an online calculator<\/a> for this, but what I really wanted was some graphs. So I made them.<\/p>\nI usually run into pulses that are best described as sech^2. That’s what these graphs are for. I made curves for several different pulse widths (FWHM), and plotted them on different scales for comparison.<\/p>\n
![\"pulseWidth-Bandwidth-00\"](\"http:\/\/labrigger.com\/blog\/wp-content\/uploads\/2015\/01\/pulseWidth-Bandwidth-00-472x1024.png\")
<\/p>\n
Here’s the code to generate the graphs above, which are for sech^2 pulses, and graphs for Gaussian pulses.<\/p>\n
\r\n%% time-bandwidth product\r\n\r\nc= 3*10^8;\r\n\r\npw = [10 25 50 100 150 200]; % pulse width in fs\r\nwl = 500:100:1500; % wavelength in nm\r\n\r\nG_bw_Hz = 0.44.\/(pw.*10^-15); % bandwidth in Hz, for Gaussian pulses\r\nS_bw_Hz = 0.32.\/(pw.*10^-15); % bandwidth in Hz, for Sech^2 pulses\r\n\r\nG_bw_nm = zeros([numel(pw) numel(wl)]);\r\nS_bw_nm = zeros([numel(pw) numel(wl)]);\r\n\r\nfor n=1:numel(wl)\r\n w=wl(n).*10^-9;\r\n G_bw_nm(:,n)=(10^9).*(G_bw_Hz.*w^2)\/c;\r\n S_bw_nm(:,n)=(10^9).*(S_bw_Hz.*w^2)\/c;\r\nend\r\n\r\nfigure\r\nsubplot(1,2,1)\r\nplot(wl,S_bw_nm)\r\nsubplot(1,2,2)\r\nplot(wl,G_bw_nm)\r\n\r\n<\/pre>\n<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"
\n
Ultrafast pulses are formed through interference of different wavelengths of light. Think of Fourier transforms, and how pulses can be generated through constructive and destructive interference of wavelengths with aligned phases. These wavelengths are close to the center wavelength, and spread over a wavelength…<\/p>\n
Read More<\/a><\/div><\/p>\n","protected":false},"author":1,"featured_media":4144,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[32,26,15],"class_list":["post-4143","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-software","tag-laser","tag-matlab","tag-optics"],"_links":{"self":[{"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/posts\/4143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/comments?post=4143"}],"version-history":[{"count":8,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/posts\/4143\/revisions"}],"predecessor-version":[{"id":4153,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/posts\/4143\/revisions\/4153"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/media\/4144"}],"wp:attachment":[{"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/media?parent=4143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/categories?post=4143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/labrigger.com\/blog\/wp-json\/wp\/v2\/tags?post=4143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"ft\"](\"http:\/\/labrigger.com\/blog\/wp-content\/uploads\/2015\/01\/ft.gif\")
<\/p>\n