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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4854–4863
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Change of self-focusing behavior of phosphate glass resulting from exposure to ultraviolet nanosecond laser pulses

Stavros G. Demos, Paul R. Ehrmann, Michael A. Johnson, Kathleen I. Schaffers, Alexander M. Rubenchik, and Michael D. Feit  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4854-4863 (2013)
http://dx.doi.org/10.1364/OE.21.004854


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Abstract

The self-focusing characteristic of 355 nm, 3.3 ns pulses propagating through phosphate glass samples is found to significantly change during repeated exposure. The results indicate this change is related to the formation of color centers in the material as well as the generation of a transient defect population during exposure to the laser pulses. A model is used to fit the experimental data and obtain an estimated range of values for the modified linear and nonlinear indices of refraction.

© 2013 OSA

1. Introduction

Phosphate and silicate glasses are some of the most important optical materials in high power laser systems [4

4. J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci. 2, 1–27 (2011).

]. Silicate glasses are most often used in the manufacturing of optical elements that require transparency in the ultraviolet (UV) spectral region. On the other hand, phosphate glasses are used in a variety of optical components but most commonly as a host material for doping ions for color filters or gain medium after doping with a lasant ion (such as neodymium). A characteristic behavior of phosphate glasses is the formation of color centers under exposure to ultraviolet light, commonly referred to as solarization [5

5. D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids 240, 263–264 (2000).

]. High energy photons cause the release of electrons and holes, which are subsequently trapped by precursors in the matrix, leading to the formation of electron and hole defect centers. These defect centers cause a red-shift the UV absorption band from about 300 nm to above 400 nm. It has been previously reported that defects can increase the second-order optical nonlinearity and change the refractive index in silica glasses implemented via a combination of thermal poling and defect generation such as via exposure to x-ray, electron-beam or UV laser irradiation [6

6. P. G. Kazansky, A. Kamal, and P. S. J. Russell, “High second-order nonlinearities induced in lead silicate glass by electron-beam irradiation,” Opt. Lett. 18(9), 693–695 (1993). [CrossRef] [PubMed]

8

8. A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys. 95(8), 4000–4006 (2004). [CrossRef]

].

The motivation for this work is to investigate if transient defects (in addition to permanent defects) formed in optical materials during exposure to high power laser pulses can significantly affect beam propagation. The formation of transient defects in various technologically important optical materials under such excitation conditions is well documented in the literature but their role in beam propagation (in addition to transmission loss) has not been explored. Such effects become increasingly important as the repetition rate of high power lasers is continuously increased in order to generate higher output average laser power. As a result, defect generation and accumulation (especially when the lifetime of the generated defects is on the same order or larger than the inverse of the repetition rate of the laser) become increasingly important. Phosphate glasses are known to create defects under UV exposure [5

5. D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids 240, 263–264 (2000).

] and therefore, they represent a good model medium to study the relevant possible phenomena.

2. Experimental design

The two CCD cameras recording the input and output beam profiles were calibrated using the following two steps: In the first calibration step, an energy meter was positioned at the location of the sample. Subsequently, 20 pulses were recorded by the reference (input) CCD camera along with the corresponding values of the energy of the pulses as recorded by the energy meter. This enabled the correlation of the counts recorded by the reference CCD to the energy recorded by the energy meter (counts per unit energy), thus the energy reaching the sample. This also enabled the estimation of the fluence at each location within the beam profile recorded by the reference camera. In the second calibration step, the sample was removed and 20 pulses were simultaneously recorded by the two CCD cameras capturing the (same) beam profile at the sample location. This step was repeated for various laser pulse energies covering the entire range of energies used in the experiments. This enabled the calibration of the second camera in terms of counts per unit energy (using the first camera as reference) and subsequently the estimation of the fluence at each location within the beam profile recorded by the output CCD camera. This configuration enabled us to monitor a) the energy and spatial profile of the input beam, b) the relative intensity of the output beam compared to the input (transmittance) and, c) the beam profile and its modification due to propagation inside the sample. These parameters also allow us to evaluate the peak intensity of the output beam if there was no distortion by its propagation inside the sample, which is referred to as “reference peak fluence”. The beam profile had a nearly Gaussian shape with a beam radius at 1/e of peak intensity of about 48 µm. The beam-to-beam stability exhibited modulation in both, the spatial dimensions of the beam and at the location of the center of the beam. Since the profiles of all pulses were recorded by the two CCD cameras, we were able to monitor the effect of these variations in the experimental data as discussed later.

Samples from three materials were used in this work. The first two were phosphate glasses, referred to as LHG-8 and LG-770, manufactured by Hoya and Schott, respectively. Detailed information on these materials is provided in Ref. 9

9. P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids 263–264, 251–262 (2000). [CrossRef]

. These materials are used as laser glasses in the main amplifiers of the National Ignition Facility laser [4

4. J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci. 2, 1–27 (2011).

] using an Nd-doping density of 4.2 1020/cm3. However, in order to avoid the absorption of the Nd doping ions at the excitation wavelength of 355 nm, the doping with Neodymium ions was replaced by Lanthanum ions, which leads to a transparent material with minimal absorption (of about 2%) at 355 nm. In addition, the LHG-8 glass was doped with Copper at about 0 – 1 mole % (< 2.7 1020/cm3) with the Cu2+ oxidation state dominating the absorption characteristics of the material. As a result, the UV absorption edge is located in the 300-350 nm range with about 5% absorption at 355 nm while a second broad absorption band located in the near infrared range is due to the Cu2+ ions [9

9. P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids 263–264, 251–262 (2000). [CrossRef]

]. The samples were cut to about 4-mm thick sections so that their thickness is more than an order of magnitude smaller than the Raleigh range (which is estimated to be about 5.9 cm) to achieve a nearly collimated propagation of the focused beam through the sample. In addition, a fused silica sample was used as a reference material under similar excitation conditions. The literature value for the nonlinear refractive index in fused silica is 3.6 ± 0.64 10−7 cm2/GW [10

10. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef] [PubMed]

] while the corresponding values for the LHG-8 and LG-770 samples are 3.13 10−7 cm2/GW and 2.85 10−7 cm2/GW, respectively [4

4. J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci. 2, 1–27 (2011).

].

3. Experimental results

Figure 2
Fig. 2 The fluence profiles of the transmitted pulses through sample LG-770 averaged along a 2 µm section that transverses the central region of the digitized image of the beam for a pristine and a pre-irradiated site under similar excitation conditions.
shows the spatial profiles of the transmitted pulses through sample LG-770. The first profile was obtained prior to exposure of this site to any 355 nm laser pulses (first exposure pulse on a pristine site of the material). The second profile was obtained after this site was previously exposed to 300 pulses of about the same energy. This pre-exposure was used in order to saturate the solarization of this site prior to performing this set of measurements. It must be noted that the laser beam pointing fluctuations result in exposure (and solarization) of an area of the sample over a radius that is about twice the size of the beam radius. Specifically, the beam center position is reproducible with an rms uncertainty of 60 µm determined by recording 300 pulses.

The profiles shown in Fig. 2 represent the average value (expressed in J/cm2) along a 2 µm in width section (2 pixels) spanning through the central region of the digitized image of the beam profile. These two profiles were selected because their input beam profiles (as recorded by the reference CCD camera) were practically identical. The profile of the pulse that propagated though the pristine site was indistinguishable (within experimental error which is on the order of a few µm in beam diameter) from that of the reference profile. The input energy for this pulse was 980.4 µJ, corresponding to a peak fluence of about 11 J/cm2. The measured losses due to reflection and absorption in the sample were about 9% indicating that the energy of the pulse after passing though the sample was about 892 µJ. In comparison, the pulse that propagated through the pre-irradiated site with 300 pulses of about the same fluence (on the order of ≈950 ± 100 µJ) was 917.7 µJ while the losses were about 14.7% indicating that the output energy was about 783 µJ. The higher losses in the latter case may be attributed to the enhanced absorption at 355 nm due to the solarization of the sample after its pre-exposure to the laser pulses. Although the transmitted energy in the second case was more than 10% lower, the beam profile exhibits a self-focusing behavior with the peak fluence of about 16 J/cm2.

This effect could be attributed to a change in the linear index of refraction, thus creating a waveguide leading to the focusing of the beam. To address this issue, we performed interferometry measurements to assess the change of the linear index of refraction (Δn0) of the material due to the localized exposure to the UV pulses and ensuing solarization. The experiments were performed using a high sensitivity in house-built interferometric microscope system having lateral resolution of 4 µm using a laser operating at 514 nm. The experimental results suggested that Δn0/n0≈10−6 at maximum for the experimental conditions used in this experiment. This change of n0 is too small to support the change of the beam propagation behavior exemplified in Fig. 2, as will be discussed in more detail later. In addition, the area of solarization and increased n0 was found to be larger than the beam spot, which is anticipated due to the beam spatial movement (discussed earlier).

The self-focusing effect can be quantified in terms of the ratio of the measured peak fluence over the estimated reference fluence as defined earlier (which represent the peak fluence at the transmitted energy if there was no self-focusing involved). We will refer to this peak fluence ratio as “Intensification” to quantify the self-focusing strength. Figure 3
Fig. 3 Intensification (ratio of the measured peak fluence over the reference peak fluence) as a function of the output energy and reference peak fluence (open circles) obtained from a pre-irradiated site (open circles) and corresponding measured transmission (solid circles) in sample LG-770. Solid line represents the fit to the data using the self-focusing model below.
shows the beam intensification as a function of the output energy and output reference peak fluence from a pre-irradiated site in sample LG-770. The experimental error in these data represents mostly the error in the CCD cameras (the error in determining the energy as obtained from the energy meter and the corresponding total detected signal by the CCD cameras) and the error in the estimation of the peak fluence. It must be noted that the peak fluence was estimated by averaging over a square area of 5X5 pixels in the digitized image of the beam profile as recorded by the CCD camera (corresponding to an area of about 25 µm2) at the position of observed peak fluence.

Figure 3 also shows the measured transmission of the laser pulses as a function of the laser pulse energy. These measurements were performed starting with the highest energy pulses and subsequently decreasing the laser pulse energy. Therefore, the observed increase in transmission as the laser pulse energy was decreased cannot be attributed to solarization of the sample (which would have led to lower transmission for the lower energy pulses in the as executed sequence of measurements). In addition, the measured transmission at higher laser pulse energies is significantly lower than that at lower laser pulse energies. For comparison, the measured absorption (using a conventional spectrophotometer) at 355 nm due to solarization (produced using a large aperture laser having a square, nearly flat-top beam profile with dimensions of about 1 cm X 1 cm) was found to be on the order of a few percent. As a result, the decrease of the transmission with increasing laser pulse energy may be attributed to the formation of transient defects during laser exposure. This, in turn, results in the appearance of a transient absorption that is dependant on the laser pulse energy (intensity). It should be noted that the additional induced absorption observed in Fig. 3 corresponds to a very small imaginary part of the refractive index, less than 10−6 in the most severe case. This estimate was arrived at by setting the relative change in transmission to 2 k (Im(n)/n0) z.

The results of the experiments using the Cu-doped LHG-8 glass were very similar to those observed in the LG-770 glass. The results shown in Fig. 4
Fig. 4 Intensification (open circles) and the corresponding measured transmission (solid circles) as a function the number of exposure pulses in sample LHG-8.
obtained using this material demonstrate the build up of the self-focusing behavior with the number of exposure to 355 nm pulses. Specifically, while the input laser pulse energy was kept constant to a measured average of 980 µJ per pulse, the ratio of the measured over the reference peak fluence (intensification) is plotted as a function of the number of exposure pulses. The as measured transmission is also plotted in the same graph. It can be appreciated that as the intensification increases due to self-focusing, the transmission loss due to the formation of color centers (solarization) increases. This suggests a direct relationship between the materials parameters governing the self –focusing process and the density of defect centers.

The measured data are affected by instrumentation errors in recording the laser pulse energy and beam profiles (as discussed earlier) as well as the beam pointing stability. Specifically, the effect of exposure to even the first few pulses is significant and can be detected as a loss of transmission. However, as the center of the beam moves around covering an area that has a diameter about twice that of the each individual laser pulse, some of the pulses will be transmitted though areas of material that exhibit lower solarization leading to slightly lower values of absorptivity (higher transmission). The same mechanism also contributes to the spread in the data of the intensification, but to a higher degree due to the nonlinearity of the process. The presence of the copper doping ions in this material does not seem to affect to a measurable degree the change of the self-focusing parameters in phosphate glass. Further increase of the laser input pulse energy above the range used in these experiments leads to laser induced damage.

As mentioned earlier, the literature value of the nonlinear index of refraction of fused silica is slightly higher than that of the phosphate glasses. For this reason, we also tested fused silica using the same excitation conditions as those used for the study of the phosphate glassbut no measurable self-focusing was detected. This indicates that no other extrinsic effects (such as self focusing in air, abnormal laser beam characteristics etc) are responsible for the experimental observations presented in this work. Therefore, it appears that the main contributor to the self-focusing effect observed in phosphate glasses is the color centers (or a sub-population of the color centers) formed during the solarization process.

4. Modeling

The results discussed above indicate the involvement of both, a steady state defect population (giving rise to what is commonly referred to as solarization) and a transient defect population, which is manifested as an increased transmission loss (absorptivity) with increasing laser intensity/fluence. Such defects can induce changes in both the linear and the nonlinear indices of refraction. It was mentioned earlier that the solarization causes a change on the linear index of refraction of about 10−6. Since the change of the refractive indices is proportional to the density of defects, which is expected to follow the beam energy distribution, such changes can lead to self-focusing behavior of the laser beam even when only the linear index is affected. The experimental results shown in Fig. 3 can be used to obtain information about the underlying mechanisms. The slowly varying envelope of the self-focusing electric field E can be described by the non-linear Schrodinger equation:
iEz=2E2kkΔn2n0(ra)2Ekn2n0|E|2E
(1)
where z is the distance propagated, and the units of E are chosen so that |E|2 is the laser intensity. Here n0 is the linear refractive index of the medium, k = 2π n0 is the wavenumber, λ the wavelength, Δn0 is the magnitude of induced linear index, a the 1/e intensity radius and n2 is the induced nonlinear coefficient. Since we don’t know the relative strength of the linear vs. nonlinear indices, we analyzed cases of pure Δn0, of pure n2, and mixed effect. We employed the method of moments [11

11. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys. 14(9), 1062–1070 (1971). [CrossRef]

] to describe the degree of intensification due solely to n2 of a Gaussian beam as a function of laser intensity. The theory predicts:
Intensification=11+(zzR)2n2I2n0(za)2=11+(zzR)2n2ϕ2n0τ(za)2
(2)
in terms of the laser intensity I or fluence φ and pulselength τ. In this expression a is the initial 1/e beam radius and zR is the Raleigh range ka2. The experimental observations were modeled using this expression with a = 48 μm, τ = 3.3 ns, n0 = 1.47 and z = 4 mm. The results are shown in Fig. 3. Note that zR = 59.9 mm so diffractive spreading is not significant during the propagation of the beam inside the sample.

The situation in which self-focusing is due solely to Δn0 was treated using the waveguide model of ref [12

12. M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett. 28(6), 331–333 (1976). [CrossRef]

]. This gives the intensification as:

Intensification=11+((azR)2n0Δn1)sin2(Δnn0za)
(3)

The resulting fit of the data was essentially indistinguishable from the fit shown in Fig. 3. Finally, we used a generalization [13

13. S. K. Turitsyn, V. K. Mezentsev, M. Dubov, A. M. Rubenchik, M. P. Fedoruk, and E. V. Podivilov, “Sub-critical regime of femtosecond inscription,” Opt. Express 15(22), 14750–14764 (2007). [CrossRef] [PubMed]

] of Eq. (2) that accounts for self-focusing of an already converging beam to treat the case in which both indices contribute. This model leads to the necessary relationships between Δn0 and n2 to be consistent with the data.

In using either Eq. (2) or Eq. (3), it is necessary to account for the entire population of defects present during the laser irradiation that contribute to the nonlinear focusing. Specifically, solarization is associated with a residual (steady-state) population of defects which is the result of the generation of a larger population of defects during the laser pulse followed by partial annihilation of this population via recombination afterward. Typically the recombination rate of the defects rapidly increases with defect density. As a result, there is an initial rapid increase of the residual population with increasing number of pulses which thereafter saturates as the population reaches a high enough density so that recombination ultimately balances the new defects generated during the laser pulse. However, the optical nonlinearity experienced during the pulse can be influenced by both the steady state and transient defect populations. Experiments have verified that the density of generated defects increases monotonically as a function of the laser fluence [14

14. Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B 166–167, 698–703 (2000). [CrossRef]

] as one would expect. Furthermore, such transient defects can contribute to both Δn0 and n2 during the laser pulse. Both the experimental results and Eqs. (2) and (3) average this effect over the duration of the laser pulse. Accordingly, in Eq. (2), we assume that Δn0 and n2 are themselves a function of intensity or fluence.

Comparison of the model fits shown in Fig. 3 to the experimental data indicate a good representation of intensification observed in our measurements. The corresponding values of either solely Δn0 or solely n2 as a function of input laser fluence, assuming generation of transient defects as necessary for the best fit in Fig. 3, is given in Fig. 5
Fig. 5 Calculated induced transient linear or nonlinear refractive indices as a function of peak input laser fluence obtained from fit to the experimental data shown in Fig. 3.
. When both indices contribute, their values lie between the limiting cases of the two curves shown. Thus the maximum induced n2 is on the order of a few times 10−5 cm2/GW and the induced Δn0/n0 is on the order of 10−4.

The background n2 in the solarized sample at low intensity is several times (≈8) larger than that for LG770 or fused silica and its increase is attributed to the presence of color centers (solarization). For reference, the accepted value of n2 for fused silica is 3.6x10−7 cm2/GW and that of LG770 is 2.8x10−7 cm2/GW. Despite the increased self-focusing with laser pulse energy, the observed increased absorption is only on the order of a few percent. Consequently, the theoretical model assumes for simplicity no change in absorption while the beam transverses the sample, which would only introduce small changes in the estimated values.

Since the value of n2 shown in Fig. 5 is derived from a fit to the observed intensifications in Fig. 3, we estimated the uncertainties in the derived values using a bootstrap method in which pseudo data sets are created with the same statistical deviations from the fit intensification as were observed experimentally and then refit these pseudo data sets. This method suggests that the nonlinearity at the highest fluences to be well determined with less than about a 5% standard deviation. The theoretical value at the lowest fluences is less well determined since the observed differences of intensification from unity are much more relatively uncertain there. A similar conclusion is obtained for the value of Δn0. Thus, the general shape of the curves in Fig. 5 with the upper values more or less fixed is well established from the experimental observations.

5. Discussion

The results demonstrate the strong effect of the transient population of defects on the propagation (and self focusing) of the laser beam. The measurement of the n0 in the solarized material (Δn0/n0≈10−6) is about two order of magnitude smaller to the peak required value to fully account for the self focusing behavior as shown in Fig. 5 (Δn0/n0 ≈1.2 10−4). As the change of n0 is generally proportional to the induced absorption [8

8. A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys. 95(8), 4000–4006 (2004). [CrossRef]

], the comparison of the transient absorption component (about 6-10% transmission loss) with the steady state component (about 3-5% transmission loss) does not support an additional change of the Δn0/n0 by the transient defects of two orders of magnitude. This may indicate that the main contributor to the self-focusing behavior is the non-linear index of refraction n2. As discussed earlier, the data fit shown in Fig. 5 suggest that the n2 of the solarized material is about 8 times higher than the pristine material (≈25 10−7 cm2/GW). A change by another factor of 20 due to the presence of the transient detects is suggested by the fit to the experimental data shown in Fig. 5. Resonance phenomena may play an important role is such process. We must also consider that the transient defects are probably different from the steady state defects as they may represent a short lived state of the photo-excited electrons and holes which are subsequently trapped by precursors in the matrix to form the color centers (solarization). Thus, the transient defects may be capable of inducing a higher change of the n2 (associated in the nonlinear polarization generated in the medium) compared to the steady state defects. Additional experiments are required in order to resolve the relative contribution of the linear and the nonlinear index of refraction and the underlying mechanisms.

The effects discussed in this work are of importance in high power laser applications. Transient defects are known to form in other optical materials under exposure to high power UV laser pulses and therefore, the behaviors discussed in this work may not be unique to the phosphate glasses but may be present in other materials currently used in high average power or high peak intensity UV laser systems.

The maximum value of n2 of ≈550 10−7 cm2/GW shown in Fig. 5 is essentially identical to the value for Cu2+-doped germano-silicate glass fibers [15

15. A. Lin, B. H. Kim, D. S. Moon, Y. Chung, and W.-T. Han, “Cu2+-doped germano-silicate glass fiber with high resonant nonlinearity,” Opt. Express 15(7), 3665–3672 (2007). [CrossRef] [PubMed]

] exhibiting high resonant nonlinearity. Various such ion-doped fibers have been developed for all optical switching applications [15

15. A. Lin, B. H. Kim, D. S. Moon, Y. Chung, and W.-T. Han, “Cu2+-doped germano-silicate glass fiber with high resonant nonlinearity,” Opt. Express 15(7), 3665–3672 (2007). [CrossRef] [PubMed]

17

17. J. W. Arkwright, P. Elango, G. R. Atkins, T. Whitbread, and J. F. Digonnet, “Experimental and theoretical analysis of the resonant nonlinearity in ytterbium-doped fiber,” J. Lightwave Technol. 16(5), 798–806 (1998). [CrossRef]

]. The phosphate glass samples used in this work demonstrate analogous nonlinear behavior but the change of the nonlinearity is introduced via the formation of long-lived or transient defects via exposure to UV laser pulses. It is therefore a material whose nonlinearity can be locally increased merely via exposure to UV irradiation, not requiring a change in stoichiometry (via doping with impurity ions as in the case of germano-silicate glass fibers). Furthermore, the defects formed due to UV exposure can be annealed via heating. Therefore, it is possible to generate three dimensional re-writable n2 structures in bulk material where the solarization via a focused or properly spatially shaped beam can be used to induce localized increases of the n2 while heating can be used to reverse such changes, even locally. One efficient method to produce such local heating may be via doping the material with an absorbing ion, such as the Cu-doped sample used in our experiments. In this case, a proper dose of localized exposure to a near infrared laser beam (to excite the absorption band of the Cu2+ ions) can deliver the localized heating. Other all-optical methods to anneal the point defects are also possible without using heating. Furthermore, the entire material can be solarized and then use localized heating (or another method to locally anneal the defects) to imprint locally decreased n2.

6. Conclusion

Acknowledgments

We thank Raluca A. Negres and Paul J. Wegner for stimulating discussions that helped improve the manuscript. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

References and links

1.

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]

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4.

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci. 2, 1–27 (2011).

5.

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids 240, 263–264 (2000).

6.

P. G. Kazansky, A. Kamal, and P. S. J. Russell, “High second-order nonlinearities induced in lead silicate glass by electron-beam irradiation,” Opt. Lett. 18(9), 693–695 (1993). [CrossRef] [PubMed]

7.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys. 88(8), 4666–4670 (2000). [CrossRef]

8.

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys. 95(8), 4000–4006 (2004). [CrossRef]

9.

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids 263–264, 251–262 (2000). [CrossRef]

10.

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef] [PubMed]

11.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys. 14(9), 1062–1070 (1971). [CrossRef]

12.

M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett. 28(6), 331–333 (1976). [CrossRef]

13.

S. K. Turitsyn, V. K. Mezentsev, M. Dubov, A. M. Rubenchik, M. P. Fedoruk, and E. V. Podivilov, “Sub-critical regime of femtosecond inscription,” Opt. Express 15(22), 14750–14764 (2007). [CrossRef] [PubMed]

14.

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B 166–167, 698–703 (2000). [CrossRef]

15.

A. Lin, B. H. Kim, D. S. Moon, Y. Chung, and W.-T. Han, “Cu2+-doped germano-silicate glass fiber with high resonant nonlinearity,” Opt. Express 15(7), 3665–3672 (2007). [CrossRef] [PubMed]

16.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27(4), 908–913 (1991). [CrossRef]

17.

J. W. Arkwright, P. Elango, G. R. Atkins, T. Whitbread, and J. F. Digonnet, “Experimental and theoretical analysis of the resonant nonlinearity in ytterbium-doped fiber,” J. Lightwave Technol. 16(5), 798–806 (1998). [CrossRef]

OCIS Codes
(140.3380) Lasers and laser optics : Laser materials
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 7, 2012
Revised Manuscript: January 23, 2013
Manuscript Accepted: February 7, 2013
Published: February 20, 2013

Citation
Stavros G. Demos, Paul R. Ehrmann, Michael A. Johnson, Kathleen I. Schaffers, Alexander M. Rubenchik, and Michael D. Feit, "Change of self-focusing behavior of phosphate glass resulting from exposure to ultraviolet nanosecond laser pulses," Opt. Express 21, 4854-4863 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4854


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References

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