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We investigate the dependence of the nonlinear optical properties of Cu-doped and Ag-doped As2Se3 glasses on the incident pulse-width at 1.064 μm using the Z-scan technique. In this work, 11.5-ns optical pulses from a Nd:YAG laser were compressed up to 1.6 ns by using stimulated Brillouin scattering in heavy fluorocarbon liquid. The measurement of the pulse-width dependence of the optical nonlinearities leads to the separation of an ultrafast Kerr nonlinearity and a slow (cumulative) nonlinearity such as a thermal nonlinearity. The measured values of the nonlinear refractive index and the nonlinear absorption coefficient of 4 at.% Cu-doped As2Se3 glass (where the normal photodarkening effect is sufficiently suppressed) and 4 at.% Ag-doped As2Se3 glass were proportional to the pulse width, showing that the cumulative nonlinearity is present in these two glasses. The cumulative nonlinearity of these doped glasses is larger than one of the undoped glass. The origin of such slow nonlinearity is presumably attributed to the photostructural changes inherent in chalcogenide glasses and is directly independent of one of photodarkening.
©2009 Optical Society of America
1. Introduction
Chalcogenide glasses have attracted significant attention as promising materials in fiber optics and integrated optics since they have many unique optical properties and exhibit a good transparency in the infrared region [1–3]. In particular, As-Se system and related glass system such as Ag-As-Se possess a high third-order Kerr nonlinearity with an ultrafast time response [4–6], a large Raman-gain coefficient [7], and a large Brillouin-gain coefficient [8,9]. These three kinds of third-order nonlinearities can be applied to all-optical switching, optical bistability, regeneration, Raman and Brillouin amplification and lasing, slow light, supercontinuum generation, and so on [3]. We recently investigated the dependence of the nonlinear refractive index and the nonlinear absorption coefficient of As2Se3 glass on the incident pulse-width in the picosecond-to-nanosecond regime using the conventional Z-scan technique and pulse compression based on stimulated Brillouin scattering in a liquid [10]. This novel approach allows the separation between an ultrafast Kerr nonlinearity and a slow (cumulative) nonlinearity such as a thermal nonlinearity [10,11]. Our experimental results show that there exists a considerable cumulative nonlinearity generated by linear (one-photon) absorption (OPA) in the As2Se3 glass, which is presumably attributed not to the thermal effects or the plasma effects of photoinduced free carriers, but to the photostructural changes inherent in chalcogenide glasses [12]. The structural changes in chalcogenide glasses generated by exposure to near bandgap light are often accompanied by photodarkening (i.e., a red-shift in the optical absorption edge and a related increase in refractive index) or photobleaching (i.e., blue-shift) [13]. The sign of the observed nonlinear changes in refractive index and absorption coefficient was positive as in case of photodarkening although illumination with below-bandgap light was used in the experiment. It is important to further investigate such a cumulative nonlinearity since its magnitude is much larger than the thermal nonlinearity and it can cause serious problems in application of chalcogenide glasses to nonlinear optical devices.
It is known that the addition of some heavy metal atoms into chalcogenide glasses inhibits the appearance of the photodarkening effect. Adding, for example, a small amount (1-5 at.%) of Cu into As2Se3 and As2S3 glasses, it is completely suppressed [14,15]. The addition of Cu or Ag is also effective in preventing or decreasing the photodecomposition and photo-oxidation (i.e., the formation of As2O3 microcrystals) [16,17].
In this paper we measure the pulse-width dependence of the nonlinear refractive index and the nonlinear absorption coefficient in Cu-doped and Ag-doped As2Se3 glasses at 1.064 μm in the nanosecond regime using our developed approach [10,11] and discuss the mechanisms of the optical nonlinearities and the relation between the slow nonlinearity and photodarkening. Every parameter describing the nonlinear optical properties is determined using a theoretical model developed in [10]. It is found that, compared with undoped As2Se3 glass, these two kinds of doped As2Se3 glasses have intense linearity of the two nonlinear coefficients against the incident pulse-width, i.e. have a large cumulative nonlinearity. The mechanism producing the cumulative nonlinearity is not directly related to the photodarkening and the magnitude of the cumulative nonlinearity increases with increasing absorption loss in the weak-absorption region.
2. Experiment
For the sake of completeness, we briefly describe the preparation of the samples used in this work and its characterization based on the Z-scan method [18].
The samples used in this work were prepared by a conventional melt-quenching method. First, glassy As2Se3 was synthesized by melting the mixture of As and Se elements of 99.9999% purity in an evacuated fused-quartz ampoule. The ampoule was placed in a rocking furnace at about 1000 °C for 25 h to increase the mixing and homogenization of the melt and then rapid cooling by putting it into water. Next, Cu(Ag)-doped As2Se3 glasses were prepared by heating the mixture of the glassy As2Se3 and appropriate amounts of Cu(Ag) of 99.999% purity in the same way. However, in order to avoid the segregation of Cu(Ag) on the surface of the quenched ingot, the melt was cooled down from 420 °C (slightly higher that the melting point). The content of Cu was selected to be 4 at.% from the following two facts; the addition of 5 at.% of Cu to As2Se3 essentially suppresses the photodarkening [14,15] and the binding energies of As and Se undergo a great change at a Cu content of 3 at.% [19]. The concentration of Ag was also selected to be 4 at.% for comparison. We obtained the sample used for Z-scan measurements by cutting the glass into a parallel plate and polishing both surfaces of it. The thickness of the samples was 1.2 mm. Although the 1.064-μm pump wavelength is longer than a band gap (Tauc gap) wavelength of 0.705 μm in case of undoped As2Se3 glass, there is still considerable absorption because of weak-absorption tail (mid-gap absorption) [12]. We have already pointed out that the cumulative nonlinearity found in the previous work would be closely related to the mid-gap absorption [10]. Therefore we measured the linear refractive index n and absorption coefficient α of three glasses used in the Z-scan experiment at 1.064 μm using a Brewster’s angle method [20]. The obtained results are given in Table 1 in Section 3. It should be noted that the Cu addition of 4 at.% increases the absorption coefficient by a factor of 11. The Cu or Ag element acts as glass structure modifier rather than glass structure former for low Ag (Cu) content, i.e. the low addition of Ag or Cu has no significant effect on the structure of As2Se3 glass [21,22]. However the optical properties are drastically changed even by the addition of low Cu content as discussed in [22] or shown in Table 1.
Table 1. The measured linear and nonlinear optical coefficients of undoped and Cu(Ag)-doped As2Se3 glasses at 1.064 μm. The concentration of Cu and Ag is 4 at.%.
In the Z-scan experiments for determining the nonlinear refractive index n 2eff and nonlinear absorption coefficient β eff of the samples [18], a nanosecond pulsed laser is used. Since the details of the SBS pulse compression of nanosecond pulses and the Z-scan experiments can be found in [11], we shall here describe them only briefly. The pump laser used in this work is an injection-seeded, Q-switched Nd:YAG laser, which provides 400-mJ, 11.5-ns Gaussian pulses at a 1.064-μm wavelength and a 10-Hz repetition rate. The optical pulses from this laser are compressed by using SBS in heavy fluorocarbon liquids from 11.5 ns to 1.6 ns. We utilize the compressed Nd:YAG laser pulses to two kinds of Z-scan measurements, i.e. open-aperture and closed-aperture Z-scans for determining the nonlinear refraction and nonlinear absorption of the sample. However a part of the cross section of the compressed pulses was used through an aperture with 1mm diameter because of their poor beam profile. The sample is mounted on a translation stage and is moved along the z-axis through the focal plane of 25-cm focal length lens. The beam waist w 0 (defined by the half width at 1/e 2 of the maximum) at focus is 40 μm. We use the aperture’s linear transmission S = 0.40 for our Z-scan experiments. Since the stability of the compressed pulses was often lost during experiment, we had to obtain Z-scan data while the stability was maintained. Therefore we display the Z-scan data on an XY recorder in a short period of time (typically 30-60 seconds), where the position of the sample is converted into voltage with a potentiometer and is fed into the X axis of the recorder. The sensitivity of the Z-scan depends on beam quality and stability of the laser system including the SBS pulse compressor as well as distortions and a tilt of the sample. Typical raw Z-scan data have been presented in Fig. 1 of [10] and Fig. 3 of [11].
Fig. 1 Dependence of (a) the effective nonlinear refractive index n 2eff and (b) the effective nonlinear absorption coefficient β eff on the incident pulse energy for the pulse width t FWHM = 11.5 ns at 1.064 μm.
Fig. 3 Dependence of (a) the effective nonlinear refractive index n 2eff and (b) the effective nonlinear absorption coefficient β eff on the incident pulse-width t FWHM. The data were obtained at an incident pulse energy of 15 μJ.
3. Results and discussion
First, we examine the dependence of the effective nonlinear coefficients n 2eff and β eff of Cu(Ag)-doped As2Se3 glasses on the incident power. Figures 1 and 2 shows the experimental results for the pulse width (defined by full width at half maximum) t FWHM = 11.5 ns and 1.6 ns at 1.064 μm, respectively. For comparison, the results for undoped As2Se3 glass given in [10] are also reproduced in the figures. The horizontal axis is shown in terms of the incident energy per pulse. An incident energy of 10-μJ leads to the on-axis peak intensity (inside the sample) I 0 = 26.7 MW/cm2 for t FWHM = 11.5 ns and I 0 = 192 MW/cm2 for t FWHM = 1.6 ns. Note that the peak optical intensity at t FWHM = 1.6 ns is always about 7 times as much as one at t FWHM = 11.5 ns for a given value of the incident power. In the low power region where data are not given in the figures, we could not obtain reliable results because of small Z-scan signals. The results show that the nonlinear coefficients of three kinds of glasses depend on incident pulse energy contrary to our expectation. Since the absorption coefficient α of As2Se3, Ag-As2Se3, and Cu-As2Se3 glasses is 0.621, 0.948, and 7.117 cm−1, respectively, as shown in Table 1, we can say that the measured values of n 2eff and β eff generally increase with incrasing linear absorption coefficient α. As will be discussed below, this can be expected from the fact that the cumulative nonlinearity is proportional to the absorbed photon density (see Eqs. (1) and (2)).
Fig. 2 Dependence of (a) the effective nonlinear refractive index n 2eff and (b) the effective nonlinear absorption coefficient β eff on the incident pulse energy for the pulse width t FWHM = 1.6 ns at 1.064 μm.
Next, we examine the dependence of n 2eff and β eff of Cu(Ag)-doped As2Se3 glasses on the pulse width. Figure 3 shows the experimental results when an incident average power (or energy per pulse) is fixed at 150 μW (15 μJ) for the pulse width ranging from 11.5 ns to 1.6 ns. For comparison, the results for the undoped As2Se3 glass are shown in the figure. It is found that all the measured values of n 2eff and β eff vary linearly with the pulse width t FWHM. This is to certify that a cumulative nonlinearity is present in these glasses, i.e. the photoinduced refractive index change and absorption loss are accumulated during the incident pulse. Therefore it should be noted that although this cumulative nonlinearity can be increased by increasing pulse-width, the large nonlinearity never varies in proportion to the temporal variation of the incident pulse. The effective nonlinear refractive index and nonlinear absorption coefficient when the Kerr nonlinearity and the cumulative nonlinearity coexist in the sample are given by [10]
where γ is the fast Kerr coefficient, β is the two-photon absorption (TPA) coefficient, α is the linear absorption coefficient, σ r is the change in the refractive index per unit of the absorbed photon density, and σ ab is the change in the absorption coefficient per unit photon density. The six straight lines presented in Fig. 3 are the best fit to the experimental data of n 2eff and β eff. We can obtain the values of σ r and σ ab from the slope of the fitted straight lines and the values of γ and β from the intercept (t FWHM = 0) of the straight line. The obtained results are summarized in Table 1. Although it is difficult to exactly determine the values of γ and β for Cu(Ag)-As2Se3 glasses from Fig. 3, they are largely similar to γ = 3.0 × 10−17m2/W and β = 5.0 × 10−11m/W of As2Se3 glass [10]. The σ r and σ ab values of Cu-doped As2Se3 glass are smaller than those of the undoped As2Se3 glass, whereas the σ r and σ ab values of Ag-doped As2Se3 glass are larger than those of the undoped glass.[REMOVED SHAPE FIELD]Although it is obvious that the linearity of n 2eff and β eff against the pulse width comes from a cumulative nonlinearity generated by linear absorption [10], we try to show direct evidence of it. We carried out the experiment of the time-resolved transmission done in [23] by using the setup for the open-aperture Z-scan. Figure 4(a) shows the time-varying transmission of the undoped As2Se3 glass when an 11.5-ns and 15-μJ optical pulse is incident into it. The dynamic transmittance was obtained by conforming the transmitted and incident optical pulses at the beginning of leading edge and by dividing the former by the latter. It is clearly shown that photoinduced loss is accumulated during the incident optical pulse. We also had similar results for Cu(Ag)-doped As2Se3 glasses. Figure 4(b) shows the input-output characteristics for three values of incident pulse energy. The solid (with marks) and dashed lines correspond to the leading and trailing edges, respectively and the peak power of each incident pulse is normalized to 1. We have a clockwise hysteresis loop because of a large difference in transmittance between the leading edge and trailing edge.
Fig. 4 (a) Time-varying transmission of the undoped As2Se3 glass when an 11.5-ns and 15-μJ optical pulse is incident into it. (b) The input-output characteristics for three values of incident pulse energy.
In the previous paper [10], we discussed the origin of this slow cumulative nonlinearity. The plasma effect of free-carriers generated by linear (one-photon) absorption (OPA) and the thermal effect were excluded from its possibility and we had come to the conclusion that it would be presumably attributed to the photostructural changes inherent in chalcogenide glasses. However we must again consider the possibility of the thermal effect in case of Cu-As2Se3 glass since its absorption coefficient is an order of magnitude larger than of the undoped glass as shown in Table 1. When the fast Kerr nonlinearity and the slow thermal nonlinearity exist together, n 2eff is given by [10]
where ρ is the density, C is the specific heat, and dn/dT is the thermo-optic coefficient of the material. To examine the possibility, we calculate the magnitude of the thermal contribution n 2eff−γ of Eq. (3) and compare it with the measured value. As an example, let us calculate the magnitude of n 2eff−γ at t FWHM = 11.5 ns. With the known values of α = 7.117 cm−1 for the Cu-As2Se3 glass and C = 0.27 J/gK, ρ = 4.64 gcm−3and dn/dT = 3.5 × 10−5 K−1 for As2Se3 glass [10], we have n 2eff−γ = 1.0 × 10−16 m2/W, which is 1/10 of the measured value. Moreover we cannot explain the large incident-energy dependence of n 2eff and β eff shown in Figs. 1 and 2, since the thermal nonlinearity does not depend on the incident pulse energy. Therefore we can neglect the thermal effect even for the Cu-As2Se3 glass.A plausible origin of the cumulative nonlinearity is the reversible photostructural changes [12,13,24]. The sign of both the observed nonlinear refraction and absorption is positive and is consistent with the photodarkening induced by illumination with bandgap light. However this normal photodarkening seems to be not the origin of the cumulative nonlinearity because it is essentially induced by the interband absorption. The results for Cu-As2Se3 with a Cu content of 4 at.% clearly show that the origin of the cumulative nonlinearity is not the same as one of the normal photodarkening. Belykh et al. have observed photoinduced loss with a very long response time in As2S3 glass under conditions similar to the present experiment by the experiment of the time-resolved transmission [23]. Although they conclude that the mechanism of the photoinduced loss is connected with the nonlinear excitation of interband transition in glass, which can be done by TPA or two-step absorption, we believe that the two experimental results are the same in essence. However their conclusion is inconsistent with our experimental results. If the observed cumulative nonlinearity is induced by nonlinear absorption such as TPA and two-step absorption, the values of n 2eff and β eff should be proportional to the fluence, as discussed in [10]. The observed cumulative nonlinearity is the change in optical constants due to the structural changes induced by OPA. Therefore we believe that the photoinduced structural changes are associated with defects which are responsible for weak-absorption tail. Although the process of weak-absorption tail is still speculative as well as the normal photodarkening, it seems to be dominantly caused by the wrong bond, As-As and Se-Se [25]. However, at the present stage, we do not understand how the wrong bonds relate to the observed slow nonlinearity.
We must also discuss the difference in the cumulative nonlinearity among As2Se3, Ag-As2Se3, and Cu-As2Se3 glasses. It should be remembered that the magnitude of the cumulative nonlinearity is given by the product of the linear absorption coefficient α and the microscopic parameters σ r and σ ab as shown in Eqs. (1) and (2). Therefore we can mainly explain the difference in n 2eff and β eff among three kinds of glasses by α. On the other hand, considering the microscopic parameters, the obtained σ r and σ ab values for Ag-As2Se3 glass are relatively close to those of the undoped glass. Regarding the photo-oxidation and the photodarkening effect, we have already found a distinct difference between Ag-As2Se3 and Cu-As2Se3 in [17], which is attributed to the difference in the bonding and electronic properties of Se atoms due to the difference in the coordinate number between Ag and Cu atoms. In Ag-As-Se glasses, the Ag atom is coordinated by two Se atoms. On the other hand, when Cu is added into As2Se3 glass, the coordination is changed from two-fold to four-fold for Se atoms since the Cu atom is always tetrahedrally coordinated. Although the cumulative nonlinearity is independent of the photodarkening effect directly, we believe that the origin of the difference in the magnitude of σ r and σ ab the between Ag and Cu addition is the same as one of the two effects mentioned above in essentials.
4. Conclusion
We have investigated the nonlinear optical properties of 4 at.% Cu-doped and 4 at.% Ag-doped As2Se3 glasses for pulse durations on the order of nanoseconds at 1.064 μm using the Z-scan method. In this experiment, the duration of incident optical pulses was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in liquid Fluorinert. We measured the pulse-width dependence of the effective nonlinear refractive index n 2eff and the effective nonlinear absorption coefficient β eff at an incident pulse energy of 15 μJ. It has been found that the measured values of n 2eff and β eff increase linearly with pulse width, showing that a cumulative nonlinearity is present in these two glasses as well as undoped As2Se3 glass. It has been confirmed that the magnitude of the cumulative nonlinearity increases with the absorption loss α in the weak-absorption region. Therefore it can be expected that the cumulative nonlinearity decreases with increasing optical wavelength. Moreover we determined the Kerr coefficient γ, the TPA coefficient β, and the changes in the refractive index and absorption coefficient per unit absorbed photon density, σ r and σ ab using a theoretical model developed in the previous paper [10]. The mechanism of the cumulative nonlinearity is presumably attributed to photostructural changes inherent in chalcogenide glasses. The relation among the cumulative nonlinearity, photodarkening, and photo-oxidation was also discussed.
Acknowledgments
This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology in Japan. The authors would like to thank Dr. M. Kitao retired from Shizuoka University for providing As2Se3 glasses.
References and link
1. A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]
2. K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005). [CrossRef]
3. V. G. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007). [CrossRef] [PubMed]
4. F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274(1-3), 232–237 (2000). [CrossRef]
5. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]
6. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29(3), 265–267 (2004). [CrossRef] [PubMed]
7. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004). [CrossRef]
8. K. Ogusu, H. Li, and M. Kitao, “Brillouin-gain coefficients of chalcogenide glasses,” J. Opt. Soc. Am. B 21(7), 1302–1304 (2004). [CrossRef]
9. K. S. Abedin, “Observation of strong stimulated Brillouin scattering in single-mode As2Se3 chalcogenide fiber,” Opt. Express 13(25), 10266–10271 (2005). [CrossRef] [PubMed]
10. K. Shinkawa and K. Ogusu, “Pulse-width dependence of optical nonlinearities in As2Se3 chalcogenide glass in the picosecond-to-nanosecond region,” Opt. Express 16(22), 18230–18240 (2008). [CrossRef] [PubMed]
11. K. Ogusu and K. Shinkawa, “Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 microm,” Opt. Express 16(19), 14780–14791 (2008). [CrossRef] [PubMed]
12. K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. 44(6), 475–588 (1995). [CrossRef]
13. G. Pfeiffer, M. A. Paesler, and S. C. Agarwal, “Reversible photodarkening of amorphous arsenic chalcogens,” J. Non-Cryst. Solids 130(2), 111–143 (1991). [CrossRef]
14. J. Z. Liu and P. C. Taylor, “Absence of photodarkening in bulk, glassy As2S3 and As2Se3 alloyed with copper,” Phys. Rev. Lett. 59(17), 1938–1941 (1987). [CrossRef] [PubMed]
15. J. Z. Liu and P. C. Taylor, “Effect of Cu alloying on metastable photoinduced absorption in Cux(As0.4Se0.6)1-x and Cux(As0.4S0.6)1-x glasses,” Phys. Rev. B 41, 3163–3171 (1990). [CrossRef]
16. K. Ogusu, Y. Hosokawa, S. Maeda, M. Minakata, and H. Li, “Photo-oxidation of As2Se3, Ag-As2Se3, and Cu-As2Se3 chalcogenide films,” J. Non-Cryst. Solids 351(37-39), 3132–3138 (2005). [CrossRef]
17. K. Ogusu, T. Hagihara, Y. Hosokawa, and M. Minakata, “Dependence of photo-oxidation on Ag(Cu)-content in Ag(Cu)-As2Se3 films,” J. Non-Cryst. Solids 353(11-12), 1216–1220 (2007). [CrossRef]
18. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
19. A. Gheorghiu-de La Rocque, E. Belin-Ferré, M. F. Fontaine, and G. J. Adriaenssens, “XPS studies of Cu incorporation in arsenic chalcogenides,” J. Non-Cryst. Solids 299-302, 953–957 (2002). [CrossRef]
20. K. Ogusu, K. Suzuki, and H. Nishio, “Simple and accurate measurement of the absorption coefficient of an absorbing plate by use of the Brewster angle,” Opt. Lett. 31(7), 909–911 (2006). [CrossRef] [PubMed]
21. K. Ogusu, T. Kumagai, Y. Fujimori, and M. Kitao, “Thermal analysis and Raman scattering study on crystallization and structure of Agx(As0.4Se0.6)1-x glasses,” J. Non-Cryst. Solids 324, 118–126 (2003). [CrossRef]
22. K. Ogusu, S. Maeda, M. Kitao, H. Li, and M. Minakata, “Optical and structural properties of Ag(Cu)-As2Se3 chalcogenide films prepared by a photodoping,” J. Non-Cryst. Solids 347, 159–165 (2004). [CrossRef]
23. A. V. Belykh, O. M. Efimov, L. B. Glebov, Yu. A. Matveev, A. M. Mekryukov, M. D. Mikhailov, and K. Richardson, “Photo-structural transformation of chalcogenide glasses under non-linear absorption of laser radiation,” J. Non-Cryst. Solids 213-214, 330–335 (1997). [CrossRef]
24. K. Tanaka, “Reversible photostructural change: Mechanisms, properties and applications,” J. Non-Cryst. Solids 35-36, 1023–1034 (1980). [CrossRef]
25. K. Tanaka, “Midgap photon effects in As2S3 glass,” Philos. Mag. Lett. 84(9), 601–606 (2004). [CrossRef]
