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1ω noise in refractive-index fluctuations in As2Se3 glass
15 October 1997
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 142 (1997) 220-222
1/w noise in refractive-index fluctuations in As,Se, glass B.P. Antonyuk, Institute
of Spectroscop?;. Russian
S.F. Musichenko,
V.B. Podobedov
Academy of Sciences. Troitsk, Moscow~ Region 142092, Russian Federation
Received 3 March 1997; accepted 17 June 1997
Abstract Refractive-index fluctuation in As,Se, under excitation by an Arf laser was measured by an optical grating method. After 50 min exposition with a power of 9.5 mW and diameter of the spot of N 0.25 mm, the diffracted signal became considerably noisy. The Fourier transform of the signal reveals a I/w spectrum, predicted for self-organized (ordered) electron-hole systems. 0 1997 Elsevier Science B.V.
1. Introduction High energy photons generate electrons and holes in extended states. After fast relaxation to trapped states (ps time scale) a slow recombination of electrons and holes, separated in space, takes place. Trap populations (change of electron states) result in a change of the refractive-index and therefore may be investigated by an optical method. The relative variation An/n is of the order of the relative number of electrons, changing the state ANe/N, (A N,/N, ==K1). So the density of trapped electrons AN, manifests itself in the refractive index variation An and one can find trap population, recombination and its temporal ( t) fluctuation by the measurement of the An(r) kinetics. In general, both the real and imaginary parts of the dielectric constant vary, but this does not change our arguments. The investigation of time fluctuations An(t) is interesting because it allows to draw a conclusion about the state of electrons and holes. Our previous studies [ 1,2] have shown that the electron-hole system under light pumping with “band gap” photons transits to an ordered state: in spite of Coulomb repulsion the carriers form electron and hole domains. The density of trapped particles (and refractive index) fluctuates in this case with universal spectrum 1/LO, while the spectrum of fluctuations in random state of independent particles is a white noise. For the first time we have found this I/w noise in As,S, glass [3] in the measurement of power fluctuations on a diaphragm. Here we present the experimental results for As,Se, glass measured by the optical grating method. We have also found in 0030.4018/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII s0030-4018(97)00335-0
this case a l/w tions.
spectrum
in the refractive-index
fluctua-
2. Experimental The main peculiarity of the present method (see also Ref. [4]) compared with most previous experiments (see, for example, Refs. [5]) is related to the back-scattering geometry for the diffracted light and the use of the same laser for both preparing the grating and its study by the probe beam. The choice of such a geometry was due to the relatively high absorption coefficient of the As,Se, material [6]. The radiation of an Ar+ laser at A = 5 14.5 nm divided into two beams of approximately equal intensity was directed to the sample. At 0 = 22” used here the period of the interference pattern was A = A, l/2 sin( 0/2) u I350 nm. This pattern creates a periodic disturbance in the refractive index of the sample. If both beams are on, one can observe the sum of two diffracted orders of the grating. If only one beam is on, it serves as a probe and the detector located at the correct position measures the intensity of only one diffracted order. The gratings were induced in the focused beams, a lens of F = 400 mm was used in this case and the diameter of these gratings was = 0.25 mm. The detectors used here were silicon diodes combined with a digital system, providing a total precision of mea-
B.P. Antonyk
surements of = 1%. Full power of order was measured. The incident beams was maintained at a constant precision. The power of the diffracted beam An ((nL/~cos0)‘(An)’ < I) is [7]
et al. /Optics
Commur~ications
(1)
3. Results and discussion Our previous paper 141 was devoted to the regular (smoothed) part of the diffracted signal. We examined the preparation and erasure of the state and we have found that the density of the trapped electrons and holes depended only on the number of transmitted photons, but the relative distribution of the particles is controlled by the light power. After a long exposure. a weak beam creates a high-ordered state (strong correlated), where electrons and
.+T-c,~.
l/I 0.00
0
200
400
,
600
,
/
/
,
800
1000
1200
,
,
1400
(
(
1600
l+-:-\;i.r.___.“,
_.._.
-- __i-Yi
lllllll~I/III./I,
0.05
0.10
0.15
0.20
0.25
Fig. 2. Spectrum of the diffraction refractive-index fluctuation).
0.35
0.30
0.40
0.45
0.50
signal
(the same
for the
holes are extremely separated. For this reason this state is long living: it recombines one order of magnitude slower than that prepared by a powerful beam during a short exposure. Here we pay attention to the fluctuations of the diffracted signal, driven by a refractive-index fluctuation. Our experiment has shown that after = 50 min exposure by radiation of an Ar+ laser at h = 514.5 nm, with a power of 9.5 mW and diameter of the spot of = 0.25 mm, the diffracted signal became noisy as shown in Fig. 1 (see also Fig. 8 of Ref. [4]). The amplitude of the noise exceeds considerably the accuracy of the measurement but it is lo-20 times less than the average level of the diffraction signal. It allows to treat it in the frame of perturbation theory: the amplitude of the incident field is constant at any point; the diffracted field is given by the above formula (11, as a first order on small perturbation An(r) = (An(t)> + 6n(tJ (SE(~) i< (An(t)), ((An(j)) is the average level, 6~l(f) is the noise). So the noise in the diffraction signal I is proportional to 6n(t). i.e. the noise
r
41'
I
,,L!Lj7
Frequency (s-l)
6
r
I
221
220-222
I at a small value of
where f, is the incident beam power, Arz is the refractive index change, L is the grating effective thickness, which depends on the absorption coefficient. Thus, the efficiency of the grating l//Cl may be found from a measurement of the detected current, which is proportional to the intensity of the diffracted beam. The refractive index change All consists of two parts, An = Arz, + A+, where Arz, is the electron contribution due to a partial change of the electronic states, and An, is due to temperature variations. A tlT was measured directly by comparison of the diffracted beam power in the presence of two pumping beams with the signal, when only one beam was on. We have found that Arl, and A.n, have opposite signs and An, is always small (Ar~,/Art, < IO-‘). Moreover, the An, grating vanishes with a rate yT = gX_‘/cp, - 10’ SC’, after switching off one of the pumping beams (,CCis the thermal conductivity coefficient, c is the thermal capacity, p. is the material density).
I.
f 19Y7)
i
the first diffraction power of the laser level with the same
/= (+‘hcos0)‘(Ar1)‘/,.
600
142
~ :_
In(F)
~
..: _.
-0.64-0.94ln(o)
, :,
-4 1 /
I
-6
-5
,,,/,,,,,/,// -4
-3
-2
-,
0
1
Time (seconds) Fig. I. Fluctuation tion.
of the diffraction
signal after 50 min exposi-
Fig. 3. 1/co noise in diffraction signal and refractive-index ation (double log scale. experiment).
fluctu-
222
B.P. Antonyuk et al. / Optics Communications
300.0
F
-
to the well-known phenomenon of self-organization in Ge-doped silica fibers, resulting in second harmonic generation [S-12]. We believe that both phenomena have the same background and may be described within the frame of our approach.
-1 i
200.0
142 f 1997) 220-222
: Acknowledgements This work is supported 161 13A.
100.0
by RFFI under Grant 96-02-
References
6,
0.0
0.00
[I] B.P. Antonyuk, 11111/I,,II//~,,,,,,,II~I,III///III,,~//11111/
0.20
0.40
0.60
0.80
1.00
(21
w
Fig. 4. l/o
noise in refractive-index
fluctuations
(theory).
in An(r). The Fourier transform of the diffracted signal reveals a l/o spectrum as shown in Fig. 2 and Fig. 3. According to our theory [1,2], this frequency dependence is inherent for a self-organized system. The theory predicts l/w noise in the refractive-index fluctuations for the ordered system shown in Fig. 4, while in a random system of independent particles the theory gives white noise. This universal behavior is valid for the Fourier transform of the time dependence including the initial part (growth) of the signal as well as for a “stationary” stage of fluctuations. So, the experimental result presented here supports the idea of light-driven electron-hole self-organization (ordering) in As,Se, glass, proposed in our previous papers [l-4]. The self-organization of electrons and holes in amorphous semiconductors discussed here is very similar
[3] [4] [5]
SF. Musichenko, Optics Comm. 99 (1993) 365. B.P. Antonyuk, SF. Musichenko, Phys. Lett. A 193 (1994) 403. B.P. Antonyuk, S.F. Musichenko, M. Bertolotti, R. Li Voti, C. Sibilia, G.L. Liakhou, Phys. Lett. A 201 (1995) 77. B.P. Antonyuk, S.F. Musichenko, V.B. Podobedov, J. Mod. Optics 42 (199.5) 2551. M.J. Pelletler, H.R. Thorshelm. J.M. Harris, Anal. Chem. 54 (1982) 239.
[6] J.B. Ramirez-Malo, E. Marquez, C. Corrales. P. Vilares, R. Jimenez-Garay, Materials Science Eng. B 25 (1994) 53. [7] R.J. Coller, Ch.B. Burckhardt, L.H. Lin Optical Holography (Academic, New York. 1971). [8] U. Osterberg, W. Marqulis, Optics Lett. 11(1986) 516. [9] Q.H. Stolen, H.W.K. Tom, Optics Lett. 12 (1987) 585. [lo] E.M. Dianov, P.G. Kazanskii, D.Y. Stepanov, Sov. J. Quantum Electron. 19 (1989) 575. [ll] N.B. Baranova, A.N. Chudinov. B.Y. Zel’dovich. Optics Comm. 79 (1990) 116. [I21 Z. Anderson, V. Mizrahi, J.E. Sipe, Proc. Intern. Workshop on Photoinduced Self-organization Effects in Optical Fibers. 1991, Quebec City.
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 142 (1997) 220-222
1/w noise in refractive-index fluctuations in As,Se, glass B.P. Antonyuk, Institute
of Spectroscop?;. Russian
S.F. Musichenko,
V.B. Podobedov
Academy of Sciences. Troitsk, Moscow~ Region 142092, Russian Federation
Received 3 March 1997; accepted 17 June 1997
Abstract Refractive-index fluctuation in As,Se, under excitation by an Arf laser was measured by an optical grating method. After 50 min exposition with a power of 9.5 mW and diameter of the spot of N 0.25 mm, the diffracted signal became considerably noisy. The Fourier transform of the signal reveals a I/w spectrum, predicted for self-organized (ordered) electron-hole systems. 0 1997 Elsevier Science B.V.
1. Introduction High energy photons generate electrons and holes in extended states. After fast relaxation to trapped states (ps time scale) a slow recombination of electrons and holes, separated in space, takes place. Trap populations (change of electron states) result in a change of the refractive-index and therefore may be investigated by an optical method. The relative variation An/n is of the order of the relative number of electrons, changing the state ANe/N, (A N,/N, ==K1). So the density of trapped electrons AN, manifests itself in the refractive index variation An and one can find trap population, recombination and its temporal ( t) fluctuation by the measurement of the An(r) kinetics. In general, both the real and imaginary parts of the dielectric constant vary, but this does not change our arguments. The investigation of time fluctuations An(t) is interesting because it allows to draw a conclusion about the state of electrons and holes. Our previous studies [ 1,2] have shown that the electron-hole system under light pumping with “band gap” photons transits to an ordered state: in spite of Coulomb repulsion the carriers form electron and hole domains. The density of trapped particles (and refractive index) fluctuates in this case with universal spectrum 1/LO, while the spectrum of fluctuations in random state of independent particles is a white noise. For the first time we have found this I/w noise in As,S, glass [3] in the measurement of power fluctuations on a diaphragm. Here we present the experimental results for As,Se, glass measured by the optical grating method. We have also found in 0030.4018/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII s0030-4018(97)00335-0
this case a l/w tions.
spectrum
in the refractive-index
fluctua-
2. Experimental The main peculiarity of the present method (see also Ref. [4]) compared with most previous experiments (see, for example, Refs. [5]) is related to the back-scattering geometry for the diffracted light and the use of the same laser for both preparing the grating and its study by the probe beam. The choice of such a geometry was due to the relatively high absorption coefficient of the As,Se, material [6]. The radiation of an Ar+ laser at A = 5 14.5 nm divided into two beams of approximately equal intensity was directed to the sample. At 0 = 22” used here the period of the interference pattern was A = A, l/2 sin( 0/2) u I350 nm. This pattern creates a periodic disturbance in the refractive index of the sample. If both beams are on, one can observe the sum of two diffracted orders of the grating. If only one beam is on, it serves as a probe and the detector located at the correct position measures the intensity of only one diffracted order. The gratings were induced in the focused beams, a lens of F = 400 mm was used in this case and the diameter of these gratings was = 0.25 mm. The detectors used here were silicon diodes combined with a digital system, providing a total precision of mea-
B.P. Antonyk
surements of = 1%. Full power of order was measured. The incident beams was maintained at a constant precision. The power of the diffracted beam An ((nL/~cos0)‘(An)’ < I) is [7]
et al. /Optics
Commur~ications
(1)
3. Results and discussion Our previous paper 141 was devoted to the regular (smoothed) part of the diffracted signal. We examined the preparation and erasure of the state and we have found that the density of the trapped electrons and holes depended only on the number of transmitted photons, but the relative distribution of the particles is controlled by the light power. After a long exposure. a weak beam creates a high-ordered state (strong correlated), where electrons and
.+T-c,~.
l/I 0.00
0
200
400
,
600
,
/
/
,
800
1000
1200
,
,
1400
(
(
1600
l+-:-\;i.r.___.“,
_.._.
-- __i-Yi
lllllll~I/III./I,
0.05
0.10
0.15
0.20
0.25
Fig. 2. Spectrum of the diffraction refractive-index fluctuation).
0.35
0.30
0.40
0.45
0.50
signal
(the same
for the
holes are extremely separated. For this reason this state is long living: it recombines one order of magnitude slower than that prepared by a powerful beam during a short exposure. Here we pay attention to the fluctuations of the diffracted signal, driven by a refractive-index fluctuation. Our experiment has shown that after = 50 min exposure by radiation of an Ar+ laser at h = 514.5 nm, with a power of 9.5 mW and diameter of the spot of = 0.25 mm, the diffracted signal became noisy as shown in Fig. 1 (see also Fig. 8 of Ref. [4]). The amplitude of the noise exceeds considerably the accuracy of the measurement but it is lo-20 times less than the average level of the diffraction signal. It allows to treat it in the frame of perturbation theory: the amplitude of the incident field is constant at any point; the diffracted field is given by the above formula (11, as a first order on small perturbation An(r) = (An(t)> + 6n(tJ (SE(~) i< (An(t)), ((An(j)) is the average level, 6~l(f) is the noise). So the noise in the diffraction signal I is proportional to 6n(t). i.e. the noise
r
41'
I
,,L!Lj7
Frequency (s-l)
6
r
I
221
220-222
I at a small value of
where f, is the incident beam power, Arz is the refractive index change, L is the grating effective thickness, which depends on the absorption coefficient. Thus, the efficiency of the grating l//Cl may be found from a measurement of the detected current, which is proportional to the intensity of the diffracted beam. The refractive index change All consists of two parts, An = Arz, + A+, where Arz, is the electron contribution due to a partial change of the electronic states, and An, is due to temperature variations. A tlT was measured directly by comparison of the diffracted beam power in the presence of two pumping beams with the signal, when only one beam was on. We have found that Arl, and A.n, have opposite signs and An, is always small (Ar~,/Art, < IO-‘). Moreover, the An, grating vanishes with a rate yT = gX_‘/cp, - 10’ SC’, after switching off one of the pumping beams (,CCis the thermal conductivity coefficient, c is the thermal capacity, p. is the material density).
I.
f 19Y7)
i
the first diffraction power of the laser level with the same
/= (+‘hcos0)‘(Ar1)‘/,.
600
142
~ :_
In(F)
~
..: _.
-0.64-0.94ln(o)
, :,
-4 1 /
I
-6
-5
,,,/,,,,,/,// -4
-3
-2
-,
0
1
Time (seconds) Fig. I. Fluctuation tion.
of the diffraction
signal after 50 min exposi-
Fig. 3. 1/co noise in diffraction signal and refractive-index ation (double log scale. experiment).
fluctu-
222
B.P. Antonyuk et al. / Optics Communications
300.0
F
-
to the well-known phenomenon of self-organization in Ge-doped silica fibers, resulting in second harmonic generation [S-12]. We believe that both phenomena have the same background and may be described within the frame of our approach.
-1 i
200.0
142 f 1997) 220-222
: Acknowledgements This work is supported 161 13A.
100.0
by RFFI under Grant 96-02-
References
6,
0.0
0.00
[I] B.P. Antonyuk, 11111/I,,II//~,,,,,,,II~I,III///III,,~//11111/
0.20
0.40
0.60
0.80
1.00
(21
w
Fig. 4. l/o
noise in refractive-index
fluctuations
(theory).
in An(r). The Fourier transform of the diffracted signal reveals a l/o spectrum as shown in Fig. 2 and Fig. 3. According to our theory [1,2], this frequency dependence is inherent for a self-organized system. The theory predicts l/w noise in the refractive-index fluctuations for the ordered system shown in Fig. 4, while in a random system of independent particles the theory gives white noise. This universal behavior is valid for the Fourier transform of the time dependence including the initial part (growth) of the signal as well as for a “stationary” stage of fluctuations. So, the experimental result presented here supports the idea of light-driven electron-hole self-organization (ordering) in As,Se, glass, proposed in our previous papers [l-4]. The self-organization of electrons and holes in amorphous semiconductors discussed here is very similar
[3] [4] [5]
SF. Musichenko, Optics Comm. 99 (1993) 365. B.P. Antonyuk, SF. Musichenko, Phys. Lett. A 193 (1994) 403. B.P. Antonyuk, S.F. Musichenko, M. Bertolotti, R. Li Voti, C. Sibilia, G.L. Liakhou, Phys. Lett. A 201 (1995) 77. B.P. Antonyuk, S.F. Musichenko, V.B. Podobedov, J. Mod. Optics 42 (199.5) 2551. M.J. Pelletler, H.R. Thorshelm. J.M. Harris, Anal. Chem. 54 (1982) 239.
[6] J.B. Ramirez-Malo, E. Marquez, C. Corrales. P. Vilares, R. Jimenez-Garay, Materials Science Eng. B 25 (1994) 53. [7] R.J. Coller, Ch.B. Burckhardt, L.H. Lin Optical Holography (Academic, New York. 1971). [8] U. Osterberg, W. Marqulis, Optics Lett. 11(1986) 516. [9] Q.H. Stolen, H.W.K. Tom, Optics Lett. 12 (1987) 585. [lo] E.M. Dianov, P.G. Kazanskii, D.Y. Stepanov, Sov. J. Quantum Electron. 19 (1989) 575. [ll] N.B. Baranova, A.N. Chudinov. B.Y. Zel’dovich. Optics Comm. 79 (1990) 116. [I21 Z. Anderson, V. Mizrahi, J.E. Sipe, Proc. Intern. Workshop on Photoinduced Self-organization Effects in Optical Fibers. 1991, Quebec City.