1. Introduction

Photonic nanostructured materials with artificially designed spatial orders such as photonic crystals and metamaterials have been paid much attention for their novel optical properties [1,2]. Another class of nanostructured materials involves random arrangements of nanoscale materials (i.e., nanoparticles) embedded in a host material (Maxwell Garnett geometry) and two different materials either finely interspersed with one another (Bruggeman geometry) or layered alternatively (layered composite geometry) [3]. Such nanocomposite materials exhibit the local-field effect that can control and enhance the linear and nonlinear optical properties [4]. However, they are usually photo-insensitive so that no light control of their arrangements is possible.

In 2002 we introduced a novel photopolymerizable nanocomposite material [5] acting as a photo-configurable nanostructured material, the so-called photopolymerizable nanoparticle-polymer composite (NPC) [6], for volume holographic recording. The mechanism of holographic grating formation in an NPC material is shown in Fig. 1. Prior to holographic exposure nanoparticles are uniformly dispersed in host monomer capable of radical photopolymerization as shown in Fig. 1(a).Spatially non-uniform light illumination generates free radicals from photo-initiators to initiate the photopolymerization reaction of free radicals with monomer molecules in the bright regions of the light intensity-interference fringe pattern. Since the chemical potential (more generally, Gibbs free energy) of monomer molecules is lowered in the bright regions due to their transformation to the formed polymer, the diffusion of monomer molecules from the dark to the bright regions takes place during holographic exposure. At the same time photo-insensitive nanoparticles experience the counterdiffusion from the bright to the dark regions since they are not consumed by light and their chemical potential increases in the bright regions [see Fig. 1(b)]. This holographic assembly of nanoparticles [7] as a result of polymerization-driven mutual diffusion process continues until the photopolymerization process completes. When refractive indices of the formed polymer and nanoparticles are different each other, a refractive index grating is created owing to their compositional and density differences between the bright and the dark regions.

 

Fig. 1. Schematic of distributions of constituents (monomer, formed polymer and nanoparticles) in an NPC material (a) before and (b) during holographic exposure.

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So far, holographic recording in NPCs dispersed with inorganic nanoparticles such as TiO$_2$ [5,8], SiO$_2$ [9], ZrO$_2$ [8,10], ZnS [11], zeolites [12] and semiconducor quantum dots [13,14] has been reported. Refractive indices of these inorganic nanoparticles are generally much different from those of organic photopolymer hosts so that a volume holographic grating with large saturated refractive index modulation amplitude ($\Delta n_\textrm {sat}$) and high dimensional stability [15] is generally available. Various volume holographic applications such as holographic data storage [16], 3D head-mounted display [17], holographic optical elements [18] and holographic spatial-spectral filters [19] can be considered with NPC volume gratings. To prepare NPC films in good optical quality, however, one must require that inorganic nanoparticles be uniformly dispersed without substantive aggregation and unwanted chemical reaction with a photopolymer host. To this end some special surface treatment on inorganic nanoparticles is always necessary to realize the uniform and high dispersion without any other chemical reactions before photopolymerization.

One can relax this somewhat severe requirement by using nanostructured polymers that possess highly branched main chains such as dendrimers [20] and hyperbranched polymers (HBPs) [21] acting as another candidate for size controllable organic nanoparticles. Among them HBPs are preferable from a viewpoint of the ease of preparation as well as of the uniform dispersion in monomer without any substantive aggregation and unwanted chemical reaction/geometrical entanglement with host monomer, so that NPC films with good optical quality are easily available. It is also possible to control their refractive indices and to add photonic functionalities (photochromism, optical nonlinearities etc.) by means of their chemical treatment of functional end groups. So far, we developed NPCs incorporated with various types of HBPs in photopolymer systems possessing different photopolymerization processes such as free radical mediated chain-growth, cationic ring-opening and thiol-ene polymerizations [22–24]. For example, we showed that (meth)acrylate monomer-based NPCs incorporated with hyperbranched poly(ethyl methacrylate) (HPEMA) having the refractive index of 1.51 could record a transmission volume holographic grating having $\Delta n_\textrm {sat}$ as large as 8$\times 10^{-3}$ at a wavelength of 532 nm and at a recording intensity of 100 mW/cm$^2$ [22]. Later, we developed a new NPC system incorporated with HBP having the ultrahigh refractive index of 1.82 at a wavelength of 532 nm [25]. This work was primarily motivated by strong demands for developments of highly efficient volume holographic optical elements (VHOEs) for wearable displays for augmented and mixed reality [26–28]. Volume holographic gratings as VHOEs must provide high diffraction efficiencies with wide Bragg apertures (e.g., $\Delta n_\textrm {sat}>2\times 10^{-2}$ and the grating thickness of 10-$\mu$m order or thinner). We showed that $\Delta n_\textrm {sat}$ could reach as large as $2.2\times 10^{-2}$ at a wavelength of 532 nm. It was also found that the out-of-plane fractional thickness change due to polymerization shrinkage in such an NPC system could also be suppressed significantly [25]. However, the recording intensity was rather high (200 mW/cm$^2$). Subsequently, we showed that the use of crosslinking monomer with higher photochemical reactivity and lower viscosity as compared with the previous NPC formulation gave $\Delta n_\textrm {sat}$ as large as $2.3\times 10^{-2}$ at a recording intensity of 75 mW/cm$^2$ [29]. Holographic recording in NPCs dispersed with other organic nanoparticles using carbon allotropes such as carbon nanotubes and nanodiamonds were also reported very recently [30,31].

In this paper we describe volume holographic recording in a new ultrahigh refractive index HBP-dispersed NPC codoped with an electron donor/acceptor photo-initiator system, more efficient than a green-sensitive titanocene photoinitiator system used in all of our previous works mentioned above. It is shown that the NPC dispersed with 23 vol.% HBP in a new acrylate monomer blend having low viscosity gives $\Delta n_\textrm {sat}$ as large as 4.5$\times 10^{-2}$ at a wavelength of 532 nm and at a recording intensity of 5 mW/cm$^2$.

2. Materials and methods

2.1 Materials

The ultrahigh refractive index HBP was synthesized by the polycondensation of a diamine monomer with 2, 4, 6-trichloro-1, 3, 5-triazine in N, N-dimethylacetamide. It was further processed by the end-capping reaction with aniline [Fig. 2(a)]. Details of the synthesis process and the material properties of such an end-capped HBP are described in Ref. [25]. The refractive index was found to be 1.82 at a wavelength of 532 nm, much higher than 1.51 and 1.61 of HPEMA and hyperbranched polystyrene, respectively, that were used in our previous NPC systems [22]. The ultrahigh refractive index can be attributed to incorporation of the triazine and aromatic ring unit structure. Host monomers, 4-hydroxybutyl acrylate (4-HBA, purity > 97.0%) [Figs. 2(b)] and tetrahydrofurfryl acrylate (THF-A, purity > 98.0%) [Figs. 2(c)] were obtained from Tokyo Chemical Industry Co. Ltd. N-vinyl-pyrrolidone (NVP, purity $\ge$ 99.0%) [Figs. 2(d)] was obtained from Sigma-Aldrich. Ethoxylated dipentaerythritol hexaacrylate (A-DPH, purity $\ge$ 99.0%) [Figs. 2(e)] was received from Shin-Nakamura Chem. Co. Ltd. Rose Bengal ester (RB) [Figs. 2(f)] and N-phenyl glycine (NPG, purity > 97.0%) [Figs. 2(g)] were obtained from Tokyo Chemical Industry Co. Ltd. A green-sensitive radical titanocene photoinitiator (Irgacure 784) [Figs. 2(h)] was received from BASF. All of them were used as received without additional purification steps.

 

Fig. 2. Chemical structures of (a) HBP, (b) 4-HBA, (c) THF-A, (d) NVP, (e) A-DPH, (f) RB, (g) NPG and (h) Irgacure 784.

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2.2 Sample preparation for spectral absorption and holographic recording

We added HBP in a power form to a monomer blend consisting of single functional 4-HBA as host monomer with low viscosity and multifunctional A-DPH as crosslinking monomer with high photochemical reactivity. A-DPH possessing ethylene oxide chains also lowers the viscosity of a monomer blend and thus facilitates crosslinking reactions effectively. Refractive indices of 4-HBA and A-DPH were 1.452 and 1.478, respectively, at 589 nm. The concentration ratio, 4-HBA:A-DPH, was 74: 3 in vol.% at the HBP concentration of 23 vol.% when $\Delta n_\textrm {sat}$ was maximized, as shown later. We employed a radical electron-donor/acceptor photoinitiator system consisting of RB as a blue-green sensitive dye and NPG as a coinitiator at their concentrations of 2 and 4 wt.%, respectively, with respect to A-DPH. This photo-initiator system has been widely employed in holographic polymer-dispersed liquid crystals (HPDLCs) [32,33]. It is known that an photo-excited singlet state RB$^*$(S) from the ground singlet state RB(S) under illumination of green light decays by intersystem crossing to an excited triplet state RB$^*$(T) with a high triplet quantum yield ($\sim$ 0.7). Then, it forms the encounter complex with NPG. Such a complex state changes to the exciplex state by longitudinal relaxation and finally dissociates into an ionic radical pair, an anionic RB radical (RB$^{\bullet -}$) as an electron acceptor and a cationic NPG radical (NPG$^{\bullet +}$) as an electron donor. RB$^{\bullet -}$ acts as an inhibition radical and provides the delay in gelation during photopolymerization [11], keeping the viscosity of the NPC prepolymer syrup low and thereby facilitating the mutual diffusion of HBP and monomer molecules during holographic exposure. NPG$^{\bullet +}$ is continuously decomposed into the phenyl-amino-alkyl radical (PhNHCh$_2^{\bullet }$) as well as a proton and a carbon dioxide by decarboxylation [34–36]. This phenyl-amino-alkyl radical acts as an initiation radical for chain-growth polymerization under green light illumination. The mixture of HBP, 4-HBA, A-DPH and RB was put in a vial and mixed by a tube roller mixer at 50$^\circ$ C and at 60 rpm for approximately 72 hours. Then, the addition of NPG to the vial was carried out by three sets of mixing with a planetary centrifugal mixer and leaving to stand for 2 min. each. The resultant uniformly mixed syrup was cast on a glass substrate loaded with a $\sim$5-$\mu$m spacer and was covered with another glass substrate to prepare an NPC film sample. It is referred to as Sample #1.

For comparison we also prepared other two types of the ultrahigh refractive index HBP-dispersed NPCs, Samples #2 and #3, with a different monomer blend from Sample #1. The host monomer blend consisted of two single functional monomers, THF-A and NVP, which was the same formula as the one used in Ref. [29]. These refractive indices were 1.455 and 1.507, respectively, at 589 nm. A-DPH was also added as crosslinking monomer. The concentration ratio, HBP: THF-A: NVP: A-DPH, was 27: 65: 5: 3 in vol.%. Sample #2 incorporated RB and NPG at the same wt.% concentrations (with respect to A-DPH) as those in Sample #1 in order to see a difference in the monomer blend from Sample #1. The mixture of the monomer blend and RB were put in a vial and mixed by a planetary centrifugal mixer for several minutes at a time. Then, NPG was added to the mixture. Sample #3 incorporated Irgacure 784 [37] at the concentration of 3 wt.% with respect to A-DPH in order to see a difference in the photo-initiator system from Samples #1 and #2. The mixed syrup was cast on a glass plate loaded with a $\sim$5 (10)-$\mu$m-thick spacer for Sample #2 (Sample #3) and was finally covered with another glass plate. The thicker spacer was employed for Sample #3 since Sample #3 gave $\Delta n_\textrm {sat}$ substantively smaller than those of Samples #1 and #2 as shown later. All the preparation procedures for Samples #1, #2 and #3 were performed in a room illuminated by a red fluorescent light tube.

2.3 Spectral absorption

Linear absorption measurements at varied HBP concentrations were done before and after uniform curing by an incoherent green LED light source with its peak wavelength of 525 nm by using UV-visible spectrometer (V-630, JASCO).

2.4 Photopolymerization kinetics

We evaluated the photopolymerization kinetics of Samples #1, #2 and #3 by the photocalorimeter measurement to quantify their photo-induced polymerization rates ($R_\textrm {p}$s) and conversions ($\alpha _\textrm {p}$s) in real time. We used a commercially available photocalorimeter (Q200, TA instrument) equipped with a refrigerated cooling system (RCS 90, TA instrument) in order to accurately maintain the isotherm condition at 25$^\circ$ C. Each nanoparticle-monomer syrup of Samples #1, #2 and #3 at the same formulations as those for holographic recording was dripped on an uncovered Tzero aluminum pan (TA instrument). The weight of the baked syrup in the pan was approximately 5 mg. The sample chamber of the photocalorimeter was purged with nitrogen gas prior to light irradiation to avoid oxygen inhibition. Photopolymerization was initiated by a loosely focused light beam from a 200W Hg-Xe lump through a 532 nm bandpass filter and a light-guiding fiber. The light intensity on the baked syrup was varied from 5 to 75 mW/cm$^2$ during the photo-DSC experiment. Since $R_\textrm {p}$ is proportional to the number of reacted monomer units that can be measured from the reaction heat flow as a function of curing time ($t$) in seconds, $R_\textrm {p}$($t$) in s$^{-1}$ for a blend of acrylate monomers is given by [38]

2.5 Viscosity measurement

Viscosity measurement was conducted by a viscometer (HBDV-II+P CP, Brookfield) for Samples #1, #2 and #3 before curing at varied HBP concentrations and at the rotation speed of 100 r.p.m.

2.6 Holographic recording and characterization

We used the same two-beam interference setup as that used in Ref. [42] to write unslanted and plane-wave transmission phase gratings at either 1- or 0.5-$\mu$m spacing by two mutually coherent beams of equal intensities from a diode-pumped frequency-doubled Nd:YVO$_4$ laser operating at a wavelength of 532 nm. A low-intensity He-Ne laser beam operating at a wavelength of 633 nm was employed as a probe beam to monitor the buildup dynamics of the grating since all the photo-initiator systems employed were insensitive in the red. All the beams were s-polarized. We measured the diffraction efficiency ($\eta$) that was defined as the ratio of the 1st-order diffracted signal to the sum of the 0th- and 1st-order signals. Three to five repeated measurements were done under each experimental condition. The grating thickness ($\ell$) and $\Delta n_\textrm {sat}$ were extracted by least-squares curve fits to the Bragg-angle detuning ($\Delta \theta _B$) data of the saturated $\eta$ ($\eta _\textrm {sat}$) with the following analytical formula of $\eta _\textrm {sat}$ as a function of $\Delta \theta _B$ for an unslanted and uniform transmission phase grating by Kogelnik’s coupled-wave theory [43,44]:

3. Results and discussion

3.1 Spectral absorption

Figure 3 shows spectral absorption coefficients ($\alpha$) of Sample #1 at varied HBP concentrations before and after uniform curing by an incoherent green LED light source with its peak wavelength of 525 nm. The concentration of A-DPH was kept 3 vol.%. It can be seen that $\alpha$ has a characteristic absorption peak of RB near 560 nm before curing but it diminishes after curing due to the dissociation of photoexcited RB molecules. Available thicknesses defined as $\alpha ^{-1}$ are approximately 240 and 680 $\mu$m at a holographic recording wavelength of 532 nm and at the 23 vol.% HBP dispersion before and after curing, respectively.They are sufficiently thick enough to uniformly record a phase grating of 10-$\mu$m thickness or thinner along the film thickness direction without substantive absorption loss in our experiment. Sample #2 doped with the RB/NPG photo-initiator system has the same spectral absorption curve as Sample #1. Sample #3 has a typical spectral absorption characteristics of Irgacure 784; $\alpha$ monotonically decreases with increasing wavelength and the available thickness is thicker than 3 mm [25].

 

Fig. 3. Spectral absorption coefficients of Sample #1 dispersed at different HBP concentrations before and after uniform curing by an incoherent green LED light source.

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3.2 Photopolymerization kinetics

Figure 4 shows parametric plots of $R_\textrm {p}$ vs. $\alpha _\textrm {p}$ at a curing intensity of 5 mW/cm$^2$ for Samples #1 and #2 and at a curing intensity of 75 mW/cm$^2$ for Sample #3. These curing intensities are the same as those in holographic recording as shown later. It can be seen that Sample #1 has the maximum final conversion of approximately 0.9 among all three samples. It can also be seen that the decay of $R_\textrm {p}$ to 0 (i.e., the final conversion point) after the peak of $R_\textrm {p}$ (near the gelation point) is gradual for Sample #1 as compared to other samples. In contrast, although the maximum $R_\textrm {p}$ for Sample #3 is the highest among all three samples, the decreasing rate of $R_\textrm {p}$ to the final conversion after the peak is the highest for Sample #3. These behaviors indicate that Sample #1 has the longest delay in the gelation throughout the formation of cross-linking networks during the photopolymerization process. This trend results in the facilitation of the mutual diffusion of HBP nanoparticles and monomer molecules to form a large spatial density modulation of the HBP nanoparticle density during holographic recording. This characteristic results in large $\Delta n_\textrm {sat}$ for Sample #1.

 

Fig. 4. Polymerization rate vs. conversion for Samples #1 (23 vol.% HBP), #2 (27 vol.% HBP) and #3 (27 vol.% HBP).

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3.3 Holographic recording characteristics

Figure 5 shows photographs of a typical plane-wave transmission grating of 1-$\mu$m spacing (approximately 10 mm in diameter) recorded in Sample #1 at 23 vol.% HBP dispersion. It can be seen that the grating is highly transparent (with slight reflection from it due to very large $\Delta n_\textrm {sat}$) [Fig. 5(a)] and produces bright diffracted light [Fig. 5(b)], showing the high performance of a volume holographic grating recorded in Sample #1 as described below.

 

Fig. 5. Photographs of a plane-wave transmission grating recorded in Sample #1. Views (a) from diagonally above and (b) through the sample.

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Figure 6 shows the buildup dynamics of Bragg-matched $\eta$ at a recording intensity of 5 mW/cm$^2$ for Sample #1 of 1-$\mu$m grating spacing at 23 vol.% HBP dispersion and 3 vol.% A-DPH. It can be seen that $\eta$ monotonically increases until $\sim 0.8$ at a probe wavelength of 633 nm. The inset in Fig. 6 shows measured angular selectivity (Bragg-angle detuning) data of $\eta _\textrm {sat}$. Two solid curves correspond to least-squares fits to the Bragg-angle detuning data of $\eta _\textrm {sat}$ with the coupled-wave theory and the rigorous coupled-wave analysis (RCWA) that treats the multiple-beam diffraction process [45]. The Bragg-angle detuning plots indicate that the recorded NPC grating is in the first quadrant phase modulation regime (i.e., no overmodulation [46] takes place). The data fitting with the coupled-wave theory gave the best fit values for $\ell$ and $\Delta n_\textrm {sat}$ to be 5.3 $\mu$m and 4.2$\times 10^{-2}$ at 633 nm, respectively, while the data fitting with RCWA did the best fit values for $\ell$ and $\Delta n_\textrm {sat}$ to be 5.4 $\mu$m and 4.2$\times 10^{-2}$ at 633 nm, respectively. We found excellent curve fits with both the coupled-wave theory and RCWA that gave very close values for $\ell$ and $\Delta n_\textrm {sat}$. It indicates that the recorded NPC grating is uniformly formed along the thickness direction and that the diffraction from the $\sim$5-$\mu$m thick phase grating of 1-$\mu$m spacing can be considered nearly in the Bragg diffraction regime. This result would validate our analysis in evaluating $\ell$ and $\Delta n_\textrm {sat}$ by means of the simpler and analytical coupled-wave theory despite the fact that the NPC grating is rather thin and has very large $\Delta n_\textrm {sat}$.

 

Fig. 6. Buildup dynamics of Bragg-matched $\eta$ for Sample #1 at a recording intensity of 5 mW/cm$^2$ and at a probe wavelength of 633 nm. The inset is measured data ($\circ$) of $\eta _\textrm {sat}$ as a function of Bragg-angle detuning, where solid curves are least-squares fits of the measured data to the Kogelnik’s coupled-wave theory and RCWA.

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In order to discuss the above result in terms of three diffraction regimes, let us consider the Klein-Cook parameter ($Q$) and the grating strength parameter ($\nu$) [47,48]. They are given by $Q=2\pi \lambda \ell /n\Lambda ^2$ and $\nu =\pi \ell \Delta n_\textrm {sat}/\lambda \cos \theta _\textrm {B}$, respectively, where $n$ is the average refractive index of a phase grating. When the conditions of $Q\nu /\cos \theta _\textrm {B}>\sim 1$ and $Q/\nu \cos \theta _\textrm {B}>\sim 20$ are met, diffraction occurs in the Bragg diffraction regime [49]. In contrast, when the conditions of $Q\nu /\cos \theta _\textrm {B}<\sim 1$ and $Q/\nu \cos \theta _\textrm {B}<\sim 20$ are met, diffraction is in the Raman-Nath diffraction regime [50], which features many overlapping diffraction orders in a thin grating, almost independently of the angle of incidence. Otherwise, diffraction is in the intermediate diffraction regime that must be described by the RCWA treatment. In our case, Sample #1 of 1-$\mu$m grating spacing shown in Fig. 4 has $Q\nu /\cos \theta _\textrm {B}$ and $Q/\nu \cos \theta _\textrm {B}$ of 16.1 and 12.2, respectively, with $\ell$ = 5.4 $\mu$m, $\Delta n_\textrm {sat}$ = 4.2$\times 10^{-2}$, $n$=1.563 (23 vol.% HBP) and $\cos \theta _\textrm {B}$=0.98 at $\lambda =$ 633 nm. This means that light diffraction by Sample #1 is strictly in the RCWA diffraction regime but is near the boundary between the RCWA and Bragg diffraction regimes as we found from the fitting result in Fig. 4.

Figure 7 shows the buildup dynamics of the refractive index modulation amplitude ($\Delta n$) evaluated at a wavelength of 532 nm for Sample #1 as shown in Fig. 6, together with those for Samples #2 and #3 of 1-$\mu$m grating spacing for comparison. Holographic recording was made at recording intensities of 5 mW/cm$^2$ for Sample #2 and 75 mW/cm$^2$ for Sample #3, owing to a difference between the two photo-initiator systems. The recording intensities and doping concentrations of A-DPH for all samples are the optimum ones maximizing $\Delta n_\textrm {sat}$. The buildup dynamics of $\Delta n$ for each sample at a wavelength of 532 nm were plotted. The reason for the evaluation at 532 nm is that one may usually evaluate the performance of light diffraction at the same wavelength as the recording one in a more generic case of non-plane wave recording where readout has to be done at the same Bragg-matched wavelength. To plot a curve in Fig. 7 for each sample, we first calculated time-dependent $\Delta n$ at 633 nm from the measured dynamics of $\eta$ at 633 nm with the extracted $\ell$ as done in the inset of Fig. 6 and with Eq. (3) at $\Delta \theta _B$=0. Then, the buildup dynamics of $\Delta n$ at 532 nm were found by multiplying time-dependent $\Delta n$ at 633 nm by a factor being the ratio of $\Delta n_\textrm {sat}$ measured at 532 nm to that measured at 633 nm. It can be seen that Sample #1 possesses the largest value for $\Delta n_\textrm {sat}$, 4.5$\times 10^{-2}$, at 532 nm. This value corresponds to $\eta _\textrm {sat}$ near 100% just before overmodulation. It is approximately a 1.3-fold (1.9-fold) increase as compared with that of Sample #2 (#3) and a 15-fold reduction in the recording intensity as compared with that of Sample #3. It is now clear that while an increase in $\Delta n_\textrm {sat}$ with Sample #1 is gained partly by use of the monomer blend with lower viscosity and partly by use of the radical electron-donor/acceptor photo-initiator system in comparison with Samples #2 and #3, respectively.

 

Fig. 7. Buildup dynamics of $\Delta n$ at a wavelength of 532 nm for Samples #1, #2 and #3 at recording intensities of 5, 5 and 75 mW/cm$^2$, respectively.

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Such drastic improvements in $\Delta n_\textrm {sat}$ with Sample #1 essentially result from differences in simultaneous radical/inhibitor generation and mutual diffusion of HBP and monomer during holographic recording. A drastic reduction in recording intensity stems from the fact that the use of highly efficient co-generation of RB$^{\mathbf{\bullet}-}$ and NPG$^{\mathbf{\bullet}+}$ provides the delay in gelation due to the action of inhibition by RB$^{\mathbf{\bullet}-}$ during photopolymerization, facilitating the mutual diffusion of HBPs and monomer. This effect would lead to an increase in the density modulation of transporting HBP by holographic assembly of nanoparticles during holographic exposure. We can express $\Delta n_\textrm {sat}$ of a holographic phase grating (the first-order periodic spatial modulation formed in an NPC material) by [5,6]

Figure 8 shows HBP-concentration dependence of $\Delta n_\textrm {sat}$ at different recording intensities for Sample #1 of 1-$\mu$m grating spacing. The concentration of A-DPH was fixed at 3 vol.%, which gave the maximum value for $\Delta n_\textrm {sat}$ as shown in Fig. 9. It can be seen that $\Delta n_\textrm {sat}$ of the order of 4$\times 10^{-2}$ are obtained at the HBP concentrations in the range of 20-23 vol.% and at 5 mW/cm$^2$. An increase in $\Delta n_\textrm {sat}$ with increasing the HBP concentration can be explained by an increase in $a\Delta f$ [see Eq. (4)]. We also find that a noticeabledecrease in $\Delta n_\textrm {sat}$ at HBP concentrations higher than 23 vol.% occurs due to a rapid increase in the viscosity of the prepolymer syrup (700 cP at 25 vol.% HBP and at 297 K) and to unwanted nonuniformity of the NPC mixture in sample preparation, resulting in a decrease in $a\Delta f$ due to increased light scattering.

 

Fig. 8. Dependence of $\Delta n_\textrm {sat}$ at 532 nm on HBP concentration at different recording intensities for Sample #1. The concentration of A-DPH was fixed at 3 vol.%.

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Fig. 9. A-DPH-concentration dependence of $\Delta n_\textrm {sat}$ at different recording intensities for Sample #1. The concentration of HBP was fixed at 20 vol.%.

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Figure 9 shows A-DPH-concentration dependence of $\Delta n_\textrm {sat}$ at different recording intensities for Sample #1 of 1-$\mu$m grating spacing. The concentration of HBP was fixed at 20 vol.%. It can be seen that $\Delta n_\textrm {sat}$ is peaked at the A-DPH concentration of 3 vol.%, more or less independently of recording intensity. This trend was insensitive to HBP concentrations in the range of 20-23 vol.% HBP. The existence of the optimum A-DPH concentration may be related to the interplay between polymerization and mutual diffusion rates.

Figure 10 shows a dependence of recording intensity on $\Delta n_\textrm {sat}$ for Sample #1 of 0.5-$\mu$m grating spacing at 20 vol.% HBP and 3 vol.% A-DPH. It can be seen that measured values for $\Delta n_\textrm {sat}$ at 0.5-$\mu$m grating spacing are lower than those at 1-$\mu$m grating spacing, more or less independently of recording intensity. Such a trend in grating-spacing dependence of $\Delta n_\textrm {sat}$ was reported in multi-component photopolymer including NPCs and HPDLCs [10,52–56].It is attributed to the grating formation process associated with mutual diffusion and phase separation of reactive monomers and unreacted secondary species (HBP nanoparticles in our case): When unreacted secondary species migrate to the dark fringe region of the light intensity-interference fringe pattern of submicron-order shorter grating spacing during holographic exposure, the contrast of the spatial density modulation of transporting secondary species is lowered since clusters of secondary species and growing polymer chains may extend over an adjacent light intensity-interference fringe region [56,57]. Moreover, the diffusion of photo-initiating molecules from the bright to the dark regions tends to causes polymerization in the dark region, inhibiting the mutual diffusion of secondary species [55].

 

Fig. 10. Dependence of $\Delta n_\textrm {sat}$ on recording intensity for Sample #1 at grating spacing of 0.5 $\mu$m. The concentration of HBP was fixed at 20 vol.%.

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3.4 Holographic grating formation in a thick NPC film

So far, we have shown that our NPC volume gratings (Sample #1) provide high diffraction efficiency with a very large $\Delta n_\textrm {sat}$ and a large Bragg aperture due to the 5-$\mu$m order thickness, useful for its use in VHOEs, particularly its use in wearable headsets for augmented and mixed reality. What happens when the thickness of such a very high contract NPC volume grating becomes of the order of a few tens of $\mu$m or thicker ? An interesting phenomenon of overmodulation associated with holographic scattering observed in our very high contrast NPC gratings is described below.

Holographic recording in a thick photo-sensitive material with a large light-induced refractive index modulation exhibits overmodulation [58] when the phase modulation exceeds $\pi /2$ during recording. Characteristic holographic scattering due to the formation of noise gratings onset of recording may also take place in such a material. Holographic scattering was reported in various photonic recording media such as all-organic photopolymers [59,60], HPDLCs [61] and photorefractive crystals [62]. It was also observed in SiO$_2$ nanoparticle-dispersed NPCs [63]. In these media, coherent scattering of an incident laser beam takes place due to randomly distributed scattering centers such as supramolecular assemblies of polymerizing radical monomer complexes of several-tens-of-nanometers size in photopolymer, microscopic polymer domains (liquid crystal droplets) formed during the transient phase-separation process in HPDLCs, intrinsic impurities and inhomogeneities in photorefractive crystals, and supramolecular assemblies and aggregated nanoparticles, if any, in NPCs. Randomly scattered waves interfere with the incident radiation, leading to the formation of parasitic noise gratings in these media. A common consequence from noise gratings is the appearance of scattering rings on a screen placed after the transmission of a beam [59,63]. Also, the varied grating modulation along the grating thickness direction would also be induced by the contrast degradation of the intensity-interference fringe pattern due to the formation of noise gratings.

Figure 11 shows an example of Bragg-angle detuning data of $\eta _{sat}$ for Sample #1 (20 vol.% HBP) loaded with a thick spacer ($\sim$ 20 $\mu$m) at grating spacing of 1 $\mu$m. It can be seen that minima of side lobes do not exhibit well-defined null points but apodized sidelobe variations, indicating that the recorded NPC volume grating is nonuniform along the thickness direction due to holographic scattering. Moreover, the slight asymmetry in the Bragg-detuning curve is seen. This asymmetry may be attributed to the bending distortion of the recorded NPC volume grating due to polymerization shrinkage along the transversal direction in a thick photopolymer film [64]. The solid curve in red corresponds to the least-squares fit of the Uchida’s coupled-wave theory [65] to the data. This theory provides an analytical expression of the diffraction efficiency for an exponentially decaying plane-wave volume grating with $\Delta n_{sat}(z)$ given by $\Delta n_0\exp {(-\alpha _gz)}$ along the thickness direction $z$, where $n_0$ is $\Delta n_{sat}$ without the spatial grating decay and $\alpha _g$ is a decay constant of the exponentially decaying grating. We define the effective grating thickness ($\ell _\textrm {eff}$) as given by $[1-\exp {(-\alpha _g\ell )}]/\alpha _g$. It was found that $\Delta n_0=4.0\times 10^{-2}$, $\ell = 21.7$ $\mu$m and $\alpha _g$ = 0.0731 $\mu$m ($\ell _\textrm {eff}$ = 10.9 $\mu$m). Therefore, the recorded NPC volume grating is overmodulated since the effective phase modulation $\phi$ ($\equiv \pi \Delta n_0\ell _\textrm {eff}/\lambda \cos \theta _B]$) is 2.16 radian and is in the second quadrant region ($\pi /2<\phi \le \pi$) as a result of very large $\Delta n_{sat}$ of our NPC volume grating. We note that grating apodization due to linear absorption of the recording beams [66] can be ruled out here since available thickness at a recording wavelength of 532 nm (240 $\mu$m before exposure) is much longer than $\ell$ as seen in Fig. 3. The solid curve in green is the least-squares fit of RCWA calculation using the exponential form of $\Delta n_{sat}(z)$ given above to the data. The best values for the fitting parameters were found to be the same as those of the Uchida’s coupled-wave theory as seen in Fig. 11 where the fitted curve in green was nearly the same as that in red. The solid curve in black is the least-squares fit of RCWA calculation using the stretched exponential form of $\Delta n_{sat}(z)$ given by $\Delta n_0\exp {(-\alpha _gz^\beta )}$ to the data, where $\beta (>0)$ is a stretching exponent. Such a phenomenological expression is usually used in a description of relaxation processes in disordered systems [67–69]. It was found that $\Delta n_0 = 4.1\times 10^{-2}$, $\ell = 22.0$ $\mu$m, $\alpha _g$ = 0.0667 $\mu$m ($\ell _\textrm {eff}$ = 11.5 $\mu$m) and $\beta$ = 1.05, similar to those of the Uchida’s coupled-wave theory and the RCWA calculation using the exponential form of $\Delta n_{sat}(z)$. Fair agreement with the data within the first sidelobe variations indicates that the grating decay is not exactly exponential owing to random holographic scattering. Fair agreement with the data within the first sidelobe variations indicates that the grating decay is not exactly exponential owing to random holographic scattering [70].

 

Fig. 11. Measured Bragg-angle detuning data ($\circ$) of $\eta _{sat}$ for Sample #1 of 1 $\mu$m grating spacing at a probe wavelength of 633 nm. Solid curves correspond to least-squares fits of the Uchida’s coupled-wave theory (red), the RCWA calculation with the exponential form (green), the RCWA calculation with the stretched exponential form (black) and the empirical formula (blue) to the measured data.

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In Fig. 11 we also plotted the solid curve in blue by use of the following empirical formula for the Bragg-mismatched diffraction efficiency deduced from Eq. (3) in the main text and the Uchida’s coupled-wave theory:

4. Conclusion

We have demonstrated volume holographic recording in NPCs incorporated with the ultrahigh refractive index HBP in a mixture of the acrylate monomer blend with low viscosity and the electron donor/acceptor photo-initiator system with high photosensitivity. We have found that the NPC transmission volume grating of 1-$\mu$m spacing possesses $\Delta n_\textrm {sat}$ as large as 4.5$\times 10^{-2}$ at 532 nm and at a recording intensity of 5 mW/cm$^2$. Such an increase in $\Delta n_\textrm {sat}$ can be attributed to a large difference between $n_n$ and $n_p$ and to the delay in gelation and high conversion by highly efficient co-generation of RB$^{\mathbf{\bullet}-}$ and NPG$^{\mathbf{\bullet}+}$ associated with appropriately low viscosity of the monomer blend. The later results in efficient mutual diffusion of HBP and monomer molecules under holographic exposure. We have also shown that reducing the grating spacing down to 0.5 $\mu$m still provides $\Delta n_\textrm {sat}$ of the order of 3$\times 10^{-2}$. These results suggest the potential use of our newly developed HBP-dispersed NPC gratings (Sample #1) for photonic applications such as security holograms and VHOEs including wearable headsets for augmented and mixed reality. Our studies on recording of volume reflection gratings with high $\eta _\textrm {sat}$ and volume holographic recording with large $\Delta n_\textrm {sat}$ in the red and the blue are also underway. These results will be reported elsewhere.