Dear Stephen, Thank you for your extremely thorough explanation. You and your colleagues are really helping move the field ahead with these wonderful tools. Supporting them is a nice bonus.
I should have realized to do |E* dot E| first as well. I searched more this afternoon and stumbled across this other relevant thread, cited here for others to cross reference: http://www.mail-archive.com/[email protected]/msg00318.html I will also check your book as well. Chad Quoting "Steven G. Johnson" <[EMAIL PROTECTED]>: > On Dec 1, 2008, at 11:25 PM, Chad Husko wrote: >> real >> h5topng -Zc dkbluered -C epsilon.h5:data-new -d x.r-new ex.band14.h5 >> imaginary >> h5topng -Zc dkbluered -C epsilon.h5:data-new -d x.i-new ex.band14.h5 >> >> give basically the same results --> modes that do not look like they >> propagate. > > I don't know what you mean by "modes that do not look like they > propagate". Maybe the field is not oriented in the x direction for > the mode you are interested in? It is usually easier to see what is > going on by looking at a scalar field like epsilon*|E|^2 first. > > I have calculated modes of photonic crystal fibers many times with MPB > without a problem. > >> Aeff = int ( int ( |Ex|^2 dy dz ))^2 / int ( int ( |Ex|^4 >> dy >> dz )) in octave/matlab? > > Note that this definition of "effective area" was derived as a figure > of merit for Kerr nonlinearities in the scalar approximation for low > index contrasts. If you are interested in Kerr nonlinearities in high- > contrast media like photonic-crystal fibers, this formula is incorrect > (except in certain limits). If you are interested in other things > like bending losses, etcetera, be aware that formulas derived based on > this effective area are generally from the scalar low-contrast limit > and are inapplicable to photonic-crystal fibers. (In general, a lot of > formulas from the fiber literature, e.g. in the Snyder and Love book, > were derived in the scalar approximation, and it is dangerous to use > them blindly.) > > The correct formula for effective area in high-contrast fibers, as a > figure of merit for Kerr nonlinearities (i.e. the parameter that goes > into the nonlinear Schrodinger equation), was derived by Tzolov in > 1995; the formula and reference are in chapter 9 of our book (ab- > initio.mit.edu/book) > > Note also that you can compute the effective area directly in MPB with > the field integration routines. The following computes the effective > area for a band b for a photonic crystal fiber consisting of an index > n material with a constant Kerr coefficient, and air (with Kerr > coefficient zero), using Tzolov's formula: > > (define (Aeff b) > (define (Aeff-integrand r eps E) > (* (/ eps 3) (/ (- eps 1) (- (sqr n) 1)) > (+ (sqr (magnitude (vector3-dot E E))) > (* 2 (sqr (real-part (vector3-cdot E E))))))) > (define (zflux-integrand r E H) > (real-part (vector3-z (vector3-cross (vector3-conj E) H)))) > (get-efield b) > (let ((E (field-copy cur-field))) > (get-epsilon) > (let ((denom (integrate-fields Aeff-integrand cur-field E))) > (get-hfield b) > (/ (sqr (integrate-fields zflux-integrand E cur-field)) > denom)))) > > Note that Tzolov's formula reduces to the one you quoted in the scalar > limit (either low-contrast materials or propagation constant beta -> > infinity). > > Steven > > _______________________________________________ > mpb-discuss mailing list > [email protected] > http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss > > _______________________________________________ mpb-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
