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Field-assisted patterned dissolution of silver nanoparticles in phosphate glassA. Andreyuk and J. Albert Citation: Journal of Applied Physics 116, 113106 (2014); doi: 10.1063/1.4896135 View online: http://dx.doi.org/10.1063/1.4896135 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Periodic nanostructuring of Er ∕ Yb -codoped IOG1 phosphate glass by using ultraviolet laser-assisted selectivechemical etching J. Appl. Phys. 100, 114308 (2006); 10.1063/1.2396715 Bulk photochromism in a tungstate-phosphate glass: A new optical memory material? J. Chem. Phys. 125, 161101 (2006); 10.1063/1.2364476 Poling-assisted bleaching of soda-lime float glasses containing silver nanoparticles with a decreasing filling factoracross the depth J. Appl. Phys. 100, 044318 (2006); 10.1063/1.2234813 Waveguide fabrication in phosphate glasses using femtosecond laser pulses Appl. Phys. Lett. 82, 2371 (2003); 10.1063/1.1565708 Space-selective precipitation of metal nanoparticles inside glasses Appl. Phys. Lett. 81, 3040 (2002); 10.1063/1.1509095

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Field-assisted patterned dissolution of silver nanoparticles in phosphateglass

A. Andreyuka) and J. AlbertDepartment of Electronics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

(Received 9 July 2014; accepted 9 September 2014; published online 19 September 2014)

Phosphate glass samples doped with silver ions through a Naþ-Agþ ion-exchange process were

treated in a hydrogen atmosphere at temperatures near 430 �C for durations ranging from 4 to 5 h.Such treatment causes metallic silver precipitation at the surface as well as nanoclustering of silver

atoms under the surface under conditions very similar to those used for silicate glasses. The pres-

ence of silver clusters resulted in a characteristic coloring of the glass and was verified by the

observation of a plasmon resonance peak near 410–420 nm in the absorption spectra. Applying a

DC voltage between 1.4 and 2 kV at temperatures between 120 and 130 �C led to dissolution of theclusters in the area under the positive electrode, thereby bleaching the glass color. The use of a pat-

terned doped-silicon electrode further led to the formation of a 300 nm thick surface relief on the

glass surface and of a volume complex permittivity grating extending at least 4 lm under the sur-face. Such volume complex refractive index gratings may find applications in passive or active

(laser) photonic devices in rare-earth doped phosphate glasses, where conventional bulk grating

formation techniques have limited applicability. VC 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4896135]

I. INTRODUCTION

Phosphate glasses meet several material requirements

for integrated optics applications. Due to the high solubility

of its glass matrix it can accommodate high concentrations

of rare earth ions (Erþ, Ybþ) homogeneously, i.e., without

forming aggregates and thus keeping scattering at a low

level.1,2 The typical rare earth ion concentrations that can be

achieved without clustering are 10–20 times higher than in

silicate glasses. This feature is important because Er/Yb co-

doped glasses can transfer 980 nm pump photon energy into

the 1550 nm emission band with a long upper state lifetime,

10 ms compared to nanoseconds in semiconductors. This

makes Er/Yb doped glass fiber and waveguide lasers more

favorable than semiconductor lasers in telecommunication

applications,3,4 and the emission line widths of such lasers

can be as narrow as 10 kHz (Ref. 5). The higher concentra-

tions of active material (the rare earth ions) that can be

achieved in phosphate glasses provide more gain per unit

length and thus allow compact device sizes and high power

output. In addition, phosphate glasses have low optical loss

in the near infrared and can also be modified by ion-

exchange to form waveguides.2,6

In order to fabricate a waveguide laser in a glass sub-

strate, a pair of low loss narrowband reflectors must be cre-

ated to form a laser cavity. The best way to do this is to use

volume refractive index gratings, a well-developed technique

in certain types of silica glasses.7,8 However, in phosphate

glasses the standard method of making gratings with UV ex-

posure through a diffractive phase mask does not work well

because this glass does not contain photosensitive

molecules.9,10 While gratings have been successfully pro-

duced by a related thermally assisted UV irradiation pro-

cess,11,12 the index modulation amplitudes of the gratings

remained small.

Here, we present work that investigates the possibility

of achieving a relatively large periodic modulation in both

the real and imaginary parts of the phosphate glass bulk per-

mittivity by means of dissolved and partially clustered silver

nanoparticles inside the glass matrix. We used ion-exchange

to introduce silver into the glass, precipitated some of it into

clusters and then used field assisted bleaching with a pat-

terned electrode to locally bleach the nanoparticles and

hence to modify the complex permittivity of the material.

Field assisted bleaching of soda-lime glass doped with

silver clusters has been known since 2004,13,14 and later

observed in other types of silicate-based glasses such as sol-

gel, borosilicate N-BK7, K8, and VO73.15–17 Furthermore,

other embedded nanoparticles such as gold and copper were

successfully dissolved with high electric fields15–21 in those

glasses. We report on similar effects and the conditions

required for observing them in a silica-free phosphate glass

especially designed for integrated optics applications, in

particular waveguide and waveguide laser fabrication.

II. EXPERIMENTAL PROCEDURE LEADING TO SILVERCLUSTERING IN PHOSPHATE GLASS

A. Ion-exchange, annealing in air followed byannealing in H2

The glass substrate used is an active (Er/Yb doped)

IOG-1 phosphate glass from Schott Glass Technologies Inc.,

with a mol. % composition of 60% P2O5, 13% Al2O3, 24%

Na2O, 1.1% La2O3, 1.5% Yb2O3, and 0.4% Er2O3 (Ref. 22).

Silver ions were introduced into the glass by the dry

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected].

0021-8979/2014/116(11)/113106/9/$30.00 VC 2014 AIP Publishing LLC116, 113106-1

JOURNAL OF APPLIED PHYSICS 116, 113106 (2014)


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silver-film ion-exchange technique, also known as field-

assisted ion diffusion and electromigration (see Refs. 23–25

for descriptions of these techniques). The goal in preparing

the sample is to optimize the size distribution of silver clus-

ters embedded in the glass matrix, i.e., the mean value of the

cluster diameter and its standard deviation that leads to the

strongest plasmon resonance.

The sample was first prepared by depositing silver films

on both sides of a 1.5 mm thick IOG-1 phosphate glass,

400 nm of Ag on the side towards the positive electrode (top

side, the side where ion-exchange will take place), and

100 nm on the side towards the negative electrode (bottom

side). The silver film on the bottom side of the glass is only

used to ensure a good electrical contact with the electrode

during ion-exchange. Upon heating with the imposition of a

high voltage between the electrodes, silver ions from the top

side diffuse into the substrate by ion-exchange, replacing so-

dium ions that move towards the negative bottom electrode.

An ion-exchanged layer results under the top surface, with

sodium accumulating on the bottom side. Depositions on

both sides of the sample were performed individually by E-

beam evaporation using a Balzers BA 510 system. The de-

posited thickness of the silver film is controlled by the dura-

tion of the process, as calibrated beforehand on dummy

samples.

For the ion-exchange process, the sample was sand-

wiched between two 10 cm diameter circular polished alumi-

num electrodes weighting 1.7 kg each. The pressure from the

top electrode ensured good electrical contact between the

electrodes and the silver films on both sides of the sample.

The sample assembly with electrodes was placed in an oven

and kept at 95 �C with an applied DC voltage of 380 V for 28h. This unusually long lasting ion-exchange is needed in our

case for the precipitation of enough silver in the form of

clusters. After this period, the oven was turned off to let the

ion-exchanged glass cool down to room temperature over

4–5 h with the DC voltage kept on. Then the DC voltage was

switched off, the electrodes removed, any remaining silver

film dissolved chemically by immersion in a cleaning solu-

tion made up of 6 parts of deionized water (DI), 1 part of

30% ammonium hydroxide (NH4OH), and 1 part of 30%

hydrogen peroxide (H2O2). Then the sample was annealed in

air at 300 �C for 7 h to allow silver to diffuse and homoge-nize further down under the glass surface. Finally, the sam-

ple was annealed a second time but in a H2 atmosphere in

the furnace with a constant hydrogen flow to ensure 100%

hydrogen concentration at 400 �C for 30 min followed by 4 hat 430 �C. These particular conditions were chosen (afterseveral trials, some of which are described below) to obtain

a large absorption peak in the processed glass at the wave-

lengths of the plasmon resonance while maximizing the

bleaching caused by poling. During annealing in H2, it was

observed that silver atoms precipitate on the top side of the

glass surface (where the positive electrode was located),

forming a shiny metallic silver layer. It is assumed that the

silver ions nearest to the surface capture an electron from the

H2 gas and neutralize into a smooth layer of pure Ag0 (see

Ref. 26), thereby leaving room in the glass for other ions to

diffuse back towards the top surface. Reduction of silver

ions to metallic (neutral) silver atoms takes place according

to the chemical reaction

2Agþ þ H2 ! 2Ag0 þ 2Hþ: (1)

It was observed in separate experiments that such pre-

cipitation does not occur in silver ion-exchanged silicate

glasses (such as microscope slide glass). Silver precipitation

on the surface is an undesired effect that lowers the amount

of silver available inside the glass for cluster formation. The

precipitation of silver out of the glass is thought to be one of

the reasons why the ion-exchange process has to be pro-

longed from 1.5–2 h (typical for silicate type glasses27) to

20–40 h for phosphate glass in order to keep enough silver in

the glass to get significant clustering. Finally, the glass surfa-

ces were cleaned in a cleaning solution to remove the pre-

cipitated silver from the surface and any residue on the other

side. The final appearance of the initially transparent samples

was yellowish, thus confirming visually the formation of

nanoscale metal clusters inside the glass. Fig. 1(a) shows the

final absorbance spectrum of this sample, measured with a

Cary 3 UV-Visible spectrophotometer in the range from 300

to 900 nm. The absorbance was not corrected for reflection

off the sample faces.

B. Influence of ion-exchange time and temperature

The conditions described above were chosen following

several tests to be described presently. One set of samples

was prepared with ion-exchange durations from 22 h up to

64 h under the same remaining parameters: T¼ 95 �C andV¼ 350 V, followed by annealing in air at T¼ 300 �C fort¼ 6 h, then reduction in H2 at T¼ 400 �C for t¼ 1.5 h fol-lowed by a ramping temperature to 430 �C, which was keptfor 3 h (Fig. 2). Another pair of samples was used to check

the effect of the ion-exchange temperature between 85 �C

FIG. 1. UV-vis absorption spectra and TEM image inset of the IOG-1 glass

sample that underwent ion-exchange (T¼ 95 �C, t¼ 28 h, V¼ 380 V),annealing in air (T¼ 300 �C, t¼ 7 h), and reduction in H2 (T¼ 400 �C,t¼ 30 min followed by T¼ 430 �C, t¼ 4 h). The inset shows a TEM imagetaken on a thinned slice from a typical sample with 20–30 nm silver clusters.

113106-2 A. Andreyuk and J. Albert J. Appl. Phys. 116, 113106 (2014)


and 95 �C, with the other parameters of ion-exchange set as:t¼ 25 h and V¼ 410 V, annealing in air: T¼ 300 �C, t¼ 6 h,and reduction in H2: T¼ 400 �C, t¼ 1.5 h followed byT¼ 430 �C, t¼ 3 h (Fig. 3).

C. Influence of anneal conditions

Samples with different times and temperatures of

annealing in H2 are shown in Fig. 4, with other parameters

fixed (ion-exchange: T¼ 95 �C, t¼ 28 h, V¼ 350 V; anneal-ing in air: T¼ 300 �C, t¼ 6 h). Finally, the effect of the airanneal was explored in the following conditions: ion-

exchange T¼ 105 �C, t¼ 45 h, V¼ 400 V, annealing in H2:T¼ 400 �C, t¼ 30 min followed by T¼ 430 �C, t¼ 4 h. Forthe 400 �C cases, it was found that a second step at 430 �Cwas necessary to increase the absorption peak to useful lev-

els while still allowing for their subsequent bleaching. Those

results are shown in Fig. 5.

D. Discussion of the clustering results

All the samples have a single well-defined peak centered

near 410 nm, with absorbances often exceeding 6 (the limit

of our measurement system), and no other notable spectral

features between 300 and 900 nm. The 410 nm peak is

known to correspond to a localized plasmon resonance of

nanoscale silver aggregates in glass,14,26 and this was veri-

fied by Transmission Electron Microscope (TEM) image of

cleaved slivers from the sample shown in the inset of Fig. 1.

That image reveals the presence of rounded silver clusters

with diameters near 20–30 nm. The plasmon peak increases

with ion-exchange time or temperature, likely because such

increases lead to larger amounts of silver ions being intro-

duced in the glass. Results further indicate that it is not bene-

ficial to increase temperature of annealing in H2 beyond

400 �C, otherwise the plasmon peak starts to decrease andshift towards longer wavelengths (corresponding to smaller

FIG. 2. Absorption spectra of the samples with different ion-exchange time

from 22 h (lowest curve) to 64 h with T¼ 95 �C, V¼ 350 V (other parame-ters), annealing in air: T¼ 300 �C, t¼ 6 h, reduction in H2: T¼ 400 �C,t¼ 1.5 h followed by T¼ 430 �C, t¼ 3 h.

FIG. 3. Absorption spectra of the samples with different ion-exchange tem-

perature, 85 �C and 95 �C with t¼ 25 h, V¼ 410 V (other parameters),annealing in air: T¼ 300 �C, t¼ 6 h, reduction in H2: T¼ 400 �C, t¼ 1.5 hfollowed by T¼ 430 �C, t¼ 3 h.

FIG. 4. Absorption spectra of the samples with different treatments of

annealing in H2: 400�C for 30 min followed by 430 �C for 4 h, 400 �C for

1.5 h followed by 430 �C for 3 h, 450 �C for 4 h, 415 �C for 4 h. Other param-eters, ion-exchange: T¼ 95 �C, t¼ 28 h, V¼ 350 V, annealing in air:T¼ 300 �C, t¼ 6 h.

FIG. 5. Absorption spectra of the samples with different treatments of

annealing in air: 300 �C for 6 h, 350 �C for 3 h, and 350 �C for 6 h. Other pa-rameters, ion-exchange: T¼ 105 �C, t¼ 45 h, V¼ 400 V, annealing in H2:T¼ 400 �C, t¼ 30 min followed by T¼ 430 �C, t¼ 4 h.



densities of larger clusters). Finally, the absorption spectra

for different time-temperature pairs the annealing in air

show that temperature has a strong effect but not so much

time, in the range studied.

In summary, by properly adjusting the parameters of the

three phases of the clustering processes (ion-exchange,

annealing in air, and annealing in H2) the shape of the

induced absorption can be controlled, namely, the height,

width, and to a certain extent, position of the plasmon reso-

nance peak. This was more or less expected and led us to the

conditions necessary to prepare samples with the largest pos-

sible concentration of silver clusters, to be used in bleaching

experiments. Such sample is shown in Fig. 6 (ion-exchange:

T¼ 95 �C, t¼ 70 h, V¼ 370 V, annealing in air: T¼ 300 �C,t¼ 6 h, and annealing in H2: T¼ 400 �C, t¼ 30 min followedby T¼ 430 �C, t¼ 4 h).

III. HIGH VOLTAGE BLEACHING OF THE SILVERCLUSTER PLASMON ABSORPTION PEAK

A. Field-assisted dissolution of silver clusters

Metal clusters can be fully or partially dissolved if a

glass sample containing such clusters is subjected to high

voltage electric field at an elevated temperature.13,14 The

cluster dissolution process starts with electron tunneling

through the metal-dielectric barrier which leads to atomic sil-

ver ionization and in turn to a silver ion leaving the cluster.

It was shown that tunneling sharply depends on distance

between clusters and therefore on their filling factor, as well

as on the temperature and voltage applied.14 Full cluster dis-

solution is achieved when the glass becomes transparent

again, or “bleached.” This is shown in Fig. 6, with bleaching

conditions determined from Figs. 8(a) and 8(b) and the same

electrode configuration (without the deposited silver films)

that was used for the ion-exchange. These results show that

the phosphate glass host does not behave differently com-

pared to silicate glasses for the high voltage dissolution

process.

It is therefore possible to dissolve the clusters locally if

a patterned electrode is used, as was shown in Refs. 28 and

29. In particular, since electron tunneling strongly depends

on the voltage applied, there is a threshold voltage that trig-

gers the clusters dissolution. Therefore, a periodically corru-

gated anode may lead to a potential modulation around the

threshold voltage over a certain region of the glass and thus

to a spatially modulated dissolution. Our goal is to investi-

gate how deeply such periodic modulation of the dissolution

reaches under the surface and hence to investigate the possi-

bility of making volume gratings of complex permittivity

(refractive index and absorption).

An n-type silicon wafer was patterned with a periodic

array of rectangular grooves made by anisotropic plasma

etching (Fig. 7(a)). The grating period was 7.4 lm and thegroove depth 5.7 lm. The patterned wafer was placed grooveside down on the glass surface containing the silver clusters

and then the wafer-glass pair was pressed between two stain-

less electrodes with the wafer on the positive electrode side.

The whole assembly was placed in the oven. When the tem-

perature in the oven reached 120–140 �C, the voltage wasincreased in steps of 100 V every 15 min up until reaching

the 1.3–1.8 kV levels. It was found that such gradual voltage

increase is necessary to prevent the excessive current that

otherwise would permanently damage the glass sample if the

high voltage was applied instantaneously.

The side view SEM images shown in Fig. 7 also reveal

that a surface relief pattern remains after the bleaching pro-

cess, as was previously observed when a microstructured

anode was used to pattern the dissolution of a silicate glass-

metal nanocomposite sample.28,29 It was shown in Refs. 28

and 29 that the spatial relief appearing on the surface of

soda-lime glass results from internal mechanical stresses;

they alter the volume of the glass because the top surface of

the sample is free to expand and contract. The stresses arise

as a result of the ionization of Ag0 atoms since the Agþ ion

occupies a smaller volume and also as a result of the replace-

ment of larger ions such as Naþ, Ca2þ, and Agþ by smaller

Hþ ions that penetrate under the surface from the air envi-

ronment. The local change in the volume is stronger in the

region of direct contact between the glass surface and the

protruded part of the corrugated electrode. The field-assisted

dissolution of silver clusters in phosphate glass matrix used

here results in similar surface relief but its depth is estimated

to be �300 nm, almost 10 times larger than reported in Refs.14 and 15. This difference is likely due to the fact that the

periodicity of our electrodes is also about one order of mag-

nitude larger than in those references (thereby allowing more

space between the electrodes and more volume of glass

impacted by the high voltage). Also for IOG-1 glass the sur-

face relief is expected to be more pronounced because its

elastic modulus is smaller, 61 GPa, versus 68 GPa for a typi-

cal silicate glass.

Figures 8(a) and 8(b) present the evolution of the electri-

cal properties of the glass sample, bleached with the pat-

terned electrode with a period of 8 lm. The absorption ofthis sample measured after the bleaching process was pre-

sented in Fig. 6. Following each voltage increment the cur-

rent experienced a sudden increase, but beginning at the 5th

FIG. 6. Absorption spectra before and after bleaching of the sample with the

following parameters, ion-exchange: T¼ 95 �C, t¼ 70 h, V¼ 370 V, anneal-ing in air: T¼ 300 �C, t¼ 6 h, and annealing in H2: T¼ 400 �C, t¼ 30 minfollowed by T¼ 430 �C, t¼ 4 h. Parameters of bleaching presented in Figs.8(a) and 8(b).



FIG. 8. Bleaching voltage (a) and cur-

rent (b) vs. time of IOG-1 glass sample

whose absorption plot is shown in Fig.

6. Bleaching voltage (c) and current

(d) vs. time of silicate glass (micro-

scope slide) sample. Dashed vertical

lines indicate time when furnace was

turned off. The voltage was supplied

by a DC high voltage programmable

power supply (Matsusada AU10R6),

and the current drawn from the power

supply was measured by its built-in

ammeter.

FIG. 7. (a) SEM image of periodic Si

electrode produced by plasma etching.

(b) and (c) SEM image of IOG-1 glass

bleached with periodic electrode. (d)

SEM image of surface relief of IOG-1

glass bleached with periodic electrode.



increment this increase was followed by a relatively slow

decay until the next voltage step increase. When the voltage

reached its maximum value of 1800 V the peak current

reached 90 lA then monotonically decayed. After 5 h oftreatment, the decay rate increased because the oven was

turned off and sample started cooling, thereby decreasing the

ionic conductivity of the glass. After 9.4 h the voltage started

to drop off with a rate of 1 V/s and reached zero at 10 h. For

comparison, the bleaching dynamics of a silicate glass sam-

ple containing silver clusters is shown in Figures 8(c) and

8(d) where the current decay after each voltage increment is

more pronounced and the overall current value is larger

(with the same electrode area in both cases). So while the

conductivity of the phosphate glass is significantly lower

than that of the comparative silicate glass, the overall effect

of bleaching is similar. (The lower conductivity also helps to

explain the need for much longer exchange times to diffuse

enough silver in the phosphate glasses). For reference, the

silicate glass sample was prepared as follows: 1 h. of ion-

exchange at 130 �C and 400 V, 6 h 30 min of annealing in airat 300 �C and finally annealing in hydrogen at 400 �C for30 min ramped to 430 �C for 4 h.

B. EDX sample measurements and observations

Relative concentrations of the local chemical content of

the sample were determined at several locations of the pat-

terned samples by a scanning electron microscope (SEM)

equipped with an energy dispersive X-ray spectrum analyzer

(EDX). This allows the identification of the chemical com-

pounds and the measurement of their concentration within a

depth of about 1 lm, with a lateral accuracy also of the orderof 1 lm. The theoretical detection limit of the EDX measure-ments is 0.08 wt. % while in practice the limit is estimated to

0.1 wt. % according to Ref. 30.

Performing measurements in the various locations indi-

cated in Fig. 9 reveal the concentration changes across the

sample and therefore the magnitude of the permittivity gra-

ting contrast. In order to evaluate the reach of the permittivity

modulation under the sample surface, additional measure-

ments were carried out on the sample after removing the top-

most �4 lm of the sample by polishing.The thickness of material removed by polishing

(x1¼ 4 lm) was derived from the 4 measurements made on

the single sample by solving 4 equations with 4 unknowns:

the surface concentrations A1 and A2 in the bleached and

unbleached regions, respectively, the exponential decay

length d, and the depth removed by polishing x1 (as shown

in Fig. 9). This derivation assumes that the Ag concentration

follows a decaying exponential, as reported in Ref. 14.

The atomic silver concentration measurements at the

four spots shown in Fig. 9 are given as weight fractions. The

values at points 1, 2, 3, 4 are 0.0714, 0.0883, 0.0237, 0.0211,

respectively. If we assume that the depth profile of the con-

centration of atomic silver in the bleached and unbleached

regions is identical apart from a different amplitude factor,

each pair of points can be used to fit a simple exponentially

decaying function from the surface, and, respectively, for the

bleached and unbleached regions. Given the height differ-

ence observed on the SEM pictures of the sample cross-

section (300 nm), the fits have 4 unknowns, A1, A2, d, and x1(where x1 is the thickness that was removed by polishing).

With this approach the thickness that was polished away was

found to be 4 lm, and the estimated penetration depth d was3 lm. A representative SEM image of the glass sample andcorresponding EDX spectroscopy results at the point number

4 in Fig. 9 is shown in Fig. 10.

C. Calculation of the complex permittivity grating bythe Maxwell-Garnett mixing formula

The effective complex permittivity of a medium that has

two components, a host medium and spherical particle inclu-

sions, is described by the Maxwell-Garnett mixing formula

as31

eef f ¼ eh þ 3f ehei � eh

ei þ 2eh � f ei � ehð Þ; (2)

where eh is the dielectric constant of the host medium, ei isthe dielectric constant of particles embedded in the host me-

dium, and f is the volume density of the embedded particlesin the mixed medium. We used the particular form of the

Maxwell-Garnett mixing formula for particles of spherical

shapes, based on the results of TEM imaging, and this for-

mula is valid regardless of the sizes of the particles as long

as that the size of each particle is much smaller than

FIG. 9. Illustration of the methodology used to determine the Ag distribution

profile by EDX measurements at four points (two each in the original and

polished samples). See text for details.

FIG. 10. SEM of the polished sample surface near the location of the EDX

measurements. A variation of the SEM brightness at the electrode period

confirms the existence of pattern formation at least 4 lm below the originalsurface.



wavelength of the incident light, which is clearly the case

here. The polarizability of the particles is assumed to be

electrostatic.

In order to use this formula, the weight fractions fm ofsilver particles obtained by EDX at specified points 1–4

(in Fig. 9) are converted to volume fractions fv (withthe same assumption about exponential decay from the sur-

face as before) through the following expression fv ¼ fm=ðfm þ ð1� fmÞqAg=qIOGÞ, where qAg and qIOG are the den-sities of silver and IOG-1 glass: qAg ¼ 10:49g=cm3 andqIOG ¼ 2:74g=cm3 (Ref. 32). The permittivity of the glass asa function of wavelength is real and it was obtained from the

Sellmeier coefficients of Er-doped phosphate glass provided

by Ref. 33 in the visible and near infrared range

eIOG�1 kð Þ ¼ 1þX3

i¼1

Aik2

k2 � B2i; (3)

where A1¼ 1.239990, A2¼ 0.09958, A3¼ 2.43925,B1¼ 0.05557, B2¼ 0.24132, and B3¼ 15.8609.

At a wavelength of 1534 nm, this formula yields a glass

refractive index of 1.5235.

For the permittivity of metal inclusions, we use the size

dependent dielectric constant for silver based on the Drude

model and a size dependent mean free path given by34

eAg x; rð Þ ¼ ebulk þx2p

x2þ ixc0�

x2px2þ ix c0þA tF=rð Þð Þ

; (4)

where xp is the plasma frequency, xp ¼ 9:17 eV (Ref. 35);c0 is the damping constant, c0 ¼ 0:021 eV (Ref. 35); A is asize factor, A ¼ 1 for a spherical particle (Ref. 36); tF is theFermi velocity for Ag, tF ¼ 1:39� 106m=s (Ref. 36); r isthe silver cluster radius; and ebulk is the dielectric constant ofbulk silver, data from Ref. 37.

The effective dielectric constants of the bleached and

unbleached regions can now be calculated as a function of

distance from the surface (where we used the same exponen-

tial decay fitting functions as for the measured fm values).Finally, we can calculate the contrast in the real and

imaginary parts of the refractive index between the

bleached and unbleached areas of the glass as ReðDnðkÞÞ¼ Reð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieeff ;unbðkÞ

pÞ � Reð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieeff ;blðkÞ

pÞ and ImðDnðkÞÞ

¼ Imðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieeff ;unbðkÞ

pÞ � Imð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieeff ;blðkÞ

pÞ.

Plots of the real and imaginary refractive index grating

contrast versus wavelength at a depth of 4 lm below the sur-face are shown in Fig. 11. The peak values are 0.01 and 0.02

for the real and imaginary parts, respectively, and they decay

away from the resonance wavelength. For near infrared

wavelengths around 1550 nm, the values are 1.7 � 10�3 and1.3 � 10�5 for the real and imaginary parts of the index mod-ulation. Further down into the sample, these fits predict that

the real index modulation 10 lm below the surface is still aslarge as 2.6 � 10�4 at 1550 nm, more than sufficient to fabri-cate high reflectivity Bragg gratings (this index modulation

gives a reflectivity 99.9% for grating lengths of 10 mm and

more if the grating periodicity can be reduced to near 1 lm).Of course, these numerical estimates depend on the validity

of the various assumptions made in deriving them, namely,

the exponential shape of the ion-exchanged Ag distribution

under the surface, the Drude model for the dispersion of the

permittivity of the Ag clusters, and the Maxwell-Garnett

effective medium theory. These assumptions and models are

widely used and validated for similar configurations

In order to further visualize the two-dimensional

structure of the index modulation pattern resulting from

the corrugated electrode, electrostatic calculations of the

voltage were performed using conformal mapping techni-

ques.38 Figure 12(a) shows how the initially rectangular

voltage distributions rapidly washes out with distance from

the surface. Actually, a section of Fig. 12(a) at a depth of

4 lm in the sample, shown in Fig. 12(b), indicates that thepeak-to-peak voltage modulation at this depth is less than

5 V, while experimental results show a silver colloid vol-

ume fraction of about 10%. This supports the hypothe-

sis13,14,21 that field-assisted bleaching is highly nonlinear

with imposed voltage and may in fact be driven by a

threshold process.

The real part of the index modulation under the sam-

ple surface is one order of magnitude larger than the best

results obtained in phosphate glasses by UV-induced pho-

tosensitive processes12 but the simultaneous formation of

a significant absorption grating may prove detrimental to

most applications of these kinds of gratings (as frequency

selective mirrors for waveguide lasers for instance in

Ref. 39). However, the periodic modulation of the con-

centration of silver clusters in rare-earth doped phosphate

glasses may find new applications associated with

enhancement of the pump or signal electromagnetic

fields due to plasmonic excitations around the metal

nanoparticles.

FIG. 11. Refractive index change vs. wavelength of bleached IOG-1 glass

with corrugated electrode based on EDX measurements and modelling of

the dispersion of the effective permittivity of the Ag diffused glass. The

peak value (0.01 for real part and 0.02 for imaginary part) decays away from

resonance as Lorentzian. (a) Real part, (b) imaginary part.



IV. CONCLUSIONS

In conclusion, we have investigated the formation of a

complex permittivity volume grating in phosphate glass

doped with silver nanoclusters formed by ion-exchanged fol-

lowed by hydrogenation and bleaching with a periodically

modulated electric field. The main findings include the fact

that the conditions required for the formation of the silver

nanoclusters were significantly different from those of the

well studied silica glasses. In particular, because solubility of

Ag (as well as Er and Yb) in phosphate glass, due to proper-

ties of its matrix, is grater than in silica based glass much

longer (by an order of magnitude) ion-exchange times are

required to achieve insoluble residue and form the Ag clus-

ters. Another difference is the migration of silver ions

towards the top surface and the reformation of a thin atomic

silver layer there during the thermal annealing in hydrogen.

On the other hand, the conditions of the high voltage bleach-

ing process that is used to dissolve the silver nanoclusters

were found to be identical to those used in silica glasses.

Based on these findings, an attempt has been made to

build a volume grating in the IOG-1 phosphate glass by field

assisted bleaching of silver clusters with a periodically corru-

gated electrode. While the lateral modulation amplitude of

the DC voltage at a depth of under the surface was calculated

to be relatively small (of the order of a few volts, relative to

an imposed total voltage difference of 1800 V between the

top and bottom of the sample), a significant modulation of

the material properties was obtained. Since the electron and

ion tunneling current from nanoclusters depend exponen-

tially on the imposed potential difference, even a weak mod-

ulation of the voltage can induce a moderate modulation of

tunneling current and of the corresponding bleaching of the

nanoparticles. Based on concentration measurements by

EDX, modeling by the Maxwell-Garnett theory and Drude

model for silver, extrapolated to near infrared wavelengths,

an indirect estimation of the distribution of refractive index

generated by a periodic bleaching electrode (period of

10 lm) showed that the real part of the index had a modula-tion amplitude of 1.7 � 10�3 at a depth of 4 lm under thesurface and still as much as 2.6 � 10�4 at 10 lm below thesurface, for optical wavelengths near 1550 nm. In the middle

of the glass layer studied, i.e., near 4 lm, the imaginary partof the complex refractive index was estimated to be of the

order of 10�5, which corresponds to a loss of about 1 cm�1

at 1550 nm. While this loss is quite large and may prevent

practical uses of these gratings in applications such as wave-

guide lasers, the presence of a periodic array of metal nano-

particles may find other applications in plasmonics and

nonlinear optics. In particular, the presence of metallic silver

enhances Kerr-type nonlinearities and furthermore, imposing

a large DC field during bleaching has the effect of breaking

the inversion symmetry of glass and inducing a second-order

nonlinearity by a process called poling. The second harmonic

generation efficiency of poled IOG-1 glass was studied in

Ref. 40. Finally, in rare-earth phosphate glass, periodic

bleaching also could lead to periodic energy transfer from

silver to erbium and ytterbium as discussed in Refs. 41 and

42 for other glass systems.

ACKNOWLEDGMENTS

This work was supported by the Natural Sciences and

Engineering Research Council of Canada. We would like to

thank Professor S. Honkanen and his group from Aalto

University for the TEM image of the glass sample.

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