the beam some distance away to a focussing mirror, which produces a waist slightly before (or after) the PR\/SR mirror, potentially with another folding mirror in between.<\/p>\n\n\n\n<p>Since we start with an almost collimated beam, the only significant Gouy phase will be picked up close to the resultant focus, which is necessarily close to the PR\/SR mirror. Depending on the focussing distance, one obtains a more or less strong focus and therefore high intensities on the PR\/SR mirror.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>virgo = finesse.Model()\n\nlength_of_recycling_cavity = 100.0\n\nvirgo.parse(f\"\"\"\nl l1 P=1.0\nlink(l1, 1.0, mEM)\n\n# arm cavity (with Phase II parameters)\nm mEM R=0.99 L=0 Rc=-1683\ns sAC mEM.p2 mIM.p1 L=2999.8\nm mIM R=0.99 L=0 Rc=1420\ns sIM mIM.p2 mIM_AR.p1 nr=1.44 L=0.2\nm mIM_AR R=0.0 L=0.0 Rc=1420\ncav cAC mIM.p1.o\n\n# focussing lens, then looking at beam parameters a certain distance away\ns sIM_lens mIM_AR.p2 mPR2.p1\nlens mPR2 f=49.0\nnothing mPR\ns slens_PR mPR2.p2 mPR.p1\n\nbp w_PR mPR.p1.i w\nbp w0_PR mPR.p1.i w0\n\"\"\")\nvirgo.modes(maxtem=0)\nvirgo.slens_PR.L = length_of_recycling_cavity<\/code><\/pre>\n\n\n\n<p>Let&#8217;s scan the lens focal length around the length of the cavity (roughly we have a collimated beam, so distance to waist after lens is roughly the same as the focal length). Note, in principle the propagate_beam function can return a symbolic formula where it is then easy to directly insert a linspace array &#8212; but for some reason the parameter substitution does not work right now.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>focal_lengths = np.linspace(length_of_recycling_cavity - 10.0, length_of_recycling_cavity, 11)\nfor focal_length in focal_lengths:\n    virgo.mPR2.f = focal_length\n    trace = virgo.propagate_beam(from_node=virgo.mIM.p2.o, to_node=virgo.mPR.p1)\n    print(f'f={focal_length}m: {trace.total_acc_gouy:.2f}deg')<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>f=90.0m: 160.64deg\nf=91.0m: 153.35deg\nf=92.0m: 139.16deg\nf=93.0m: 108.77deg\nf=94.0m: 65.30deg\nf=95.0m: 38.82deg\nf=96.0m: 26.46deg\nf=97.0m: 19.92deg\nf=98.0m: 15.96deg\nf=99.0m: 13.34deg\nf=100.0m: 11.48deg<\/code><\/pre>\n\n\n\n<p>Here we have a specific value of f=90.0m, which results in a beam radius of 2.1mm on the recycling mirror, for an accumulated Gouy phase of 20deg. Note that there&#8217;s basically two symmetric solutions, one with waist shortly before the recycling mirror, requiring a concave RoC; and one slightly behind the recycling mirror, requiring a convex RoC. Which one is better can surely be a topic of much debate \ud83d\ude42<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>virgo.mPR2.f = 90.0\nout = virgo.run()\nprint(f\"w @ PR = {out&#091;'w_PR']*1000.0:.3f}mm\\nw0 = {out&#091;'w0_PR']*1000.0:.3f}mm\")\ntrace = virgo.propagate_beam(from_node=virgo.mIM_AR.p2.o, to_node=virgo.mPR.p1)\ntrace.plot();<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"432\" src=\"https:\/\/logbooks.ifosim.org\/finesse\/wp-content\/uploads\/sites\/5\/2023\/06\/output.png\" alt=\"\" class=\"wp-image-235\" srcset=\"https:\/\/logbooks.ifosim.org\/finesse\/wp-content\/uploads\/sites\/5\/2023\/06\/output.png 587w, https:\/\/logbooks.ifosim.org\/finesse\/wp-content\/uploads\/sites\/5\/2023\/06\/output-300x221.png 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Investigating here whether the &#8220;simple&#8221; external solution with just one focussing element can work at all. Idea is that after BS, one would have a 45deg plane mirror to direct the beam some distance away to a focussing mirror, which produces a waist slightly before (or after) the PR\/SR mirror, potentially with another folding mirror [&hellip;]<\/p>\n","protected":false},"author":89,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ssl_alp_hide_revisions":false,"footnotes":"","ssl_alp_hide_crossreferences_to":false},"categories":[14],"tags":[62,60,61],"ssl-alp-coauthor":[59],"class_list":["post-233","post","type-post","status-publish","format-standard","hentry","category-finesse3","tag-beam-trace","tag-gouy-phase","tag-recycling"],"_links":{"self":[{"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/posts\/233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/users\/89"}],"replies":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/comments?post=233"}],"version-history":[{"count":5,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/posts\/233\/revisions"}],"predecessor-version":[{"id":240,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/posts\/233\/revisions\/240"}],"wp:attachment":[{"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/media?parent=233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/categories?post=233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/tags?post=233"},{"taxonomy":"ssl-alp-coauthor","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/finesse\/wp-json\/wp\/v2\/ssl-alp-coauthor?post=233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}