Download pdf - Comparison of a new photosensitizer with erythrosine B in an AA/PVA-based photopolymer material

Comparison of a new photosensitizer with erythrosineB in an AA/PVA-based photopolymer material

Yue Qi,1 Haoyu Li,1 Jean Pierre Fouassier,2 Jacques Lalevée,3 and John T. Sheridan1,*1School of Electrical, Electronic and Communications Engineering,

Communications and Optoelectronic Research Centre,The SFI-Strategic Research Cluster in Solar Energy Conversion,

College of Engineering and Architecture,University College Dublin, Belfield, Dublin 4, Ireland

2Université de Haute Alsace, Mulhouse, France3Institut de Science des Matériaux de Mulhouse IS2M—LRC CNRS 7228- Université de Haute Alsace,

15, rue Jean Starcky, 68057 Mulhouse Cedex, France

*Corresponding author: [email protected]

Received 15 November 2013; revised 18 December 2013; accepted 30 December 2013;posted 3 January 2014 (Doc. ID 200981); published 12 February 2014

Dyes often act as the photoinitiator PI/photosensitizer PS in photopolymer materials and are therefore ofsignificant interest. The properties of the PI/PS used strongly influences grating formation when thematerial layer is exposed holographically. In this paper, the ability of a recently synthesized dye,D 1, to sensitize an acrylamide/polyvinyl alcohol (AA/PVA) based photopolymer is examined, and thematerial performance is characterized using an extended nonlocal photopolymerization-driven diffusionmodel. Electron spin resonance spin-trapping (ESR-ST) experiments are also carried out to characterizethe generation of the initiator/primary radical, R•, during exposure. The results obtained are then com-pared with those for the corresponding situation when using a xanthene dye, i.e., erythrosine B, underthe same experiment conditions. The results indicate that the nonlocal effect is greater when this newphotosensitizer is used in the material. Analysis indicates that this is the case because of the dye’s (D 1)weak absorptivity and the resulting slow rate of primary radical production. © 2014 Optical Society ofAmericaOCIS codes: (050.0050) Diffraction and gratings; (090.0090) Holography; (090.2900) Optical storage

materials; (160.5470) Polymers; (160.5335) Photosensitive materials.http://dx.doi.org/10.1364/AO.53.001052

1. Introduction

Over the past decades, photopolymer materials[1–11] have been studied for use in applications, suchas holography [12,13], data storage [14,15], solar con-centration [16], and self-trapping [17]. Dyes [18,19]functioning as the initiator in acrylamide/polyvinylalcohol (AA/PVA) based photopolymer materials leadto the production of primary radicals. The rateof radical production is critically important in

determining how many and the lengths of the poly-mer chains formed. The amount of polymer formed isclosely related to the refractive indexmodulation cre-ated inside the material when holographic exposureis applied.

In this paper, a recently developed photosensitizer,2-(4-(N,N-dimethylamino)benzylidene)-1H-indene-1,3(2H)-dione, which will be referred to as D 1 [20],is examined when it is used with AA/PVA photopol-ymer material. D 1 is synthesized following thedetailed instructions given in [20]. Briefly, 1 g∕6.84 mmol 4-N,N-dimethylaminobenzaldehyde and1 g∕6.84 mmol indane-1,3-dione are suspended in

1559-128X/14/061052-11$15.00/0© 2014 Optical Society of America

1052 APPLIED OPTICS / Vol. 53, No. 6 / 20 February 2014

http://dx.doi.org/10.1364/AO.53.001052

20 ml absolute ethanol, and a few drops of piperidineare added. The solution is refluxed for 4 h. After cool-ing, the solution is concentrated to 1∕5 of the initialvolume. Addition of ether precipitates out a red solid,which is filtered off, washed several times withwater, and then dried under vacuum. The advantageof D 1 is that it can be used inmulticomponent photo-initiating systems for either free radical or cationicpolymerization. EB can only be used for one, i.e., freeradical [18]. The synthesis of interpenetrated poly-mer networks (IPNs) of acrylate/epoxy blends canalso be carried out using D 1, as the D 1/iodoniumsalt system can simultaneously initiate free radicalpolymerization acrylates and the ring openingpolymerization of epoxy [20]. A study of the abilityof D 1 to sensitize an AA/PVA matrix is interesting,as it demonstrates and extends the versatility of thisnew dye. The procedure to prepare the dry materiallayer is given in [18].

2. Theoretical Analysis of AA/PVA-BasedPhotopolymer Material

In this paper, a more complete nonlocal photo-polymerization-driven diffusion (NPDD) model isdeveloped. This extended model includes several ef-fects, which are neglected in previously developedversions of the model [18,19]. These effects includethe recovery of the triplet photosensitizer excitedstates and the diffusion of all the photosensitizerstates. Moreover, the model was appropriatelyadapted for D 1, as this compound works in theexcited singlet state not in the triplet state, as isthe case for other sensitizers (e.g., EB).

A. Photochemical Reactions

During free radical photo-polymerization, the ma-terial system undergoes four main processes whenilluminated [21–25]: (1) initiation; (2) propagation;(3) termination; and (4) inhibition. We now highlightthe major chemical reactions taking place associatedwith each of these processes [8–10,22,26,27].

1. InitiationDuring exposure, the ground-state photosensitizer,D, can be converted into the singlet and tripletexcited states, 1D� and 3D�, see Eqs. (1a) and (1b).We note that the ground-state dyes convert intothe singlet excited state by photon absorption, thenthe singlet state will convert into triplet state. In thispaper, we treat these two processes as one combinedprocess. This way we avoid estimating the inter-crossing rate of the dye converting from the singletto the triplet state, and the model is simple andphysical. The singlet excited state photosensitizercan recover to its original state by undergoing radi-ationless electron transfer to another molecule, suchas triethanolamine, which acts as an electron donor(ED), or by the emission of a photon by fluorescence[18,21,28] [see Eq. (1c)]. Similarly, the triplet excitedstate photosensitizer formed from the singlet stateby intersystem crossing can return to the ground

state by either radiationless energy transfer withtriplet oxygen or through collision with a ground-state photosensitizer molecule [29] [see Eq. (1d)].The reaction between the triplet excited photosensi-tizer and ED leads to the production of initiator/primary radicals, R•, Eq. (1e). These can react withthe monomer to produce chain initiators, M•

1 ,Eq. (1g). We note that for the D 1 case, the triplet ex-cited state dye is generated very slowly [20], and theprimary radicals are generated from the reaction be-tween the singlet excited state dye, 1D 1� and ED. Asa result, for D 1 case, Eq. (1e) becomes Eq. (1e′):

D� hυ→kaS1D�; (1a)

D� hυ→kaT3D�; (1b)

1D�→kr1D; (1c)

3D�→kr2D; (1d)

3D� � ED!kd R• �H� �D•− → R• �HD•; (1e)

or

1D 1� � ED→kdR• �HD•; (1e 0)

ED�HD•→kbH2D� EDint; (1f)

R• �M→ki M•

1 : (1g)

In Eq. (1a), hv indicates that energy is absorbed froma photon. The rate constants in Eqs. (1a) and (1b) canbe described as kaS � φSεdI00, kaT � φTεdI00, where,φS and φT are the quantum efficiencies of the reac-tions in which the ground-state photosensitizer isconverted into the singlet and triplet excited photo-sensitizer states, ε is the photosensitizer molar ab-sorptivity, d is the thickness of the material layer,and I00 Einsteins∕cm3 s is the incident intensity[10]. kr1 and kr2 are the recovery rates in going fromthe singlet and triplet excited states to the groundstate, respectively. kd is the rate constant of electrontransfer through which ED becomes a free radical,R•. HD• represents a radicalized photosensitizer,which abstracted a hydrogen ion from the ED. kbis the rate constant of the photobleaching process,i.e., the rate of formation of dihydro dye, H2Dye.EDint is an intermediate form of the ED (the amino-alkyl radical generated by hydrogen transfer). ki isthe chain initiation kinetic constant, and M repre-sents the monomer molecules.

Electron spin resonance spin-trapping (ESR-ST)Measurement: in order to examine Eqs. (1e) and

20 February 2014 / Vol. 53, No. 6 / APPLIED OPTICS 1053

(1e′) for EB and D 1, we introduce and apply theESR-ST measurement technique [30].

Nowadays, the ESR-ST is recognized as beingparticularly powerful for the identification and thequantification of free radicals [30]. For short-livedradicals, (e.g., aminoalkyls), which are almost inac-cessible using classical steady-state ESR, the ESR-ST technique is highly valuable since the persistentadducts because molecules produced by the additionof the reactive radical to a spin trap [30] are easilyobserved.

Basically, in ESR-ST, the spectrometer detects theadducts (“spin adduct”), which are formed by the ad-dition of the reactive radical (e.g., aminoalkyl), to thedouble bond of the spin trap, i.e., ST, see in Eq. (2)and as illustrated in Fig. 1. This adduct (a nitroxide)is now stable enough for in situ ESR detection:

R• � ST → R − ST•: (2)

In the spin adducts (R − ST•), the spin trap islinked to the added radical. The coupling of theoxygen-centered radical, with the nuclear spin of thenitrogen and the hydrogen atoms of the ST, is depen-dent on the size and the nature of R• (Fig. 1) and canbe used as an unambiguous method for the identifi-cation and the quantification of the radicalsgenerated in the initiating system. Phenyl-N-tert-butylnitrone (PBN) is used as the spin trap in thiswork (see Fig. 1).

To produce the results presented here, the ESR-STmeasurements performed were carried out using anX-Band spectrometer (MS 400Magnettech). The rad-icals generated were characterized after the D 1 (orEB)/triethanolamine was irradiated by visible lightjust prior to the ESR-STmeasurements [see Eqs. (1e)and (1e′)]. The radicals were generated at room tem-perature by exposing the dyes in a Triethanolamine/tert-butylbenzene solution using a diode laser,λ � 532 nm, under a nitrogen gas (N2) environment.The primary radical, R•, is trapped by the PBN asdescribed in detail in [31]. The ESR spectra resultwas then interpreted using simulations carried outusing the WINSIM software [32]. We note that inthe previously reported work [20], D 1 was used incombination with iodonium salt and not an amine.

Interestingly, for D 1, the aminoalkyl radicals, R•,generated from the hydrogen abstraction reaction,Eq. (1e′), can be easily observed. The hyperfinecoupling constants value estimated from thesimulations of the spectrum using WINSIM, i.e.,aN � 14.3 Gauss (G) and aH � 2.5 Gauss (G) [where

aN and aH stand for the hyperfine coupling constantsin the PBN radical adducts for the nitrogen and thehydrogen, respectively], as shown in Fig. 2, are ingood agreement with those reported in the literature[33]. In Fig. 2, we see that no signal is detected beforeirradiation (see curve a). The signal is easily ob-served after irradiation (curve b) indicating the gen-eration of the primary radical, i.e., R•, duringexposure. This experiment was also performed forEB/triethanolamine, and the corresponding resultsobtained, i.e., the obtained aN and aH values arethe same as those for D 1 case. The results of theseexperiments indicate that the same initiating radi-cals are generated (Fig. 3) as specified in Eqs. (1e)and (1e′).

We recall that the coupling of the oxygen-centeredradical with the nuclear spin of the nitrogen and the

(a) (b)

Fig. 1. Principle of the ESR-ST experiments. (a) The reactive radical (aminoalkyl) reacts with the spin trap to give (b) the spin adduct.

B (G)3300 3310 3320 3330 3340 3350 3360

aN = 14.3 GaH = 2.5 GD_1

(a)

(b)

Fig. 2. ESR-ST spectrum recorded upon irradiation of aD 1∕triethanolamine solution in tert-butylbenzene (irradiation di-ode laser 532 nm; under N2); (a) before and (b) after irradiation.

(b)

aN = 14.3 GaH = 2.5 GEB

(a)

B (G)3300 3320 3340 3360 3380

Fig. 3. ESR-ST spectrum recorded upon irradiation of an EB/trie-thanolamine solution in tert-butylbenzene (irradiation diode laser532 nm; under N2); (a) before and (b) after irradiation.


hydrogen atoms of the ST is dependent on the sizeand nature of the radical trapped by PBN. Thusthe values of the hyperfine coupling constants, i.e.,aN and aH , depend on the radical generated fromEB or D 1. The results obtained show that the valuesaN and aH extracted for D 1 case are the same asthose estimated for the EB case. Thus the sameradical, i.e., R•, is generated from D 1 and EB,respectively, and Eqs. (1e) and (1e′) are confirmedas being appropriate.

2. PropagationThe chain initiator, M•

1 will attach itself to anothermonomer molecule, M, by addition to the C � Cbond, yielding a growing polymer radical with an ac-tive tip. Through propagation, polymer chain growthtakes place [22]:

M•

n �M!kp M•

n�1: (3)

In this equation, kp is the rate constant of propaga-tion, andM•

n andM•

n�1 are the growing macroradicalchains of length n and (n�1) repeat monomericunits, (n≥1).

3. TerminationTermination can occur by disproportionation andcombination; both involve two growing macroradi-cals interacting to stop growth, i.e., the bimoleculartermination mechanism:

M•

n �M•

m!ktcMn�m; (4a)

M•

n �M•

m→ktdMn �Mm; (4b)

where ktc and ktd are the rate constants of combina-tion and disproportionation termination, respec-tively. Mn, Mm, and Mm�n represent terminatedchains, which no longer have radical tips, i.e., deadpolymer. In this analysis, ktc and ktd will be treatedas a single lumped rate constant, i.e., kt � ktc�ktd �cm3 mol−1 s−1�, since the specificmode of termina-tion does not affect the polymerization kinetics [8].

Another possible termination mechanism involvesprimary radical termination [9,29]:

M•

n �R•!ktpMnR; (4c)

where ktp is the rate constant of primary radical ter-mination. In this step, a growing macroradical chainreacts with a primary radical (initiator radical), lead-ing once again to the production of inactive or deadpolymer chains [8].

4. InhibitionInhibitors are chemicals that react with the initiat-ing and propagating radical species and rapidly re-move or scavenging such radicals. Polymerization

is effectively halted until they are all consumed[27]. Several possible inhibitor reaction mechanismsare listed below:

R• � Z !kz;R•�RZ•; and∕or R� Z•�; (5a)

3D� � Z !kz;Dye�

leuco − dye� Z�; (5b)

M•

n � Z !kz;M•

�MnZ•; and∕or Mn � Z•�; (5c)

where Z is the inhibitor species, e.g., oxygen, with Z•

being the concentration of singlet oxygen [10,23,27],and kz;R• , kz;Dye� , and kz;M• are the rate constants ofinhibition of the primary radicals, the photosensi-tizer and the macroradicals, respectively[21,23,34–36]. Inhibition typically leads to a deadband at the start of exposure, i.e., stopping gratingformation during the initial exposure. The effectsof inhibitors are especially significant when lowerexposure energies are used; for example, when largeareas must be exposed (low intensities) or shortduration (pulsed) exposures are used [10].

B. Inclusion in the NPDD Model

Based on the analysis present above, a set of coupleddifferential equations representing the spatial andtemporal evolutions of the material concentrationsassociated with Eqs. (1) and (3)–(5) can be derivedusing the same notation and following the samemethodology as in [8,9,27]. Noting that for D 1 case,Eqs. (7)–(11) become Eqs. (7′)–(11′).

d�D�x; t��dt

� ddx

�DD�x; t�

d�D�x; t��dx

�� kr1�1D��x; t��

� kr2�3D��x; t�� − kaS�D�x; t�� − kaT �D�x; t��;(6)

d�1D��x; t��dt

� −

ddx

�D1D� �x; t�d�

1D��x; t��dx

�

� kaS�D�x; t�� − kr1�1D��x; t��; (7)

d�3D��x; t��dt

� −

ddx

�D3D� �x; t�d�

3D��x; t��dx

�

� kaT �D�x; t�� − kr2�3D��x; t��− kd�3D��x; t��ED�x; t��− kz;Dye� �3D��x; t��Z�x; t��; (8)

d�ED�x; t��dt

� −kd�3D��x; t��ED�x; t��

− kb�ED�x; t��HD•�x; t��; (9)


d�R•�x; t��dt

� kd�3D��x; t��ED�x; t�� − ki�R•�x; t��u�x; t��− ktp�M•�x; t��R•�x; t��− kz;R• �R•�x; t��Z�x; t��; (10)

d�HD•�x; t��dt

� kd�3D��x; t��ED�x; t��

− kb�ED�x; t��HD•�x; t��: (11)

Or for D 1:

d�1D 1��x; t��dt

� −

ddx

�D1D� �x; t�d�

1D 1��x; t��dx

�

� kaS�D 1�x; t�� − kr1�1D 1��x; t��− kd�1D 1��x; t��ED�x; t��; (70)

d�3D 1��x; t��dt

� −

ddx

�D3D� �x; t�d�

3D 1��x; t��dx

�

� kaT �D 1�x; t�� − kr2�3D 1��x; t��− kz;Dye� �3D 1��x; t��Z�x; t��; (80)

d�ED�x; t��dt

� −kd�1D 1��x; t��ED�x; t��

− kb�ED�x; t��HD•�x; t��; (90)

d�R•�x;t��dt

�kd�1D 1��x;t��ED�x;t��−ki�R•�x;t��u�x;t��−ktp�M•�x;t��R•�x;t��−kz;R• �R•�x;t��Z�x;t��; (100)

d�HD•�x; t��dt

� kd�1D 1��x; t��ED�x; t��

− kb�ED�x; t��HD•�x; t��; (110)

and

d�u�x; t��dt

� ddx

�Dm�x; t�

d�u�x; t��dx

�− ki�R•�x; t��u�x; t��

−

Z∞

−∞kp�M•�x0; t��u�x0; t��G�x; x0�dx0: (12)

d�N�x; t��dt

�Z

∞

−∞kp�M•�x0; t��u�x0; t��G�x; x0�dx0

−

ddx

�DN�x; t�

d�N�x; t��dx

�; (13)

d�M•�x; t��dt

� ki�R•�x; t��u�x; t�� − kt�M•�x; t��2

− ktp�M•�x; t��R•�x; t��− kZ;M• �M•�x; t��Z�x; t��; (14)

d�Z�x; t��dt

� ddx

�DZ

d�Z�x:t��dx

�− kZ;Dye� �3D��x; t��Z�x; t��

− kZ;R• �R•�x; t��Z�x; t��− kZ;M• �M•�x; t��Z�x; t��: (15)

In these equations [u�x; t�], [N�x; t�], and [M•�x; t�]are the concentrations of free-monomer, polymer,and macroradical. DD�x; t�, D1D� �x; t�, D3D� �x; t�,Dm�x; t�, DN�x; t�, and DZ are the diffusion rates ofground-state photosensitizer, singlet excited statephotosensitizer, and triplet excited photosensitizer,monomer, polymer, and inhibitor, respectively. Thediffusion constant of oxygen in the dry material layeris assumed to be time and space independent. Thisassumption is reasonable, as the small oxygen mol-ecule will diffuse rapidly (compared to the othermaterial components), and we do not expect this fastrate of diffusion to be significantly affected by anysmall changes in material viscosity due to polymeri-zation.

In Eqs. (12) and (13), G�x; x0� is the nonlocalmaterial spatial response function given by [27]

G�x; x0� � 1��2πσ

p exp�−�x − x0�2

2σ

�; (16)

where σ is the constant nonlocal response parameter[22,37]. The nonlocal spatial response function repre-sents the effect of initiation at location x0 on theamount of monomer polymerized at location x [37].

Given cosinusoidal illumination of period Λ, theconcentrations of each associated chemical speciescan be presented as Fourier series:

�X�x; t�� Xmi�0

Xi�t� cos�iKx�; (17)

where [X] represents the species concentrations pre-sented in Eqs. (1) and (3)–(5),K � 2π∕Λ, and i�0 ≤ i ≤m� indicates the harmonics retained in the Fourierseries expansions. A set of first-order coupled differ-ential equations can then be derived by gathering thecoefficients of the various cosinusoidal spatial contri-butions and then writing the equations in terms ofthese time-varying spatial harmonic amplitudes.In order to numerically solve these rateequations, the following initial conditions, (at timet � 0), apply: �D�x; 0�� A0� � 1.22 × 10−6 mol∕cm3,�1D��x; 0�� 0, �3D��x;0�� 0, �ED�x; 0�� ED0� �3.18 × 10−3 mol∕cm3, �R•�x;0�� 0, �HD•�x;0�� 0,�u�x; 0�� u0� � 2.83 × 10−3 mol∕cm3, �N�x;0�� 0,�M•�x;0�� 0, and �Z0�x; 0�� 0.


3. Behaviors of the Two Photosensitizers in AA/PVA

Chemical representations of the two photosensitizersused in this study are given in Fig. 4. Due to the dif-ferent chemical structures of the photosensitizers,different solvents are chosen, i.e., deionized waterfor EB and acetonitrile for D 1.

A. Transmission Spectrum

Figure 5 shows the transmittance spectrum of EBand D 1 for visible wavelengths.

In both cases, the normalized transmittance T�t�[18] can be expressed as

T�t� � Tsf exp�−ε�A�t��d�; (18)

where Tsf is the transmission fraction, which allowsfor the boundary and scatter losses, ε is the molar ab-sorption of the photosensitizer, [A�t�] is the timevarying dye concentration, and d is the thicknessof the material layer. Taking t � 0, Eq. (18) reducesto

T0 � Tsf exp�−ε�A0�d�; (19)

where T0 is the transmittance value for one particu-lar wavelength, λ. The full absorptivity curves toT0�λ� are presented in Fig. 5, for an initial photosen-sitizer concentration �A0� � 1.22 × 10−6 mol∕cm3,

and the layer thicknesses d given in Table 1. Wedefine Tsf to be the maximum transmittance value.Using this maximum value, the molar absorption, ε,can be estimated, when λ � 532 nm, i.e., the expos-ing wavelength used in all the experiments reportedhere.

We also note that in both cases the transmittancevalue at a wavelength of 633 nm is greater than 97%,i.e., 99.98% and 97.89% for EB and D 1, respectively.This means that 633 nm laser light can be safelyused as the low-intensity monitoring probe beamduring holographic recording, as it will have little ef-fect on grating formation. The resulting parametervalues, i.e., ε, estimated using Eq. (19) and Fig. 5,are listed in Table 1. The values of the transmittanceand Tsf in Table 1 are read off directly from Fig. 5.The thickness of the material layer is measuredpostexposure mechanically using a micrometerscrew gauge.

B. Transmission

In this subsection, we begin by examining the trans-mission process [18] of the material. First, we need toexamine the effects of the two photosensitizers in thestandard AA/PVA material. We do this by measuringthe resulting transmission curves. In all cases, thesetups involve illumination by a uniform plane waveof intensity 10 mW∕cm2 at a wavelength of 532 nm,passing normally through the material layer andmeasurement of the resulting transmitted intensity.The area of illumination is 0.25 cm2. The spatial fil-ter composes a microscope objective EFL 8.00 andpinhole ∼2.5 μm. The lens placed in front of the spa-tial filter is of focal length 8 cm and diameter 4 cm.The experiment setup is shown in Fig. 6. Normalized

D_1 EB

(a) (b)

Fig. 4. Structures of the two photosensitizers studied in thispaper: (a) EB (879.87 g∕mol) and (b) D 1, (277.00 g∕mol) [18,20].

Transmittance T0(λ)

(b) D_1

(a) EB

1.0

0.8

0.6

0.4

0.2

0 400 500 600 700 800

Wavelength (nm)

Exposure532 nm

Probe633 nm

Fig. 5. Transmittance spectrum for (a) EB (red-dotted curve) and(b) D 1 (green solid curve) in AA/PVA photopolymer material. Theconcentration of photosensitizer used in both cases is 1.22 ×10−6 mol∕cm3 in a dry material layer containing triethanolamine.

Table 1. Estimated Photosensitive Parametersa

Type ofPhotosensitizer

Transmittance(%)

Tsf

(%)d

�μm�ε�108�

�cm2∕mol�EB 13.37 100.00 105 1.5707D 1 80.36 100.00 120 0.1494

aEB and D 1 (with a concentration of 1.22 × 10−6 mol∕cm3 forboth in a dry material layer containing triethanolamine),estimated using Eq. (19) from Fig. 5 when λ � 532 nm.

Laser λ = 532 nm

Neutral Density Filter (NDF)

Lens

Plate

Iris Shutter

Spatial Filter

Detector

Laser λ = 532 nm

Neutral Density Filter (NDF)

Lens

P

Iris Shutter

Spatial Filter

Detector

Shutter Controller

Fig. 6. Setup for the transmission experiments.


transmittance curves (verses time) for identical EBand D 1 photosensitizer concentrations are givenin Fig. 7.

We apply the model discussed in Section 2 andEq. (18) to estimate the dye parameter values by fit-ting these curves. All the values along with the initialconditions are mentioned in the text above exceptwhere explicitly noted. To reduce the complexity ofthe model, the diffusion, recovery, and bleaching ofthe photosensitizer and its excited states are ne-glected. We also do not distinguish the two excitedstates dyes, i.e., we assume that the singlet and trip-let state photosensitizer concentrations can betreated as a single lumped parameter. We refer tothe new excited dye state asD�, with a correspondingquantum efficiency of φ. The resulting estimatedparameter values are listed in Table 2. A meansquare error (MSE) value is also shown to quantifythe quality of the fitting.

These include the values of molar absorptivity, ε,and the quantum efficiency of the reaction by whichthe ground-state dye is converted into the excited,D�, dye states with the quantum efficiencies, φ. Wenote that φ is the quantum yield of the photon-absorption process, which together with ε representthe absorptivity of the dye.

It is worth noting that the values of molar absorp-tivity, ε, independently estimated here agree withthose presented in Section 3.A. We recall that thevalues in Section 3.A were found directly by measur-ing the spectrum, while in this section ε is estimated

numerically by fitting the normalized transmissionexperimental data. This agreement supports thevalidity of the model and procedure used.

Due to the weak absorptivity of D 1 [see Fig. 7(b)],the transmission curve, which when t � 0 has a largevalue T0 � T�t � 0� � 0.75, only increases by about0.01. In this case, the quality of the laser source (i.e.,stability of the output power) and the quality of thematerial layer (i.e., any losses due to scattering) criti-cally affect the accuracy of the results.

In order to obtain greater accuracy, either higherD 1 concentrations or thicker material layers shouldbe used to perform the experiments. However,because of the poor dissolvability of D 1 in acetoni-trile, it was found extremely difficult to increasethe concentration. Furthermore, the fabrication ofthicker material layers with smooth surfaces wasalso found to be difficult, and therefore to date no im-provement in the quality of these results has beenpossible.

4. Refractive Index Modulation

A. Volume Fraction Analysis and Refractive Index

Under holographic exposure, the spatially distrib-uted irradiance is assumed to be cosinusoidal. Thusthe incident intensity is represented as

I�x; t� � I00�1� V cos�Kx��; (20)

where V is the fringe visibility and K � 2π∕Λ, whereΛ is the grating period. I00 has the unit ofEinstein∕cm3 s. We note that the incident intensityI0 �mW∕cm2� must be converted into appropriateunits, i.e., Einstein∕cm3 s [10].

During holographic exposure [19], a weak redprobe beam is used to monitor the grating growth.To do this, the grating is replayed on-Bragg at awavelength of λp � 633 nm, to which the materialis insensitive (see Section 3). The temporal evolutionof the resulting Fresnel-corrected first-order dif-fracted intensity, Id, and the transmitted intensity,It, of the probe beam are measured. It can be shownthat the diffraction efficiency of an unslanted trans-mission holographic grating is well approximatedusing the diffraction selectivity:

η�t� ≈ Id�t�Id�t� � It�t�

: (21)

The first harmonic grating refractive index modula-tion, n1�t� [5], can then be extracted using Kogelnik’stwo-wave coupled-wave theory [38]:

η�t� � sin2

�πdn1�t�λp cos θin

�; (22)

where θin is the on-Bragg replay angle of the probebeam inside the layer.

The value of n1�t� can be related to the refractiveindices and concentrations of the various component

Fig. 7. Normalized transmission characteristics of (a) EB and in-set (b) D 1 in AA/PVA photopolymer material with the presence ofamine. The concentration of photosensitizer used in both cases is1.22 × 10−6 mol∕cm3. Both the experimental data points (circlesand triangles) and theoretical fits (solid lines) for exposure inten-sities of 10 mW∕cm2 are shown.

Table 2. Values of Dye Absorption-Related Parametersa

Type ofPhotosensitizer

d�μm�

ε�108��cm2∕mol�

φ�10−3��mol∕Einstein�

MSE(10−3)

EB 101 1.724 14.69 9.00D 1 105 0.226 1.71 0.11

aExtracted by fitting the experimental data in Fig. 7 using themodel presented in Section 2 and Eq. (18).


materials in the layers. Starting with the Lorentz–Lorenz relation [39], it can be shown that

n2− 1

n2 � 2� φ�m��t� n

2m − 1

n2m � 2

� φ�p��t� n2p − 1

n2p � 2

� φ�b��t� n2b − 1

n2b � 2

; (23)

where nm, np, and nb are the refractive indices ofmonomer, polymer, and backgroundmaterial, respec-tively [8], and φ�m�, φ�p�, and φ�b� are the correspond-ing volume fraction of these species. Neglecting anyshrinkage and swelling effects during holographicgrating formation, the sum of the volume fractionsof the individual component is assumed conserved[8,10], i.e.,

φ�m��t� � φ�p��t� � φ�b��t� � 1: (24)

In this case, the temporal evolution of the refractiveindex modulation is given by [39]

n1�t� ��n2

dark � 2�26ndark

�φ�m�1 �t�

�n2m − 1

n2m � 2

−

n2b − 1

n2b � 2

�

� φ�p�1 �t�

�n2p − 1

n2p � 2

−

n2b − 1

n2b � 2

��; (25)

where ndark is the refractive index of the photopoly-mer layer before exposure, and φ1

�m��t� and φ1�p��t�

are the time-varying first-harmonic volume fractioncomponents of monomer and polymer, respectively.Equation (25) is used to fit the experimental mea-sured growth curve in the next section.

The initial material parameter values are also re-quired: Φm, Φp, and Φb denote the initial monomer,polymer, and background volume fractions beforeexposure. These are directly found given the initialmaterial layer composition following the descriptiongiven in [8] (see Table 3).

The refractive index of each component in thematerial (nm, nP, and nb) and the mean refractive in-dex of the material before exposure, i.e., ndark, are alllisted in Table 3.

B. Experimental Verifications

In this subsection, experimental measurements aremade to examine the evolution of the index modula-tion, n1�t�, in the material layer during exposure.In performing this study, different maximum expo-sure durations were used for the two dyes, i.e.,

texpEB � 5.5 s and texpD 1 � 198.5 s for EB andD 1, respectively. Figure 8 shows the experimentalsetup used. In all cases, unslanted transmission-typevolume holographic gratings are recorded. The ex-posing fringe visibility is unity, V � 1. Two equal re-cording beams of wavelength, λ � 532 nm, deliveringa total (both beams) exposing intensity of, I0 �20 mW∕cm2. The layer is probed at λp � 633 nm.The spatial frequency of the formed gratingsis 1428 lines∕mm.

The initial conditions in the material layers areidentical to those listed in Section 2. Using the modeldeveloped in Section 2, the resulting experimentallyobtained refractive index modulation growth curvesare numerically fit.We recall that the diffusion, recov-ery, and bleaching of the photosensitizer and itsexcited states are neglected. In order to furthersimplify the fitting procedure, some assumptionsare made, i.e., ki � kp and ktp � 10kt [10,19]. Finally,the monomer diffusion rate is treated as being con-stant, i.e.,Dm, no polymer diffusion is assumed to takeplace, andno inhibitor is present. Theparameters val-ues estimated are presented in Fig. 9 and Table 4.

Examining the values in Table 4, we first note thatthe values of the independently estimated absorp-tion-related parameters, i.e., ε and φ, presentedin Table 4 agree well with those previously presentedin Section 3. The parameter values also agree wellwith those in [19] and [28] (differing by factors ofless than 2, in [28] the value of kd for EB is1.06 × 102 cm3∕mol s). However, we note that themodels used are different (with the model here beingmore physical), and there will also be some variabil-ity due to noise and environmental conditions. As aresult, the estimated parameters values are slightlydifferent. The thickness could be different due to thetemperature and humidity difference and how muchsolution is poured onto the microscope slice whenplaced down the plate. However, the thickness willnot effect the experimental results and can be mea-sured accurately using a micrometer screw gauge.

Table 3. Mean Refractive Indices for all Component Materials at theProbe Beam Wavelength and Initial Volume Fractions of Each

Component before Exposurea

ndark nb nm nP Φb Φm Φp

1.4948 1.4957 1.4719 1.520 0.8277 0.1723 0aI.e., t � 0 [10], Φb �Φm �Φp � 1.

Fig. 8. Setup for holographic exposure experiments.


Inspecting Fig. 9, we see that, in the case of D 1,the maximum saturated first-harmonic refractive in-dex modulation value, nsat, is smaller (half) than thatfound in the EB case. This is mainly due to (1) theweak absorptivity of D 1; (2) the slow constantrate of primary radical production identified; and(3) the larger nonlocal effect in the D 1 case. It isin fact reasonable that nonlocality will play a moresignificant role in materials with photosensitizersthat have weaker absorptivity. In the case of D 1,weaker absorptivity means that fewer D 1moleculesbecome excited and the lower rate, kd, results infewer radicals, R•, being produced. This, in turn,leads to fewer M•

1 molecules being available to ini-tiate polymer chains. As a result, fewer photopoly-mer chains are created, and more monomersmolecules remain available to become attached(polymerized) in the volume surrounding the grow-ing active polymer chains tips during the propaga-tion process. Since the chains have greateropportunities to grow and fewer opportunities to ter-minate, they grow longer. Therefore it is reasonablethat the nonlocal effect becomes stronger for D 1, aslonger chains result in more smearing of the recordedpattern.

5. Conclusion

In this paper, a new photosensitizer, D 1 [20] is stud-ied for use in AA/PVA photopolymer material, andthe resulting performance is examined and charac-terized using the NPDD model. The D 1 resultsare compared with the corresponding results whenthe material is sensitized using erythrosine B

(EB). The original model proposed (for EB-like dyeswhose triplet state interacts with the ED) has beenmodified to describe the behavior of a sensitizer, D 1,with an excited singlet state pathway to initiation.The advantage of D 1 compared with EB is that itcan be used to initiate both the cationic and freeradical processes [20].

In Section 2, the primary photochemical reactions[21–25], i.e., (1) initiation; (2) propagation; (3) termi-nation; and (4) inhibition, which occur during expo-sure in an AA/PVA-based photopolymer material, aredescribed. The NPDD model proposed includes theeffects of the recovery of the triplet state photosensi-tizer and the diffusion of the photosensitizer.

In Section 3, the transmittance spectrum of thematerial containing D 1 and EB are presented inFig. 5. Then, using a simplified dye model, the ab-sorption-related parameters are estimated by fittingthe normalized transmission curve as measured dur-ing exposure. In order to simplify the developedNPDD model, assumptions are made, i.e., the valuesfor diffusion, recovery, and bleaching of the photosen-sitizer and its excited states are set to be zero. Wealso assume that the two excited photosensitizersstate can be treated as being identical. The keyparameters extracted by fitting the experimentaldata using the NPDD model agree well with the val-ues previously estimated from the transmittancespectrum in Fig. 5.

In Section 4, the refractive indices and the initialvolume fractions of the main components of thematerial are presented. The first harmonic of gratingrefractive index modulation, n1�t�, is calculated fromthe experimentally obtained diffraction efficiencydata using Kogelnik’s two-wave coupled-wave theory.The temporal evolution of the grating refractive in-dex modulation is modeled by applying a volumefraction analysis and using the Lorentz–Lorenz rela-tion. The refractive indices and the initial volumefractions of the main components of the materialare given.

Under holographic recording, the measured dif-fraction efficiencies (gratings growth curves) are ex-amined for samples containing the two dyes: D 1 andEB. The refractive index modulation is then ex-tracted from the intensity data obtained (diffractionefficiency curves). Then, fitting the experimental re-sults using the NPDD model, key material parame-ters, i.e., the nonlocal response parameter, σ, theconstant rate of production of the primary radical,R•, kd, are extracted. For the D 1 case, the maximumsaturated first-harmonic refractive index modula-tion value, nsat, is half that found for the correspond-ing EB case. Based on our results, it is shown that

Fig. 9. Refractive index modulation for the material layer con-taining (a) EB and inset (b) D 1, for I0 � 20 mW∕cm2 andλ � 532 nm. In both cases, the experimental data points (circlesand triangles) and theoretical fits (solid lines) for a spatial fre-quency of 1428 lines∕mm are shown.

Table 4. Spatial Frequency Parameter Estimations of EB and D 1 for 1428 Lines∕mm

Photo-sensitizer

d�μm�

ε�108��cm2∕mol�

φ�10−3��mol∕Einstein�

kd�cm3∕mol s�

��σ

p�nm�

Dm�10−10��cm2∕s�

DZ�10−8��cm2∕s�

ki�107��cm3∕mol s�

kt�108��cm3∕mol s�

MSE(10−5)

EB 125 1.890 14.00 70.01 84 5 1 0.40 0.10 3.79D 1 120 0.199 1.60 0.08 169 6.11


D 1 has weak absorptivity and a slow constant rateof primary radical production compared to EB. As aresult, the nonlocal effect plays a more significantrole for D 1 than for EB. We note that the valuesof the independently estimated absorption-relatedparameters, i.e., ε and φ, presented in Section 4 agreewell with those previously presented in Section 3.

In order to more clearly differentiate the dyebehaviors, future work must involve more accuratelycharacterizing the absorptivity of D 1 by either in-creasing the D 1 concentration by finding a bettersolvent (we recall D 1 is not well dissolved in aceto-nitrile) or, alternately, by making thicker materiallayers (containing D 1) having smoother surfaces.Themany simplifying assumptionmade in Sections 3and 4, i.e., the neglecting of the recovery of the tripletstate photosensitizer and the diffusion of the photo-sensitizer, might then be avoided and the neglectedeffects studied in detail.

We acknowledge the financial support of the EUERUSMAS Mundus fund. Y. Q. and J. T. S. acknowl-edge the support of Enterprise Ireland, ScienceFoundation Ireland (SFI), and the Irish ResearchCouncil for Science, Engineering and Technology(IRCSET) under the National Development Plan(NDP). J. P. F. and J. L. thank the Institut Universi-taire de France (IUF) for financial support.

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