Re: efield vs. dpwr, field definition --> follow up on old thread

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
>
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