Holographic photopolymers have been studied extensively because of their advantages such as the dry processing capability, the flexible film formation in large size, and large refractive index changes at high spatial frequencies. Their versatile applications include 3D displays, headup/headmount displays, passive and active holographic diffractive devices, narrowband optical filters, holographic sensors, and holographic data storage [1–7]. While these applications generally require large saturated refractive index modulation amplitudes ($\mathrm{\Delta }{n}_{\mathrm{sat}}$) to achieve high diffraction efficiencies near 100%, other conditions such as the angular/wavelength selectivities (i.e., the angular aperture/spectral bandwidth of the Bragg diffraction) are also demanded. Since such selectivities are inversely proportional to the thickness of a volume grating, thick volume gratings (say, $>100\mathrm{\mu m}$) are preferable for narrowband optical filters, holographic sensors, and holographic data storage. On the other hand, thin volume gratings ($\sim 10\mathrm{\mu m}$) are preferable for some display and diffractive device applications that require high diffraction efficiencies at wide acceptable angles (i.e., with low angular selectivities).

Here we describe the fabrication of transmission volume holographic gratings of approximately 10 μm thickness with diffraction efficiencies near 100% at a readout wavelength of 532 nm. A straightforward calculation based on Kogelnik’s two-wave coupled-wave theory [8] requires that $\mathrm{\Delta }{n}_{\mathrm{sat}}$ for a 10 μm thick transmission volume grating of 1 μm spacing be at least $2\times {10}^{-2}$ for this purpose in the first quadrant phase modulation region. To realize this requirement, we employ photopolymerizable nanocomposites, the so-called nanoparticle-polymer composite (NPC), in which nanoparticles having a large refractive-index difference from the formed polymer are dispersed in photopolymer [9–12]. So far, we showed that NPC volume gratings dispersed with inorganic nanoparticles gave $\mathrm{\Delta }{n}_{\mathrm{sat}}$ as large as $1\times {10}^{-2}$. In this case, the surface treatment on nanoparticles was inevitable for their uniform dispersion in photopolymer to avoid unwanted aggregation. To relax this severe requirement, we also reported on the use of nanostructured polymers, the so-called hyperbranched polymers (HBPs) [13], acting as size and refractive-index controllable organic nanoparticles; they possess highly branched main chains and behave like well-shaped nanoparticles (i.e., hard nanospheres) [14] that are immersed in monomer. We demonstrated that (meth)acrylate monomer-based NPCs, dispersed with either 34 vol.% hyperbranched poly(ethyl methacrylate) (HPEMA) having a low refractive index of 1.51 or 34 vol.% hyperbranched polystyrene (HPS) having a high refractive index of 1.61, gave $\mathrm{\Delta }{n}_{\mathrm{sat}}$ as large as $7.9\times {10}^{-3}$ and $4.0\times {10}^{-3}$, respectively, at a wavelength of 532 nm [15]. In this Letter, we introduce new HBPs that possess the ultrahigh refractive index of 1.82 as organic nanoparticles in NPCs. We show that a transmission NPC volume grating of approximately 10 μm thickness gives $\mathrm{\Delta }{n}_{\mathrm{sat}}$ as large as $2.2\times {10}^{-2}$ at 532 nm, giving the diffraction efficiency near 100%.

Figure 1 shows our synthesized HBP containing triazine and aromatic ring units, which was prepared by the following synthesis scheme: we first added and dissolved 2, 4, 6-trichloro-1, 3, 5-triazine (Evonik Degussa Japan Co., Ltd.) of 3.69 g in N, N-dimethylacetamide (DMAc, Junsei Chemical Co., Ltd.) of 20.3 g placed in a four-necked flask kept at $-10°\mathrm{C}$. Subsequently, a separately prepared solution of m-phenylenediamine (m-PDA, Sigma-Aldrich) of 2.70 g and DMAc of 13.3 g was added dropwise and stirred for 30 min. Then the heated mixture of dimethylacetamide of 27.0 g and aniline of 0.630 g kept at 85°C was added dropwise to the above mixed solution over 1 h by a feed pump. The resultant mixture was stirred for 1 h to conduct their polycondensation. Subsequently, aniline of 4.95 g was added to this mixture for the end-capping reaction, followed by the dropwise addition and stirring (30 min) of triethylamine of 5.07 g at room temperature to quench hydrochloric acid. The precipitated hydrochloride salt was filtered out, and the remaining reacted mixture was precipitated in a 28% aqueous solution of ammonia of 12.2 g and ion-exchanged water of 387 g. The precipitates collected by filtration were dissolved in THF of 39.3 g and then precipitated again in ion-exchanged water of 306 g. The resultant precipitates collected by filtration were dried at 150°C for 25 h in a vacuum dryer, giving the target high-molecular compound (i.e., HBPs) of 4.08 g. The average size of the synthesized HBP was estimated to be approximately 12 nm by a small angle X-ray scattering method. The heterogeneity index, defined as $M_w/M_n$ (where $M_w$ and $M_n$ are the weight-average molar mass and the number-average molar mass, respectively) [15], which indicates the relative size distribution of polymers, was estimated to be 4.4 by the gel permeation chromatography. The glass transition and decomposition temperatures were found to be 200°C and 430°C, respectively. The refractive index ($n_{\mathrm{HBP}}$) of the HBP was estimated by an Abbe refractometer with which we measured the refractive index of a polymer film uniformly incorporated with the HBPs and extracted $n_{\mathrm{HBP}}$ from it by using the Lorentz–Lorenz formula. It was found to be 1.82 at a wavelength of 532 nm. Such an ultrahigh value as organic materials, much higher than those of HPEMA and HPS [15], can be attributed to the incorporation of triazine and aromatic ring units to the HBP structure shown in Fig. 1.

 

Fig. 1. Molecular structure of the synthesized HBP.

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To achieve high dispersion of the HBPs, we mixed them with tetrahydrofurfuryl acrylate (THF-A, TCI) and N-vinylpyrrolidone (NVP, Junsei Chemical Co., Ltd.) used as plasticizers, as well as single functional monomers. These refractive indices were 1.45 and 1.51, respectively, at 589 nm. We added multifunctional acrylate monomer, dipentaerythritol penta-/hexa-acrylate (DPHA, TOAGOSEI Co., Ltd.), to the mixture of the HBPs, THF-A and NVP to form the high cross-linked structure after curing. The refractive index of DPHA was 1.49 at 589 nm. The relative concentration ratio, THF-A: NVP: DPHA, was 68: 5: 2 in vol.% near the optimum HBP concentration of 25 vol.% maximizing $\mathrm{\Delta }{n}_{\mathrm{sat}}$, as shown later. We also added titanocene (Irgacure 784, Ciba) as a green-sensitive radical photoinitiator at 1 wt.% concentration with respect to the monomer blend of THF-A, NVP, and DPHA. They were put in a vial and mixed by a planetary centrifugal mixer for several minutes at a time. The mixed syrup was cast on a glass plate loaded with a 10 μm thick spacer and was finally covered with another glass plate to prepare NPC film samples. Figure 2 shows spectral absorption coefficients $\alpha$ of an NPC film sample with 22 vol.% HBP dispersion before and after uniform curing by an incoherent LED light source at a wavelength of 532 nm. It can be seen that values for $\alpha$ slightly increase after curing at wavelengths longer than 510 nm due, probably to the reaction of dissociated Irgacure 784 with monomers. However, these values are smaller than $3{\mathrm{cm}}^{-1}$, corresponding to the available film thickness ${\alpha }^{-1}$ thicker than 3 mm, sufficiently thick enough to uniformly record $\sim 10\mathrm{\mu m}$ thick volume gratings along the thickness direction without substantive absorption and scattering loss in our experiment.

 

Fig. 2. Spectral absorption coefficients of an NPC film sample with 22 vol.% HBP dispersion.

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In the holographic recording measurement, we used a two-beam interference setup to write an unslanted and plane-wave transmission volume grating of 1 μm spacing by two mutually coherent beams of equal intensities from a diode-pumped frequency-doubled and s-polarized $\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ laser operating at a wavelength of 532 nm. A low-intensity and s-polarized He-Ne laser beam at a photoinitiator-insensitive wavelength of 633 nm was employed as a readout beam to monitor the buildup dynamics of the grating being recorded. We measured the diffraction efficiency $\eta$, defined as the ratio of the first-order diffracted signal to the sum of the zeroth- and first-order signals. Figure 3 shows photographs of a plane-wave transmission grating ($\sim 10\mathrm{mm}$ in diameter) recorded in an NPC film sample with 25 vol.% HBP dispersion.

 

Fig. 3. Photograph of a recorded plane-wave transmission grating under white light illumination.

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Figure 4 shows the buildup dynamics of $\eta$ for an NPC film sample with 25 vol.% HBP dispersion that gave the maximum $\mathrm{\Delta }{n}_{\mathrm{sat}}$ at a recording intensity $I_0$ of $200\mathrm{mW}/{\mathrm{cm}}^2$ as shown later. It can be seen that the saturated $\eta$ (${\eta }_{\mathrm{sat}}$) is 86.4% for the NPC film sample with the effective grating thickness $\ell$ of merely 11.4 μm.

 

Fig. 4. Buildup dynamics of $\eta$ at a readout wavelength of 633 nm. The inset is ${\eta }_{\mathrm{sat}}$ as a function of $\mathrm{\Delta }{\theta }_B$, where the solid curve corresponds to the least-squares fit of the theoretical formula to the measured data (open circles).

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The value for $\ell$ was estimated by the least-squares fit to the measured data for ${\eta }_{\mathrm{sat}}$ as a function of the external Bragg detuning angle $\mathrm{\Delta }{\theta }_B$ with a theoretical formula using the beta-value method (Uchida’s formalism) for an unslanted transmission grating [16,17], as shown in the inset of Fig. 4.

The buildup dynamics of the refractive index modulation amplitude $\mathrm{\Delta }n$ at a readout wavelength of 633 nm was obtained from measured values for $\eta$ (Fig. 4) given theoretically by ${\sin }^2(\pi \mathrm{\Delta }n\ell /\lambda \cos {\theta }_B)$ [8], where $\lambda$ is a readout wavelength in vacuum, and ${\theta }_B$ is the internal Bragg angle given by $\sqrt{1-{\lambda }^2/4n^2{\mathrm{\Lambda }}^2}$ in which $n$ is the film’s refractive index and $\mathrm{\Lambda }$ is grating spacing. Then the buildup dynamics of $\mathrm{\Delta }n$ at 633 nm was converted to that at a recording wavelength of 532 nm by multiplying the former by a factor being the ratio of $\mathrm{\Delta }{n}_{\mathrm{sat}}(=2.2\times {10}^{-2})$ extracted from ${\eta }_{\mathrm{sat}}$ ($=99.6\%$), measured at 532 nm to $\mathrm{\Delta }{n}_{\mathrm{sat}}$ ($=2.1\times {10}^{-2}$) extracted from that ($=86.4\%$) measured at 633 nm. The result is shown in Fig. 5. For comparison, the buildup dynamics of $\mathrm{\Delta }n$ for (meth)acrylate monomer-based NPC film samples dispersed with 34 vol.% ${\mathrm{SiO}}_2$ inorganic nanoparticles [10], 34 vol.% HPEMA and HPS, [15] is also plotted.

 

Fig. 5. Buildup dynamics of $\mathrm{\Delta }n$ at 532 nm for NPC film samples dispersed with 25 vol.% HBP (red solid curve), 34 vol.% ${\mathrm{SiO}}_2$ inorganic nanoparticles (blue dashed curve), 34 vol.% HPEMA organic nanoparticles (black chain curve), and 34 vol.% HPS organic nanoparticles (black dotted curve) at their optimum recording intensities of 200, 100, 100, and $200\mathrm{mW}/{\mathrm{cm}}^2$, respectively.

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Fig. 6. Dependences of $\mathrm{\Delta }{n}_{\mathrm{sat}}$ at 532 nm on HBP concentration at different values for $I_0$.

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It can be seen that while the NPC film sample with 25 vol.% HBP dispersion gives $\mathrm{\Delta }{n}_{\mathrm{sat}}$ of $2.2\times {10}^{-2}$, NPC film samples dispersed with 34 vol.% ${\mathrm{SiO}}_2$, HPEMA, and HPS nanparticles produce those of $7.7\times {10}^{-3}$, $7.9\times {10}^{-3}$, and $4.0\times {10}^{-3}$, respectively. The observed large difference in $\mathrm{\Delta }{n}_{\mathrm{sat}}$ between the three NPCs can be primarily attributed to a large difference in the refractive index between the formed polymer and nanoparticles: they are approximately 0.30, 0.13, 0.08, and 0.13 for the NPC film samples dispersed with HBP, ${\mathrm{SiO}}_2$, HPEMA, and HPS nanoparticles, respectively. It can also be seen that although $I_0$ of $200\mathrm{mW}/{\mathrm{cm}}^2$ is high, the buildup time constant of $\mathrm{\Delta }n$ for the NPC film sample with the HBP dispersion is longer than those of the other NPCs due, possibly due to the low polymerization rate as a result of the relatively large viscosity of the HBP-dispersed NPC film sample before and during curing.

Figure 6 shows HBP-concentration dependences of $\mathrm{\Delta }{n}_{\mathrm{sat}}$ at various values for $I_0$. It can be seen that the highest $\mathrm{\Delta }{n}_{\mathrm{sat}}$ is obtained at the HBP concentration of 25 vol.% and at $I_0=200\mathrm{mW}/{\mathrm{cm}}^2$. Such strong nanoparticle-concentration dependences can also be found in other NPC systems [9–12,15]. An increase in $\mathrm{\Delta }{n}_{\mathrm{sat}}$ with increasing HBP concentrations up to 25 vol.% is explained by an increase in the concentration modulation of HBPs and the formed polymer. On the other hand, a rapid decrease in $\mathrm{\Delta }{n}_{\mathrm{sat}}$ at HBP concentrations higher than 25 vol.% is primarily caused by an increase in the viscosity of NPC film samples, which prevents HBPs and monomers from their efficient mutual diffusion during holographic exposure [18]. The occurrence of the optimum value for $I_0$ may be explained as follows: $\mathrm{\Delta }{n}_{\mathrm{sat}}$ increases with an increase in $I_0$ since photopolymerization overtakes thermal polymerization [19] so that the mutual diffusion process efficiently facilitates. However, $\mathrm{\Delta }{n}_{\mathrm{sat}}$ generally decreases with a further increase of $I_0$ due to an increase in the polymerization rate that leads to the increased nonlinear response (i.e., the distortion) of a recorded grating [20].

We also evaluated the material recording sensitivity $S$ defined as $(1/I_0\ell )d\sqrt{\eta }/dt{|}_{t=t_{\mathrm{ind}}}$ ($t_{\mathrm{ind}}$ is the induction period). We found that, although $S$ generally increased with increasing HBP concentrations, it was of the order of 100 cm/J, lower than those of other NPCs dispersed with inorganic nanoparticles reported so far. Doping of an appropriate sensitizer system would reduce $I_0$, maximizing $\mathrm{\Delta }{n}_{\text{sat}}$, and increase $S$ by more than one order of magnitude, as demonstrated in other NPCs dispersed with ${\mathrm{SiO}}_2$ and ${\mathrm{ZrO}}_2$ nanoparticles [21,22]. Our effort of such sensitivity improvement is currently under way. We also evaluated the out-of-plane fractional thickness change $\sigma$ due to polymerization shrinkage during recording by means of the holographic method [23]. It was found that $\sigma$ is reduced from 11 to $\sim 1\%$ for NPC film samples without and with 25 vol.% HBP dispersion, respectively.

Finally, we discuss the diffraction properties of our $\sim 10\mathrm{\mu m}$ thick NPC grating. Various situations in diffraction from transmission gratings can be categorized into the following three cases [24]: (1) the Raman-Nath regime (many high-order diffracted waves), (2) the Bragg regime (only transmitted and the first-order diffracted waves), and (3) the rigorous coupled-wave analysis regime [25]. Criteria for these regimes are numerically found as the following conditions [26]: $Q\nu /\cos {\theta }_B\le 1$ and $Q/(2\nu \cos {\theta }_B)\le 10$ for case (1), $Q\nu /\cos {\theta }_B\ge 1$ and $Q/(2\nu \cos {\theta }_B)\ge 10$ for case (2), and otherwise for case (3), where $Q$ is the Klein–Cook parameter given by $2\pi \lambda \ell /n{\mathrm{\Lambda }}^2$, and $\nu$ is the grating strength given by $\pi \ell \mathrm{\Delta }{n}_{\mathrm{sat}}/(\lambda \cos {\theta }_B)$. In our case, $Q=25.2$ and $\nu =1.6$ for the NPC volume grating with 25 vol.% HBPs having $\mathrm{\Lambda }=1\mathrm{\mu m}$, $\cos {\theta }_B=0.97$, $n=1.59$, $\mathrm{\Delta }{n}_{\mathrm{sat}}=2.2\times {10}^{-2}$, and $\ell =12\mathrm{\mu m}$ that give ${\eta }_{\mathrm{sat}}=1$ at $\lambda =532\mathrm{nm}$. It follows that $Q\nu /\cos {\theta }_B=41.6$ and $Q/(2\nu \cos {\theta }_B)=8.1$. While the former is well above the Bragg regime boundary, the latter is close to it. Therefore, our use of the two-wave coupled-wave theory for the extraction of $\mathrm{\Delta }{n}_{\mathrm{sat}}$ is adequate.

In conclusion, we have demonstrated volume holographic recording in an NPC dispersed with ultrahigh-refractive-index HBPs. We have shown that $\mathrm{\Delta }{n}_{\mathrm{sat}}$ can be as large as $2.2\times {10}^{-2}$ in the green at 25 vol.% HBP dispersion. This is the largest among NPC volume gratings recorded in the green and gives ${\eta }_{\mathrm{sat}}$ near 100% with $\sim 10\mathrm{\mu m}$ thickness that provides wide angular apertures. We have also shown that a substantive reduction in $\sigma$ is possible by increasing HBP concentrations.