OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 1 — Jan. 8, 2007
  • pp: 143–149
« Show journal navigation

Deep and shallow trap contributions to the ionic current in the thermal-electric field poling in soda-lime glasses

A. L. Moura, M. T. de Araujo, E. A. Gouveia, M. V. D. Vermelho, and J. S. Aitchison  »View Author Affiliations


Optics Express, Vol. 15, Issue 1, pp. 143-149 (2007)
http://dx.doi.org/10.1364/OE.15.000143


View Full Text Article

Acrobat PDF (368 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper, we investigate the contribution of deep and shallow trapped ions on the second-order nonlinearity during typical poling procedures in soda-lime glass. The zero-electric field potential barriers of each contribution were estimated. The shallow traps, measured through the electrical ionic current, was determined as ~0.34 eV; while deep trap activation energy, measured by means of the thermal/electric field activated luminescence, was estimated ~3.8 eV. The traps show different dependence on its thermal energy onset for different applied electric field. The ionic current is linearly dependent on the electric field. The luminescence has a minimum electric field ~3.6 kV/cm and thermal energy ~31 meV (~87°C) to occur. The average ionic jump lengths for both processes are also estimated, and the deep trap length is about ten times shorter than the shallow trap one. Samples poled at the border of the luminescence onset parameters revealed that the higher its contributions the more stable the induced second order nonlinearity.

© 2007 Optical Society of America

1. Introduction

The poling model in the approximation of single carriers diffusion explains many of the experimental observations, but there are a number of incompatibilities with experiments namely, a detailed spatial distribution of the nonlinearity, the observation of multiple time scales of the poling, and the dependence of the nonlinearity on the sample thermal poling history. Furthermore, in ref. [5

5. Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: Evidence of a voltage threshold for the onset on the second-order nonlinearity,” Phys. Rev. A 65,043816-1–043816-14 (2002). [CrossRef]

], Quiquempois et al. suggests the contribution of orientation of hyperpolarizable moieties (bonds and defects) to the ionic diffusion current to explain the large SON.

Recently Corbari et al. [6

6. C. Corbari, P.G. Kazansky, S. A. Slattery, and D. N. Nikogosyan, “Ultraviolet poling of pure silica by high-intensity femtosecond radiation,” Appl. Phys. Lett. 86,071106-1–071106-3 (2005)

] have demonstrated the ultraviolet poling of a pure silica sample by applying simultaneously intense electric field (~200 kV/cm) and ultra short laser pulses at 264 nm (~4.8 eV). This procedure induced estimated second order nonlinearity ~0.02 pm/V. This experimental result makes evident the participation of ions subjected to potential with activation energy higher than the reported to the Na+ ions. Usually the activation energy attributed to the diffusion of Na+ ions in silica based glass is ~1.0 eV. Moreover, it has been observed in our soda-lime glass poling experiments, under certain poling conditions, a blue-violet luminescence generation [7

7. A. L. Moura, M. T. de Araujo, M V. D. Vermelho, and J. S. Aitchison, “Stable induced second-order nonlinearity in soft glass by thermal poling,” J. Appl. Phys. 100,033509-1–033509-5 (2006). [CrossRef]

]. This luminescence suggests the existence of ions subjected to potential deeper than the expected for Na+. Ions subjected to deeper potential barrier should also corroborate the existence of different carrier motions. Godbout and Lacroix theoretically investigated this assumption in poling dynamic simulations considering two kinds of carries (one fast and one slow) [8

8. N. Godbout and S. Lacroix, “Characterization of thermal poling in silica glasses by current measurements,” J. Non-Cryst. Solids 316,338–348 (2003). [CrossRef]

]. They predicted an eminent cations formation near the anode owing to the accumulation of slow carriers, which does not migrate over the whole volume. Such an accumulation was experimentally observed using different techniques, namely, the “layer peeling” using acid attack [9

9. Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I.C.S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled InfrasilTM glasses,” Appl. Phys. Lett. 86,181106-1–181106-3 (2005). [CrossRef]

], or the visualization of the nonlinearity profile using atomic force microscopy [10

10. T. G. Alley and S. R. J. Brueck, “Visualization of the nonlinear optical space-charge region of the bulk thermally poled fused-silica glass,” Opt. Lett. 23,1170–1172 (1998). [CrossRef]

], and visualizing the second harmonic in optical microscopy [11

11. H. An, S. Fleming, and G. Cox, “Visualization of the second-order nonlinear layer in thermally poled fused silica glass,” Appl. Phys. Lett. 85,5819–5821 (2004). [CrossRef]

].

Thus, the aim of this work is to investigate the role played by different contributions to the ionic current in soda-lime glass. The samples undergo similar poling conditions as reported elsewhere, being the furnace replaced by electrode/heating elements so that we are able to acquire the optical and electrical signals simultaneously.

2. Glass framework and ionic conduction theory

To estimate the contributions of both, the shallow and deep traps, the current density equation defined from the mechanism of drift of ions due to jumps over potential barriers among defects in glasses was applied [14

14. C. P. Bean, J. C. Fisher, and D. A. Vermilyea, “Ionic conductivity of tantalum oxide at very high fields,” Phys. Rev. 101,551–554 (1956) [CrossRef]

]. In such case, the individual ionic current exhibits dependences upon potential energy and applied electric field through a relation of the form [14

14. C. P. Bean, J. C. Fisher, and D. A. Vermilyea, “Ionic conductivity of tantalum oxide at very high fields,” Phys. Rev. 101,551–554 (1956) [CrossRef]

,15

15. J. Vermeer, “The electrical conduction of glass at high field strengths,” Physica 22,1257–1268 (1956) [CrossRef]

]

ji=j0iexp[(ΦiαiEkBT)]
(1)

3. Experiments

3.1. Experimental Setup

The typical experimental procedure for thermal-electric field poling (TEFP) is reported elsewhere [1–4

1. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused-silica,” Opt. Lett. 16,1732–1734 (1991). [CrossRef] [PubMed]

]. The apparatus used in this research consists of a DC high voltage power supply (GLASSMAN) with the output voltage (0-5kV) and the short-circuit output current (0-25mA) independently set. These power supply voltage and current outputs are computer controlled to set and read by means of an Analog-Digital board. The samples are pressed on two 1.0 × 3.0 cm2 stainless-steel electrodes which are heated up by temperature controlled heating elements. The leakage-surface current is negligible did not requiring the use of guard-electrode. It become evident when the very low dipole orientation current was measured as previously reported [7

7. A. L. Moura, M. T. de Araujo, M V. D. Vermelho, and J. S. Aitchison, “Stable induced second-order nonlinearity in soft glass by thermal poling,” J. Appl. Phys. 100,033509-1–033509-5 (2006). [CrossRef]

]. Furthermore, the poling conditions used in the present research are less critical than the one reported in ref. [7

7. A. L. Moura, M. T. de Araujo, M V. D. Vermelho, and J. S. Aitchison, “Stable induced second-order nonlinearity in soft glass by thermal poling,” J. Appl. Phys. 100,033509-1–033509-5 (2006). [CrossRef]

]. Thermocouple type N and a digital multimeter (AGILENT 34401) acquire the sample temperature during the TEFP. The induced ionic current, the electrodes temperature, and the visible luminescence are simultaneously acquired during each poling procedure and digitally recorded. The luminescence was detected by an S-20 photomultiplier tube and acquired by an SR-530 Stanford Research lock-in amplifier coupled to the microcomputer. When applicable a McPherson 0.67m monochromator, with resolution ~0.1nm, is used to the light dispersion. A resistor voltage in series with the applied voltage and the samples follows the dynamics of the induced current. The typical samples compositions (commercial soda-lime) are 73%SiO2– 13%Na2O–9%CaO–4%MgO and small amount of other oxides. They are cut in pieces of about 25.0×40.0mm and (1.0±0.2) mm thick.

Fig. 1. Typical thermal-electric field luminescence spectra of soda-lime glass.
Fig. 2: Activation energies of the luminescence (solid circle) and the induced ionic current (solid square). The solid lines are only guide to the eyes.

3.2 Results and Discussion

The typical luminescence spectra in the region 300–450 nm is reported in Fig. 1. The signal was not corrected to the photomultiplier spectral efficiency. Three main contributions at 338 nm (3.77 eV), 358 nm (3.56 eV), and a double peak at 375/380 nm (3.40/3.34 eV) were observed. No radiation up to 2100 nm has been detected. The visible luminescence spectrum peaks obeyed an exponential growth upon fixed ionic currents ranging from 54μA to 700μA. But it was not noticed substantial change in their normalized luminescence spectra. The visible signal showed in Fig. 1 was recorded setting the induced ionic current to 300 μA. The temporal behavior of the ionic current and the signal in our measurements agree with the current in silicate glass reported in ref. [8

8. N. Godbout and S. Lacroix, “Characterization of thermal poling in silica glasses by current measurements,” J. Non-Cryst. Solids 316,338–348 (2003). [CrossRef]

]. It was also observed that within a certain range of temperature and applied electric field both, the total luminescence collected by the photomultiplier tube, and the induced ionic current have shown similar exponential dependence obeying the simple theory of ionic conduction in crystalline materials described by eq. (1).

Fig. 3: The minimum electric field for the onset of the induced electrical ionic current in soda-lime glass.
Fig. 4: The minimum electric field for the onset of the luminescence in soda-lime glass. The numbers inside circles correspond to distinct samples poling conditions

The electrical current (solid squares) has shown saturation like behaviour above the critical field ~8 kV/cm. The current was also estimated considering the two linear fitting regions. This procedure followed the determination of the luminescence signal activation energy. The zero-field potential barrier of the induced current was found ϕ~ 0.34 eV, letting an activation energy ~0.71 eV for electric fields above 10 kV/cm. This result is also in good agreement with the activation energy attributed to the Na+ ions inducing ionic current at high electric field as reported in the literature [15

15. J. Vermeer, “The electrical conduction of glass at high field strengths,” Physica 22,1257–1268 (1956) [CrossRef]

]. These results make evident the contribution of ions trapped in deeper potential well to the ionic current. Referee 2 – Questão 1

The ionic current and luminescence showed distinct thermal energy onset dependence on the electric field strength. They are depicted in Fig. 3 and Fig. 4, respectively. The ionic current has shown a linear dependence given by the relation kBT = (46-11 E) meV, where electric field E is given in kV/cm. However, for the luminescence onset it was required a minimum thermal energy even for intense electric field regimes. The minimum thermal energy to activate the luminescent signal was found around kBT ≈31 meV. The insert of Fig. 4 shows normalized signals and the location of the minimum temperature for two applied electric field strength. This trend was checked by applying electric fields as high as 50 kV/cm at room temperature (kBT ≈ 25 meV) and it was not observed neither luminescence nor induced current at all. It was also an indication that leakage-surface current contribution is negligible. Conversely, for electric field strengths lower than ~3.5 kV/cm there is no blue-violet luminescence even in the high thermal energy regime. This minimum applied electric field reminds the threshold voltage to the formation of the depletion region as reported in ref. [3

3. M. Qiu, S. Egawa, K. Horimoto, and T. Mizunami, “The thickness evolution of the second-order nonlinearity layer in thermally poled fused silica,” Opt. Commun. 189,161–166 (2001). [CrossRef]

,7

7. A. L. Moura, M. T. de Araujo, M V. D. Vermelho, and J. S. Aitchison, “Stable induced second-order nonlinearity in soft glass by thermal poling,” J. Appl. Phys. 100,033509-1–033509-5 (2006). [CrossRef]

], or the minimum voltage to the second harmonic generation reported in refs. [5

5. Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: Evidence of a voltage threshold for the onset on the second-order nonlinearity,” Phys. Rev. A 65,043816-1–043816-14 (2002). [CrossRef]

].

Fig. 5: The minimum electric field for the onset of the induced electrical ionic current in soda-lime glass.
Fig. 6: Second harmonic decay of samples poled under conditions shown in numbered circles in Fig. 4.

The influence of the deep traps in the poling stability in soda-lime glass was also investigated. Three samples were poled under conditions close to the boundary of the curve shown in Fig. 4. The samples poling conditions are depicted in Fig. 4 as red circles numbered from 1–3. Note that, according to Fig. 3, the shallow traps contribute to the ionic current in all cases. The efficiency of the processes was measured through the second harmonic generation using the maker fringes technique. A Q-Switched-Mode-Locked (QSML) Nd:YAG laser @1064 nm, operating at 1 kHz/100MHz repetition rates, respectively, was the radiation source. The main results are: no second harmonic was generated by the samples poled under the parameters of the position 2 (4 kV/cm – 125 °C). Conversely, unstable second harmonic signals were detected in the other two positions. The decays of the SON when these samples were exposed to the laser radiation are shown in Fig. 6. Both have shown second order exponential decays with two time constants. Their respective slow and fast decays are (1.2 ± 0.3) h and (0.22 ± 0.08) h for curve 1, and (0.052 ± 0.003) h and (0.0100 ± 0.0003) h for curve 3. Note that, the fast and slow decay rates are different by a factor of five in both curves. This suggests the participation of at least two carriers in the formation of the SON [22

22. M. Guignard, V. Nazabal, F. Smektala, H. Zeghlache, A. Kudlinski, Y. Quiquempois, and G. Martinelli, “High second-order nonlinear susceptibility induced in chalcogenide glasses by thermal poling,” Opt. Express 14,1524–1532 (2006). [CrossRef] [PubMed]

]. Another remarkable difference was observed in the erasure time of the SON. Curve 3 has erased more than 20× faster than curve 1, and during the poling process the maximum luminescence of the former is ~10× smaller than the latter. These results agree with the assumption of deep and shallow traps suggested above. The shallow traps are more likely to be thermally excited with the poling parameter of curve 3 than the deep traps. Consequently, the thermal effect of the laser pumping radiation erases the SON, due to Coulombian repulsion caused by the internal poling charge distribution. The poling parameters applied to the curve 1 enable both processes. However, the high activation energy of the deep traps causes a slow down in the erasure time.

4. Conclusions

It was investigated the contribution of the luminescence on the ionic current in the soda-lime glass under poling condition. It was seen that the luminescence contributes to the ionic current as ions subjected to deeper potential barriers. Thus, the total current density is due to the combination of deep and shallow traps like jT = jDeep + jShallow. The activation energies associated to these traps were measured ~0.34 eV, owing to the shallow traps, and ~3.8 eV for the deep traps. The luminescence onset required a minimum thermal energy (kBT ≈ 31 meV) even for intense electric field regimes, as well as, a minimum electric field strength (~3.5 kV/cm) regardless of the thermal energy. Poling samples with electric fields and temperatures close to the border of the luminescence onset have shown that the occurrence of the luminescence is essential to the induction of second-order nonlinearity. Furthermore, the higher the luminescence contribution the more stable is the SON. These results were witnessed by the second-harmonic decay owing to thermal effect of the laser pumping. These decay curves also suggested the contribution of the more than one carrier to the ionic current. Finally, the average ionic jump length infers the signal contribution to the ionic current showing a substantial change in the potential barrier distance for temperature above the luminescence onset. Numerical modeling of poling using these assumptions has being extended and will appear elsewhere.

Acknowledgments

The financial support for this research by FINEP, CNPq, CAPES, PADCT, FAPEAL (Fundação de Amparo à Pesquisa do Estado de Alagoas), and PRONEX, Brazilian Agencies, are gratefully acknowledged. One of the authors A.L.M. is supported by undergraduate studentship from CNPq (PIBIC).

References and Links

1.

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused-silica,” Opt. Lett. 16,1732–1734 (1991). [CrossRef] [PubMed]

2.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrain, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76,2496–2498 (2000) [CrossRef]

3.

M. Qiu, S. Egawa, K. Horimoto, and T. Mizunami, “The thickness evolution of the second-order nonlinearity layer in thermally poled fused silica,” Opt. Commun. 189,161–166 (2001). [CrossRef]

4.

X. M. Liu and M.De Zhang, “Theoretical Study for thermal/electric field poling of fused silica,” Jpn. J. Appl. Phys. 40,4069–4076 (2001). [CrossRef]

5.

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: Evidence of a voltage threshold for the onset on the second-order nonlinearity,” Phys. Rev. A 65,043816-1–043816-14 (2002). [CrossRef]

6.

C. Corbari, P.G. Kazansky, S. A. Slattery, and D. N. Nikogosyan, “Ultraviolet poling of pure silica by high-intensity femtosecond radiation,” Appl. Phys. Lett. 86,071106-1–071106-3 (2005)

7.

A. L. Moura, M. T. de Araujo, M V. D. Vermelho, and J. S. Aitchison, “Stable induced second-order nonlinearity in soft glass by thermal poling,” J. Appl. Phys. 100,033509-1–033509-5 (2006). [CrossRef]

8.

N. Godbout and S. Lacroix, “Characterization of thermal poling in silica glasses by current measurements,” J. Non-Cryst. Solids 316,338–348 (2003). [CrossRef]

9.

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I.C.S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled InfrasilTM glasses,” Appl. Phys. Lett. 86,181106-1–181106-3 (2005). [CrossRef]

10.

T. G. Alley and S. R. J. Brueck, “Visualization of the nonlinear optical space-charge region of the bulk thermally poled fused-silica glass,” Opt. Lett. 23,1170–1172 (1998). [CrossRef]

11.

H. An, S. Fleming, and G. Cox, “Visualization of the second-order nonlinear layer in thermally poled fused silica glass,” Appl. Phys. Lett. 85,5819–5821 (2004). [CrossRef]

12.

L. J. Henry, “Correlation of Ge E′ defect sites with second-harmonic generation in poled high-water fused silica,” Opt. Lett. 20,1592–1594 (1995). [CrossRef] [PubMed]

13.

R. A. B. Devine and C. Fiori, “Thermally activated peroxy radical dissociation and annealing in vitreous SiO2,” J. Appl. Phys. 58,3368–3372 (1985). [CrossRef]

14.

C. P. Bean, J. C. Fisher, and D. A. Vermilyea, “Ionic conductivity of tantalum oxide at very high fields,” Phys. Rev. 101,551–554 (1956) [CrossRef]

15.

J. Vermeer, “The electrical conduction of glass at high field strengths,” Physica 22,1257–1268 (1956) [CrossRef]

16.

M. Tomozawa and D. W. Shin, “Charge carrier concentration and mobility of ions in a silica glass,” J. Non-Cryst. Solids 241,140–148 (1998) [CrossRef]

17.

A. Pitarch, J. Bisquert, and G. Garcia-Belmonte, “Mobile cation concentration in ionically conducting glasses calculated by means of Mott-Schottky capacitance-voltage characteristics,” J. Non-Cryst. Solids 324,196–200 (2003) [CrossRef]

18.

T. S. Hutchison and D. C. Baird, “Diffusion in Solids,” in The physics of engineering solids, (2nd Edition - A John Wiley and Sons, NY, London, Sydney, 1968)

19.

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second-order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72,3252–3254 (1998). [CrossRef]

20.

T. G. Alley, S.R.J. Brueck, and R.A. Myers, “Space Charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242,165–176 (1998) [CrossRef]

21.

M. Qiu, E. Pi, G. Orriols, and M. Bibiche, “Signal damping of second-harmonic generation in poled soda-lime silicate glass,” J. Opt. Soc. Am. B 15,1362–1365 (1998). [CrossRef]

22.

M. Guignard, V. Nazabal, F. Smektala, H. Zeghlache, A. Kudlinski, Y. Quiquempois, and G. Martinelli, “High second-order nonlinear susceptibility induced in chalcogenide glasses by thermal poling,” Opt. Express 14,1524–1532 (2006). [CrossRef] [PubMed]

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Materials

History
Original Manuscript: September 29, 2006
Revised Manuscript: December 2, 2006
Manuscript Accepted: December 18, 2006
Published: January 8, 2007

Citation
A. L. Moura, M. T. de Araujo, E. A. Gouveia, M. V. Vermelho, and J. S. Aitchison, "Deep and shallow trap contributions to the ionic current in the thermal-electric field poling in soda-lime glasses," Opt. Express 15, 143-149 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-1-143


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. A. Myers, N. Mukherjee, S. R. J. Brueck, "Large second-order nonlinearity in poled fused-silica," Opt. Lett. 16, 1732-1734 (1991). [CrossRef] [PubMed]
  2. A. L. C. Triques, C. M. B. Cordeiro, V. Balestrain, B. Lesche, W. Margulis, I. C. S. Carvalho, "Depletion region in thermally poled fused silica," Appl. Phys. Lett. 76, 2496-2498 (2000) [CrossRef]
  3. M. Qiu, S. Egawa, K. Horimoto, T. Mizunami, "The thickness evolution of the second-order nonlinearity layer in thermally poled fused silica," Opt. Commun. 189, 161-166 (2001). [CrossRef]
  4. X. M. Liu, M. De Zhang, "Theoretical Study for thermal/electric field poling of fused silica," Jpn. J. Appl. Phys. 40, 4069-4076 (2001). [CrossRef]
  5. Y. Quiquempois, N. Godbout, S. Lacroix, "Model of charge migration during thermal poling in silica glasses: Evidence of a voltage threshold for the onset on the second-order nonlinearity," Phys. Rev. A 65, 043816-1-043816-14 (2002). [CrossRef]
  6. C. Corbari, P.G. Kazansky, S. A. Slattery, D. N. Nikogosyan, "Ultraviolet poling of pure silica by high-intensity femtosecond radiation," Appl. Phys. Lett. 86, 071106-1-071106-3 (2005)
  7. A. L. Moura, M. T. de Araujo, M V. D. Vermelho, J. S. Aitchison, "Stable induced second-order nonlinearity in soft glass by thermal poling," J. Appl. Phys. 100, 033509-1-033509-5 (2006). [CrossRef]
  8. N. Godbout, S. Lacroix, "Characterization of thermal poling in silica glasses by current measurements," J. Non-Cryst. Solids 316, 338-348 (2003). [CrossRef]
  9. Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, I.C.S. Carvalho, "Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil ™ glasses," Appl. Phys. Lett. 86, 181106-1 - 181106-3 (2005). [CrossRef]
  10. T. G. Alley, S. R. J. Brueck, "Visualization of the nonlinear optical space-charge region of the bulk thermally poled fused-silica glass," Opt. Lett. 23, 1170-1172 (1998). [CrossRef]
  11. H. An, S. Fleming, G. Cox, "Visualization of the second-order nonlinear layer in thermally poled fused silica glass," Appl. Phys. Lett. 85, 5819-5821 (2004). [CrossRef]
  12. L. J. Henry, "Correlation of Ge E´ defect sites with second-harmonic generation in poled high-water fused silica," Opt. Lett. 20, 1592-1594 (1995). [CrossRef] [PubMed]
  13. R. A. B. Devine, C. Fiori, "Thermally activated peroxy radical dissociation and annealing in vitreous SiO2," J. Appl. Phys. 58, 3368-3372 (1985). [CrossRef]
  14. C. P. Bean, J. C. Fisher, and D. A. Vermilyea, "Ionic conductivity of tantalum oxide at very high fields," Phys. Rev. 101, 551-554 (1956) [CrossRef]
  15. J. Vermeer, "The electrical conduction of glass at high field strengths," Physica 22, 1257-1268 (1956) [CrossRef]
  16. M. Tomozawa, D. W. Shin, "Charge carrier concentration and mobility of ions in a silica glass," J. Non-Cryst. Solids 241, 140-148 (1998) [CrossRef]
  17. A. Pitarch, J. Bisquert, G. Garcia-Belmonte, "Mobile cation concentration in ionically conducting glasses calculated by means of Mott-Schottky capacitance-voltage characteristics," J. Non-Cryst. Solids 324, 196-200 (2003) [CrossRef]
  18. T. S. Hutchison, D. C. Baird, "Diffusion in Solids," in The physics of engineering solids, (2nd Edition - A John Wiley and Sons, NY, London, Sydney, 1968)
  19. F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, B. Lesche, "Inducing a large second-order optical nonlinearity in soft glasses by poling," Appl. Phys. Lett. 72, 3252-3254 (1998). [CrossRef]
  20. T. G. Alley, S.R.J. Brueck, R.A. Myers, "Space Charge dynamics in thermally poled fused silica," J. Non-Cryst. Solids 242, 165-176 (1998) [CrossRef]
  21. M. Qiu, E. Pi, G. Orriols, M. Bibiche, "Signal damping of second-harmonic generation in poled soda-lime silicate glass," J. Opt. Soc. Am. B 15, 1362-1365 (1998). [CrossRef]
  22. M. Guignard, V. Nazabal, F. Smektala, H. Zeghlache, A. Kudlinski, Y. Quiquempois, G. Martinelli, "High second-order nonlinear susceptibility induced in chalcogenide glasses by thermal poling," Opt. Express 14, 1524-1532 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited