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Photorefractive effects in the cubic phase of potassium tantalate-niobate
PHOTOREFRACTIVE
October 1980
OPTICS COMMUNICATIONS
Volume 35, number 1
EFFECTS IN THE CUBIC PHASE OF
POTASSIUM TANTALATE-NIOBATE
R. ORLOWSKI Philips GmbH Forschungslaboratorium
Hamburg, 02 Hamburg 54, Germany
L.A. BOATNER Solid State Division, Oak Ridge National Laboratory
*, Oak Ridge, Tennessee 37830,
USA
and E. KtiTZIG Fachbereich
4 der Universitit Osnubriick, 045
Osnabriick, Germany
Received 25 June 1980
Photorefractive effects associated with quadratic electro-optic mechanisms are studied in the cubic phase of potassium tantalate-niobate. The results of holographic measurements are compared with theory to explain the influence of writing and read-out electric fields and to determine the dominant charge carriers.
1. Introduction
The Curie point of single crystals of potassium tantalate-niobate (i.e., KTa,,Nb,03 or KTN) can be varied by controlling the niobium/tantalum ratio, and, accordingly, the electro-optic properties of these substances can be effectively “tailored” by means of a variation of this type. The ability to exercise such control over the eletitro-optic properties makes the KTN system particularly interesting for the storage of volume phase holograms via photorefractive effects. The linear electro-optic effect can be employed when the Nb/Ta ratio and crystal temperature are such that the system is in the ferroelectric tetragonal phase, and the quadratic electro-optic effect can be utilized when conditions correspond to the presence of the non-ferroelectric cubic phase. Recent measurements using incoherent light [l ] have shown that the storage properties of KTN are very attractive in both cases. * Operated by Union Carbide Corporation for the U.S. Department of Energy under contract W-7405-eng-26.
Although photorefractive effects have been extensively investigated using materials with linear electrooptic properties, only a few experiments have been reported for materials whose photorefractive properties resulted from quadratic electro-optic effects. These experiments include Investigations of the electric-fieldinduced birefringence in KTN [2,3] and demonstration of the electrical control of photoferroelectric materials using PLZT (lead-lanthanum zirconate-titanate) ceramics [4] . Additionally, the mixing of linear and quadratic electro-optic effects in Sr 1_XBa,Nb206 has been used to implement a novel layered optical memory having electrical access for the purpose of writing or reading in selected layers [5] . In the present work holographic techniques have been used to study photorefractive effects associated with quadratic electro-optic mechanisms in the cubic phase of KTN. An expression for the dependence of the refractive index change produced by external writing and reading electric fields was derived, and the validity of the expression was examined by means of two-beam interference experiments. Additionally, the light-induced charge transport in KTN was investigated. 45
Volume 35, number 1
OPTICS COMMUNICATIONS
2. Experimental Single crystals of KTa,_,Nb,O, employed in this work were grown using a variation of the flux technique. The Curie temperature, T,, of each sample was determined from measurements of the temperature dependence of the static dielectric constant. These value of T, were then used in determining the Nb/Ta ratio from the phase diagram of Triebwasser [6] . In order to achieve the desired combination of high sensitivity and long storage time, it is necessary to operate near the transition temperature T,. Accordingly, for measurements of quadratic electro-optic effects in the cubic phase of KTN tinder ambient conditions, T, must be slightly lowei than room temperature. Unfortunately, most of the KTN single crystals with a transition temperature in the range between 1.5 and 20°C were not suitable for holographic experiments, due to the production of a large amount of stray light. For this reason, KTN crystals with T, values ranging from 0 to 10°C were selected for use in the present investigation. While the storage properties in this case were more unfavorable than those reported previously [I] by about an order of magnitude, the high crystal quality of spe-
October 1980
cimens with a reduced value of T, made the desired quan titative evaluations possible. The two-beam interference arrangement shown in the inset of fig. 1 was employed in making the holographic measurements. By superimposing two coherent light beams of equal intensity Zo, it is possible to generate a sinusoidal light pattern in the crystal whose intensity is given by: Z(z) = Zo(l + m cos Kz).
(1)
The modulation index m was reduced to values smaller than 0.5 by simultaneous illumination with a third, incoherent beam. The spatial frequency K = 47r (sin /3)/h is determined by the wavelength of light h and the halfangle of interference 0. In the present work the 4.5% nm line of an Ar ion laser was employed. In order to apply the required external electric fields to the KTN single crystals, edge electrodes were formed using silver paste.
3. Theory Light-induced
changes in the index of refraction
(i.e.,
photorefractive effects) arise as a result of optically generated space-charge fields. When an electro-optic crystal is exposed to a light interference pattern, electrons in the regions of high light intensity are excited and displaced. The internal electric fields Ei generated by this charge transport then modulate the refractive index by means of the electro-optic effect. Uniform illumination of the specimen produces a corresponding uniform re-distribution of the charge and returns the crystal to its original state. For the sinusoidal light-intensity distribution described in eq. (l), the saturation value of an optically generated internal space-charge field Ei,(z)is given by [7,8] : E&)
read-out
field E,
Fig. 1. Saturation value of the refractive index change An, as a function of the read-out electric field ER for various writing fields Ew (crystal thicknessd = 0.13 cm, 0 = 3.2 degrees, and m = 0.34). The inset shows the holographic arrangement.
46
= EkO cos (Kz + $),
(2)
with E, = m’(E& + Eh)l12, 4 = -n/2 - arc tan E,/E, , and m’ = m/(1 + od/op). Here Ew is the intensity of the writing field, ED the diffusion field strength, od the dark conductivity, and up the photoconductivity. For the case of pure electronic conductivity, ED is given by kTK/e. If these are additional contributions from holes, then ED is modified by the factor [9] 6 = (upe - uph)/(ope + oph), where
Volume 35, number 1
for Ope and Oph are the values of the photoconductivity electrons and holes, respectively. The quadratic qlectro-optic effect, which is present in cubic KTN crystals, can be described by a fourthrank tensor, and the refractive index change An can be written as An = -in3g(e
- 1)2e$!?2,
(3)
where g is the corresponding quadratic electro-optic component and e is the static dielectric constant. The effective electric field E may contain contributions from an internal space-charge field Ei and an externally applied read-out field E, (i.e., E = Ei + ER). In this case eqs. (2) and (3) can be used to obtain the following saturation value Arl,(z) for the refractive index change: An S(z) = -$n3g(c
- 1)2e2 0
X (E; •t 2E,E,(z)
+ E;(z)).
(4)
Only the second term Ans(z) = -n3g(e
- l)2~i
X m’E RW(E2 + E2D )1’2 cos(Kz + 4)
(9
yields a first-order diffraction component, since the required spatial frequency term appears. This shows that, unlike measurements utilizing linear electro-optic effects, an external electric “read-out field” ER must be applied to obtain a non-zero read-out efficiency when the quadratic electro-optic effect is employed. Since E increases significantly near T,, large An values are expected in this region.
4. Experimental
October 1980
OPTICS COMMUNICATIONS
results and discussion
The saturation value of the refractive index change An, versus the readout field ER is shown in fig. 1 for various values of the writing field Ew and an interference angle 0 = 3.2 degrees. The linear dependence of An, on ER predicted by eq. (5) is clearly confirmed. The dependence of An, on Ew is also found as predicted by eq. (5). For large external fields and when EW = ER , the refractive index change is proportional to E&. For Ew = 0, only the diffusion of excited charge carriers can contribute to the light-induced charge transport and no fundamental component of the refractive index change is measured during the writing process.
Accordingly, optical coupling due to the superposition of many holograms at the same site but recorded under different angles is greatly reduced. The dynamics of the writing and reading process (i.e., the increase and decrease of the refractive index) are controlled by an exponential time dependence which is determined by the dielectric relaxation time 7 = EEO/ (up t ad). For the KTN crystal used to obtain the results shown in fig. 1, the results of holographic experiments and the experimental value of e = 7200 were used to obtain a value of 9 X lo-l1 cm/V2 for the quantity up/IO. T’he dark conductivity was measured as od = 9 X lo-l6 (a cm)-I , and this value was consistent with the dark storage time of about one week. The quantity A = n3gll (E - 1)2~i, which describes the electro-optic properties of the crystal, was determined using the slope aAn,/aE, of fig. 1 and was found to be A = 4.1 X lo-” cm2/V2. A direct calculation of A using the experimentally determined [lo] values of n = 2.4, E = 7200, and g1 I = 1.36 X lo7 cm4/A 2s2 yielded a value of A = 7.6 X lo-I1 cm2/V2. Based on the experimental results for. a number of KTN crystals with different Curie temperatures, the holographic measurements were found to result in values of A that were consistently smaller than the calculated values. A satisfactory explanation of this discrepancy has not been found at the present time. The sign of the dominant light-induced charge carriers was determined by means of beam coupling experiments carried out in the absence of an applied writing electric field (i.e., Ew = 0). If both electrons and holes contribute to the diffusion process, then the refractive index changes which produce the grating can be expressed as [9] :
AnDi
= -AE,
[ ;;
; ;;][T]K
sin@)
(6)
in accordance with eq. (2). For positive values of the read-out field ER , the phase shift of the induced refractive index grating is t n/2 for electrons and -n/2 for holes with respect to the intensity distribution given by eq. (1). This phase shift gives rise to beam coupling effects and alters the intensity Zw and IR of the transmitted beams. For the experimental arrangement shown in fig. 1 and for normalized initial values of lo = ZRo = 1, the transmitted intensities are given by [l l] : IR w = 1 + 2(r)(l - T$)I’2 sin $J,
(7) 47
Volume 35, number 1
OPTICS COMMUNICATIONS
where Q is the diffraction efficiency of the induced volume grating. For the KTN crystal used to obtain the results shown in fig. 1, positive read-out fields ER produce an increase in 1, and a decrease in Zw . This indicates that the phase shift is @J= t n/2 and that, accordingly, electrons are the dominant carriers in the charge transport in this case. It should be noted, however, that in the present experiments undoped (nominally pure) KTN crystals were used. Accordingly, it is difficult to provide a complete interpretation for these results. Nevertheless, holographic coupling experiments of this type are a powerful tool for the determination of the relative electron or hole contributions to light-induced charge transport, even when the precise nature of the centers and transitions involved in the transport process is unknown. The investigations have shown that for KTN single crystals in the cubic phase, the dependence of An, on the writing and read-out electric fields can satisfactorily be described by eq. (5) and that the diffraction efficiency of the stored holograms can be completely controlled by the external read-out field. The quantity A as determined by means of holographic experiments is consistently smaller than the calculated value, and additional work will be necessary in order to reconcile this
48
October 1980
discrepancy. It has been shown that holographic coupling experiments [9] can also be successfully applied in the case of quadratic electro-optic effects. The results of such experiments in the present case show that electrons are the dominant charge carriers.
References [l] L.A. Boatner, E. Kratzig and R. Orlowski, Ferroelectrics 27 (1980) 247. [2] F.S. Chen, J. Appl. Phys. 38 (1967) 3418. [3] D. von der Linde, A.M. Glass and K.F. Rodgers, Appl. Phys. Lett. 26 (1975) 155. [4] F. Micheron, C. Mayeux and J.C. Trotier, Appl. Optics 13 (1974) 784. [S] J.B. Thaxter and M. Kestigian, Appl. Optics 13 (1974) 913. [6] S. Triebwasser, Phys. Rev. 101 (1956) 993. [7] G.A. Alphonse, R.C. Alig, D.L. Staebler and W. Phillips, RCA Review 36 (1976) 213. [S] R. Orlowski and E. Kratzig, Ferroelectrics 26 (1980) 831. [9] R. Orlowski and E. K&zig, Solid State Commun. 27 (1978) 1351. [lo] F.S. Chen, J.E. Geusic, S.K. Kurtz, J.G. Skinner and S.H. Wemple, J. Appl. Phys. 37 (1966) 388. [ll] D.L. Staebler and J.J. Amodei, J. Appl. Phys. 43 (1972) 1042.
October 1980
OPTICS COMMUNICATIONS
Volume 35, number 1
EFFECTS IN THE CUBIC PHASE OF
POTASSIUM TANTALATE-NIOBATE
R. ORLOWSKI Philips GmbH Forschungslaboratorium
Hamburg, 02 Hamburg 54, Germany
L.A. BOATNER Solid State Division, Oak Ridge National Laboratory
*, Oak Ridge, Tennessee 37830,
USA
and E. KtiTZIG Fachbereich
4 der Universitit Osnubriick, 045
Osnabriick, Germany
Received 25 June 1980
Photorefractive effects associated with quadratic electro-optic mechanisms are studied in the cubic phase of potassium tantalate-niobate. The results of holographic measurements are compared with theory to explain the influence of writing and read-out electric fields and to determine the dominant charge carriers.
1. Introduction
The Curie point of single crystals of potassium tantalate-niobate (i.e., KTa,,Nb,03 or KTN) can be varied by controlling the niobium/tantalum ratio, and, accordingly, the electro-optic properties of these substances can be effectively “tailored” by means of a variation of this type. The ability to exercise such control over the eletitro-optic properties makes the KTN system particularly interesting for the storage of volume phase holograms via photorefractive effects. The linear electro-optic effect can be employed when the Nb/Ta ratio and crystal temperature are such that the system is in the ferroelectric tetragonal phase, and the quadratic electro-optic effect can be utilized when conditions correspond to the presence of the non-ferroelectric cubic phase. Recent measurements using incoherent light [l ] have shown that the storage properties of KTN are very attractive in both cases. * Operated by Union Carbide Corporation for the U.S. Department of Energy under contract W-7405-eng-26.
Although photorefractive effects have been extensively investigated using materials with linear electrooptic properties, only a few experiments have been reported for materials whose photorefractive properties resulted from quadratic electro-optic effects. These experiments include Investigations of the electric-fieldinduced birefringence in KTN [2,3] and demonstration of the electrical control of photoferroelectric materials using PLZT (lead-lanthanum zirconate-titanate) ceramics [4] . Additionally, the mixing of linear and quadratic electro-optic effects in Sr 1_XBa,Nb206 has been used to implement a novel layered optical memory having electrical access for the purpose of writing or reading in selected layers [5] . In the present work holographic techniques have been used to study photorefractive effects associated with quadratic electro-optic mechanisms in the cubic phase of KTN. An expression for the dependence of the refractive index change produced by external writing and reading electric fields was derived, and the validity of the expression was examined by means of two-beam interference experiments. Additionally, the light-induced charge transport in KTN was investigated. 45
Volume 35, number 1
OPTICS COMMUNICATIONS
2. Experimental Single crystals of KTa,_,Nb,O, employed in this work were grown using a variation of the flux technique. The Curie temperature, T,, of each sample was determined from measurements of the temperature dependence of the static dielectric constant. These value of T, were then used in determining the Nb/Ta ratio from the phase diagram of Triebwasser [6] . In order to achieve the desired combination of high sensitivity and long storage time, it is necessary to operate near the transition temperature T,. Accordingly, for measurements of quadratic electro-optic effects in the cubic phase of KTN tinder ambient conditions, T, must be slightly lowei than room temperature. Unfortunately, most of the KTN single crystals with a transition temperature in the range between 1.5 and 20°C were not suitable for holographic experiments, due to the production of a large amount of stray light. For this reason, KTN crystals with T, values ranging from 0 to 10°C were selected for use in the present investigation. While the storage properties in this case were more unfavorable than those reported previously [I] by about an order of magnitude, the high crystal quality of spe-
October 1980
cimens with a reduced value of T, made the desired quan titative evaluations possible. The two-beam interference arrangement shown in the inset of fig. 1 was employed in making the holographic measurements. By superimposing two coherent light beams of equal intensity Zo, it is possible to generate a sinusoidal light pattern in the crystal whose intensity is given by: Z(z) = Zo(l + m cos Kz).
(1)
The modulation index m was reduced to values smaller than 0.5 by simultaneous illumination with a third, incoherent beam. The spatial frequency K = 47r (sin /3)/h is determined by the wavelength of light h and the halfangle of interference 0. In the present work the 4.5% nm line of an Ar ion laser was employed. In order to apply the required external electric fields to the KTN single crystals, edge electrodes were formed using silver paste.
3. Theory Light-induced
changes in the index of refraction
(i.e.,
photorefractive effects) arise as a result of optically generated space-charge fields. When an electro-optic crystal is exposed to a light interference pattern, electrons in the regions of high light intensity are excited and displaced. The internal electric fields Ei generated by this charge transport then modulate the refractive index by means of the electro-optic effect. Uniform illumination of the specimen produces a corresponding uniform re-distribution of the charge and returns the crystal to its original state. For the sinusoidal light-intensity distribution described in eq. (l), the saturation value of an optically generated internal space-charge field Ei,(z)is given by [7,8] : E&)
read-out
field E,
Fig. 1. Saturation value of the refractive index change An, as a function of the read-out electric field ER for various writing fields Ew (crystal thicknessd = 0.13 cm, 0 = 3.2 degrees, and m = 0.34). The inset shows the holographic arrangement.
46
= EkO cos (Kz + $),
(2)
with E, = m’(E& + Eh)l12, 4 = -n/2 - arc tan E,/E, , and m’ = m/(1 + od/op). Here Ew is the intensity of the writing field, ED the diffusion field strength, od the dark conductivity, and up the photoconductivity. For the case of pure electronic conductivity, ED is given by kTK/e. If these are additional contributions from holes, then ED is modified by the factor [9] 6 = (upe - uph)/(ope + oph), where
Volume 35, number 1
for Ope and Oph are the values of the photoconductivity electrons and holes, respectively. The quadratic qlectro-optic effect, which is present in cubic KTN crystals, can be described by a fourthrank tensor, and the refractive index change An can be written as An = -in3g(e
- 1)2e$!?2,
(3)
where g is the corresponding quadratic electro-optic component and e is the static dielectric constant. The effective electric field E may contain contributions from an internal space-charge field Ei and an externally applied read-out field E, (i.e., E = Ei + ER). In this case eqs. (2) and (3) can be used to obtain the following saturation value Arl,(z) for the refractive index change: An S(z) = -$n3g(c
- 1)2e2 0
X (E; •t 2E,E,(z)
+ E;(z)).
(4)
Only the second term Ans(z) = -n3g(e
- l)2~i
X m’E RW(E2 + E2D )1’2 cos(Kz + 4)
(9
yields a first-order diffraction component, since the required spatial frequency term appears. This shows that, unlike measurements utilizing linear electro-optic effects, an external electric “read-out field” ER must be applied to obtain a non-zero read-out efficiency when the quadratic electro-optic effect is employed. Since E increases significantly near T,, large An values are expected in this region.
4. Experimental
October 1980
OPTICS COMMUNICATIONS
results and discussion
The saturation value of the refractive index change An, versus the readout field ER is shown in fig. 1 for various values of the writing field Ew and an interference angle 0 = 3.2 degrees. The linear dependence of An, on ER predicted by eq. (5) is clearly confirmed. The dependence of An, on Ew is also found as predicted by eq. (5). For large external fields and when EW = ER , the refractive index change is proportional to E&. For Ew = 0, only the diffusion of excited charge carriers can contribute to the light-induced charge transport and no fundamental component of the refractive index change is measured during the writing process.
Accordingly, optical coupling due to the superposition of many holograms at the same site but recorded under different angles is greatly reduced. The dynamics of the writing and reading process (i.e., the increase and decrease of the refractive index) are controlled by an exponential time dependence which is determined by the dielectric relaxation time 7 = EEO/ (up t ad). For the KTN crystal used to obtain the results shown in fig. 1, the results of holographic experiments and the experimental value of e = 7200 were used to obtain a value of 9 X lo-l1 cm/V2 for the quantity up/IO. T’he dark conductivity was measured as od = 9 X lo-l6 (a cm)-I , and this value was consistent with the dark storage time of about one week. The quantity A = n3gll (E - 1)2~i, which describes the electro-optic properties of the crystal, was determined using the slope aAn,/aE, of fig. 1 and was found to be A = 4.1 X lo-” cm2/V2. A direct calculation of A using the experimentally determined [lo] values of n = 2.4, E = 7200, and g1 I = 1.36 X lo7 cm4/A 2s2 yielded a value of A = 7.6 X lo-I1 cm2/V2. Based on the experimental results for. a number of KTN crystals with different Curie temperatures, the holographic measurements were found to result in values of A that were consistently smaller than the calculated values. A satisfactory explanation of this discrepancy has not been found at the present time. The sign of the dominant light-induced charge carriers was determined by means of beam coupling experiments carried out in the absence of an applied writing electric field (i.e., Ew = 0). If both electrons and holes contribute to the diffusion process, then the refractive index changes which produce the grating can be expressed as [9] :
AnDi
= -AE,
[ ;;
; ;;][T]K
sin@)
(6)
in accordance with eq. (2). For positive values of the read-out field ER , the phase shift of the induced refractive index grating is t n/2 for electrons and -n/2 for holes with respect to the intensity distribution given by eq. (1). This phase shift gives rise to beam coupling effects and alters the intensity Zw and IR of the transmitted beams. For the experimental arrangement shown in fig. 1 and for normalized initial values of lo = ZRo = 1, the transmitted intensities are given by [l l] : IR w = 1 + 2(r)(l - T$)I’2 sin $J,
(7) 47
Volume 35, number 1
OPTICS COMMUNICATIONS
where Q is the diffraction efficiency of the induced volume grating. For the KTN crystal used to obtain the results shown in fig. 1, positive read-out fields ER produce an increase in 1, and a decrease in Zw . This indicates that the phase shift is @J= t n/2 and that, accordingly, electrons are the dominant carriers in the charge transport in this case. It should be noted, however, that in the present experiments undoped (nominally pure) KTN crystals were used. Accordingly, it is difficult to provide a complete interpretation for these results. Nevertheless, holographic coupling experiments of this type are a powerful tool for the determination of the relative electron or hole contributions to light-induced charge transport, even when the precise nature of the centers and transitions involved in the transport process is unknown. The investigations have shown that for KTN single crystals in the cubic phase, the dependence of An, on the writing and read-out electric fields can satisfactorily be described by eq. (5) and that the diffraction efficiency of the stored holograms can be completely controlled by the external read-out field. The quantity A as determined by means of holographic experiments is consistently smaller than the calculated value, and additional work will be necessary in order to reconcile this
48
October 1980
discrepancy. It has been shown that holographic coupling experiments [9] can also be successfully applied in the case of quadratic electro-optic effects. The results of such experiments in the present case show that electrons are the dominant charge carriers.
References [l] L.A. Boatner, E. Kratzig and R. Orlowski, Ferroelectrics 27 (1980) 247. [2] F.S. Chen, J. Appl. Phys. 38 (1967) 3418. [3] D. von der Linde, A.M. Glass and K.F. Rodgers, Appl. Phys. Lett. 26 (1975) 155. [4] F. Micheron, C. Mayeux and J.C. Trotier, Appl. Optics 13 (1974) 784. [S] J.B. Thaxter and M. Kestigian, Appl. Optics 13 (1974) 913. [6] S. Triebwasser, Phys. Rev. 101 (1956) 993. [7] G.A. Alphonse, R.C. Alig, D.L. Staebler and W. Phillips, RCA Review 36 (1976) 213. [S] R. Orlowski and E. Kratzig, Ferroelectrics 26 (1980) 831. [9] R. Orlowski and E. K&zig, Solid State Commun. 27 (1978) 1351. [lo] F.S. Chen, J.E. Geusic, S.K. Kurtz, J.G. Skinner and S.H. Wemple, J. Appl. Phys. 37 (1966) 388. [ll] D.L. Staebler and J.J. Amodei, J. Appl. Phys. 43 (1972) 1042.