Third-order nonlinear spectra and optical
limiting of lead oxifluoroborate glasses
J. M. P. Almeida, L. De Boni, A. C. Hernandes, and C. R. Mendonça*
Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, SP, Brasil
*[email protected]
Abstract: We have determined two-photon absorption and nonlinear
refraction spectra of the 50BO1.5 - (50-x)PbF2 - xPbO glasses (with x = 25,
35, 50 cationic %) at the range of the 470 and 1550 nm. The replacement of
fluor atoms by oxygen leads to an increase in the third-order susceptibility,
due to the formation of non-bridging oxygens (NBO). The nonlinear index
of refraction is one order of magnitude higher than the one for fused silica,
and it increases almost twice for the sample with x = 50. This sample has
also shown promising features for all-optical switching as well as for
optical limiting.
© 2011 Optical Society of America
OCIS codes: (190.0190) Nonlinear optics; (190.4720) Optical nonlinearities of condensed
matter; (160.2750) Glass and other amorphous materials.
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1. Introduction
The large interest in nonlinear optical materials has been motivated by their potential use in
the fabrication of all-optical photonic devices. Distinct types of materials, from polymers to
inorganic semiconductors, have been investigated as promising candidates to accomplish
such task. Therefore, studies in this area are focused on the development and optimization of
materials with the proper combination of the required features. Among several interesting
candidates for photonic applications, glasses are receiving special attention because of their
chemical and mechanical stability and wide compositional range that can be explored to tune
the desired property for a specific application. Furthermore, glasses may present fast response
times and high nonlinearities, features of foremost importance for photonic devices [1].
Glasses containing highly polarizable atoms present good nonlinear optical properties on
account of their easily deformable electron clouds [2]. Heavy-metal oxide glasses have shown
to be promising materials for all-optical devices due to the largest hyperpolarizabilities of
their heavy-metals [2,3]. Particularly, the presence of lead oxide have been investigated in
tellurite, germinate, silicate and borate glass [4–7]. Waveguide structures were produced
inside PbO-Bi2O3-Ga2O3-GeO2 glass [7]. Lead silicate glasses were used on the fabrication of
highly nonlinear and low loss fibers [5]. Studies on binary systems TeO2-PbO and B2O3-PbO
have shown an enhancement of the third-order nonlinearities with the increased of lead
content due to Pb+2 ions [4,6]. In order to evaluate the capability of a given material for
optical devices, a broadband spectral analysis of its nonlinearities, absorptive and refractive,
is required. It is known, for instance, that glasses presenting high nonlinear index of
refraction also exhibit strong two-photon absorption, which is deleterious for all-optical
switching applications. However, the majority of the studies reported on the nonlinear
characterization of glasses were carried out only in a few wavelengths or in a limited
wavelength range, independently of the glassy system [3]. The knowledge of both properties,
the nonlinear refraction and absorption, could help selecting, for example, the optimum
operational wavelength for an optical device using a certain sample.
In this paper, we report a study on the two-photon absorption and nonlinear refraction
spectra (470 and 1550 nm) of the 50BO1.5 - (50-x)PbF2 - xPbO glasses, with x = 25, 35, 50
cationic %. Lead-base borate glasses exhibit high transparency in the visible and near
infrared, low melting temperature and second harmonic generation [8,9], thus being
promising materials for optical applications. We have investigated not only the nonlinear
optical properties of the Pb oxifluoroborate glasses as a function of the wavelength, but also
how they are affected by the replacement of fluor atoms by oxygen, while the content of Pb
(heavy metal) is kept constant. Such substitution can promote the formation of B–O- bonds
[10], whose free electron can positively affect the optical nonlinearity of borate glasses [3].
The nonlinear index of refraction and the two-photon absorption coefficient, represented,
respectively, by γ (m2/W) and β (m/W), were determined by Z-scan measurements using
pulses of 120 fs, which have been a useful tool to characterize several nonlinear optical
materials [2,11,12]. The values we obtained for γ are one order of magnitude higher than the
ones determined for fused silica. Moreover, considering the two-photon absorption
coefficient, the glass with x = 50 revealed potential for all-optical switching devices in the
wavelength range of 650-800 nm (figure of merit 2βλ/γ < 1). We have also studied the optical
#151483 - $15.00 USD Received 21 Jul 2011; revised 12 Aug 2011; accepted 12 Aug 2011; published 17 Aug 2011
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limiting properties of the lead oxifluoroborate glasses, which demonstrated interesting
features that can be explored in ultrashort pulse optical limiters.
2. Experimental
The preparation process of the glasses and some of their physical properties are described in
[13]. Polished flat samples with 1 mm of thickness were used for the Z-scan measurements
with femtosecond laser pulses. A Ti:sapphire chirped pulse amplified system (150-fs, 775 nm
and 1 kHz) was used as the excitation source for an optical parametric amplifier, which
provides 120-fs pulses from 460 up to 2000 nm. To ensure a Gaussian profile for the laser
beam used in the experiments, spatial filtering is performed before the Z-scan setup. The
output signal was monitored by a silicon or germanium photodetector, depending on the
wavelength region, coupled to a lock-in amplifier that integrates 1000 shots for each point of
the Z-scan trace. The laser pulse energies and beam waist size used in this experiment range
from 5 to 200 nJ and 14 to 27 µm, respectively, according to the excitation wavelength.
Details about the Z-scan technique, developed by Sheik-Bahae et al. can be found in [14]. For
comparison purposes, we have also measured the nonlinear index of refraction, γ, for fused
silica at the visible and infrared regions, and found values of approximately 1.9 x10−20 m2/W,
which are in accordance to results from the literature [15]. In our Z-scan measurement, the
estimated error was ± 10% for open aperture and ± 30% for closed aperture configuration. A
Cary 17 spectrophotometer was used to measure the linear absorption spectra of the samples.
Optical limiting measurements were performed at 650 nm, using the optical parametric
amplifier, previously described as the excitation source. The excitation light intensity was
controlled using two polarizers. To obtain a reference signal for the input intensity, the
incident laser light was separated by a beam splitter located after the second polarizer. Then,
the laser beam is focused at the sample position with a f = 15 cm lens (w0 = 13 µm). Fused
silica was used as a reference material for the optical limiting experiments.
3. Results and discussions
The linear (left axis) and nonlinear (right axis) absorption spectra of the 50BO1.5 - (50-x)PbF2
- xPbO glasses, with x = 25, 35, 50 cationic %, are shown in Fig. 1. One can notice that the
linear absorption shifts to red when PbF2 is replaced by PbO. For oxide glasses, it has been
shown that an increase in non-bridging oxygens (NBO) leads to a red shift in the sample
absorption spectra [3,16]. These NBOs are oxygen atoms bonded to only one network cation
and negatively charged, which is important for nonlinear optical materials. Changes in the
NBO content can be checked through Raman spectroscopy. Pan et al. reported that the
addition of PbX2 (X = F, Cl, Br or I) in (65-x)PbO-xPbX2-35B2O3 glasses leads to a reduction
of the B–O- vibration, and to the disappearance of the Raman peak at 570 cm−1, which has
been attributed to metaborate groups [10]. Each metaborate unit has three NBOs. Therefore,
the red shift observed in the linear absorption spectra (Fig. 1) is attributed to the increase of
the NBO in the glassy matrix. By extrapolating the linear region of the absorption, we
determined the band gap energy, Eg, that decreases from 3.63 to 3.37 and 3.14 eV for the
samples with x = 25, 35 and 50% of PbO respectively. It is important to mention that such
procedure overestimate the band-gap energy.
Two-photon absorption (2PA) was observed from 470 up to 760, 780 and 790 nm,
according to the addition of lead oxide (left axis in Fig. 1). In Fig. 1, the inset shows a typical
open aperture Z-scan signature for the lead oxifluoroborate glass with x = 50 of PbO. The
2PA spectra present a monotonous increase as the excitation energy approaches the bandgap
energy. Such process, known as resonant enhancement of the nonlinearty, occurs when the
laser frequency approaches the linear absorption of the material [2]. For the samples with x =
25, 35 and 50, we noticed that the 2PA coefficients tend to a constant value, equivalent to
0.03, 0.04 and 0.05 cm/GW, for wavelengths greater than 580, 610 and 650 nm respectively.
#151483 - $15.00 USD Received 21 Jul 2011; revised 12 Aug 2011; accepted 12 Aug 2011; published 17 Aug 2011
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This behavior indicates that the 2PA in the samples studied herein has a small dependence
with the compositional change, at regions far from one photon resonance. The differences in
the 2PA values, among the distinct samples, at the enhancement region follow the changes in
the linear absorption spectra caused by the substitution of PbF2 by PbO.
Fig. 1. Linear (line) and nonlinear (line + symbols) absorption spectra of 50BO1.5 - (50-x)PbF2
- xPbO glasses (x = 25, 35 and 50 cationic %), whose labels are defined in the figure. The
inset shows the open aperture Z-scan signature for the x = 50 sample at 700 nm.
The spectrum of the nonlinear index of refraction (γ) for the sample x = 50 is shown in
Fig. 2. A representative closed aperture Z-scan signature is presented in the inset of this
figure. As it can be seen, γ is practically constant in the range of the wavelengths analyzed,
with a value of approximately 4.7 x10−19 m2/W. Similar behaviors were obtained for samples
with x = 25 and 35, with average values for γ of 2.6x10−19 m2/W and 3.1x10−19 m2/W
respectively. Compared to the value obtained for fused silica, the γ values for the lead
oxifluoroborate glasses with x = 25, 35 and 50 of PbO, are 14, 16 and 25 times higher
respectively.
Fig. 2. Values of the nonlinear refractive index as a function of wavelength for the 50BO1.5 (50-x)PbF2 - xPbO glass with x = 50 cationic %. For this sample at 700 nm, a closed aperture
Z-scan signature is illustrated in the inset.
#151483 - $15.00 USD Received 21 Jul 2011; revised 12 Aug 2011; accepted 12 Aug 2011; published 17 Aug 2011
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An analysis on the variation of the third-order properties, as a function of the band gap
energy, is presented in Fig. 3. Both, the nonlinear refractive index and the 2PA coefficient,
increase with the decrease of the Eg. This result is a consequence of the increase in the NBO
content. Because NBO are less stable and weakly bound to the boron or lead atoms, its
valence electrons are easily deformable by the laser electromagnetic field, resulting in larger
nonlinearities [3]. In Fig. 3, one can observe a higher variation of γ than of β with the band
gap energy. Such results imply that, probably, the nonlinear index of refraction is more
sensible to the NBOs than the two photon absorption coefficient.
Fig. 3. Nonlinear index of refraction (squares) and 2PA coefficient (circles) as a function of
the band gap energy of the 50BO1.5 - (50-x)PbF2 - xPbO glasses with x = 25, 35 and 50
cationic %. The γ values represent the average of whole spectrum, and β is the average at the
range of 500-550 nm.
Distinct criteria have been proposed to analyze materials for specific applications [17].
For all-optical switching, the figure of merit F = 2βλ/γ has been used to select nonlinear
optical materials; if the condition F < 1 is satisfied, the material could be used for all-optical
switching devices [18].
In Fig. 4, we have shown the dependence on F as a function of the wavelength for the lead
oxifluoroborate glass with x = 50, since this sample is the one that presents the higher optical
nonlinearity among the ones studied herein. Figure 4 shows that F is close to 1 for
wavelengths between 650 and 800 nm, which makes this sample an interesting candidate for
photonic devices, specifically optical switches, at this region of wavelengths.
Fig. 4. Figure of merit of the 50BO1.5 - (50-x)PbF2 - xPbO glass with x = 50 at the range of
450-800 nm.
#151483 - $15.00 USD Received 21 Jul 2011; revised 12 Aug 2011; accepted 12 Aug 2011; published 17 Aug 2011
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Another possible device application for this type of glass system is in optical limiters.
Figure 5 shows optical limiting curves (closed symbols) for the three samples studied as a
function of the incident laser intensity (input intensity). One can observe that all samples
present an optical limiting behavior when compared with fused silica (open circles).
However, the sample with x = 50 presents a lower intensity threshold for optical limiting
action in comparison to the other ones. Such behavior can be explained by the gradual
replacement of PbF2 by PbO in the matrix, which increases the optical attenuation and it is
associated to the higher 2PA coefficient exhibited by the sample with x = 50. The increase of
PbO leads to a decrease in the optical limiting threshold; for the samples with x = 25, 35 and
50, the limiting process starts to occur for intensities of 90, 72 and 40 GW/cm2 respectively.
In Fig. 5, the solid lines represent the modeling of the optical limiting curves considering only
the 2PA mechanism [19], where the 2PA coefficient was the one obtained from the Z-scan
measurements. We can notice that the 2PA process solely does not describe the optical
limiting behavior. The dashed lines in Fig. 5 represent the modeling carried out considering
both processes, 2PA and three-photon absorption (3PA) [19,20]. The values of the 3PA
coefficient were estimated to be around 1.2 x10−4 cm3/GW2. Although such mechanism has
been shown to be adequate to fit results for silicon waveguides [21], it does not properly
describe the optical limiting behavior presented here. We believe that the differences between
the experimental data and the modeling indicate that other mechanisms, rather than 2PA and
2PA + 3PA, are contributing to the limiting processes. Therefore, the lead oxifluoroborate
glasses investigated in this work could be used in the development of optical limiting devices
for ultrashort laser pulses.
Fig. 5. Optical limiting curves for 50BO1.5 - (50-x)PbF2 - xPbO glass(closed symbols), with x
= 25 (a), 35 (b) and 50 (c) and silica fused (open circles) at 650 nm. The solid lines correspond
to the fittings obtained using 2PA, while de dashed line represent the fitting considering 2PA
and 3PA processes [19].
4. Conclusion
In summary, we have investigated the third-order optical nonlinearities of lead
oxifluoroborate glasses (50BO1.5 - (50-x)PbF2 - xPbO, x = 25, 35 and 50% mol) at visible and
infrared wavelength. In addition, changes of the optical nonlinearities were investigated as a
function of the oxygen content for a fixed lead (heavy metal) concentration. Our results
revealed that non-bridge oxygens have an important role in the nonlinear optical properties of
heavy metal oxide glasses; the presence of this oxygen improves both, the nonlinear index of
refraction and the 2PA coefficient. The nonlinear index of refraction was determined to be
14, 16 and 25 times higher than fused silica, respectively for the glasses with x = 25, 35 and
50. The samples have also shown interesting optical limiting features at 650 nm. Moreover,
the figure of merit analyses for the sample with x = 50 reveals this sample as being a potential
material for the development of all-optical switching at the wavelength range of 650–800 nm.
Acknowledgments
The authors wish to acknowledge the financial support from FAPESP, CAPES and CNPq.
#151483 - $15.00 USD Received 21 Jul 2011; revised 12 Aug 2011; accepted 12 Aug 2011; published 17 Aug 2011
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