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Light scattering in bismuth silicate: matching of experimental results
__ __ !!B
15 September
CQa
1996
OPTICS COMMUNICATIONS
ELSEVIER
Optics Communications
130 (1996) 85-88
Light scattering in bismuth silicate: matching of experimental results H.C. Ellin, L. Solymar Holography Group, Department ofEngineering Science, University of Ux&rd, Parks Road, Oxford, UK Received
17 August 1995; accepted 27 February
1996
Abstract The scattering pattern of a coherent light beam incident ~~endicularly on a bismuth silicate crystal in the presence of an applied electric field is investigated. A theoretical model is shown to give good agreement with the measurements provided the piezoelectric and photoelastic effects are incorporated into the usual coupled wave equations.
the results with a theory which takes into account the
1. Introduction
piezoelectric It
is well known
upon
a photorefractive
distortion,
that an optical material
may
beam suffer
and photoelastic
effects.
incident serious
2. Ex~rim~nts
usually
referred to as fanning or scattering. This property was stated already in the very first paper [l] written on photorefractive materials. The first consistent study of scattering was made much later, by Voronov et al. [2] in SBN, confirming that the strength of the scattering pattern reflected the angular distribution of two-wave gain. Following this article many interesting results were reported in materials where the anisotropy played an essential roIe (for a review see Ref. [3]). Most of the experimental observations have by now been accounted for but scattering in bismuth silicate (BSO) is still one of the unsolved problems. The scattering patterns measured by Imbert [4] and Rajbenbach et al. [5] have not so far been satisfactorily explained, although a tentative explanation was suggested by Ellin et al. [63. The aim of the present Communication is to present further experiments on scattering in BSO and match 0030~4018/96/$12.00 Copyright PII SOO30-4018(96)00169-l
A schematic representation of the experimental set-up is shown in Fig. 1. A single expanded beam from an argon laser operating at a wavelength of 514.5 nm was directed, at normal incidence, onto the (ilO> face of a BSO crystal having dimensions 5 mm X 5 mm X 10 mm (interaction length). A voltage of 5 kV was applied across the (001) faces of the crystal and the emerging pattern (shown in the inset) was observed on a screen located approximately 1 m behind the crystal. The scatter pattern as observed on the screen is shown schematically in the inset of Fig. 1, and in more detail in Fig. 2, taken from a video still. It must be emphasized that the pattern is not in the plane of incidence although one knows that there are strong enough scattered beams in that plane to enable one (see e.g. Ref. [7]) to set up ring resonators.
0 1996 Elsevier Science B.V. All rights reserved.
H.C. Elk
86
L. Solymur/Optics
Communications
130 (1996) 85-88
Y ‘v
>
I
Fig.
I. Schematic representation
of the experimental
set-up. Inset: the light pattern shown on the screen.
We have observed similar patterns in a number of crystals under similar conditions. The pattern, as may be expected, was voltage dependent. The higher the voltage, the greater the extent of the lobes in the x and y directions. The observed scatter was found to depend strongly on the angle of the incident beam as well. A small deviation from the perpendicular (of the order of lo> yielded a different type of scattering mechanism in which noise gratings were read by the boundary reflected beam. These observations were reported earlier [6].
3. Theoretical modelling
Fig. 2. A video still of the scatter pattern (the directly transmitted beam is not shown).
Can the pattern be explained by mapping the two-wave gain for BSO? Traditional theories which include only the electro-optic effect would not be able to do it because they would predict maximum gain in the plane of incidence. Some new theories could however help. First, we have to refer here to the experimental results of Ellin [8] and Ellin et al. [9] (two waves incident, one is detuned in order to
H.C. Ellin, L. Solymar/Optics
0
2
4
6
8
10
12
14
16
18
20
xdirection(~)
Fig. 3. Theoretical prediction of the relative intensity (normalized to 100) on the screen using the experimental parameters.
obtain maximum gain) in BSO in which they showed that two-wave gain may actually be higher when the incident wave vectors create a grating which is not in the xz plane (i.e. the grating vector has an arbitrary y component). It was also possible to match their experimental results by solving numerically the vector differential equations [8,9] for the interaction between the two waves but incorporating, in addition to the electro-optic effect, the piezo-electric and photo-elastic effects as suggested by Stepanov et al. [lo], Shandarov et al. [l 11, Gunter and Zgonik [12] and Pauliat et al. [13]. The theory used in the present paper is exactly the same as that in Refs. [8,9] so there seems to be no point repeating here the rather lengthy equations. The relevant interaction takes place between the beam incident perpendicularly upon the crystal and
Communicurions 130 11996) 85-88
87
light which is scattered throughout the crystal. The scattered light may then be represented by an infinite number of small amplitude waves propagating in all possible directions. Those waves will be observed which are optimally amplified. In order to find that we calculate the two-wave gain in all possible directions. In our model we take into account detuning, attenuation, optical activity and the relevant electrooptic, piezoelectric and photoelastic coefficients, and we solve numerically the corresponding coupled wave equations [8,9]. Having found the gain in a particular direction we repeat the calculations for a range of detuning values in order to find the maximum gain. The argument is that the frequency of the scattered beam will cover a range of frequencies and that it will not be restricted to the frequency of the input beam. Out of this range of scattered beams only the one with the highest amplitude will be observed, and that is the reason why we must find the optimum detuning. Where would the additional frequency come from? From the reservoir of space charge waves which are present owing to the application of a d.c. electric field (see e.g. Ref. [14]). The concept of Space Charge Wave Scattering has not sufficiently permeated the literature yet but it can be easily appreciated by people familiar with Brillouin or Raman scattering. It is the same kind of thing. Having performed the calculations for all possible directions the normalized output intensity (maximum equal to 100) is plotted in Figs. 3a and 3b for positive and negative y coordinates respectively. The experimental pattern of Fig. 2 may be seen to be reproduced with good approximation.
4. Conclusions
We have measured experimentally the scatter pattern due to a single coherent laser beam incident perpendicularly upon the (ilO> face of a BSO crystal. We have shown that this pattern can be matched by a model calculating the two-wave gain which (i) considers an optimally detuned scattered beam, and (ii) incorporates both th e piezoelectric and photoelastic effects.
88
H.C. Ellin, L. Solymar/Optics
References [l] A. Ashkin, G.D. Boyd, J.M. Dziedzic, R.G. Smith, A.A. Ballman, J.J. Levinstein and K. Nassau, Appl. Phys. Lett. 9 ( 1966172. [2] V.V. Voronov, I.R. Dorosh, YuS. Kuz’minov and N.V. Tkachenko, Sov. J. Quantum Electron. 10 (1980) 1346. [3] S.G. Odoulov, and M. Soskin, Chapter 2 in Photorefractive materials and their applications, Springer, 1989, eds. P. Gunter and J.P. Huignard. [4] B. Imbert, Etude de la sensibilite des cristaux BSO a A = 633 nm et A = 840 nm, Rapport de stage, Universite de Paris Xl, DEA d’optique et Photonique, 1986, pp. l-34. [5] H. Rajbenbach, A. Delboulbe and J.P. Huignard, Optics Len. 14 (1989) 1275.
Communications
130 (1996) 85-M
[6] H.C. Ellin, J. Takacs and L. Solymar, Appl. Optics 33 (19941 4125. [7] H. Rajbenbach and J.P. Huignard, Optics Lett. 10 (1985) 137. [8] H.C. Ellin, Aspects of wave interactions in photorefractive materials, D. Phil. thesis, Dept. Eng. SC. Univ. Oxford, 1994. 191 H.C. Ellin, A. Gnmnet-Jepsen, L. Solymar and J. Takacs, Proc. SPIE 2321 (19941 107. [lo] S.I. Stepanov, S.M. Shandarov and N.D. Khatkov, Sov. Phys. Solid State 29 (19871 1754. [l l] S.M. Shandarov, V.V. Shepelevich and N.D. Khatkov, Opt. Spectrosc. 70 (19911 627. [12] P. Gunter and M. Zgonik, Optics Lett. 16 (19911 1826. 1131 G. Pauliat, M. Mathey and G. Roosen, J. Opt. Sot. Am. B 8 (19911 1942. [14] A.S. Furman, Sov. Phys. JETP 67 (1988) 1034.
15 September
CQa
1996
OPTICS COMMUNICATIONS
ELSEVIER
Optics Communications
130 (1996) 85-88
Light scattering in bismuth silicate: matching of experimental results H.C. Ellin, L. Solymar Holography Group, Department ofEngineering Science, University of Ux&rd, Parks Road, Oxford, UK Received
17 August 1995; accepted 27 February
1996
Abstract The scattering pattern of a coherent light beam incident ~~endicularly on a bismuth silicate crystal in the presence of an applied electric field is investigated. A theoretical model is shown to give good agreement with the measurements provided the piezoelectric and photoelastic effects are incorporated into the usual coupled wave equations.
the results with a theory which takes into account the
1. Introduction
piezoelectric It
is well known
upon
a photorefractive
distortion,
that an optical material
may
beam suffer
and photoelastic
effects.
incident serious
2. Ex~rim~nts
usually
referred to as fanning or scattering. This property was stated already in the very first paper [l] written on photorefractive materials. The first consistent study of scattering was made much later, by Voronov et al. [2] in SBN, confirming that the strength of the scattering pattern reflected the angular distribution of two-wave gain. Following this article many interesting results were reported in materials where the anisotropy played an essential roIe (for a review see Ref. [3]). Most of the experimental observations have by now been accounted for but scattering in bismuth silicate (BSO) is still one of the unsolved problems. The scattering patterns measured by Imbert [4] and Rajbenbach et al. [5] have not so far been satisfactorily explained, although a tentative explanation was suggested by Ellin et al. [63. The aim of the present Communication is to present further experiments on scattering in BSO and match 0030~4018/96/$12.00 Copyright PII SOO30-4018(96)00169-l
A schematic representation of the experimental set-up is shown in Fig. 1. A single expanded beam from an argon laser operating at a wavelength of 514.5 nm was directed, at normal incidence, onto the (ilO> face of a BSO crystal having dimensions 5 mm X 5 mm X 10 mm (interaction length). A voltage of 5 kV was applied across the (001) faces of the crystal and the emerging pattern (shown in the inset) was observed on a screen located approximately 1 m behind the crystal. The scatter pattern as observed on the screen is shown schematically in the inset of Fig. 1, and in more detail in Fig. 2, taken from a video still. It must be emphasized that the pattern is not in the plane of incidence although one knows that there are strong enough scattered beams in that plane to enable one (see e.g. Ref. [7]) to set up ring resonators.
0 1996 Elsevier Science B.V. All rights reserved.
H.C. Elk
86
L. Solymur/Optics
Communications
130 (1996) 85-88
Y ‘v
>
I
Fig.
I. Schematic representation
of the experimental
set-up. Inset: the light pattern shown on the screen.
We have observed similar patterns in a number of crystals under similar conditions. The pattern, as may be expected, was voltage dependent. The higher the voltage, the greater the extent of the lobes in the x and y directions. The observed scatter was found to depend strongly on the angle of the incident beam as well. A small deviation from the perpendicular (of the order of lo> yielded a different type of scattering mechanism in which noise gratings were read by the boundary reflected beam. These observations were reported earlier [6].
3. Theoretical modelling
Fig. 2. A video still of the scatter pattern (the directly transmitted beam is not shown).
Can the pattern be explained by mapping the two-wave gain for BSO? Traditional theories which include only the electro-optic effect would not be able to do it because they would predict maximum gain in the plane of incidence. Some new theories could however help. First, we have to refer here to the experimental results of Ellin [8] and Ellin et al. [9] (two waves incident, one is detuned in order to
H.C. Ellin, L. Solymar/Optics
0
2
4
6
8
10
12
14
16
18
20
xdirection(~)
Fig. 3. Theoretical prediction of the relative intensity (normalized to 100) on the screen using the experimental parameters.
obtain maximum gain) in BSO in which they showed that two-wave gain may actually be higher when the incident wave vectors create a grating which is not in the xz plane (i.e. the grating vector has an arbitrary y component). It was also possible to match their experimental results by solving numerically the vector differential equations [8,9] for the interaction between the two waves but incorporating, in addition to the electro-optic effect, the piezo-electric and photo-elastic effects as suggested by Stepanov et al. [lo], Shandarov et al. [l 11, Gunter and Zgonik [12] and Pauliat et al. [13]. The theory used in the present paper is exactly the same as that in Refs. [8,9] so there seems to be no point repeating here the rather lengthy equations. The relevant interaction takes place between the beam incident perpendicularly upon the crystal and
Communicurions 130 11996) 85-88
87
light which is scattered throughout the crystal. The scattered light may then be represented by an infinite number of small amplitude waves propagating in all possible directions. Those waves will be observed which are optimally amplified. In order to find that we calculate the two-wave gain in all possible directions. In our model we take into account detuning, attenuation, optical activity and the relevant electrooptic, piezoelectric and photoelastic coefficients, and we solve numerically the corresponding coupled wave equations [8,9]. Having found the gain in a particular direction we repeat the calculations for a range of detuning values in order to find the maximum gain. The argument is that the frequency of the scattered beam will cover a range of frequencies and that it will not be restricted to the frequency of the input beam. Out of this range of scattered beams only the one with the highest amplitude will be observed, and that is the reason why we must find the optimum detuning. Where would the additional frequency come from? From the reservoir of space charge waves which are present owing to the application of a d.c. electric field (see e.g. Ref. [14]). The concept of Space Charge Wave Scattering has not sufficiently permeated the literature yet but it can be easily appreciated by people familiar with Brillouin or Raman scattering. It is the same kind of thing. Having performed the calculations for all possible directions the normalized output intensity (maximum equal to 100) is plotted in Figs. 3a and 3b for positive and negative y coordinates respectively. The experimental pattern of Fig. 2 may be seen to be reproduced with good approximation.
4. Conclusions
We have measured experimentally the scatter pattern due to a single coherent laser beam incident perpendicularly upon the (ilO> face of a BSO crystal. We have shown that this pattern can be matched by a model calculating the two-wave gain which (i) considers an optimally detuned scattered beam, and (ii) incorporates both th e piezoelectric and photoelastic effects.
88
H.C. Ellin, L. Solymar/Optics
References [l] A. Ashkin, G.D. Boyd, J.M. Dziedzic, R.G. Smith, A.A. Ballman, J.J. Levinstein and K. Nassau, Appl. Phys. Lett. 9 ( 1966172. [2] V.V. Voronov, I.R. Dorosh, YuS. Kuz’minov and N.V. Tkachenko, Sov. J. Quantum Electron. 10 (1980) 1346. [3] S.G. Odoulov, and M. Soskin, Chapter 2 in Photorefractive materials and their applications, Springer, 1989, eds. P. Gunter and J.P. Huignard. [4] B. Imbert, Etude de la sensibilite des cristaux BSO a A = 633 nm et A = 840 nm, Rapport de stage, Universite de Paris Xl, DEA d’optique et Photonique, 1986, pp. l-34. [5] H. Rajbenbach, A. Delboulbe and J.P. Huignard, Optics Len. 14 (1989) 1275.
Communications
130 (1996) 85-M
[6] H.C. Ellin, J. Takacs and L. Solymar, Appl. Optics 33 (19941 4125. [7] H. Rajbenbach and J.P. Huignard, Optics Lett. 10 (1985) 137. [8] H.C. Ellin, Aspects of wave interactions in photorefractive materials, D. Phil. thesis, Dept. Eng. SC. Univ. Oxford, 1994. 191 H.C. Ellin, A. Gnmnet-Jepsen, L. Solymar and J. Takacs, Proc. SPIE 2321 (19941 107. [lo] S.I. Stepanov, S.M. Shandarov and N.D. Khatkov, Sov. Phys. Solid State 29 (19871 1754. [l l] S.M. Shandarov, V.V. Shepelevich and N.D. Khatkov, Opt. Spectrosc. 70 (19911 627. [12] P. Gunter and M. Zgonik, Optics Lett. 16 (19911 1826. 1131 G. Pauliat, M. Mathey and G. Roosen, J. Opt. Sot. Am. B 8 (19911 1942. [14] A.S. Furman, Sov. Phys. JETP 67 (1988) 1034.