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Self induced gratings in ternary SiO2:SnO2:Na2O bulk glasses by UV light seeding

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Abstract

The diffraction efficiency of gratings written in ternary SnO2:SiO2:Na2O bulk glasses rises dramatically with time after the occultation of the cw 244nm light used to write the thick hologram. This self-induced behavior lasts for several hours and ultimately leads to refractive index changes as high as 3 10-3.

©2005 Optical Society of America

1. Introduction

Using UV lasers with a view of inducing refractive index change Δn of order a few 10-3 after a reasonable exposure time (≈15 min) remains a key for fabricating most photosensitivity -based devices. To increase the photosensitivity of glasses, researchers have followed two main strategies that are not exclusive. The first one consists in using hydrogen treatment (H2-loading [1], OH-flooding [2], UV hypersensitization [3]….), the second one in directly manufacturing glass with intrinsic high photosensitivity. For this last purpose, researchers have used different methods such as changing the composition of glasses (e.g. germanium concentration) and/or the technology involved in the glass fabrication. Up to now, GeO2 remains the most prominent doping for highly photosensitive silica glass. However, other doping (such as boron, lead, tin…) have been efficiently used to dope silicate or to co-dope germanosilicate (or phospho-silicate) glass For example, SnO2, has been incorporated in silica glass [4], in phosphosilicate [5] or germanosilicate [6] fibers as a doping through the MCVD process. Exposing these fibers to ≈ 0.6–20 kJ/cm2 at 248 nm light enables one to obtain photo-induced index changes ranging from 3 10-4 to 1.4 10-3. Similarly, optical fibers, produced by the rod-in-tube technique, have been designed with SiO2:SnO2:Na2O cores and SiO2 cladding for getting a high photosensitivity. As a result strong Bragg Gratings (BGs) (Δn ≈ 6.2 10-4, 30 kJ/cm2, λp=248 nm) could be written in these fibers [7]. Unlike other techniques (boron co-doping, H2-loading…), addition of tin does not introduce significant loss in the third telecommunication window near 1.55 μm. Moreover, it leads to a better thermal grating stability, is less time consuming and is potentially cheaper. Unfortunately, the incorporation of SnO2 into silica raises several problems. For example, a limit for binary glasses based on SiO2:SnO2 is given by the crystallization process that takes place for SnO2 concentration higher than 0.4 mol % [8]. Yet, previous papers [7, 9] have shown that alkaline elements like Na increase the solubility of SnO2 in bulk silica glass (up to 20% without crystallization). Furthermore, the introduction of Na2O allows the ion exchange process to be used for waveguides fabrication [10, 11]. However, little is known about the influence of Na2O on the glass photosensitivity.

Hence, in this paper, we report a study on the photosensitivity of highly Sn-doped bulk ternary SnO2:SiO2:Na2O glasses under exposure to cw 244nm laser light. Two manufacturing procedures have been investigated. Strong BG modulations between 6.10-4 and 3.10-3 associated with a self-formation of the BG have been demonstrated. Furthermore, microscopic investigations at the grating place carried out by means of optical or TEM microscopy revealed the presence of a phase separation at the UV-exposed places of the BGs.

2. Experiments

Tables Icon

Table 1. Glasses fabrication conditions.

The glasses were designed and fabricated at the Politecnico di Torino. Tin doped Na-silicate glasses were prepared via melt-quenching technique. Powders of SiO2, Na2O and SnO2 have been melted for 1 h at 1500°C and consolidated at 1700°C for 1h in a Pt crucible. To produce the most homogeneous possible glasses, two combinations of procedures have been used: melt mixing and casting upon a Cu-plate at room temperature (sample P1) or melt mixing and cooling in the Pt crucible until room temperature (sample P2). The transparent glasses have been annealed for up to 10h at 500°C to reduce the residual stresses and assure the necessary mechanical stability. The molar composition of the batch powders was [SiO2] = 75 mol%, [SnO2] = 5 mol%, and [Na2O] = 20 mol%. The resulting bulk glass was cut into plates that were then polished to reach an optical quality.

The glass refractive index was measured with an Abbe refractometer and found to be 1.52. In order to get a better knowledge of the glass characteristics, UV absorption measurements has been carried out in the pristine P1 preform plate (thickness = 100μm). The investigated spectral range spanned from 190 nm to 700 nm. Figure 1 displays the corresponding optical density spectrum. This figure shows that there exists a main peak of absorption located near ≈ 260 nm, associated with a strong absorption tail that spreads towards the VUV range. Furthermore, it is also worth noticing that the absorption coefficients near 633 nm (He-Ne laser) and near 244 nm are equal to 7.5 cm-1 and 250 cm-1 respectively.

 figure: Fig. 1.

Fig. 1. UV absorption spectrum of the SnO2:SiO2:Na2O P1 sample (t = 100 μm) before UV exposure.

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Bragg gratings have then been written in the 100 μm thick plates using the Lloyd interferometer method [5]. The set-up involving a Lloyd’s mirror type interferometer is described in Fig. 2. The sample was set perpendicularly to the plane of the interferometer mirror. The UV beam from a cw intracavity frequency-doubled Ar-ion laser (Coherent inc. FRED 244 nm) was first expanded through a spherical telescope providing an expansion ratio of 5. After spatial filtering, the UV beam was then focused onto the sample by means of a cylindrical lens to an approximately rectangular spot (4 mm wide by 20 μm in height), the UV beam optical axis impinging onto the vertical apex of the mirror. The crossing angle between the two interfering UV beams was chosen to get a grating pitch Λ of 5 μm. A mechanically chopped TEM00 He-Ne laser was used to monitor the temporal growth of the hologram in the course of its inscription. To this end, the He-Ne probe beam direction was tuned to the Bragg angle in order to get the phase-matching conditions leading to a maximum in the diffraction efficiency. Two plano-cylindrical lenses with crossed axis were used to focus the 633 nm beam onto the sample to get spot sizes (0.3 mm wide by 20 μm in height) that match these of the grating. The cylindrical lenses are not shown in Fig. 2 for sake of clarity. Both the UV and visible beams were linearly polarized along a direction perpendicular to the plane of Fig. 2 (s-polarization). The optical power, diffracted by the grating, was detected by a photomultiplier tube and a lock-in amplifier. The diffraction efficiency η of the gratings was obtained using the relation η = I 1/I 0 where I1 is the diffracted power and I 0 the incident power of the He-Ne beam. Microscopic investigations of the gratings were performed using an optical microscope, a phase-shift interferometer or a transmission Electron Microscope (TEM).

 figure: Fig. 2.

Fig. 2. Top-side view of the experimental set up (PM: photomultiplier).

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3. Results

The development of the diffraction efficiency of sample P1 (thickness = 100 μm) is shown in Fig. 3 for two gratings carried out at different laser powers (G1=57W/cm2 and G2=260W/cm2) as a function of the UV-exposure time. For these gratings, the evolution of the diffraction efficiency proved to be not monotonous with exposure time. Indeed, a steady rise in the diffraction efficiency was followed after saturation by an equally steady decline. It is worth noticing that the higher the power density, the higher the maximum in the diffraction efficiency and the longer the exposure time for which the saturation occurred. For example, the diffraction efficiency reached the maximum at 6.5 % (1000 s) for the G2 grating and at 1% (100 s) for the G1 grating.

 figure: Fig. 3.

Fig. 3. Growth of diffraction efficiencies as a result of UV exposure of SnO2:SiO2:Na2O P1 sample at two power densities.

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The growth of the diffraction efficiency corresponding to the G1 grating (sample P1) is displayed in Fig. 4 versus recording time during and after the exposure of the sample to UV light. The first section of the curve corresponds to the UV exposure at a power density of 57 W/cm2. This part of the plot witnesses a small growth (less than 1%) in the diffraction efficiency as it was already reported in Fig. 3. The second part of the curve corresponds to the switching-off of the UV exposure. A huge increase in diffraction efficiency is observed despite the fact that the UV was blocked throughout the recording time. The intensity of the diffracted beam increased during several hours, the diffraction efficiency reaching 33 % after a recording time of 4800 s. After the sharp stop-point at 4800 s, the steady rise in the diffraction efficiency was followed by a weak decrease. The long term measurements in η after it reached the plateau show a decrease of ≈3% after a few hours and no significant evolution for longer recording time (3 h ≤ t ≤ 4 weeks).

On the other hand, in the course of the second growth of the diffraction efficiency (the UV exposure being off since a time delay Δt.), the He-Ne beam has been blocked for a time δt (Section “A” in Fig. 4 illustrates the effect of an occultation for δt = 250 s after Δt =1500 s). Different times for δt and Δt have been tried ranging respectively from 10 s to 400 s and from 0 s to 1500 s. After being blocked, the He-Ne beam was launched again to be in position of measuring again the diffraction efficiency. An increase in diffraction efficiency could always be observed despite the fact that no light was impinging onto the grating (UV and He-Ne beam blocked). These results are indicative of a grating self-formation triggered by UV light. Moreover, by looking at the part of the plot corresponding to “UV off, He-Ne beam on”, in Fig. 4, it can be noticed that the noise level significantly increased as a function of the recording time (i.e. the “noise” at 2500 s is smaller than the “noise” at 4000 s). Yet, the rise in the noise level came in proportion with that of the intensity of the scattered beam so that the signal to noise ratio was nearly constant during the time of the record.

 figure: Fig. 4.

Fig. 4. Evolution of the grating diffraction efficiency, demonstrating the formation of a self induced grating in SnO2:SiO2:Na2O P1 sample (260W/cm2). “A” indicates the part where the He-Ne beam was blocked.

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It is also worth noticing that UV exposure inducing a BG in the P2 plate of a not casted glass (a drilled glass, i.e. more homogeneous than the P1 poured glass), no further self-induced grating formation could be detected in this plate. In contrast, the self-induced formation of a grating has been observed in the P1 sample provided the UV power density was higher that 50 W/cm2 (investigated power density < 300 W/cm2) and the UV exposure time was longer than 1 min. More specifically, the influence of the UV exposure time on the kinetics of grating growth is illustrated in Fig. 5. Indeed, the growth of the diffraction efficiency corresponding to two gratings written in the P1 sample is shown in Fig. 5 as a function of the recording time, the parameter of the two plots being the UV exposure time. As it can be observed, the initial rate of the second growth (UV off) depends on the UV exposure time initially used to expose the sample: the longer the exposure time, the larger the initial rate of the second growth.

 figure: Fig. 5.

Fig. 5. Growth of diffraction efficiencies as a result of self induced gratings in SnO2:SiO2:Na2O P1 sample. The parameter of the experiment is the UV exposure time before the self induced grating growth. (□: exposure time = 1850s, ♦: exposure time =900s)

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One can also note that a visual inspection of the sample at the time of the record of the second part of the plot in Fig. 4 did not enable us to detect any signal of luminescence emerging from the sample exposed to the 633 nm light. With a view of clarifying a possible role of a light-induced photochromism in the grating formation, we have carried out further measurements. Firstly, the He-Ne beam was launched at normal incidence onto the surface of a pristine plate. The transmitted intensity was measured as a function of time without observing any significant change neither in the transmitted intensity nor in the signal to noise ratio. Secondly, a part of the sample has been uniformly exposed to UV light for 120 min (power density = 200W/cm2). After the exposure, the transmission factor of the sample at the exposed spot was monitored as a function of the recording time (probe wavelength = 633 nm). It appeared that the UV exposure had no significant effect on the transmission factor (and on the signal to noise ratio S/N) that remained constant versus recording time to within 1%.

Microscopic inspections of the P1 plate surface at the grating position were carried out by means of a phase-shift interferometer microscope a few weeks after the end of the BG inscription. These inspections revealed the presence of periodic humps at the grating period Λ. The corrugation appeared above the surface of the non exposed part of the plate, indicating that the corrugation arose from a local volume expansion. The measured peak to valley depth of the corrugation ranged from 5 nm to 10 nm. Furthermore, optical microscopy inspection of the G1 grating indicated the formation of small particles (after the end of the UV exposure) in the UV bright fringes whereas no formation of clusters could be detected during the UV exposure or in the P2 plate. The difference between the two observations is illustrated by means of micrographs displayed in Fig. 6(a). To clarify the nature of the clusters in the bright fringes in Fig 6(a), a TEM analysis has been carried out at an accelerated voltage of 300 keV. The samples were prepared by ion beam polishing. Figure 6(b) shows a TEM picture of a bright fringe at the exposed P1 sample. As it can be seen, small size (between 100 nm and 1 μm) particles that give bright contrast developed in the UV treated region. An EDS spectrum shows that these particles are a Na-rich chemical composition. TEM inspections of a non-exposed part of the P1 plate or of the P2 plate (exposed or non-exposed parts) did not reveal any formation of cluster. These results indicate that the formation of these clusters is specific of the exposed part of the P1 plate.

 figure: Fig. 6.

Fig. 6. a) Optical microscope image of G1 Bragg grating written in the P1 sample; b) TEM picture of small particles in the UV-exposed region of the G1 grating on P1 sample.

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4. Discussion

We have shown that the diffraction efficiency of a grating written in ternary SnO2:SiO2:Na2O P1 sample rises dramatically with time after the end of the inscription of the thick hologram by means of 244 nm cw laser light. Moreover, the probe beam at 633 nm has no significant influence on the kinetics of the new growth. To our best knowledge, it is the first material in which such growth behavior is reported. Yet, Strasser et al. [12] have observed a waiting time for the growth of gratings in D2 loaded UV-exposed Ge-doped waveguides, the UV beams being on. The above-mentioned experimental observations provide some evidence about the possible origin of grating formation in multicomponent tin-silicate glasses.

Thus, the invariance of the sample transmission factor under UV exposure yields an upper limit for the UV-induced loss near 633nm: Δαi (633nm) < 0.1 cm-1. Furthermore, this figure enables us to disregard the formation of an absorption grating as giving a significant contribution to the diffraction efficiency. Indeed, the diffraction efficiency η of an absorption grating is given by Eq. (1):

η=I1I0=sinh2(Δα.teff2.cosθB)

where ϑB is the internal Bragg angle, Δα is the amplitude of the sinusoidal loss along the grating wavevector, teff is the effective grating depth and n the glass refractive index. With a view of determining η, one can obtain a rough estimate of teff through the assumption that the effective grating depth is equal to the UV penetration depth. Assuming further that the absorption coefficient α(λp) at the pump wavelength (λp = 244nm) does not depend on the optical power, one can merge teff to 1/α(λp). The absorption coefficient at the peak of the 244nm band is α(λp) =250 cm-1 in our P1 sample before the UV exposure (see Fig. 1). Thus, the value of 1/α(λp) that can be deduced from this analysis is equal to ≈ 40 μm. On the other hand, the effective thicknesses t eff of the thick holograms can also be estimated through the measurement of the angular acceptance (ΔθB) of the gratings: ΔΘB ≈ 2Λ/teff. This measurement method led to values of t eff located within the range [30 – 40 μm] depending on the power density (measurement carried out at the end of the scanning time). Thus, there exists a good agreement between the estimations from the two methods. Consequently, to calculate the diffraction efficiency of an absorption grating we have fixed the effective thickness teff at 40 microns. As a result of this figure, the UV-induced loss Δαi can be held to be responsible for a diffraction efficiency of less than 0.1%. This figure is lower than the accuracy of our η measurement.

As a periodic corrugation has been observed at the sample surface, it seems necessary to estimate the contribution of such grating to the diffraction efficiency. Indeed, high diffraction efficiency has already been reported for corrugation gratings written either in high germanium or lead doped glasses [13]. Thus, Eq. (2) has been used to calculate the diffraction efficiency of a corrugation grating [14].

η=(π.Δn.hλpr.cosθB)2

In Eq. (2), Δn is the refractive index difference between the glass and air, h the measured corrugation depth and λpr ≈ 633nm is the probe wavelength. Making allowance for a maximum value of 10nm for h and taking Δn = 0.52, we find that η is inferior to 1 %. This figure is at least one order in magnitude lower than the measured value of ≈30 %, suggesting that the contribution of the surface relief grating to the diffracted signal can be neglected.

Eventually, we have to consider that the main part of the diffraction efficiency comes from the formation of a thick phase hologram. When the Bragg condition is satisfied, the diffraction efficiency of a Bragg grating η is given by Eq. (3) [15]:

η=sin2(π.Δnmod.teffλpr.cosθB)

In Eq. (3), λpr ≈ 633nm, t eff is the effective thickness of the hologram and Δnmod the amplitude of the refractive index modulation. Assuming that neither surface relief grating nor absorption grating was induced at the time of the grating writing, we have used Eq. (3) to estimate the order of magnitude of Δnmod (teff ≈ 40 μm). As a result, the amplitude of the refractive index modulation calculated at the end of the self-induced grating growth (recording time = 5000s) was found to be ≈ 3 10-3. The evolution of Δnmod with recording time is shown in Fig. 7. As for the evolution of the diffraction efficiency, one can note that the quasi-linear growth of Δnmod with recording time in the range [2500 s – 5000 s] suddenly stopped at a recording time of 5000 s. After this stop-point, Δnmod leveled off.

 figure: Fig. 7.

Fig. 7. Evolution of the modulation index calculated using teff = 40μm in SnO2:SiO2:Na2O P1 sample. “A” indicates the part where the He-Ne beam was blocked.

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Another possibility to account for the diffraction efficiency starts from the assumption that the UV-induced grating growth is governed by the thermal diffusion of Na ions in the glass. Indeed, this correlates well with the observation of Na-rich clusters in the bright fringes and with the enhanced effect at higher UV power density (higher temperature in the sample). Now, it is well established that our Sn-doped glass has a strong absorption coefficient near 244nm (αinit (244nm) = 250 cm-1) and thus UV exposure at this wavelength should lead to an increase of the sample temperature T. This figure is in agreement with the thermal diffusion hypothesis. However, this conclusion proves to be contrary to our observation since the formation of the clusters seems not occur during the UV exposure but rather after the end of the UV exposure. On the other hand, the initial level of the loss near 633nm was only near to 7.5 cm-1 and the UV-induced loss near 633nm proves to change less than 1%. This indicates that the probe He-Ne laser does not induce an elevation of the temperature of the sample. So the above-mentioned assumption looks inconsistent with one of our observations. Yet, it cannot be definitively disregarded, as little is known about 1/ the evolution of the linear absorption coefficient at 244nm under UV exposure at the cumulated power density used in the experiment (< 0.5 MW/cm2) and 2/ the dynamic of the clusters formation.

Our microscopic investigations achieved a few weeks after the grating inscription show that there exists a phase separation in the P1 plate glass in the UV exposed zone. This observation looks similar to those reported in Ref. [16 , 17]. Indeed, phase separation associated with UV irradiation (KrF laser light) has been observed in a SnO2 rich phosphosilicate [16] or germanosilicate [17] optical fiber preform. Yet, the complete absence of particles in exposed tin-silica fiber (SnO2 < 1 mol %) seems to indicate that phase separation occurs only at high SnO2 concentrations. One can account for our observations through the assumption that the P1 sample glass network is frozen in a metastable state because of the rapid cooling (casting upon Cu plate) at the time of the bulk glass fabrication. One has also to postulate that the UV exposure triggers the formation of precursors of a spontaneous network rearrangement that occurs in the absence of UV light and leading to phase separation. Yet, the time when the phase separation occurs is at the present time under investigation. More specifically it looks necessary to establish whether or not the formation of the clusters is correlated to the self-induced growth of the grating or to the stop point of this growth. On the opposite, in the sample P2 (slower cooling rate in the Pt crucible) or in low SnO2 concentration fiber, the Sn is inserted in the silica network in a stable substitutional position [18] and it does not undergo any structural reorganization through or after exposure of the glass to UV light.

5. Conclusion

In summary, we have reported the fabrication of bulk ternary SnO2:SiO2:Na2O glasses that can allow for SnO2 concentration (5 mol %) significantly above the crystallization limit in silica glasses. Significant photosensitivity (up to 3.10-3) has been achieved in bulk ternary SnO2:SiO2:Na2O glasses. Measurements at different power densities indicate that the kinetics of the UV-induced refractive index changes depend strongly of this parameter. On one hand, self induced grating growth could be observed in the sample cooled at a high rate. Inspection of this glass after the grating formation revealed the presence of a phase separation (Na rich particles). On the other hand, in the drilled sample, no self induced grating, no corrugation and no phase separation were observed. In this sample, photo-induced refractive index modulation up to 6 10-4 extending 40 μm into the glass have been achieved with a cw 244 nm laser.

References and links

1. R. M. Atkins, P.J. Lemaire, T. Erdogan, and V. Mizrahi, “Mechanisms of enhanced UV photosensitivity via hydrogen loading in germanosilicate glasses,” Electron. Lett. 29, 1234 (1993) [CrossRef]  

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3. G.E. Kohnke, D. W. Nightingale, P. G. Wigley, and C. R. Pollock, “Photosensitization of optical fiber by UV exposure of hydrogen loaded fiber,” Optical Fiber Communication Conference (OFC’99), PD20 (1999)

4. G. Brambilla, V. Pruneri, and L. Reekie, “Photorefractive index gratings in SnO2:SiO2 optical fibres,” Appl. Phys. Lett. 76 (7), 807 (2000) [CrossRef]  

5. L. Dong, J.L. Cruz, J.A. Tucknott, L. Reekie, and D.N. Payne, “Strong photosensitive gratings in tin-doped phosphosilicate optical fibers,” Opt. Lett. 20, 1982 (1995) [CrossRef]   [PubMed]  

6. L. Dong, J.L. Cruz, L. Reekie, M. G. Xu, and D.N. Payne, “Enhanced photosensitivity in tin-doped germanosilicate optical fibers,” IEEE Photonics Technol. Lett. 7, 1048 (1995) [CrossRef]  

7. G. Brambilla, V. Pruneri, L. Reekie, C. Contardi, D. Milanese, and M. Ferraris, “Bragg gratings in ternary SnO2:SiO2:Na2O optical glass fibers,” Opt. Lett. 25 (16), 1153 (2000) [CrossRef]  

8. N. Chiodini, F. Morazzoni, A. Paleari, R. Scotti, and G. Spinolo, “Sol-gel synthesis of monolithic tin-doped silica glass,” J. Mater. Chem. 9, 2653 (1999) [CrossRef]  

9. O. V. Mazurin, M. V. Streltsina, and T. P. Shvaiko-ShvaikovskayaHandbook of glass data, Elsevier, Amsterdam (1985)

10. G. Perrone, D. Berger, L. Cognolato, M. Ferraris, G. Motta, D. Pircalaboiu, and I. Montrosset, Proc. SPIE 3283, 31 (1998) [CrossRef]  

11. D. Milanese, M. Ferraris, Y. Menke, M. Olivero, G. Perrone, C. B. E. Gawith, G. Brambilla, P. G. R. Smith, and E. R. Taylor, “Photosensitive properties of a tin-doped sodium silica glass for direct ultraviolet writing,” Appl. Phys. Lett. 84, 3259 (2004) [CrossRef]  

12. T. A. Strasser, T. Erdogan, A. E. White, V. Mizrahi, and P. J. Lemaire, “Ultraviolet laser fabrication of strong, nearly polarization-independent Bragg reflectorsin germanium-doped silica waveguides on silica substrates,” Appl. Phys. Lett. 65, 3308 (1994) [CrossRef]  

13. X. C. Long and S. R. J. Brueck, “Large photosensitivity in lead-silicate glasses,” Appl. Phys. Lett. 74, 2110 (1999) [CrossRef]  

14. N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. A 62, 280 (1973)

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16. G. Brambilla and P. Hua, “Phase separation in highly-photosensitive tin-doped and codoped silica optical fibers and preforms,” Bragg Gratings Photosensitivity and Poling in Glass Waveguides (BGPP), Stresa, Italy, Technical Digest, BthA1 (2001)

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Figures (7)

Fig. 1.
Fig. 1. UV absorption spectrum of the SnO2:SiO2:Na2O P1 sample (t = 100 μm) before UV exposure.
Fig. 2.
Fig. 2. Top-side view of the experimental set up (PM: photomultiplier).
Fig. 3.
Fig. 3. Growth of diffraction efficiencies as a result of UV exposure of SnO2:SiO2:Na2O P1 sample at two power densities.
Fig. 4.
Fig. 4. Evolution of the grating diffraction efficiency, demonstrating the formation of a self induced grating in SnO2:SiO2:Na2O P1 sample (260W/cm2). “A” indicates the part where the He-Ne beam was blocked.
Fig. 5.
Fig. 5. Growth of diffraction efficiencies as a result of self induced gratings in SnO2:SiO2:Na2O P1 sample. The parameter of the experiment is the UV exposure time before the self induced grating growth. (□: exposure time = 1850s, ♦: exposure time =900s)
Fig. 6.
Fig. 6. a) Optical microscope image of G1 Bragg grating written in the P1 sample; b) TEM picture of small particles in the UV-exposed region of the G1 grating on P1 sample.
Fig. 7.
Fig. 7. Evolution of the modulation index calculated using teff = 40μm in SnO2:SiO2:Na2O P1 sample. “A” indicates the part where the He-Ne beam was blocked.

Tables (1)

Tables Icon

Table 1. Glasses fabrication conditions.

Equations (3)

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η = I 1 I 0 = sinh 2 ( Δ α . t eff 2 . cos θ B )
η = ( π . Δn . h λ pr . cos θ B ) 2
η = sin 2 ( π . Δ n mod . t eff λ pr . cos θ B )
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