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The electrogyration effect is the spatial dispersion phenomenon, that consists in the change of optical activity (gyration) of crystals by a constant or time-varying electric field. A phenomenon (from Greek φαινόμενoν, pl φαινόμενα - phenomena) is any observable occurrence Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can Being a spatial dispersion effect, the induced optical activity exhibit different behavior under the operation of wave vector reversal, when compare with the Faraday effect: the optical activity increment associated with the electrogyration effect changes its sign under that operation, contrary to the Faraday effect. In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic

The electrogyration effect linear in the electric field occurs in crystals of all point groups of symmetry except for the three cubic – m3m, 432 and \overline{4}3m\, . In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The effect proportional to the square of the electric field can exist only in crystals belonging to acentric point groups of symmetry. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Mathematics, a point group is a group of geometric symmetries ( isometries) leaving a point fixed

Contents

The historical background of discovery of electrogyration

The changes in the optical activity sign induced by the external electric field have been observed for the first time in ferroelectric crystals LiH3(SeO4)2 by H. Futama and R. Pepinsky in 1961 [1], while switching enantiomorphous ferroelectric domains (the change in the point symmetry group of the crystal being 2/m«m). The observed phenomenon has been explained as a consequence of specific domain structure (a replacement of optic axes occurred under the switching), rather than the electrogyration induced by spontaneous polarization. The first description of electrogyration effect induced by the biasing field and spontaneous polarization at ferroelectric phase transitions has been proposed by K. Aizu in 1963 on the basis of third-rank axial tensors [2] (the manuscript received on September 9, 1963). Probably, K. Aizu has been the first who defined the electro-gyration effect (”the rate of change of the gyration with the biasing electric field at zero value of the biasing electric field is provisionally referred to as “electrogyration””) and introduced the term “electrogyration” itself. Almost simultaneously with K. Aizu, I. S. Zheludev has suggested tensor description of the electrogyration in 1964 [3] (the manuscript received on February 21, 1964). In this paper the electrogyration has been referred to as “electro-optic activity”. In 1969, O. G. Vlokh has measured for the first time the electrogyration effect induced by external biasing field in the quartz crystal and determined the coefficient of quadratic electro-gyration effect [4] (the manuscript received on July 7, 1969).
Thus, the electrogyration effect has been predicted simultaneously by Aizu K. and Zheludev I. S. in 1963–1964 and revealed experimentally in quartz crystals by Vlokh O. G. in 1969. [5] [6] [7] [8].

Description

Electrodynamics relations

The electric field and the electric displacement vectors of electromagnetic wave propagating in gyrotropic crystals may be written respectively as:

E_{i}=B_{ij}^{0}D_{j}+\tilde\delta_{ijk}\frac{\partial D_{j}}{\partial x_{k}}=B_{ij}^{0}D_{j}+(ie_{ijl}\tilde{g}_{lk}k_k)D_{j}\, ,                             (1)

or

D_{i}=\epsilon_{ij}^{0}E_{j}+\delta_{ijk}\frac{\partial E_{j}}{\partial x_{k}}=\epsilon_{ij}^{0}E_{j}+(ie_{ijl}{g}_{lk}k_k)E_{j}\, ,                           (2)

where B_{ij}^{0} is the optical frequency impermeability tensor, \epsilon_{ij}^{0} the dielectric permittivity tensor, \tilde{g}_{lk}\overline{n}=g_{kl}, \overline{n} the mean refractive index, D_{j}\, - induction, \delta_{ijk}\, , \tilde\delta_{ijk} polar third rank tensors, e_{ijl}\, the unit antisymmetric Levi-Civit pseudo-tensor, k_k\, the wave vector, and g_{lk}\, , \tilde{g}_{lk} the second rank gyration pseudo-tensors. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually A wave vector is a vector representation of a Wave. The wave vector has magnitude indicating Wavenumber (reciprocal of Wavelength) and the The specific rotation angle of the polarization plane \rho\, caused by the natural optical activity is defined by the relation:

\rho=\frac{\pi}{\lambda n}g_{lk}l_{l}l_{k}=\frac{\pi}{\lambda n}G\, ,                                                  (3)

where n\, is the refractive index, \lambda\, the wavelength, l_{l}\, , l_{k}\, the transformation coefficients between the Cartesian and spherical coordinate systems (l_{1}=\sin \Theta \cos \varphi\, , l_{2}=\sin \Theta \sin \varphi, l_{3}=\cos \Theta), and G\, the pseudo-scalar gyration parameter. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials The electro-gyration increment of gyration tensor occurred under the action of electric field E_{m}\, or/and E_{n}\, is written as:

\Delta g_{lk}=\gamma _{lkm}E_{m}+\beta _{lkmn}E_{m}E_{n}\, ,                                           (4)

where \gamma _{lkm}\, and \beta _{lkmn}\, are third- and fourth-rank axial tensors describing the linear and quadratic electrogyration, respectively. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually In the absence of linear birefringence, electrogyration increment of the specific rotatory power is given by:

\Delta \rho=\frac{\pi}{\lambda n}g_{lk}l_{l}l_{k}=\frac{\pi}{\lambda n}\Delta G=\frac{\pi}{\lambda n}(\gamma _{lkm}E_{m}+\beta _{lkmn}E_{m}E_{n})l_{l}l_{k}. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray                    (5)

The electrogyration effect may be also induced by spontaneous polarization P_{m}^{s}P_{n}^{s}\, appearing in the course of ferroelectric phase transitions [9]:

\Delta \rho=\frac{\pi}{\lambda n}g_{lk}l_{l}l_{k}=\frac{\pi}{\lambda n}\Delta G=\frac{\pi}{\lambda n}(\tilde\gamma _{lkm}P_{m}^{s}+\tilde\beta _{lkmn}P_{m}^{s}P_{n}^{s})l_{l}l_{k}.                    (6)

Explanation on the basis of symmetry approuch

The electrogyration effect can be easy explained on the basis of Curie and Neumann symmetry principles. In the crystals that exhibit centre of symmetry, natural gyration can not exist, since, due to the Neumann principle, the point symmetry group of the medium should be a subgroup of the symmetry group that describes the phenomena, which are properties of this medium. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating As aresult, the gyration tensor possessing a symmetry of second-rank axial tensor - \infty 2\, is not a subgroup of centrosymmetric media and so the natural optical activity cannot exist in such media. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials According to the Curie symmetry principle, external actions reduce the symmetry group of the medium down to the group defined by intersection of the symmetry groups of the action and the medium. When the electric field (with the symmetry of polar vector, \infty mm\, ) influences the crystal which possess the inversion centre, the symmetry group of the crystal should be lowered to the acentric one, thus permitting the appearance of gyration. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can However, in case of the quadratic electrogyration effect, the symmetry of the action should be considered as that of the dyad product E_{m}E_{n} \, or, what is the same, the symmetry of a polar second-rank tensor (\infty /mmm\, ). History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Such a centrosymmetric action cannot lead to lowering of centrosymmetric symmetry of crystal to acentric states. This is the reason why the quadratic electrogyration exists only in the acentric crystals.

Eigenwaves in the presence of electrogyration

In a general case of light propagation along optically anisotropic directions, the eigenwaves become elliptically polarized in the presence of electrogyration effect, including rotation of the azimuth of polarization ellipse. Then the corresponding ellipticity \kappa \, and the azimuth \chi \, are defined respectivelly by the relations

\kappa =\frac{\Delta G}{2\Delta n\overline{n}}\, ,                                                             (7)
\tan 2(\alpha -\chi )=\frac{2\kappa }{1+\kappa ^2}\tan \boldsymbol{\Gamma } \left ( 1+\frac{P\tan 2\alpha +(1-R)}{R+\tan ^22\alpha } \right )\,  ,                  (8)

where \alpha \, is the polarization azimuth of the incident light with respect to the principal indicatrix axis, \Delta n\, the linear birefringence, \boldsymbol\Gamma \, the phase retardation, P=\frac{(1-\kappa ^2)^2}{2\kappa (1+\kappa ^2)}\, , and R=\left (\frac{2\kappa }{1+\kappa ^2}\right )^2+\left (\frac{1-\kappa ^2}{1+\kappa ^2}\right )^2\, . Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray In the case of light propagation along optically isotropic directions (i. e. , the optic axes), the eigenwave become circularly polarized (\kappa =1\, ), with different phase velocities and different signs of circular polarization (left and right ones). In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the Hence the relation (8) may be simplified so as to describe a pure polarization plane rotation:

2(\alpha -\chi )=\boldsymbol\Gamma \, ,                                                                (9)

or

\rho d=\alpha -\frac{\boldsymbol\Gamma}{2}\, ,                                                 (10)

where d\, - is the sample thickness along the direction of light propagation. For the directions of light propagation far from the optic axis, the ellipticity \kappa \, is small and so one can neglect the terms proportional to \kappa ^2\, in Eq. (8). Thus, in order to describe the polarization azimuth at \alpha =0\, and the gyration tensor, simplified relations

\tan 2\chi =-2\kappa \sin \boldsymbol\Gamma\, ,                                                        (11)

or

g_{kl}=2\chi \Delta n\overline{n}\, .                                                           (12)

are often used. According to Eq. (11), when the light propagates along anisotropic directions, the gyration (or the electro-gyration) effects manifest themselves as oscillations of the azimuth of polarization ellipse occurring with changing phase retardation \boldsymbol\Gamma\, . Gyration is another term for Rotation. A center of actual rotation as well as Rotational symmetry may be called gyration center gyration point or rotocenter

Experimental results

The electrogyration effect has been revealed for the first time in quartz crystals [2] as an effect quadratic in the external field. Later on, both the linear and quadratic [10] electrogyrations has been studied in the dielectric (\alpha -\, HIO3 [11], LiIO3 [12], PbMoO4 [13], NaBi(MoO4)2, Pb5SiO4(VO4)2, Pb5SeO4(VO4)2, Pb5GeO4(VO4)2 [14], alums [15] [16] [17] etc. ) semiconductor (AgGaS2, CdGa2S4) [18], ferroelectric (TGS, Rochelle Salt, Pb5Ge3O11 and KDP families etc. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent ) [19] [20] [21] [22] , as well as the photorefractive (Bi12SiO20, Bi12GeO20, Bi12TiO20) materials [23] [24] [25]. The photorefractive effect is a nonlinear optical effect seen in certain Crystals and other materials that respond to Light by altering their The electro-gyration effect induced by a powerful laser radiation (a so called self-induced or dynamic electro-gyration) has been studied in the works [26] [27]. The influence of electro-gyration on the photorefraction storage has been investigated in [28] [29], too. The photorefractive effect is a nonlinear optical effect seen in certain Crystals and other materials that respond to Light by altering their From the viewpoint of nonlinear electrodynamics, the existence of gradient of the electric field of optical wave in the range of the unit cell corresponds to macroscopic gradient of the external electrical field, if only the frequency transposition [30] is taken into account. In that sense, the electrogyration effect represents the first of the gradient nonlinear optical phenomena ever revealed.

References

  1. ^ [1]Futama H. and Pepinsky R. (1962) "Optical activity in ferroelectric LiH3(SeO3)2", J. Phys. Soc. Jap. 17, 725
  2. ^ [2]Aizu K. (1964) “Reversal in optical rotatory power – “gyroelectric” crystals and “hypergyroelectric” crystals”, Phys. Rev. 133 (6A) A1584–A1588
  3. ^ [3]Zheludev I. S. (1964), "Axial tensors of the third rank and the physical effects they describe", Kristallografiya 9, 501-505. [(1965). Sov. Phys. Crystallogr. 9,418]
  4. ^ [4]Vlokh O. G. (1970). "Electrooptical activity of quartz crystals", Ukr. Fiz. Zhurn. 15(5), 758-762. [Blokh O. G. (1970). "Electrooptical activity of quartz crystals", Sov. Phys. Ukr. Fiz. Zhurn. 15, 771. ]
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  14. ^ [14]Vlokh O. G. (1984) Spatial dispersion phenomena in parametric crystal optics. Lviv: Vyshcha Shkola (in Russian).
  15. ^ [15]Weber H. J. and Haussuhl S. (1974), "Electric-Field-Induced Optical Activity and Circular Dichroism of Cr-Doped KAl(SO4)2 · 12H2O " Phys. Stat. Sol. (b) 65, 633-639.
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  17. ^ [17]Weber H. J. , Haussuhl S. (1976) "Electrogyration effect in alums", Acta Cryst. A32 892-895
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  19. ^ [19]Kobayashi J. , Takahashi T. , Hosakawa T. and Uesu Y. (1978). "A new method for measuring the optical activity of crystals and the optical activity of KH2PO4 ", J. Appl. Phys. 49, 809-815.
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  21. ^ [21]Uesu Y. , Sorimachi H. and Kobayashi J. (1979), "Electrogyration of a Nonenantiomorphic Crystal, Ferroelectric KH2PO4 " Phys. Rev. Lett. 42, 1427-1430.
  22. ^ [22]Vlokh O. G. , Lazgko L. A. , Shopa Y. I. (1981), "Electrooptic and Electrogyration Properties of the Solid Solutions on the Basis of Lead Germanate", Phys. Stat. Sol. (a) 65: 371-378.
  23. ^ [23]Vlokh O. G. , Zarik A. V. (1977), "The effect of electric field on the polarization of light in the Bi12SiO20, Bi12GeO20, NaBrO3 crystals", Ukr. Fiz. Zhurn. 22(6), 1027-1031.
  24. ^ [24]Deliolanis N. C. , Kourmoulis I. M. , Asimellis G. , Apostolidis A. G. , Vanidhis E. D. , and Vainos N. A. (2005), "Direct measurement of the dispersion of electrogyration coefficient of photorefractive Bi12GeO20", J. Appl. Phys. 97, 023531.
  25. ^ [25]Deliolanis N. C, Vanidhis E. D, and Vainos N. A. (2006), "Dispersion of electogyration in sillenite crystals", Appl. Phys. B 85(4), 591-596.
  26. ^ [26]Akhmanov S. A. , Zhdanov B. V. , Zheludev N. I. , Kovrigin N. I. , Kuznetsov V. I. (1979). "Nonlinear optical activity in crystals", Pis. ZhETF. 29, 294-298.
  27. ^ [27]Zheludev N. I. , Karasev V. Yu. , Kostov Z. M. Nunuparov M. S. (1986) "Giant exciton resonance in nonlinear optical activity", Pis. ZhETF, 43(12), 578-581.
  28. ^ [28]Brodin M. S. , Volkov V. I. , Kukhtarev N. V. and Privalko A. V. (1990), "Nanosecond electrogyration selfdiffraction in Bi12TiO20 (BTO) crystal", Optics Communications, 76(1), 21-24.
  29. ^ [29]Kukhtarev N. V. , Dovgalenko G. E. (1986) "Self-diffraction electrogyration and electroellipticity in centrosymmetric crystals", Sov. J. Quantum Electron. , , 16 (1), 113-114.
  30. ^ [30]Vlokh R. O. (1991). "Nonlinear medium polarization with account of gradient invariants. ", Phys. Stat. Sol (b), 168, k47-K50.

See also

Piezo-gyration
Faraday effect

In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic
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