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Temperature dependence of refractive index and absorption coefficient of GaSe at 633 nm
1.5July 1995 OPTICS
COMMUNICATIONS ELSEVIER
Optics Communications
118 ( 1995) 335-337
Temperature dependence of refractive index and absorption coefficient of GaSe at 633 nm M.A. Hernindez, M.V. And&, A. Segura, V. Mufioz Departumento de Fkica Aplicada. Universidad de Valencia. Dr. Moliner 50. 46100 Burjasot (Valencia), Spain
Received 6 February 1995
Abstract Measurements of the ordinary refractive index and the absorption coefficient (E I to c axis) of gallium selenide at 633 nm, in the temperature range [ 20,100] “C, are reported. Useful analytical approximations obtained after a least squares fitting process are provided, as well. These results are basic for any theoretical model of nonlinear and bistable optical devices based on Case.
1. Introduction The layered semiconductor gallium selenide (GaSe), with a band gap of about 2.0 eV at room temperature [ I], exhibits an exciton peak in its absorption edge at this temperature. The HeNe laser light (633 nm) has a photon energy very close to the exciton peak, making the GaSe an interesting material for nonlinear optical devices at 633 nm and room temperature. In fact, Iwamura et al. [2,3] and Segura et al. [4] have discussed some nonlinear optical effects, in Au/GaSe/Au devices, based on a combination of optical absorption, photoconductivity and Joule effect, Velikovich [ 51 has investigated the characteristics of GaSe/air/mirror devices and Stadnik [ 61 has reported the formation of moving absorption domains in GaSe samples. Moreover, we have observed nonlinear optical transmission and bistability in thin GaSe samples and GaSe/Au devices [ 71. GaSe is a birefringent uniaxial crystal with a strong anisotropy [ 11. The difference between the ordinary (E I to c axis) and the extraordinary (E )I to c axis)
00X0-4018/95/$09.50
refractive indices is about 0.3 in most of the visible and near infrared ranges and the difference between the ordinary and the extraordinary absorption coefficients is larger than an order of magnitude. The origin of the above referred optical nonlinearities is thermal and, therefore, any theoretical analysis of such devices requires an accurate knowledge of the temperature dependence of the optical constants. In this paper we report measurements of both the ordinary refractive index and absorption coefficient in GaSe, at 633 nm in the temperature range 20-100 “C.
2. Experimental
Laminar GaSe single crystals (e-hexagonal politype) were grown by the Bridgman-Stockbarger method from the material previously synthesized from direct combination of the elements (nominal purity 6N). Samples with faces parallel to the layers were cleaved from the ingot, with thicknesses between 5 and 100 pm. The samples were mounted on an aluminium holder with a hole of 2 mm diameter.
@ 1995 Elsevier Science B.V. All rights reserved
s!?D/0030-4018(95)00315-O
arrangement
336
M.A. Herndndez et al. /Optics
Communications 118 (1995) 335-337
The sample-holder, equipped with a heating element, was supported by a rotating plate, which in turn was controlled by a synchronous motor. Two series of transmission spectra were recorded, both as functions of temperature. The first series was a set of standard absorption wavelength spectra with normal incidence and recorded with a halogen light source and a Jovin-Yvon monochromator. The second series was a set of transmission spectra as a function of the angle of incidence, and was recorded using a polarized HeNe laser with the electric field aligned normal to the plane of incidence (E I to c axis). Fig. 1. Transmission spectrum as a function of the angle of incidence, d=25.6 pm, T = 35.7 ‘C.
3. Refractive index measurements The refractive index spectrum at room temperature has been accurately measured by Le Toullec et al. [ 11. The sample thickness and the interference order nearest to the HeNe wavelength can then be obtained from a fit to the transmission spectrum over a large wavelength interval. Once the thickness, d, and interference order, k,,, are accurately known, the transmission spectra at fixed wavelength (633 nm) are recorded as functions of angle of incidence at different temperatures and analyzed to yield the refractive index dependence on the temperature. The transmission spectra as functions of the angle of incidence can be regarded as interference fringe patterns, whose maxima satisfy the condition
(1) in which k is the interference order that corresponds to the angle of incidence i, n, is the ordinary refractive index, d is the thickness of the sample and A is the wavelength. The value of n, at each temperature is obtained from the value of the ordinate at the origin of the plot k2 versus sin2 i. The linear thermal expansion coefficient is about 10v5 K-*, so the relative change of d in the temperature range 20-l 00 “C is 0.8 x 10m3 and has been neglected. Fig. 1 gives an example of a transmission spectrum as a function of the angle of incidence for T = 35.7”C. In this example, d = 25.6 pm and ko = 233. Heating the GaSe samples, we covered the range 25-100 “C. The results for the refractive index are given in Fig. 2.
2.956
./+
2.952
.’ . :
/y .,;
2.948 1 E0 2.944 -
/
*
I 2.940 I/ 2.936
.
~~~~~~~~~‘~~~~~~~~~1~~~‘~~~~~~~~~~~~~~’~~ “a 20 40 60 80 100
t (“C) Fig. 2. GaSe ordinary refractive index as a function of temperature. (0) experimental points, (-) polynomial fit, (- - -) extrapolation from [8].
A least squares polynomial T gives n, = 2.93323+2.55921
fit of n, as a function
x lo-9-3.26264x
+ 8.06267 x 10-8T3 - 5.20204 x 10-top,
of
lo-&r2 (2)
where T is in “C and the correlation coefficient R = 0.99852. This polynomial fit is plotted in Fig. 2. We can compare our results with those provided by Antonioli et al. [8], who measured the temperature variation of the ordinary refractive index between 300 K and 75 K and in the energy range 0.5-2.5 eV. In principle, we could extrapolate their results to the temperature range 300-380 K, as we show in Fig. 2. The extrapolation nearly fits our experimental results up to 50 “C. At higher temperatures, the Antonioli et
M.A.Hernhdezet al. /Oprics Communications
I18 (1995) 335-337
331
We have found that the continuity of the first two derivatives is critical when using the analytical approximation to calculate the nonlinear optical transmission and the power required to observe optical bistability. The absorption coefficient shown in Fig. 3, as the refractive index of Fig. 2, exhibits a peculiar temperature variation. Again this is related to the exciton peak. In fact, the maximum that can be observed in Fig. 3 shows up the presence of the exciton.
I
.
LIII)
. 1,.
”
. L
l
7;)
~~~ #I
,,,I I cIIqlel.lllllc
X,, I”(
100
,111
1
,
Fig. 3. GaSe ordinary absorption coefficient as a function of temperature. ( l) Experimental points, (-) analytical approximation.
al. mode1 cannot fit the experimental results since it does not take into account the exciton contribution to the refractive index.
4. Absorption
coefficient measurements
The absorption edge of GaSe at different temperatures was obtained through standard transmission measurements, in the wavelength interval from 700 to 550 nm. From those spectra, the temperature dependence of the absorption coefficient at a given wavelength can be obtained [ I]. Fig. 3 gives the ordinary absorption coefficient as a function of the temperature at A=633 nm. This figure includes an analytical aproximation given by ( 7.39 e”~058s-r, a(T)
10 5 T 5 70,
5
=
c
a,(T n=cl
- 70)“,
70 5 T < 120,
where a and T are in cm-’ and “C, respectively. The coefficients of the polynomial series are ao = 453.11, al = 26.64, a2 = 0.7833, a3 = -0.06366, a4 = 0.001225 and u5 = -7.792 x 10m6. The polynomial aproximation that covers the temperature range [ 70,12O]“C has been fitted to insure continuity of a(T), da/dT and d2a/dT2, at T = 70°C.
5. Conclusion We provide experimental values for the refractive index and the absorption coefficient of GaSe, as a function of temperature, at A = 633 nm, for light polarized perpendiculary to the crystallographic axis c . We provide, as well, useful analytical approximations for these coefficients, covering the temperature range [ 20,100] “C. These results are required to mode1 the nonlinear optical devices based on GaSe, e.g. to determine the power threshold for optical bistability or the time response.
References Ill R. Le. Toullec, N. Piccioli, M. Mejatty and M. Balkanski, I1 Nuovo Cimento 38 (1977) 159. 121 Y. Iwamura, M. Moriyama and N. Watanabe, Jap. J. Appl. Phys. 29 (1990) L975. 131 Y. Iwamura, M. Moriyama and N. Watanabe, Jap. J. Appl. Phys. 30 (1991) I-42. [41 A. Segura, M.V. And& and V. Muiioz, Jap. J. Appl. Phys. 30 (1991) L608. [51 A.L. Velikovich, G.P. Golubev, V.P. Golubchenko and D. G. Luchinsky, Optics Comm. 80 (1991) 444. [61 V.A. Stadnik, Sov. Phys. Solid State 30 (1988) 2052. [71 M.A. Hemtidez, J.F. Unchez, M.V. And& A. Segura and V. Muiioz, Optica Pura y Aplicada 26 ( 1993) 152. [81 G. Antonioli, D. Bianchi and P. Franzosi, Appl. Optics 18 (1979) 3847.
COMMUNICATIONS ELSEVIER
Optics Communications
118 ( 1995) 335-337
Temperature dependence of refractive index and absorption coefficient of GaSe at 633 nm M.A. Hernindez, M.V. And&, A. Segura, V. Mufioz Departumento de Fkica Aplicada. Universidad de Valencia. Dr. Moliner 50. 46100 Burjasot (Valencia), Spain
Received 6 February 1995
Abstract Measurements of the ordinary refractive index and the absorption coefficient (E I to c axis) of gallium selenide at 633 nm, in the temperature range [ 20,100] “C, are reported. Useful analytical approximations obtained after a least squares fitting process are provided, as well. These results are basic for any theoretical model of nonlinear and bistable optical devices based on Case.
1. Introduction The layered semiconductor gallium selenide (GaSe), with a band gap of about 2.0 eV at room temperature [ I], exhibits an exciton peak in its absorption edge at this temperature. The HeNe laser light (633 nm) has a photon energy very close to the exciton peak, making the GaSe an interesting material for nonlinear optical devices at 633 nm and room temperature. In fact, Iwamura et al. [2,3] and Segura et al. [4] have discussed some nonlinear optical effects, in Au/GaSe/Au devices, based on a combination of optical absorption, photoconductivity and Joule effect, Velikovich [ 51 has investigated the characteristics of GaSe/air/mirror devices and Stadnik [ 61 has reported the formation of moving absorption domains in GaSe samples. Moreover, we have observed nonlinear optical transmission and bistability in thin GaSe samples and GaSe/Au devices [ 71. GaSe is a birefringent uniaxial crystal with a strong anisotropy [ 11. The difference between the ordinary (E I to c axis) and the extraordinary (E )I to c axis)
00X0-4018/95/$09.50
refractive indices is about 0.3 in most of the visible and near infrared ranges and the difference between the ordinary and the extraordinary absorption coefficients is larger than an order of magnitude. The origin of the above referred optical nonlinearities is thermal and, therefore, any theoretical analysis of such devices requires an accurate knowledge of the temperature dependence of the optical constants. In this paper we report measurements of both the ordinary refractive index and absorption coefficient in GaSe, at 633 nm in the temperature range 20-100 “C.
2. Experimental
Laminar GaSe single crystals (e-hexagonal politype) were grown by the Bridgman-Stockbarger method from the material previously synthesized from direct combination of the elements (nominal purity 6N). Samples with faces parallel to the layers were cleaved from the ingot, with thicknesses between 5 and 100 pm. The samples were mounted on an aluminium holder with a hole of 2 mm diameter.
@ 1995 Elsevier Science B.V. All rights reserved
s!?D/0030-4018(95)00315-O
arrangement
336
M.A. Herndndez et al. /Optics
Communications 118 (1995) 335-337
The sample-holder, equipped with a heating element, was supported by a rotating plate, which in turn was controlled by a synchronous motor. Two series of transmission spectra were recorded, both as functions of temperature. The first series was a set of standard absorption wavelength spectra with normal incidence and recorded with a halogen light source and a Jovin-Yvon monochromator. The second series was a set of transmission spectra as a function of the angle of incidence, and was recorded using a polarized HeNe laser with the electric field aligned normal to the plane of incidence (E I to c axis). Fig. 1. Transmission spectrum as a function of the angle of incidence, d=25.6 pm, T = 35.7 ‘C.
3. Refractive index measurements The refractive index spectrum at room temperature has been accurately measured by Le Toullec et al. [ 11. The sample thickness and the interference order nearest to the HeNe wavelength can then be obtained from a fit to the transmission spectrum over a large wavelength interval. Once the thickness, d, and interference order, k,,, are accurately known, the transmission spectra at fixed wavelength (633 nm) are recorded as functions of angle of incidence at different temperatures and analyzed to yield the refractive index dependence on the temperature. The transmission spectra as functions of the angle of incidence can be regarded as interference fringe patterns, whose maxima satisfy the condition
(1) in which k is the interference order that corresponds to the angle of incidence i, n, is the ordinary refractive index, d is the thickness of the sample and A is the wavelength. The value of n, at each temperature is obtained from the value of the ordinate at the origin of the plot k2 versus sin2 i. The linear thermal expansion coefficient is about 10v5 K-*, so the relative change of d in the temperature range 20-l 00 “C is 0.8 x 10m3 and has been neglected. Fig. 1 gives an example of a transmission spectrum as a function of the angle of incidence for T = 35.7”C. In this example, d = 25.6 pm and ko = 233. Heating the GaSe samples, we covered the range 25-100 “C. The results for the refractive index are given in Fig. 2.
2.956
./+
2.952
.’ . :
/y .,;
2.948 1 E0 2.944 -
/
*
I 2.940 I/ 2.936
.
~~~~~~~~~‘~~~~~~~~~1~~~‘~~~~~~~~~~~~~~’~~ “a 20 40 60 80 100
t (“C) Fig. 2. GaSe ordinary refractive index as a function of temperature. (0) experimental points, (-) polynomial fit, (- - -) extrapolation from [8].
A least squares polynomial T gives n, = 2.93323+2.55921
fit of n, as a function
x lo-9-3.26264x
+ 8.06267 x 10-8T3 - 5.20204 x 10-top,
of
lo-&r2 (2)
where T is in “C and the correlation coefficient R = 0.99852. This polynomial fit is plotted in Fig. 2. We can compare our results with those provided by Antonioli et al. [8], who measured the temperature variation of the ordinary refractive index between 300 K and 75 K and in the energy range 0.5-2.5 eV. In principle, we could extrapolate their results to the temperature range 300-380 K, as we show in Fig. 2. The extrapolation nearly fits our experimental results up to 50 “C. At higher temperatures, the Antonioli et
M.A.Hernhdezet al. /Oprics Communications
I18 (1995) 335-337
331
We have found that the continuity of the first two derivatives is critical when using the analytical approximation to calculate the nonlinear optical transmission and the power required to observe optical bistability. The absorption coefficient shown in Fig. 3, as the refractive index of Fig. 2, exhibits a peculiar temperature variation. Again this is related to the exciton peak. In fact, the maximum that can be observed in Fig. 3 shows up the presence of the exciton.
I
.
LIII)
. 1,.
”
. L
l
7;)
~~~ #I
,,,I I cIIqlel.lllllc
X,, I”(
100
,111
1
,
Fig. 3. GaSe ordinary absorption coefficient as a function of temperature. ( l) Experimental points, (-) analytical approximation.
al. mode1 cannot fit the experimental results since it does not take into account the exciton contribution to the refractive index.
4. Absorption
coefficient measurements
The absorption edge of GaSe at different temperatures was obtained through standard transmission measurements, in the wavelength interval from 700 to 550 nm. From those spectra, the temperature dependence of the absorption coefficient at a given wavelength can be obtained [ I]. Fig. 3 gives the ordinary absorption coefficient as a function of the temperature at A=633 nm. This figure includes an analytical aproximation given by ( 7.39 e”~058s-r, a(T)
10 5 T 5 70,
5
=
c
a,(T n=cl
- 70)“,
70 5 T < 120,
where a and T are in cm-’ and “C, respectively. The coefficients of the polynomial series are ao = 453.11, al = 26.64, a2 = 0.7833, a3 = -0.06366, a4 = 0.001225 and u5 = -7.792 x 10m6. The polynomial aproximation that covers the temperature range [ 70,12O]“C has been fitted to insure continuity of a(T), da/dT and d2a/dT2, at T = 70°C.
5. Conclusion We provide experimental values for the refractive index and the absorption coefficient of GaSe, as a function of temperature, at A = 633 nm, for light polarized perpendiculary to the crystallographic axis c . We provide, as well, useful analytical approximations for these coefficients, covering the temperature range [ 20,100] “C. These results are required to mode1 the nonlinear optical devices based on GaSe, e.g. to determine the power threshold for optical bistability or the time response.
References Ill R. Le. Toullec, N. Piccioli, M. Mejatty and M. Balkanski, I1 Nuovo Cimento 38 (1977) 159. 121 Y. Iwamura, M. Moriyama and N. Watanabe, Jap. J. Appl. Phys. 29 (1990) L975. 131 Y. Iwamura, M. Moriyama and N. Watanabe, Jap. J. Appl. Phys. 30 (1991) I-42. [41 A. Segura, M.V. And& and V. Muiioz, Jap. J. Appl. Phys. 30 (1991) L608. [51 A.L. Velikovich, G.P. Golubev, V.P. Golubchenko and D. G. Luchinsky, Optics Comm. 80 (1991) 444. [61 V.A. Stadnik, Sov. Phys. Solid State 30 (1988) 2052. [71 M.A. Hemtidez, J.F. Unchez, M.V. And& A. Segura and V. Muiioz, Optica Pura y Aplicada 26 ( 1993) 152. [81 G. Antonioli, D. Bianchi and P. Franzosi, Appl. Optics 18 (1979) 3847.