Thank you Ian for the comment ! Apparently, I was a bit too quick in my answer. By the way, my mentioning of Fresnel's theory was of pure historical interest and not at all to say that the whole story was written at that time.
I went back to my "Born & Wolf" (some kind of a bible in the optics field) and I am somewhat surprised of not seeing any comment on that topics. May be the comments exist, but implicitly in the cited litterature... Now, I am still wondering whether external "stresses" on biological crystals could indeed induce such unexpected birefringence. Philippe Dumas IBMC-CNRS, UPR9002 15, rue René Descartes 67084 Strasbourg cedex tel: +33 (0)3 88 41 70 02 [EMAIL PROTECTED] -----Message d'origine----- De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la part de Ian Tickle Envoyé : Thursday, June 12, 2008 9:20 PM À : CCP4BB@JISCMAIL.AC.UK Objet : Re: [ccp4bb] birefringent spacegroups But it seems that Hendrik Lorentz was the first to realise that symmetry breaking of the isotropy of the refractive index & other optical properties could occur in cubic crystals at sufficiently short wavelength even in the absence of a distorting force - the "spatial-dispersion-induced birefringence" effect referred to in the paper. Note that this is an intrinsic effect, it has nothing to do with external stress, electric field etc., and if you read the paper you'll see that such external effects were specifically eliminated as the cause of the observed effect. -- Ian > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Philippe DUMAS > Sent: 12 June 2008 19:20 > To: Ian Tickle; CCP4BB@JISCMAIL.AC.UK > Subject: RE: [ccp4bb] birefringent spacegroups > > Hello, > > A short comment of historical interest: the first theory about "double > refraction in crystals" (with explicit calculation of the > index ellipsoid) > goes back to 3 memoirs by A. Fresnel in 1821 and 1822. So, we > are even in > "older regions". > > This being said, in cubic crystals the index ellipsoid can > only be a sphere. > An so, no birefringence should exist (unless there is some > external cause of > anisotropy: mecanical stress, electric field,...). See Born & Wolff > (principles of optics) p. 703. May be, our "biological > crystals" might quite > easily develop such "stress birefringence"... > > Philippe Dumas > IBMC-CNRS, UPR9002 > 15, rue René Descartes 67084 Strasbourg cedex > tel: +33 (0)3 88 41 70 02 > [EMAIL PROTECTED] > > > > -----Message d'origine----- > De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la > part de Ian > Tickle > Envoyé : Thursday, June 12, 2008 7:19 PM > À : CCP4BB@JISCMAIL.AC.UK > Objet : Re: [ccp4bb] birefringent spacegroups > > > PS in case you missed it, here's the bottom line from the paper: > > "Interestingly, a cubic crystal has seven nonbirefringent > axes, four in > the <111> > directions and three in the <100> directions, with > birefringence maxima > in the twelve <110> directions." > > So it would appear that the optical properties of cubic crystals are > *more* complicated than those of lower symmetry systems, not > less! - and > previous conclusions about isotropy of cubic crystals probably arose > because the measurements were simply not precise enough (or > not carried > out at short enough wavelength) to detect the effect. However the > relevant theory goes back to Lorentz (1878) so it's not exactly new! > > Cheers > > -- Ian > > > -----Original Message----- > > From: [EMAIL PROTECTED] > > [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle > > Sent: 12 June 2008 17:50 > > To: Ethan A Merritt; Jacob Keller > > Cc: CCP4BB@jiscmail.ac.uk > > Subject: RE: [ccp4bb] birefringent spacegroups > > > > Hi Ethan > > > > You could be right, see this paper: > > > > > http://physics.nist.gov/Divisions/Div842/Gp2/DUVMatChar/PDF/In > tBiref.pdf > > > > Cheers > > > > -- Ian > > > > > > > -----Original Message----- > > > From: [EMAIL PROTECTED] > > > [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt > > > Sent: 12 June 2008 15:46 > > > To: Multiple recipients > > > Cc: CCP4BB@jiscmail.ac.uk > > > Subject: Re: [ccp4bb] birefringent spacegroups > > > > > > On Wednesday 11 June 2008 23:55, Robin Owen wrote: > > > > Hi Jacob, > > > > > > > > The birefringence of a crystal is determined by a three > > dimensional > > > > shape (the indicatrix) describing how refractive index > > varies with > > > > direction within the crystal. You can think of this as a 3d > > > ellipse and > > > > the birefringence is given by the difference in length of > > > the two axes > > > > of the ellipse 'seen' by light as it passes through the crystal. > > > > > > > > The orientation and shape of the indicatrix are constrained > > > by the point > > > > group symmetry of the crystal. In the case of cubic > crystals, the > > > > indicatrix is characterised by four 3-fold axes. The > > > indicatrix for all > > > > cubic crystals is thus a sphere and cubic crystals are > > > non-birefringent. > > > > Hexagonal, trigonal and tetragonal crystals are uniaxial and the > > > > indicatrix is an ellipsoid of revolution > > > > - there is one direction in which the crystal appears > > > non-birefringent. > > > > Orthorhombic, monoclinic and triclinic systems are biaxial > > > -two axes in > > > > which the crystal appears non-birefringent. > > > > > > I have wondered about this in the past. > > > That argument only appears to hold if "birefringent" is > > taken to mean > > > "different optical index at two angles 90 degrees apart". I think > > > even in a cubic crystal you can find non-equivalent > > directions if you > > > are not limited to a right angle between the two vectors. > Does this > > > not count as birefringence? Or am I misunderstanding the > > definition? > > > > > > Ethan > > > > > > and then there's the issue of anomalous dispersion... > > > > > > > A good reference is > > > > Nye (1984). Physical Properties of crystals. Their > > > representation by > > > > tensors and matrices. Clarendon Press, Oxford. > > > > There is a more detailed list of space groups and their > > > tensor optical > > > > properties in there I think. > > > > > > > > Cheers, > > > > Robin > > > > > > > > > > > > Jacob Keller wrote: > > > > > Dear Crystallographers, > > > > > > > > > > is there a list somewhere of spacegroups which can and > > cannot be > > > > > birefringent? Upon what feature of the spacegroup does > > > this depend? > > > > > > > > > > Jacob Keller > > > > > > > > > > ******************************************* > > > > > Jacob Pearson Keller > > > > > Northwestern University > > > > > Medical Scientist Training Program > > > > > Dallos Laboratory > > > > > F. Searle 1-240 > > > > > 2240 Campus Drive > > > > > Evanston IL 60208 > > > > > lab: 847.491.2438 > > > > > cel: 773.608.9185 > > > > > email: [EMAIL PROTECTED] > > > > > ******************************************* > > > > > > > > > > -- > > > Ethan A Merritt > > > Biomolecular Structure Center > > > University of Washington, Seattle 98195-7742 > > > > > > > > > > > > Disclaimer > > This communication is confidential and may contain privileged > > information intended solely for the named addressee(s). It > > may not be used or disclosed except for the purpose for which > > it has been sent. If you are not the intended recipient you > > must not review, use, disclose, copy, distribute or take any > > action in reliance upon it. 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