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Abstract
The experimental and theoretical study of continuous UV laser beam propagation through thick silver-containing photo-thermo-refractive glass is presented. It is shown for the first time that self-action of UV Gaussian beam in glass results in its self-focusing. The observed linear effect is non-reversible and is caused by the transformation of subnanosized charged silver molecular clusters to neutral state under UV laser radiation. Such transformation is accompanied by the increase of molecular clusters polarizability and the refractive index increase in irradiated area. As a result, an extended positive lens is formed in glass bulk. In a theoretical study of linear self-focusing effect, the “aberration-free” approximation was used, taking into account spatial distribution of induced absorption.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photo-thermo-refractive (PTR) glasses are the class of photosensitive silver-containing glasses [1,2], which is used for recording commercially available volume holograms and Bragg gratings [3–7]. Silver-containing glasses also possess non-linear optical properties [8–10], and can be used for optical information recording [11–14]. Silver in PTR glasses can exist in the states of ions, neutral atoms, charged or neutral subnanosized molecular clusters (MCs) Agn, and silver nanoparticles (NPs) [1,2,11,12]. As a rule, in addition to silver, PTR glasses contain photosensitizer (Ce3+ ions) and reducer (Sb5+ or Sn2+ ions). UV irradiation and thermal treatment of such glasses can transform the state of silver in them, changing their optical properties [1,11,12]. UV irradiation into the absorption band of Ce3+ ions (λ = 305-330 nm) results in photoionization of Ce ions. Some part of free electrons is trapped by charged silver components, and another part – by ions of reducer. The subsequent thermal treatment results in the release of trapped electrons from the reducer and in the increase of neutral silver components, or in silver NPs growth, depending on treatment temperature. These effects are used for the synthesizing in PTR glasses neutral silver MCs, which possess intense luminescence in visible spectral range, silver NPs with plasmon resonance [15,16], and for recording of volume holograms and Bragg gratings.
It was shown in [17] experimentally that the transformation of charged silver MCs to the neutral state by continuous UV irradiation results not only in the increase of glass luminescence intensity, but also in the increase of glass refractive index in the irradiated area. This makes possible to record optical waveguides and holograms using only local UV irradiation of PTR glasses. The effect of PTR glass refractive index increase during silver MCs transformation to the neutral state is caused by the fact that the polarizability of neutral silver MCs is larger than the polarizability of charged ones. Such change of polarizability was confirmed in [17] by computer simulation. Here the question appears: if UV irradiation of PTR glass results in the increase of refractive index, can this effect manifest itself in linear self-focusing of UV radiation?
To answer this question we experimentally studied the propagation of continuous UV laser radiation through thick PTR glass samples, and the influence of the subsequent thermal treatments on their optical properties. We also performed brief theoretical explanation of the observed effects.
2. Experimental methods
PTR glasses based on the Na2O-ZnO-Al2O3-Si2O-NaF-NaCl system, doped with Ag2O (0.12 mol.%), photosensitizer - CeO2 (0.07 mol.%) and reducer - Sb2O3 (0.04 mol.%) were synthesized in ITMO University. As-prepared the glass is transparent in a spectral range of 350-1500 nm and has the refractive index of 1.52 in a spectral range of 400-800 nm. The glass transition temperature Tg was measured with STA6000 (PerkineElmer) differential scanning calorimeter, its magnitude being found to be Tg = 494 °C. It must be noted, that during the glass synthesis some part of Ce ions changes the valence state from IV to III, and some part of Sb ions changes the valence state from III to V. The samples to be investigated were prepared in the form of the plane-parallel polished plates 5 mm thick and 21 mm long. The laser input and output edges were also polished.
The samples were irradiated through their edge by continuous UV single-mode He-Cd laser (λ = 325 nm) Kimmon IK3501R-G with parallel beam. The wavelength of laser radiation matches the absorption band of Ce3+ ions. Laser power density on a samples surface during irradiation was 425 mW/cm2, irradiation dose was 6 J/cm2. Laser beam diameter on the samples was 2.5 mm. For the visualization of laser beam trace after irradiation semiconductor laser with λ = 405 nm was used. Its radiation excite neutral silver MCs and their luminescence mark the beam trace. This wavelength was chosen because it does not match the absorption band of Ce3+ ions, so it does not change optical properties of the studied glasses.
Thermal treatment of the samples was performed in a muffle furnace (Nabertherm) at T = 350 °C (less than Tg) during 1 h and at T = 550 °C (higher than Tg) during 1 and 2 h. It is known that the thermal treatment at temperature higher than Tg results in transformation of silver VCs into silver NPs [1,11]. Optical density spectra of the glass samples were measured using Lambda 650 (Perkine-Elmer) spectrophotometer. Luminescence spectra were recorded by LS-55 spectrofluorimeter (Perkin-Elmer). Spectral measurements were performed at room temperature.
3. Experimental results
The transformation of charged silver MC to the neutral state by UV irradiation makes them luminescent. It makes possible to trace the excitation laser beam (λ = 405 nm) and to discover in a sample the areas with high concentration of neutral silver MCs. Figure 1 shows photos of luminescence of the sample before He-Cd laser irradiation, after irradiation and after thermal treatment at T = 350 °C during 1 h. Before laser irradiation the sample was homogenously irradiated by UV mercury lamp during 10 s. So the weak luminescence appears in the whole sample bulk. One can see from Fig. 1(a) that before laser irradiation parallel excitation laser beam remains parallel in the whole its path in the sample. Only the luminescence intensity decreases along the beam path, because of excitation radiation absorption. After He-Cd laser irradiation luminescent area became conical, and luminescence intensity decreases along the excitation laser path [Fig. 1(b)]. This indicates that during He-Cd laser action self-focusing of its beam takes place. After the thermal treatment at 350 °C luminescence intensity increases by 3-5 times, and the whole luminescent area along laser beam path can be observed [Fig. 1(c)].
Fig. 1 Luminescence of PTR glass excited by semiconductor laser with parallel beam and λ = 405 nm. (a): before He-Cd laser irradiation; (b): after He-Cd laser irradiation; (c): after He-Cd laser irradiation and thermal treatment at T = 350 °C during 1 h. The directions of He-Cd and semiconductor laser beams were from right to left.
The dependence of luminescent area diameter on distance from the laser beam input after the thermal treatment at 350 °C is shown in Fig. 2 (curve 1). These data were obtained by processing of the images in Fig. 1(b,c) mathematically. It can be seen from Fig. 2 that the curvature of the curve at first increases, and for distance z > 7.5 mm the curve becomes more sloping.
Fig. 2 1 - Diameter of luminescent area via distance after He-Cd laser irradiation and thermal treatment at T = 350 °C during 1 h.
Figure 3 shows the luminescence spectra of irradiated area before He-Cd laser irradiation (curve 1), after laser irradiation (curve 2), and after laser irradiation and thermal treatment at T = 350 °C (less than Tg) (curve 3). The excitation wavelength of 360 nm was chosen because it matches the maximum of excitation band of neutral silver MCs [11]. One can see from Fig. 3 that after laser irradiation and thermal treatment the luminescence intensity increases and maximum of luminescence band shifts from 480 nm to 500 nm. On base of the data, presented in [18–21], we can make the conclusion that for excitation wavelength λ = 360 nm the contribution to the luminescence band make neutral MCs Ag2, Ag3, and Ag4. The contribution to luminescence in spectral range of 350-490 nm make MCs Ag2 and Ag4, in the spectral range of 550-600 nm – MC Ag3. The spectral shift of luminescence maximum after the thermal treatment is caused by redistribution of different MCs concentration during their growth.
Fig. 3 Luminescence spectra of PTR glass before He-Cd laser irradiation (1), after He-Cd laser irradiation (2), and after He-Cd laser irradiation and thermal treatment at T = 350 °C during 1 h (3). Excitation wavelength is 360 nm.
Figure 4 shows the optical density spectra of irradiated area before He-Cd laser irradiation (curve 1), after laser irradiation (curve 2), and after laser irradiation and thermal treatment at T = 350 °C (curve 3). The absorption band in spectral range of 300-330 nm is the absorption band of Ce3+ ions. It can be seen from Fig. 3 that UV laser irradiation causes the increase of the absorption in spectral range of 250-450 nm. This is the result of transformation of charged silver MCs to neutral state, which have the absorption bands in that spectral region. The thermal treatment leads to the further increase of the absorption in that spectral region, caused by the increase of neutral MCs concentration [11]. The thermal treatment at T = 550 °C (higher than glass transition temperature, Tg) results in the intense brown coloring of the first part of the irradiated area [Fig. 5(a)], and in the appearance on optical density spectrum of the absorption band in a spectral range of 380-500 nm with maximum at λ = 420 nm [Fig. 4, curve 4]. This absorption band is caused by the plasmon resonance [15,16] of metal silver NPs, which are formed in PTR glass during thermal treatment.
Fig. 4 Optical density spectra of PTR glasses before He-Cd laser irradiation (1); after He-Cd laser irradiation (2); after He-Cd laser irradiation and thermal treatment at T = 350 °C during 1 h (3); and after He-Cd laser irradiation and thermal treatment at T = 550 °C during 2 h (3).
Fig. 5 Photos of the sample (a) and its luminescence (b) after He-Cd laser irradiation and thermal treatment at T = 550 °C during 2 h. Excitation wavelength is 405 nm. Scale is 10 mm. Insets: views in glass cross-section.
The appearance of silver NPs leads to the disappearance of luminescence in the central part of the beam trace [Fig. 5(b)], because in this area silver MCs are transformed to silver NPs. This transformation results also in decrease of optical density in spectral range of 250-350 nm, because of the decrease of silver MCs concentration. It is known that silver NPs possess luminescent properties in red spectral range. But as it was shown in [11,23] the presence of halogenide shells leads to luminescence bleaching. It can be seen from Fig. 5(b) that at the periphery of the area with silver NPs the luminescence of silver MCs remains. This indicates that at low concentration neutral silver MCs are stable and do not transform to silver NPs during heating up to 550 °C. Luminescence spectrum in this area is the same, as shown in Fig. 3 (curve 3). The reason of luminescence presence in this area is a low intensity of He-Cd laser radiation there during irradiation. Therefore only small part of silver ions was transformed to neutral silver atoms. As silver atoms are the building material for silver NPs growth, very few silver NPs can be formed in this area.
Silver MCs play the role of seed centers for silver NPs growth. The shape and spectral position of plasmon resonance band makes possible to define that silver NPs have spherical shapes, their diameters are approximately 2-20 nm and they have dielectric shells with high refractive index [11,15,16,22]. As it was shown in [11,22] in the studied PTR glasses these shells consist of crystalline NaxAgyClz. The diameter of the region with silver NPs decreases with the distance [Fig. 6, curves 1 and 2] and the dependence is approximately linear.
Fig. 6 Diameters of absorbing areas via distance after He-Cd laser irradiation and thermal treatment at T = 550 °C during 1 h (2) and 2 h (3) (see also Fig. 4).
4. Discussion
The experiments, described above have shown that during irradiation of PTR glass by continuous UV laser radiation with parallel Gaussian laser beam the self-focusing effect takes place. The main condition of this effect appearance is matching of laser radiation wavelength with the absorption band of Ce3+ ions. The described result is consistent with the results, which we described in [17]. It was shown in [17] that the transformation of charged silver MCs to neutral state results in the increase of silver MCs polarizability, and in the increase of refractive index of PTR glass by Δn = + (0.2-0.76)·10−4. Small value of Δn is explained by low concentration of silver in PTR glasses. As the samples were irradiated by single-mode He-Cd laser with Gaussian distribution in laser beam cross-section, the positive lens is formed in the track of laser beam, which focuses the beam. The reason of this is the larger radiation intensity on the beam axis, which produces more neutral silver MCs in the center of laser beam than on its periphery. It is known that the action of pico- or nanosecond laser pulses on materials with third-order optical non-linearity or semiconductors results in self-focusing or self-defocusing effects [24–30]. Self-focusing in PTR glasses, caused by third-order non-linearity, was also observed during IR femtosecond laser irradiation [10,31]. Unlike these “classical” non-linear optical effects the effect of refractive index increase, described above, is non-reversible, and remains after the laser action.
For the qualitative description of linear self-focusing effect in PTR glasses the “aberration-free” approximation [28–30] can be used. In this approximation the Gaussian beam propagating through the thick medium keeps its Gaussian shape. The condition of this is the parabolic spatial distribution of medium refractive index in a beam cross-section. So for the change of refractive index in a beam cross-section the following expression can be used [30]:
where Δn(0) is the refractive index change on a beam axis; R is the local beam radius; a is the correction factor to account higher order terms in the expansion of exponent. For thin medium the parabolic approximation of refractive index change correlates with a thin spherical lens. In this case a thick medium can be described as the sequence of m thin layers, each layer representing a thin lens, and the properties of the next lens depend on the properties of previous lenses. The effective focal length fm of each lens in the sequence can be written as [29,30]:Here Rm and Δnm are the beam radius and on-axis refractive index change respectively; ΔL is the distance between two adjacent lenses. In this model thick medium can be described by ABCD-matrix formalism, defining m’th element in the sequence as [30]:
The transformation of charged silver MCs to neutral state is accompanied not only by the increase of refractive index, but also by the increase of the absorption at He-Cd laser wavelength (see Fig. 4). So, the intensity of laser beam decreases along the laser beam path. The decrease of laser beam intensity results in the decrease of neutral silver MCs concentration, and in the decrease of absorption coefficient and refractive index change in m’th layer. But there is a concurring process: self-focusing causes the decrease of beam diameter, and, as a result, the increase of laser radiation intensity. To take into account these processes self-consistent model was used in calculations. Figure 7 shows the intensity distribution along laser beam for the cases of constant absorption coefficient (curve 1), taking into account the dependence of absorption coefficient on intensity for constant beam diameter (curve 2), and taking into account the dependence of absorption coefficient on intensity and self-focusing effect (curve 3). It can be seen from Fig. 7 that the absorption processes, discussed above, influence on the laser intensity distribution considerably.
Fig. 7 Calculated normalized radiation intensity (λ = 325 nm) via distance. 1 – for constant absorption coefficient, 2 – taking into account the dependence of absorption coefficient on intensity for constant beam diameter, 3 - taking into account the dependence of absorption coefficient on intensity and self-focusing.
Figure 8 shows the beam diameter and radius curvature of wavefront via distance, calculated for Δn0 = 0.5·10−4, and taking into account the processes, noted above. One can see from Fig. 8 that beam diameter dependence for distance z < 7.5 mm have a good qualitative agreement with experimental dependence, shown in Fig. 2 (curve 1). Chosen volume of Δn0 is nearby the volumes of Δn, measured in [17] experimentally. For z > 7.5 mm the calculated dependence considerably differs from the experimental one. The reason of this is the following. As in Gaussian beam the radiation intensity is a maximum at beam axis, the induced absorption is a maximum in this area too. So during the beam penetration through the sample the distortion of beam shape takes place: at the beam axis the intensity distribution flattens. This distortion causes the distortion of refractive index profile in a beam cross section. So the “aberration-free” approximation is not valid for the long distances.
Fig. 8 Calculated dependence of beam diameter (1) and radius curvature of wavefront (2) on distance.
Thus, during irradiation of PTR glass by parallel single-mode He-Cd laser beam self-focusing effect takes place, and the conical gradient luminescent waveguide is formed along the laser beam path. The subsequent thermal treatment at T = 550 °C transforms this optical structure to the conical waveguide with high refractive index on the periphery and low refractive index in central part. Some possible applications of refractive index modulation by the described method were discussed in [17].
5. Conclusions
The experiments have shown that the self-action of UV Gaussian laser beam in silver-containing PTR glass results in its linear self-focusing in glass bulk. This effect is non-reversible and is caused by the transformation of subnanosized charged silver MCs to neutral state. Such transformation is accompanied by the increase of MCs polarizability, and the refractive index increase in irradiated area. Estimation gives the increment of refractive index of approximately 0.5·10−4. As a result, the extended positive lens is formed in glass bulk. The theoretical analysis has shown that the observed effect depends on radiation-induced absorption considerably. The observed effect can be used for luminescent waveguides recording in PTR glasses.
Funding
Ministry of Education and Science of Russian Federation (project # 16.1651.2017/4.6).
Acknowledgment
The authors thank V.D. Dubrovin for PTR glass synthesis.
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