May 1, 2010 / Vol. 35, No. 9 / OPTICS LETTERS 1359

On the existence of Jones birefringenceand Jones dichroism

Oriol ArteagaFEMAN Group, Departament de Física Aplicada i Òptica, IN2UB, Universitat de Barcelona, Barcelona 08028, Spain

(oarteaga@ub.edu)

Received February 2, 2010; revised March 10, 2010; accepted March 11, 2010;posted March 16, 2010 (Doc. ID 123645); published April 23, 2010

We claim that the so-called Jones birefringence and Jones dichroism effects, understood as new optical phe-nomena of difficult experimental observation, cannot be deduced from Jones publications and were proposeddue to a misinterpretation of his original work. © 2010 Optical Society of America

OCIS codes: 260.1440, 260.1180.

In 1948 Jones published the seventh paper of his fa-mous series [1]. It was devoted to a matrix calculusbased on infinitesimal matrices, the 2�2 N matrices,which allows one to describe the linear optical effectsof a system. This formalism has been widely appliedin crystal optics and in spectroscopy of oriented mol-ecules. It is worthwhile to note that some time laterAzzam [2] developed an analogous infinitesimal for-malism based on Mueller matrices. In [1] Jonesstated that eight real constants (the real and imagi-nary parts of each one of the four complex matrix el-ements) are required to specify an N matrix. Accord-ing to him these constants were chosen so that eachone of them corresponded to a simple type of opticalbehavior, namely, phase retardation, amplitude ab-sorption, circular birefringence, circular dichroism,linear birefringence, and linear dichroism parts par-allel to the coordinate axes and linear birefringenceand linear dichroism parts parallel with the bisectorsof the coordinate axes.

In 1983 Graham and Raab published a paper [3]stating that in Jones’ 1948 work a new kind of linearbirefringence, together with its corresponding dichro-ism, had been postulated and proposed the namesJones birefringence and Jones dichroism for such ef-fects. They argued that the linear birefringence andthe linear dichroism parallel with the bisectors of thecoordinate axes were new types of optical effects thatwere unknown up to that date. In this work they pre-dicted that Jones birefringence can occur naturally incertain uniaxial and biaxial nonmagnetic crystals,where it should accompany the “familiar” linear bire-fringence. They also predicted the presence of Jonesbirefringence in liquids subjected to parallel electricand magnetic fields. Later, in [4] they found, by usinga multipole approach to the electromagnetic effects,that Jones birefringence would be typically 4 ordersof magnitude smaller than the usual linear birefrin-gence.

To our knowledge no experimental observations ofthe Jones birefringence in crystals have been re-ported. According to [5], Jones birefringence occur-ring naturally in crystals is probably too weak to bemeasurable. However, the first experimental obser-vation of Jones birefringence in systems with parallelelectric and magnetic fields was published in 2000

[6], and, in 2003, the first experimental observation

0146-9592/10/091359-2/$15.00 ©

of Jones dichroism was reported [7]. Since then, theinterest on the subject of Jones birefringence andJones dichroism seems to increase [8–13], and recentbooks [14–16] review the subject. Much like [3], mostof these publications state that these supposed neweffects were deduced by Jones, and even, in [6], it issaid that their experimental observation constitutesthe final validation of the Jones formalism in polar-ization optics.

We argue that in his 1948 paper Jones did not in-troduce neither deduce any intriguing new opticalphenomenon. We think that linear birefringence andlinear dichroism parallels with the bisectors of thecoordinate axes that Jones used are not new opticaleffects of difficult experimental observation and thatthe controversy about these effects stems from a mis-interpretation of the coordinated system used in theoriginal Jones publication, misinterpretation thatprobably started with [3].

Jones calculus can be developed for an arbitrarybasis, although the most usual choice is a laboratoryCartesian coordinate system in which light propa-gates along the positive z axis. The optical elementdescribed by Jones had plane and parallel surfaceslying in the xy plane. Keeping the same notation usedin [1], the definitions that Jones gave for the twoparts (g0 and g45) of the linear birefringence are

g0 =�

��ny − nx�, g45 =

�

��n−45 − n45�, �1�

where � is the wavelength of light and ni is the indexof refraction on the stated directions. Consideringthese equations and the laboratory coordinate systemit is easy to realize that, for example, any uniaxialoptical element with the optical axis not lying paral-lel to the x, y, and z axes will have a g45 differentfrom zero. Thus, rather than a new type of birefrin-gence, g45 is only a measure of the part of the linearbirefringence that is parallel to the bisector of the co-ordinate axes, and it does not supposes any new find-ing. We suspect that the confusion must have arisenwith the incorrect assumption that Jones used a co-ordinate system based on the optical axis of the opti-cal element under study. It is important to stressthat, in general, neither g0 nor g45, as defined in Eqs.

(1), are equivalent to the usual definition of linear bi-

2010 Optical Society of America

1360 OPTICS LETTERS / Vol. 35, No. 9 / May 1, 2010

refringence given in crystal optics,

� =2�

��ne − no�, �2�

because this definition is given for the natural basisof the birefringent element, i.e., a coordinate systembased on the crystallographic (ordinary and extraor-dinary) axes of the optical element. If the optic axislies in the xy plane (this may be not always the case)the relation between � and g0 and g45 clearly showsthat g0 and g45 can be understood as measurementsof the “projected” of birefringence,

g0 = −�

2cos�2��, g45 = −

�

2sin�2��, �3�

where � is the angle shown in Fig. 1. For an arbitraryorientation of the optic axis, the correspondence be-tween � and g0 and g45 is more complex and involvesthe complete set of Euler angles.

To our knowledge there are no further and solid ar-guments proving the existence of a supposed newtype of birefringence or dichroism independent fromthe “usual” one. Theoretical works on this subject arenot aimed to demonstrate the Jones birefringenceand Jones dichroism as new phenomena independentfrom the standard linear birefringence; instead, theyassume that they exist by citing Jones work and fo-cus their attention on identifying systems in whichthese effects may be possible.

According to our thesis, experimental observationsof that part of the linear birefringence or the lineardichroism parallel to the bisector of the laboratory co-

Fig. 1. For an optical element with the optic axis lying inthe xy plane, the laboratory coordinates x and y (referencebasis) are related to the crystallographic coordinates (natu-

ral basis) by a simple rotation.

ordinate axes can be easily done with polarimetrictechniques, as is shown, for example, in [17], and itdoes not involve any special difficulty. Probably, mostof the reported experimental results on Jones bire-fringence or Jones dichroism could be interpreted asmeasurements of “projected” birefringence or dichro-ism, and, therefore, their physical meaning would begiven by their correspondence, in terms of Eulerangles, to the birefringence or dichroism of the natu-ral basis. To conclude, we advise against the use ofthe terms of “Jones birefringence” and “Jones dichro-ism,” as we consider that they were proposed follow-ing a misinterpretation of Jones’ work.

The author thanks Daniel Arteaga for his Englishrevision of the manuscript and acknowledges finan-cial support from the Ministerio de Educacion ofSpain through FPU AP2006-00193.

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