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The Borrmann effect and extinction in holography
Volume
28A, number
THE
10
PHYSICS
BORRMANN
EFFECT
LETTERS
AND
24 February
EXTINCTION
1969
IN HOLOGRAPHY
V. V. ARISTOV, V. Sh. SHEKHTMAN, V. B. TIMOFEEV Solid State Physics
Institute,
Academy Received
of Science 25 September
of the USSR,
Chernogolovka,
USSR
1968
The structure of holograms recorded in a three-dimensional photosensitive medium, is a combination of ideal three-dimensional periodics. By reconstruction of the images of those holograms phenomena of abnormal transmission and extinction were observed, i.e. effects characteristic for diffraction of Xrays in ideal crystals.
The structure of a hologram, recorded of an object consisting of N points in a three-dimensional photosensitive medium, is a combination of three-dimensional periodics with spatial frequencies v x a& - &,I, where & and& are coordinates of two arbitrary points. Each of the said elementary periodics (total number N2 - N [l]) can be regarded as a three-dimensional diffraction lattice with sinusoidal density distribution. Thus, the ” reading” of a three-dimensional hologram is a process useful to be analysed in terms of X-ray crystallography, dealing with diffraction in three-dimensional periodic structures. As is known, the diffraction in ideal structures is especially distinguished in X-ray optics and is investigated by means of the so-called dynamical theory [2]. According to this theory; the intensity of the primary wave having transitted through an ideal crystal does not merely depend on the linear coefficient of absorption (p) and thickness (t), but assumes an extreme value when located the crystal is in the Bragg position. In particular the extinction is characteristic of an object with negligible absorption (nt
“Ir
some extra weakening of the primery wave due to interaction with diffracted waves. On the other side, in an object with high absorption (n t >>l) the atomic planes under the diffraction angle serve as a kind of waveguide, which ensures the abnormal transmission of the primery wave of a rather low absorption. This phenomenon is named the Borrmann effect. To detect the said effects in visible light appropriate experiments have been carried out, where holograms (acted as ideal crystals) recorded of the two points. Laser was the source of light (X = 0.65 Km), the hologram was located on an X-ray goniometer. The accuracy of angles was within 0.5, the intensity was measured with a precision of less than 2%. Two types hologram have been used: a) recording in a dyed crystal KBr (thickness N 2 cm), (b)
(0)
00Y
60 -60
I -40
,
I -20
c
1 0 8’
Fig. la. 700
(
1 20
(
6 40
(
1 60
00 16
24
32
e” Fig. lb.
40
48
56
PHYSICS
Volume 28A, number 10
LI”““1”“‘-“J 48
40
32
24 0’ Fig. 2.
16
8
LETTERS
24 February 1969
the maximum is very diffuse, but its existence is also undoubtless, which means that any pattern on the photo emulsion can be regarded as three-dimensional structure. In fig. 2 the decrease of intensity of the transitting wave is shown, corresponding to the case of extinction, observed by a hologram, recorded in the film. It is interesting that to analyse it, it proved enough to carry out the measurements in the most transparent pieces of the same hologram for which the Borrmann effect has been marked. The last can be used to investigate experimentally the diffraction of electromagnetic waves in ideal three-dimensional structures. Realy, by means of directing both the thickness and darkening of photo emulsion it is possible to model different experimental situations by means of holograms, including those inaccessible for X-ray analysis. In particular, the hologram being analysed on photo emulsion can be regarded as an optical analogue of zone Huinier-Preston. It is pointed out by the experimentally detected considerable extent of knots of the reciprocal lattice being correlated with the hologram in the direction of the normal towards the surface of the film.
0
b) recording on an ordinary photo emulsion (thickness of photosensitive layer some microns). The dependence of the light intensity, having transitted the hologram, plotted against the angle of rotation is given in fig. 1, and fig. 2. The shape of the curves in fig. 1 is characteristic of the effect of abnormal transmission*. In fig. la the Borrmann effect is shown, corresponding to the hologram, recorded in the dyed crystal KBr. In case of an hologram on photo emulsion (fig. lb)
References V. V. Aristov, V. L. Broude, L. V. Kovalsky, V. K. Polijnsky, V. Sh. Shekhtman, V. B. Timofeev, Doklad. Akad. Nauk 177 (1967) 1, 65. 2. P. P. Ewald, Rev. Mod. Phys. 37 (1965) 46. 3. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks and N. Massey, Appl. Opt. 8 (1966) 1303. 4. Edward J. Saccocio, Appl. Phys. 10 (1967) 3994. 1.
* The intensity increase of the “reading” beam having transitted the hologram on the condition that the angle of reading is equal to this of recording was discribed in ref. 3, where thick-layer emulsions (t N 40 pm) were utilized, In ref. 4 the relation of this phenomenon with the Borrmann effect is pointed out.
LATTICE
VIBRATIONS
J. GOVINDARAJAN Department
of Physics,
IN
ALKALI
AZIDES
and T. M. HARIDASAN
Indian Institute
of Science,
Bangalore-12,
India
Received 27 January 1969
The longwavelength lattice vibrations in potassium, rubidium and caesium azides have been using BornPs lattice dynamics.
In this note we report the lattice vibrations in KN3, RbN3 and CsN3 calculated on the basis of the rigid ion model, taking into account the long range electrostatic coupling coefficients com-
calculated
puted using the Ewald’s method and the nearest neighbour short range interaction with the Pauling potential [l] with n = 9. .The method of Gray et al. [2] has been followed in evaluating a general ra701
28A, number
THE
10
PHYSICS
BORRMANN
EFFECT
LETTERS
AND
24 February
EXTINCTION
1969
IN HOLOGRAPHY
V. V. ARISTOV, V. Sh. SHEKHTMAN, V. B. TIMOFEEV Solid State Physics
Institute,
Academy Received
of Science 25 September
of the USSR,
Chernogolovka,
USSR
1968
The structure of holograms recorded in a three-dimensional photosensitive medium, is a combination of ideal three-dimensional periodics. By reconstruction of the images of those holograms phenomena of abnormal transmission and extinction were observed, i.e. effects characteristic for diffraction of Xrays in ideal crystals.
The structure of a hologram, recorded of an object consisting of N points in a three-dimensional photosensitive medium, is a combination of three-dimensional periodics with spatial frequencies v x a& - &,I, where & and& are coordinates of two arbitrary points. Each of the said elementary periodics (total number N2 - N [l]) can be regarded as a three-dimensional diffraction lattice with sinusoidal density distribution. Thus, the ” reading” of a three-dimensional hologram is a process useful to be analysed in terms of X-ray crystallography, dealing with diffraction in three-dimensional periodic structures. As is known, the diffraction in ideal structures is especially distinguished in X-ray optics and is investigated by means of the so-called dynamical theory [2]. According to this theory; the intensity of the primary wave having transitted through an ideal crystal does not merely depend on the linear coefficient of absorption (p) and thickness (t), but assumes an extreme value when located the crystal is in the Bragg position. In particular the extinction is characteristic of an object with negligible absorption (nt
“Ir
some extra weakening of the primery wave due to interaction with diffracted waves. On the other side, in an object with high absorption (n t >>l) the atomic planes under the diffraction angle serve as a kind of waveguide, which ensures the abnormal transmission of the primery wave of a rather low absorption. This phenomenon is named the Borrmann effect. To detect the said effects in visible light appropriate experiments have been carried out, where holograms (acted as ideal crystals) recorded of the two points. Laser was the source of light (X = 0.65 Km), the hologram was located on an X-ray goniometer. The accuracy of angles was within 0.5, the intensity was measured with a precision of less than 2%. Two types hologram have been used: a) recording in a dyed crystal KBr (thickness N 2 cm), (b)
(0)
00Y
60 -60
I -40
,
I -20
c
1 0 8’
Fig. la. 700
(
1 20
(
6 40
(
1 60
00 16
24
32
e” Fig. lb.
40
48
56
PHYSICS
Volume 28A, number 10
LI”““1”“‘-“J 48
40
32
24 0’ Fig. 2.
16
8
LETTERS
24 February 1969
the maximum is very diffuse, but its existence is also undoubtless, which means that any pattern on the photo emulsion can be regarded as three-dimensional structure. In fig. 2 the decrease of intensity of the transitting wave is shown, corresponding to the case of extinction, observed by a hologram, recorded in the film. It is interesting that to analyse it, it proved enough to carry out the measurements in the most transparent pieces of the same hologram for which the Borrmann effect has been marked. The last can be used to investigate experimentally the diffraction of electromagnetic waves in ideal three-dimensional structures. Realy, by means of directing both the thickness and darkening of photo emulsion it is possible to model different experimental situations by means of holograms, including those inaccessible for X-ray analysis. In particular, the hologram being analysed on photo emulsion can be regarded as an optical analogue of zone Huinier-Preston. It is pointed out by the experimentally detected considerable extent of knots of the reciprocal lattice being correlated with the hologram in the direction of the normal towards the surface of the film.
0
b) recording on an ordinary photo emulsion (thickness of photosensitive layer some microns). The dependence of the light intensity, having transitted the hologram, plotted against the angle of rotation is given in fig. 1, and fig. 2. The shape of the curves in fig. 1 is characteristic of the effect of abnormal transmission*. In fig. la the Borrmann effect is shown, corresponding to the hologram, recorded in the dyed crystal KBr. In case of an hologram on photo emulsion (fig. lb)
References V. V. Aristov, V. L. Broude, L. V. Kovalsky, V. K. Polijnsky, V. Sh. Shekhtman, V. B. Timofeev, Doklad. Akad. Nauk 177 (1967) 1, 65. 2. P. P. Ewald, Rev. Mod. Phys. 37 (1965) 46. 3. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks and N. Massey, Appl. Opt. 8 (1966) 1303. 4. Edward J. Saccocio, Appl. Phys. 10 (1967) 3994. 1.
* The intensity increase of the “reading” beam having transitted the hologram on the condition that the angle of reading is equal to this of recording was discribed in ref. 3, where thick-layer emulsions (t N 40 pm) were utilized, In ref. 4 the relation of this phenomenon with the Borrmann effect is pointed out.
LATTICE
VIBRATIONS
J. GOVINDARAJAN Department
of Physics,
IN
ALKALI
AZIDES
and T. M. HARIDASAN
Indian Institute
of Science,
Bangalore-12,
India
Received 27 January 1969
The longwavelength lattice vibrations in potassium, rubidium and caesium azides have been using BornPs lattice dynamics.
In this note we report the lattice vibrations in KN3, RbN3 and CsN3 calculated on the basis of the rigid ion model, taking into account the long range electrostatic coupling coefficients com-
calculated
puted using the Ewald’s method and the nearest neighbour short range interaction with the Pauling potential [l] with n = 9. .The method of Gray et al. [2] has been followed in evaluating a general ra701