Light-induced oscillatory behaviors of transmission in chalcogenide glasses are investigated using a continuous wave tunable Ti-sapphire laser. It is shown that phase change, thermal fluctuation, nonlinear index change and periodic self focusing are not at the origin of light-induced oscillatory transmittance in chalcogenide glasses. Instead, results indicate that the interference of transmitting and reflecting light is at the origin of the oscillatory behaviors of transmitted light. Just like the principle of Fabry-Pérot interferometer, these interferences result in a periodic change in transmission as the related interferential beams get in and out of phase. However, this transmitting oscillatory behavior can be registered by the detector only when the change of optical path length difference initiated by photo-induced effects is slower enough compared with the corresponding response time of the detector. Several photo-structural effects contribute to that phenomenon including photo-expansion, photo-darkening, and permanent self focusing. It appears that fluctuations of the light source intensity induce a wide distribution of the oscillatory periods.
©2009 Optical Society of America
Chalcogenide glasses have been intensively investigated during the last several decades due to their potential applications in many fields such as information storage and integrated optics. Varieties of photo-induced effects in this kind of glass (for example: volume , index , phase  changes and polarization-driven anisotropic changes of optical , electric  and mechanical  properties) have been reported. Recently significant achievements have been made regarding the understanding of microscopic mechanism of some photo-induced effects [7,8]. However, the nature of many intriguing phenomena in these glasses is not well understood. In this paper we investigated the oscillating fluctuation in transmitted intensity observed during continuous irradiation of chalcogenide glasses. There is still a wide divergence of opinions concerning the origin of photo-induced transmitting oscillations. For example, observations in amorphous GeSe2 using Raman spectra , suggested that this oscillatory phenomenon be associated with a laser-induced phase change such as the reversible micro-crystallization. In another study, a periodic change of diameter of rings accompanying the oscillatory behavior  proposed that the self focusing phenomena easily occurring in chalcogenide glasses [11,12] could possibly induce a periodic change of focus therefore resulting in the oscillatory behavior. Lastly, the oscillations of transmittance were suggested to be originated from the combined effects of laser heating and photo-structural changes based on the change of absorptive coefficient and thermal “runaway” model [13,14]. Therefore, it appears that a clear understanding of the mechanism of oscillatory transmission in chalcogenide glass is still lacking.
In this letter, we suggest that optical interferences are at the origin of the transmitting oscillatory behavior based on a study of GeSe4 glasses irradiated with a continuous wave tunable Ti-sapphire laser. The gradual variation of optical path length difference between the transmitting and reflecting light is believed to produce an oscillating interferential effect similar to the principle of Fabry-Pérot interference resulting from the slowly progressing photo-structural effects in the material.
Photo-induced transmitting oscillatory behaviors are commonly observed when studying photo-darkening in many chalcogenide glassy systems such as Ge-As-Se, As-S-Se, Ge-Se. In order to study this phenomenon more closely, samples of the GeSe4 composition with two parallel polished faces and a variety of thickness ranging from 0.1mm~3mm were prepared. The GeSe4 composition was chosen because the Ge-Se glassy system is a close-to-ideal covalent glass due to the similar size and electro-negativity of its compositional elements. Based on the network rigidity of the Phillips and Thorp Model, the GeSe4 glass should be an optimally constrained glass and exhibit excellent glass-forming tendency. According to the intermediate phase theory, Boolchand  further pointed out that GeSe4 glass should possess stress-free structure. Also, based on our recent identification about the effect of network connectivity on photo-structural changes , this glass should have a moderate photosensitivity.
Glasses with optical quality were synthesized from 99.9999% purity starting element and melted in sealed silica ampoules in a rocking furnace for up to 12 hours. The resulting rods were quenched in water and annealed near the glass transition temperature. The rods were subsequently sliced and polished into discs with parallel faces.
Irradiation measurements were performed similar to  with a continuous tunable Ti-Sapphire laser S3900 (Spectra Physics) and standard silicon detectors. Raman characterization of the samples was performed with a laser con-focal Raman microscope (Type: inVia).
3. Results and discussion
Systematic adjustment of the irradiation wavelength, power as well as thickness of samples, shows that photo-induced oscillatory behaviors of transmittance can be widely and reproducibly observed in many irradiation conditions; and for a certain oscillatory condition, the oscillatory periods always have a wide distribution from several seconds to several tens of seconds in a chaotic form. Figure 1 shows that its development can be typically divided into three successive phases. In the first stage, the transmission decreases monotonically as expected from the build up of photo-darkening. The second stage however appears more chaotic and corresponds to a transitory phase associated with the initiation of the oscillatory mode. Finally the third stage corresponds to the steady oscillatory state.
3.1 Potential phase change
The oscillatory behavior of transmittance can be observed in a wide range of optical density at 785nm. In order to investigate whether a possible phase change is at the origin of these oscillations, a Raman system equipped with a 785 nm source was used to continuously (sampling interval: 5 seconds) monitor the possible change of the sample in the structure during irradiation. However, up to clear appearance of photo-expansion (Fig. 2 ) no measurable change occurs as to the profile and full width at half maximum of the GeSe4 Raman spectra. It is well known that Raman scattering technique is a sensitive probing tool for covalent structural units and can easily identify phase changes in chalcogenide glass [9,16]. Therefore, it is concluded that phase changes such as reversible optical crystallization are not at the origin of the generally observed transmitting oscillations in the present chalcogenide glasses. This is not surprising considering that GeSe4 is an excellent glass former and is not expected to crystallize easily.
3.2 Potential thermal effects
According to the theory of reference [13,14], thermally induced oscillatory behavior can only occur in a narrow range of condition including optical density, thickness and temperature. In order to investigate a potential thermal origin due to laser light absorption, a laser source with longer wavelength was used. The behavior was studied at 880nm with an absorption coefficient of only 0.2 cm−1 much lower than the optical absorptive coefficient of 2 cm−1 at 785nm (see Fig. 3 ). The oscillatory behavior was nevertheless shown to occur despite this large change in conditions and the much lower absorption. The oscillatory phenomenon was also shown to occur in a wide range of laser intensity from several to several tens of W/cm2 without altering other parameters. Finally, as shown in Fig. 1(a), the maximum decrease in transmittance in the first stages is about 4.5% at saturation. This shift in absorption could potentially be ascribed to a monotonic increase of the medium temperature due to laser heating; however, Fig. 1(c) shows that the following transmitting oscillations reach up to 9% which make them very unlikely to have a thermal origin. And it was also confirmed in  that the nature of the sub-bandgap photo-induced effects is a-thermal. Therefore, although thermal effect may have an influence in very specific conditions [13,14], the general transmitting oscillatory behavior observed in this study should not be ascribed to fluctuations of temperature in the medium. These changes are instead likely due to photo-induced phenomena.
3.3 Potential effect of self-focusing
In order to investigate whether a periodic change of focus resulting from self-focusing is at the origin of this oscillatory phenomenon, the self-focusing process in GeSe4 glass was characterized. Self focusing effects have been ascribed to the nonlinear index change which shows a great effect in ; however, the low optical density used in this study with a maximum of several tens of W/cm2 should not generate any nonlinear effects. Alternatively, according to reference , the formation of graded index ascribed to a photo-induced index change resulting from the Gaussian profile of the light source could be at the origin of self focusing. And finally the convex structure formed by photo-expansion including permanent and instantaneous parts should also have an important contribution to self focusing especially in the later period, because the saturation of photo-darkening can be obtained much more quickly compared with that of photo-expansion . In addition, in the present case, the use of a screen behind the sample instead of the detector revealed a solid circle showing periodic change of brightness and darkness following the oscillatory behavior of transmission, but no significant periodic change of circle diameter. This suggests that a defocusing effect is present as a result of the photo-induced index gradient and/or the photo-expansion; however, a periodic change of focus cannot be at the origin of the oscillatory behavior.
3.4 Effect of optical path length difference
Then what is the nature of the oscillatory phenomenon? Considering the large refractive index (2.7 at 880nm for GeSe4 glass) the optical interference between the transmitting light and the reflecting light might play a significant role in the origin of this oscillating phenomenon. The two opposite faces of the polished glass sample can act as a Fabry-Pérot cavity that can either transmit or reflect light of a given wavelength depending on the distance between the two faces, the index of the medium and the angle of incidence. In this cavity, a change of phase between the two beams could produce constructive or destructive interferences and finally lead to a change of intensity registered by the detector. The intensity on the detector is maximum when the optical path length difference between the incident and reflected beams is an integer multiple of the wavelength and becomes minimum correspondingly when the difference is half an odd multiple of the wavelength.
The phase change δ between incident and reflected light is expressed by Eq. (1) where θ is the angle of incidence, L is the sample thickness, λ the light wavelength and n is the glass index. For a normal angle of incidence cos θ = 1 and since L and λ are fixed, the incident and reflected light periodically come in and out of phase as the index n is changing during photo-darkening.
This process is initially very rapid during the first stage. As an estimate, the index drops by about Δn = 0.1 in the first 60 seconds which corresponds to 16 phase oscillations per second. However the response time of the Si detector is only 0.1 second, hence the signal is averaged and appears continuous in the first stage.
When the index change stabilizes in the second stage the phase oscillations also stabilize. Comparing the intensity of reference and glass transmission registered by the detectors, Fig. 4 shows the process from the initial strong dependence on the random power fluctuation in the laser source (for samples without any photo-induced effects, the exact dependence of the intensity between the reference and glass transmission will always come out) to larger change in the glass transmission following small jumps of less than 1mW up to the emerging of the periodic transmitting oscillations, which appears to render the effect of signal sampling gradually commensurable with a periodic variation due to interference on time.
But the question remains as to what is driving the periodic oscillation in transmission in the third stage. In the present experiment the interference conditions described above gradually change due to a combination of the slowly progressing light-induced phenomena including photo-expansion, photo-darkening, self focusing together with the fluctuation of irradiated power. It is known that photo-darkening, which leads to the concomitant change of refractive index of chalcogenide glasses, comprises permanent and transient parts . The instantaneous part will disappear following the removal of light. Both parts are directly proportional to optical density of the irradiated light. Similarly, photo-expansion also includes permanent and transient parts . The change of index and thickness of the medium together with the formation of convex structure due to the Gauss profile of laser will all lead to the gradual change of phase which can result in the intensity change on the detector.
The periodic oscillations present in the third stage can then be explained if we bear in mind that the sub-bandgap light employed in the present experiment is almost not absorbed yet can effectively induce photo-structural changes. Driven by light-induced phenomena the interference condition can be fulfilled; however, this condition will not persist because the gradually cumulative photo-induced change will further modify the phase difference, now bringing the light back in phase and restoring transmission as observed in Fig. 1. Then this behavior becomes periodic as the related beams consecutively get in and out of phase following the progression of self-generated cumulative photo-induced effects. In addition, the fluctuation of source laser intensity will lead to a non-homogeneous change of photo-induced effects mentioned above on time, which will further induce a wide distribution of the oscillatory periods.
In summary, GeSe4 glasses with varying thickness were irradiated with sub-bandgap light of varying power and wavelength. It is shown that the general oscillatory phenomena of transmittance in chalcogenide glasses is not associated with phase change, thermal fluctuation or nonlinear index change and self focusing. Instead, optical interference of the transmitting and reflecting light appears to be at the origin of the transmission oscillations. The phenomenon results from a combination of photo-induced effects and the wide distribution of the oscillatory periods appears to be triggered by the fluctuation of laser source.
This work was partially supported by the National Natural Science Foundation of China (grant No.60808024).
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