Abstract

This work demonstrates the grating formation of bulk nanoparticle polymer composites through an improved interference optical system under ultrafast nanoseconds exposure of a silver nanoprisms (NPs) dispersed photo-polymerizable mixture in the case of 532 nm wavelength. The polymerizable mixture is composed of phenathrenequinone (PQ) (photoinitiator) and methyl methacrylate (MMA) (monomer). The mechanism in this bulk nanoparticle polymer composite is analyzed by mixing nonlocal polymerization driven diffusion (NPDD) model and absorption modulation caused by the spatial concentration distribution difference of silver NPs. We find that the attenuation of diffraction efficiency under pulsed exposure is due to the reciprocity law failure. This work presents an analysis of the cause of reciprocity failure and improvement in holographic properties by doping silver NPs. The optimized photopolymer presents diffraction efficiencies as high as 51.4% with 1.8 μs cumulative pulsed exposure. Cumulative gratings strength is also enhanced by 70% while doping silver NPs under 1.5 μs cumulative pulsed exposure.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Photopolymers for holographic application have increased due to their unique properties such as high optical thickness [1], stable holographic recordings [2] and huge storage density [3,4]. Among these materials, the phenathrenequinone (PQ) doped poly (methyl methacrylate) (PMMA) photopolymer materials stand out due to their negligible shrinkage and stable diffractive efficiency (DE) [5–8]. It has been shown that PQ / PMMA photopolymer materials can be used to produce optical devices with low three-dimensional power loss, high stability and high contrast refractive index changes [9]. By doping nanoparticles, the holographic properties of PQ/PMMA polymers can be improved [10–14] As a holographic material with stable performance, its preparation methods and holographic characteristics under continuous wave (CW) exposure have been quite extensively studied [15-16]. The applicability of PQ-PMMA material in holography is already demonstrated. However, there are few studies on characteristics of bulk PQ/PMMA polymer with pulsed exposures [17-18]. In our previous work, the feasibility of recording grating in PQ/PMMA polymers under pulsed exposure has been demonstrated [19]. In the pulsed laser exposure method, the duration of information recording will be reduced from the order of seconds to the microseconds.

Low grating intensity and response time are the main disadvantages for bulk PQ-PMMA polymers. Recently, doping oxide nanoparticle components into PQ-PMMA material were shown to be more feasible than previous conventional methods [10–12]. Besides the oxide component composites, metal NPs have strongly emerged as preferable optical performances due to their localized surface plasmon resonance (LSPR) [13,14,20–22]. A plasmon-induced holographic absorption grating has been proposed to be an effective approach to enhance grating strength by dispersing metal NPs into photopolymers [13, 14]. A dynamic model would have a better interpretation of the influence on silver nanoparticles to polymerizable process during holographic exposure. NPDD model is a valid method in analyzing the photochemical dynamics of nanoparticle polymer composites [23–26]. However, when metal NPs disperse into the bulk sample, the simple diffusion of PQ molecules is broken by mutual diffusion between PQ and silver NPs. As a result, the metal NPs can improve the grating strength of holographic composites in two aspects, the refractive index modulation and the absorption modulation.

In this paper, a new kind of nanoparticles, silver NPs, are doped into PQ/PMMA photopolymer to improve its holographic characteristics. The grating formation dynamics in silver NPs dispersed into PQ-PMMA polymer composites are theoretically studied and experimentally verified. A 3D mutual diffusion process is simulated on the basis of photo-polymerizable diffusion equations with the NPDD model. The reciprocity law failure occurring under pulsed exposure is also analyzed. In the experimental aspect, an improved interference optical system is established where the DE under single pulse and continuous pulse exposure are measured. We also examine the effects of doping different size and concentration of silver NPs into bulk polymers by nanosecond pulsed exposure. Consequently, the simulation results are compared with the experimental results of bulk silver NPs dispersed PQ-PMMA photopolymers. Both single and multiplexed gratings recordings are investigated under microsecond cumulative pulsed exposure.

2. Materials and methods

A doping polymerization method is adopted to prepare PQ / PMMA photopolymers [7]. We use thermal initiator azo-di-iso-butyro-nitrile (AIBN) to promote the formation of PMMA chain matrix. In our fabricating process, PQ (0.1 wt %) and AIBN (0.05 wt %) powders were dissolved in MMA solvent. The mixture was then polymerized at 60 °C for 2-2.5h for the sake of eliminating the nitrogen caused by thermal decomposition in AIBN. The solution was finally initiated at 85 °C for 15 min and then solidified at 60 °C for 72 h. After thermal polymerization process, the samples with diameter of 6 cm and thickness of 1.1mm were fabricated. The thickness 1.1 mm is the physical thickness of sample. By comparing the simulation and the experimental results of angular selectivity as shown in Fig. 1, the optical thickness is approximately 610 μm.

 

Fig. 1 Theoretical and experimental angular selectivity curves

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However, we optimized the preparation while dispersing silver NPs. Compared to the traditional method above, here the mixture needed to be oscillating during high temperature polymerization process at 85 °C to avoid NPs clustering. Due to the preparation of silver NPs substrate is in distilled water, which was not miscible with MMA. We separated silver NPs and distilled water by centrifugation. Acetone was used as an agent to enhance the mixture of silver NPs with the polymer matrix. The maximum dissolution of silver NPs in MMA solutions is 0.0006wt% because of the presence of the distilled water in the substrate of Ag NPs. Different size and concentration of nanoparticle composites are prepared as shown in Table 1 and Fig. 2.

Tables Icon

Table 1. Sample with different silver NPs.

 

Fig. 2 TEM characterizations of three silver NP types

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Figure 3(a) shows the absorption spectra of nanoparticle composites with and without silver NPs. The 532nm wavelength pulsed laser was used for recording gratings in order to avoid strong holographic scattering. To do this, an improved interference optical two-beam coupling system with 30° geometry outside the composite was established to record unslanted transmittance gratings. The recorded beams were symmetrically incident on the surface of bulk composites. A CW laser beam with 532 nm wavelength was then used to reconstruct the recorded grating at the same optical path, as shown in Fig. 3(b).

 

Fig. 3 (a) Absorption spectra of samples. (b) Interference optical coupling system, BS, beam splitter; PBS, polarizing beam splitter.

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3. Theoretical analysis

3.1 Mechanism of mutual diffusion, phase and absorption gratings

During the pulsed exposure the photo-initiated PQ molecules react with PMMA matrix and form photoproduct in the bright region. Due to the concentration gradients and chemical potential differences between dark and bright zones, the unreacted PQ molecules are diffused from dark to bright area. MMA monomers have been polymerized to PMMA with different chain lengths during the preparation. Since the polymerization process from short chains to long chains (PMMA) of MMA monomers is mainly occurred in the fabrication process, PMMA matrix are considered as immobile components during ultrafast pulsed exposure. Meanwhile, the PQ molecules can absorb photons to react with the surrounding PMMA during exposure. PQ molecules are consumed in the bright area of interference, which leads to a concentration difference between bright area and dark area, eventually form the diffusion. In the silver NPs dispersed composite, a mutual diffusion is formed between PQ and silver NPs, the counter-diffusion of silver NPs from bright to dark region is simultaneously conducted due to its higher chemical potential in bright zone [10–12]. At the resonance wavelength of silver NPs, a strong absorption grating can be activated as a result of concentration differences of silver NPs between the bright and the dark zones [13, 14]. Coherent oscillations of surface bound conduction electrons lead to the LSPR of silver NPs, an absorption enhancement induced by LSPR can obviously improve the holographic characteristics of composites. Owing to the mutual diffusion effect, the temporal spatial distribution of silver NPs in the composite will emerge a strong absorption modulation with π phase shift to the refractive index modulation. The DE will also be enhanced by the common influence of absorption modulation and refractive index modulation, as shown in Fig. 4.

 

Fig. 4 Holographic mutual diffusion process (phase and absorption gratings).

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3.2 Mutual diffusion model with nonlocal response

In order to show the photo-induced dynamic process in the silver NPs that is dispersed in the PQ-PMMA composite, a model for multi-component kinetics of diffusion process is required. In the silver NPs doped PQ-PMMA, the diffusion process is composed of excited PQ molecules and no reacted silver NPs. Both of the diffusions contribute to the refractive index modulation. On the basis of the volume conservation law and the neglected shrinkage, the normalized volume fractions condition can be expressed as

MPQ+MAg+Mproduct+Mmatrix=1

According to [5], the 3D mutual diffusion dynamic model can be described as

U(x,z,t)t=(D(U)U+D(U))(2U(x,z,t)x2+2U(x,z,t)z2)
where U is the photo-initiator (PQ molecules) concentration, D(U) is the corresponding diffusion coefficient which depended on PQ’s concentrations. Due to the low absorption coefficient in PQ/PMMA photopolymers [5], the primary molecules diffusion along z axis can be neglected. Therefore, the 3D mutual diffusion dynamic model is simplified. The diffusion coefficient of PQ molecules is only related to the spatial evolution x and the temporal evolution t. The three dimensions include spatial evolution x, temporal evolution t and molecule diffusion coefficient. Meanwhile, dimension x is simplified as a symmetry grating period for simulating the sinusoidal distribution of optical interference. The light absorption caused the consumption of PQ molecules in the bright area of the interference. Therefore, the PQ molecules in the bright and dark areas formed a concentration gradient and eventually prompt the molecules diffusion.

In order to have a better interpretation of the mutual-diffusional processes in the nanoparticle photopolymer composites, a mutual diffusional model with nonlocal response is presented according to [9].

G(x,x')=exp[(xx')22σ]/2πσ
[PQ](x,t)t=RD(2[PQ](x,t)x2R2[Ag](x,t)x2)G(x,x')F0(x',t)[PQ](x',t)dx'
[Ag](x,t)t=RD(2[Ag](x,t)x2R2[PQ](x,t)x2)
[product](x,t)=0tG(x,x')F0(x',t')[PQ](x',t')dx'dt'
where RD is the diffusion coefficient of the system, and R is the mutual diffusion coefficient between PQ and silver NPs. The nonlocal spatial response function G(x,x')with nonlocal response length σ is selected. F0(x',t') depicts the source function.

The refractive index modulation influenced by the distribution of PQ molecules, photoproducts and silver NPs can be expressed as

Δn(t)=CpΔ[product](x,t)+CPQΔ[PQ](x,t)exp(iϕ)+CAgΔ[Ag](x,t)

According to Kogelnik’s theory [27], the mixed grating formation can be represented by the spatial modulation of the dielectric constant and the conductivity. Thus, the coupling constant κ can be expressed as

κ=πn1λ+jα12
where n1 and α1 represents the refractive index modulation and the absorption modulation. Therefore, the diffractive amplitude can be described as
S=jeα0d/cosθejε1νsinc(ν2+ε2),ε=Δθk0dsinθ,ν=πn1dλcosθ+jα1d2cosθ
where α0 is the average absorption constant, ε is the direction of the exposure, optical thickness d, Bragg angle θ, and angular derivation Δθ. The diffraction efficiency of the mixed gratings is depicted by η=SS*.Based on the investigation of NPDD process in Section 3.1, the growth of the diffraction efficiency is determined by the refractive index grating and the absorption grating. The grating refractive index modulation n(t) and the temporal absorption modulation α(t) is derived on the basis of deduction, whereas the variation of the diffraction efficiency can be simulated by using the coupled wave theory [27].

η=exp(2α0dcosθ){sin2[πdn(t)λcosθ]+sh2(α(t)d2cosθ)}

To demonstrate the mutual diffusional dynamics, the Eqs. (4), (5) and (6) were solved by taking into account the initial condition. Figure 5 shows the temporal spatial variation of different components inside the composites. In the bright zone there are obvious PQ molecules consumption and a trend in the growth of photoproduct, as shown in Figs. 5(a) and 5(b). The nonlocal response effect of different components distribution causes an obvious deviation of sine form. PQ molecules diffused from dark into bright zone as a driven source to prompt a counter diffusion of silver NPs. Therefore, it leads to an enhanced diffusion in the remaining PQ molecules and a noticeable increase in silver concentration gradient in dark zones, which is shown in Figs. 5(a), 5(c) and 5(d). The mutual-diffusion of PQ and silver NPs will be sustained and migrated until the gratings reach a steady state [28,29].

 

Fig. 5 Normalized spatial and temporal evolution of components concentrations under accumulated pulse exposure. 3D model for (a) PQ molecules, (b) Photoproducts, (c) silver NPs, and 2D model for (d) silver NPs.

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Meanwhile, the enhancement on holographic performance of materials by doping silver NPs is analyzed. By simulating the refractive index modulation and absorption modulation with and without silver NPs, as shown in Fig. 6, the diffraction enhancement of silver NP mutual diffusion can be neglected due to its low solubility. However, the LSPR effect is occurred during pulsed exposure by doping silver NPs. This effect leads to an enhancement on optical field inside the sample, which eventually makes an increment of absorption coefficient. The reason for the enhancement of diffraction efficiency is mainly because of the generation of absorption grating caused by doping silver NPs, not the contribution to the refractive index grating influenced by counter-diffusion of silver NPs, as shown in Fig. 6.

 

Fig. 6 Temporal evolution of diffraction efficiency with and without doping silver NPs, (a) the contribution of refractive index modulation. (b) the contribution of absorption modulation

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3.3 Reciprocity law failure under pulsed exposure

Reciprocity law failure occurs in nanoparticle polymer composites under ultrafast pulsed exposure [30–32], which eventually leads to a dynamic variation in refractive index modulation. Some reports have confirmed the reciprocity failure in photorefractive polymers under pulsed exposure [33]. However, photochemical mechanisms between photorefractive polymers and photopolymers are different. In the case of PQ/PMMA polymer composites, the photochemical reaction requires a sustained period. If the pulse width and photochemical reaction time do not match, the holographic reciprocity failure occurs [34].

The photochemical reaction process in PQ/PMMA polymers is depicted as follows. A PQ molecule is firstly converted to the singlet 1PQ* by absorbing a photon. Then, part of 1PQ* turns into triplet 3PQ*. The 3PQ*s react with the surrounding PMMA short chains or MMA monomers which leads to the formation of two radicals: macroradical (R) and semi-quinone radical (HPQ). Radicals react with each other, eventually forming the photo-product PQ-PMMA. The change of the refractive index is mainly due to the consumption of PQ and the formation of PQ-PMMA chains. Under pulsed exposure, the pulsed laser can produce higher density photons in interference region in the nanosecond order of magnitude. However, since the shortening of exposure time in the polymer composite, the photon absorption efficiency of PQ molecules will decrease which leads to a decline in 3PQ*s and the PQ molecule concentration modulation. Finally, it causes an attenuation in consumption of PQ molecules and concentration of PQ-PMMA chains in the exposure area [18]. The refractive index modulation is weakened compared to CW exposure. According to Kogelnik theory in Eq. (11) [27], the DE is decreased under pulsed exposure. This behavior is presented in Fig. 7.

 

Fig. 7 Photo-chemical mechanism for pulsed and CW exposures.

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PQP1Q*P3Q*+PMMA/MMAHPQ+RPQ-PMMA
η=sin2(Δnπdλcosθ)

4. Experimental details

To verify the enhancement of holographic properties by doping nanoparticles, we examined silver NPs dispersed samples for holographic gratings with different concentrations and sizes, the DE under single pulse,short time and continuous pulse exposure were measured. Polymers of four different silver NP concentrations and three different silver NP types were prepared with the thickness of 1.1 mm. An improved interference optical system was presented in Fig. 1. The pulse duration is 6 ns and one-shot energy is 20 mJ/cm2. For short time exposure, we set the repetition frequency to 10 Hz and exposed the sample for 300 times. 1 Hz repetition rate and 600 pulses were selected during continuous pulse exposure.

Figures 8 and 9 shows holographic characteristics of different silver NPs concentration dispersed PQ/PMMA polymers. In the experiment, a one-shot pulse with the energy of 20 mJ/cm2 was fluxed through the polymer composite. We examined the trend of diffraction efficiency within 30 minutes in the dark, as shown in Fig. 8.

 

Fig. 8 Dark diffusion enhancement process of diffraction efficiency with one-shot pulse exposure, (a) different silver NP concentrations, (b) different silver NP types.

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Fig. 9 Synchronous measurement of diffraction efficiency with multi pulse exposure, (a), different silver NP types (b) different silver NP concentrations.

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Meanwhile, a synchronous measurement of cumulative diffraction efficiency was implemented. Cumulative exposure flux increased from 1 to 600 with the repetition rate of 10 Hz, as shown in Fig. 9.

From the experimental results, it is indicated that the grating intensity is significantly improved by doping silver NPs. The optimal concentration of silver NPs 0.0006wt% is acquired. We achieved the maximum DE of 51.4% in 1.8 μs cumulative pulse exposure. Meanwhile, Figs. 8 and 9 exhibit the effect of silver NPs with different sizes on the DE. According to the result, particles of different sizes have very little influence on the grating strength. However, larger size nanoparticles lead to more resistance during mutual diffusion, which contribute to smaller concentration gradients between bright zone and dark zone. This may cause an attenuation of DE.

Figure 10 shows the response time with different type of silver NPs dispersed PQ/PMMA composites. The response time can reach microsecond level. There is a curtailment in response time while dispersing silver NPs into PQ/PMMA. An absorbing grating is generated because of the absorption enhancement in Ag/PQ/PMMA photopolymers induced by LSPR effect of silver NPs. Meanwhile, a mutual diffusion effect between silver NPs and PQ molecules happens. Both of these have a promoting effect on response time; i.e. the response time of Ag/PQ/PMMA composites consist of two parts, the formation of refractive index grating and absorption grating. With the response time has decreased by 67%, it brings a 156% improvement in the DE.

 

Fig. 10 The response time in silver NPs dispersed PQ/PMMA composites. (a) different silver NP concentrations, (b) different silver NP types.

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To depict the kinetic of DE influenced by refractive index grating and absorption grating under pulse exposure, the initial concentration of silver NPs are set to be 2 × 10−7 mol/cm3 for type 3A composite, 3 × 10−7 mol/cm3 for type 3B composite and 4 × 10−7 mol/cm3 for type 3C composite. As shown in Fig. 11(a), there is a general agreement between experiments and theoretical simulations as regards the DE under cumulative pulse exposure. A suitable mixed dynamic model of silver NPs dispersed composite is demonstrated. There are two reasons that lead to the small differences between simulation and experimental results. On the one hand, silver NPs may have an impact on the diffusion coefficient RD and mutual diffusion coefficient R. The other hand, as exposure time increases, holographic scattering is enhanced, silver NPs may also induce scattering. Figure 11(a) shows the differences between theory and experiment results. Figure 11(b) depicts the absorption modulation enhancement with different Ag doping concentrations. The absorption modulation of Ag type 3A, 3B and 3C are 2.7 × 10−5, 4.8 × 10−5 and 8.2 × 10−5, respectively. The refractive index modulation of PQ/PMMA polymer is 9 × 10−5. Compared with refractive index modulation, the absorption modulation increases the modulation depth by 91%. The simulations of Fig. 11 is according to Eq. (10). Therefore, the diffraction efficiency is influenced by the refractive index modulation and the absorption modulation. Figure 6 depicts that doping silver NPs has a slight influence on the strength of refractive index grating. Therefore, the diffraction efficiency is proportional to the absorption modulation.

 

Fig. 11 Diffraction efficiency differences. (a) comparisons of theoretical and experimental results under continuous pulsed exposure, (b) comparisons of different Ag doping concentration.

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After comparing theoretical analysis and experimental data, we examined the recording ability of multiplexing gratings in this nanoparticle photopolymer composite. In the recording stage, the sample was rotated at 1° interval. Each angle was exposed for 300 ns with the energy of 5 J/cm2. Five gratings were consecutively recorded by the angle multiplexing technique in 1.5 μs with the same exposure area. An obvious improvement of grating strength is shown in Fig. 12. Cumulative gratings strength was enhanced by 70% while doping silver NPs.

 

Fig. 12 Cumulative gratings strength with and without silver NPs under 1.5 μs pulsed exposure.

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5. Conclusions

A new kind of nanoparticles, silver NPs, are doped into PQ/PMMA photopolymer to improve its holographic characteristics. A mixed NPDD model with mutual diffusion and absorption modulation are proposed and applied to exhibit the grating formation in silver NPs dispersed PQ-PMMA composites. The holographic grating kinetic is then depicted by the equations of refractive index modulation and absorption modulation. The difference of refractive index change between pulse exposure and CW exposure has been analyzed. Reciprocity law failure occurs when the nanoparticle composite is illuminated by ultrafast pulse laser, which causes a decline in diffraction efficiency. A general uniformity between the simulations and the experimental results for the dynamic formation process of holographic gratings in silver NPs dispersed composites is proposed. The optimized photopolymer containing 0.0006 wt% silver NPs presents diffraction efficiencies as high as 51.4% under 1.8 μs cumulative pulsed exposure and cumulative gratings strength M# 1.2 under 1.5 μs cumulative pulsed exposure. It is indicated that doping silver NPs in PQ/PMMA photopolymer is an available method to develop its ultrafast holographic performance.

Funding

National Basic Research Program of China (2013CB328702); the National Natural Science Foundation of China (11374074).

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References

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  1. B. G. Manukhin, S. A. Chivilikhin, I. J. Schelkanova, N. V. Andreeva, D. A. Materikina, and O. V. Andreeva, “Reversible and irreversible alterations of the optical thickness of PQ/PMMA volume recording media samples. Part I: Experiment,” Appl. Opt. 56(26), 7351–7357 (2017).
    [Crossref] [PubMed]
  2. H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
    [Crossref]
  3. Y. W. Yu, C. H. Yang, T. H. Yang, S. H. Lin, and C. C. Sun, “Analysis of a lens-array modulated coaxial holographic data storage system with considering recording dynamics of material,” Opt. Express 25(19), 22947–22958 (2017).
    [Crossref] [PubMed]
  4. P. H. Wang, V. R. Singh, J. M. Wong, K. B. Sung, and Y. Luo, “Non-axial-scanning multifocal confocal microscopy with multiplexed volume holographic gratings,” Opt. Lett. 42(2), 346–349 (2017).
    [Crossref] [PubMed]
  5. H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
    [Crossref] [PubMed]
  6. D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
    [Crossref]
  7. D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
    [Crossref]
  8. S. Liu, M. R. Gleeson, J. Guo, J. T. Sheridan, E. Tolstik, V. Matusevich, and R. Kowarschik, “Modeling the photochemical kinetics induced by holographic exposure in PQ/PMMA photopolymer material,” J. Opt. Soc. Am. B 28(11), 2833–2843 (2011).
    [Crossref]
  9. A. V. Veniaminov and U. V. Mahilny, “Holographic polymer materials with diffusion development: principles, arrangement, investigation, and applications,” Opt. Spectrosc. 115(6), 906–930 (2013).
    [Crossref]
  10. D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
    [Crossref] [PubMed]
  11. Y. Luo, J. M. Russo, R. K. Kostuk, and G. Barbastathis, “Silicon oxide nanoparticles doped PQ-PMMA for volume holographic imaging filters,” Opt. Lett. 35(8), 1269–1271 (2010).
    [Crossref] [PubMed]
  12. H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
    [Crossref]
  13. C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
    [Crossref] [PubMed]
  14. C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
    [Crossref]
  15. D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
    [Crossref]
  16. D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
    [Crossref]
  17. N. V. Ionina, O. V. Andreeva, O. V. Bandyuk, V. N. Mikhailov, and A. A. Paramonov, “Recording volume holograms with nanosecond laser pulses in the Diffen polymeric medium,” J. Opt. Technol. 71(4), 265–266 (2004).
    [Crossref]
  18. X. Sun, F. Chang, and K. Gai, “Optoelectronic fast response properties of PQ/PMMA polymer,” Mater. Today: Proc. 3(2), 632–634 (2016).
    [Crossref]
  19. P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
    [Crossref] [PubMed]
  20. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
    [Crossref]
  21. P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
    [Crossref] [PubMed]
  22. R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
    [Crossref] [PubMed]
  23. K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
    [Crossref] [PubMed]
  24. H. Li, Y. Qi, and J. T. Sheridan, “Three-dimensional extended nonlocal photopolymerization driven diffusion model. Part II. Photopolymerization and model development,” J. Opt. Soc. Am. B 31(11), 2648–2656 (2014).
    [Crossref]
  25. H. Li, Y. Qi, and J. T. Sheridan, “Three-dimensional extended nonlocal photopolymerization driven diffusion model. Part I. Absorption,” J. Opt. Soc. Am. B 31(11), 2638–2647 (2014).
    [Crossref]
  26. E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008).
    [Crossref] [PubMed]
  27. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
    [Crossref]
  28. L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
    [Crossref]
  29. L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
    [Crossref]
  30. J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
    [Crossref]
  31. Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
    [Crossref]
  32. J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
    [Crossref]
  33. P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
    [Crossref] [PubMed]
  34. G. Zhao and P. Mouroulis, “Diffusion Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
    [Crossref]

2018 (2)

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
[Crossref] [PubMed]

2017 (4)

2016 (2)

X. Sun, F. Chang, and K. Gai, “Optoelectronic fast response properties of PQ/PMMA polymer,” Mater. Today: Proc. 3(2), 632–634 (2016).
[Crossref]

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

2014 (5)

2013 (2)

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

A. V. Veniaminov and U. V. Mahilny, “Holographic polymer materials with diffusion development: principles, arrangement, investigation, and applications,” Opt. Spectrosc. 115(6), 906–930 (2013).
[Crossref]

2012 (1)

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

2011 (3)

2010 (3)

2009 (2)

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

2008 (3)

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
[Crossref]

E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008).
[Crossref] [PubMed]

2007 (1)

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

2004 (1)

2003 (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

2002 (1)

Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
[Crossref]

1999 (1)

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

1994 (1)

G. Zhao and P. Mouroulis, “Diffusion Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Andreeva, N. V.

Andreeva, O. V.

Arias, E.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Balan, L.

L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
[Crossref]

Bandyuk, O. V.

Barbastathis, G.

Barbosa-García, O.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Blanche, P. A.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

Cao, L.

C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
[Crossref] [PubMed]

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Chang, F.

Chechik, V.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Chivilikhin, S. A.

Chon, J. W. M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Churin, D.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Ferrio, K. B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Funston, A. M.

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

Gai, K.

X. Sun, F. Chang, and K. Gai, “Optoelectronic fast response properties of PQ/PMMA polymer,” Mater. Today: Proc. 3(2), 632–634 (2016).
[Crossref]

Geng, Y.

K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

Gleeson, M. R.

Goldenberg, L. M.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Gu, M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Guenther, B. D.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Guo, J.

He, Q.

C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
[Crossref] [PubMed]

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Helliwell, P.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Hendrickx, E.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Herlocker, J. A.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Ionina, N. V.

Jiang, J.

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

Jiang, Y.

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

Jin, G.

C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
[Crossref] [PubMed]

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Kashin, O.

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Kieu, K.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

Kippelen, B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Kostuk, R. K.

Kowarschik, R.

Krul, L. P.

Li, C.

C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
[Crossref] [PubMed]

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Li, H.

Li, J.

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Li, L.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Li, X.

Li, Z.

Lin, S. H.

Liu, H.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

Liu, P.

Liu, S.

Liu, Z.

Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
[Crossref]

Lougnot, D. J.

L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
[Crossref]

Luo, S.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

Luo, Y.

Lynn, B.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

Mahilny, U. V.

A. V. Veniaminov and U. V. Mahilny, “Holographic polymer materials with diffusion development: principles, arrangement, investigation, and applications,” Opt. Spectrosc. 115(6), 906–930 (2013).
[Crossref]

Maldonado, J. L.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Manukhin, B. G.

Mao, D.

Materikina, D. A.

Matusevich, A.

Matusevich, V.

Matusevich, Y. I.

Meneses-Nava, M. A.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Mery, S.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Mikhailov, V. N.

Moggio, I.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Mouroulis, P.

G. Zhao and P. Mouroulis, “Diffusion Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

Mulvaney, P.

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

Murray, R. W.

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

Norwood, R. A.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

Olmos-López, M.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Paramonov, A. A.

Peyghambarian, N.

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Psaltis, D.

Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
[Crossref]

Qi, Y.

Ramos-Ortiz, G.

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Russo, J. M.

Sakhno, O. V.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Sardar, R.

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

Schatz, G. C.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Schelkanova, I. J.

Schneider, R.

L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
[Crossref]

Sheridan, J. T.

Singh, V. R.

Smirnova, T. N.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Song, Q.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Steckman, G. J.

Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
[Crossref]

Stumpe, J.

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

Sun, C. C.

Sun, X.

P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
[Crossref] [PubMed]

X. Sun, F. Chang, and K. Gai, “Optoelectronic fast response properties of PQ/PMMA polymer,” Mater. Today: Proc. 3(2), 632–634 (2016).
[Crossref]

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

Sung, K. B.

Tolstik, E.

Veniaminov, A. V.

A. V. Veniaminov and U. V. Mahilny, “Holographic polymer materials with diffusion development: principles, arrangement, investigation, and applications,” Opt. Spectrosc. 115(6), 906–930 (2013).
[Crossref]

Wang, J.

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

Wang, P. H.

Wang, S.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
[Crossref] [PubMed]

Wang, W.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

Wong, J. M.

Yang, C. H.

Yang, T. H.

Yu, D.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

Yu, Y. W.

Zhang, F.

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Zhang, S.

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Zhao, G.

G. Zhao and P. Mouroulis, “Diffusion Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Zhao, Y.

P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

Zhou, K.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

K. Zhou, Y. Geng, H. Liu, S. Wang, D. Mao, and D. Yu, “Improvement of holographic sensing response in substrate-free acrylamide photopolymer,” Appl. Opt. 56(13), 3714–3724 (2017).
[Crossref] [PubMed]

Zijlstra, P.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74(16), 2253–2255 (1999).
[Crossref]

Z. Liu, G. J. Steckman, and D. Psaltis, “Holographic recording of fast phenomena,” Appl. Phys. Lett. 80(5), 731–733 (2002).
[Crossref]

C. Li, L. Cao, J. Li, Q. He, G. Jin, S. Zhang, and F. Zhang, “Improvement of volume holographic performance by plasmon-induced holographic absorption grating,” Appl. Phys. Lett. 102(6), 061108 (2013).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Chem. Mater. (1)

L. M. Goldenberg, O. V. Sakhno, T. N. Smirnova, P. Helliwell, V. Chechik, and J. Stumpe, “Holographic composites with gold nanoparticles: nanoparticles promote polymer segregation,” Chem. Mater. 20(14), 4619–4627 (2008).
[Crossref]

J. Mod. Opt. (1)

G. Zhao and P. Mouroulis, “Diffusion Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Opt. Technol. (1)

J. Phys. Chem. B (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Langmuir (1)

R. Sardar, A. M. Funston, P. Mulvaney, and R. W. Murray, “Gold Nanoparticles: Past, Present, and Future,” Langmuir 25(24), 13840–13851 (2009).
[Crossref] [PubMed]

Mater. Today: Proc. (1)

X. Sun, F. Chang, and K. Gai, “Optoelectronic fast response properties of PQ/PMMA polymer,” Mater. Today: Proc. 3(2), 632–634 (2016).
[Crossref]

Nature (1)

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Opt. Commun. (4)

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part I: Short exposure,” Opt. Commun. 330, 191–198 (2014).
[Crossref]

D. Yu, H. Liu, Y. Geng, W. Wang, and Y. Zhao, “Radical polymerization in holographic grating formation in PQ-PMMA photopolymer part II: Consecutive exposure and dark decay,” Opt. Commun. 330, 199–207 (2014).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (2)

H. Liu, D. Yu, J. Wang, J. Jiang, and X. Sun, “Holographic grating formation in SiO2 nanoparticle-dispersed PQ-PMMA photopolymer,” Opt. Laser Technol. 44(4), 882–887 (2012).
[Crossref]

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Opt. Lett. (2)

Opt. Mater. (1)

J. L. Maldonado, G. Ramos-Ortiz, M. A. Meneses-Nava, O. Barbosa-García, M. Olmos-López, E. Arias, and I. Moggio, “Effect of doping with C60 on photocurrent and hole mobility in polymer composites measured by using the time-of-flight technique,” Opt. Mater. 29(7), 821–826 (2007).
[Crossref]

Opt. Spectrosc. (1)

A. V. Veniaminov and U. V. Mahilny, “Holographic polymer materials with diffusion development: principles, arrangement, investigation, and applications,” Opt. Spectrosc. 115(6), 906–930 (2013).
[Crossref]

Prog. Org. Coat. (1)

L. Balan, R. Schneider, and D. J. Lougnot, “A new and convenient route to polyacrylate/silver nanocomposites by light-induced cross-linking polymerization,” Prog. Org. Coat. 62(3), 351–357 (2008).
[Crossref]

Sci. Rep. (1)

P. A. Blanche, B. Lynn, D. Churin, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Diffraction response of photorefractive polymers over nine orders of magnitude of pulse duration,” Sci. Rep. 6(1), 29027 (2016).
[Crossref] [PubMed]

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Figures (12)

Fig. 1
Fig. 1 Theoretical and experimental angular selectivity curves
Fig. 2
Fig. 2 TEM characterizations of three silver NP types
Fig. 3
Fig. 3 (a) Absorption spectra of samples. (b) Interference optical coupling system, BS, beam splitter; PBS, polarizing beam splitter.
Fig. 4
Fig. 4 Holographic mutual diffusion process (phase and absorption gratings).
Fig. 5
Fig. 5 Normalized spatial and temporal evolution of components concentrations under accumulated pulse exposure. 3D model for (a) PQ molecules, (b) Photoproducts, (c) silver NPs, and 2D model for (d) silver NPs.
Fig. 6
Fig. 6 Temporal evolution of diffraction efficiency with and without doping silver NPs, (a) the contribution of refractive index modulation. (b) the contribution of absorption modulation
Fig. 7
Fig. 7 Photo-chemical mechanism for pulsed and CW exposures.
Fig. 8
Fig. 8 Dark diffusion enhancement process of diffraction efficiency with one-shot pulse exposure, (a) different silver NP concentrations, (b) different silver NP types.
Fig. 9
Fig. 9 Synchronous measurement of diffraction efficiency with multi pulse exposure, (a), different silver NP types (b) different silver NP concentrations.
Fig. 10
Fig. 10 The response time in silver NPs dispersed PQ/PMMA composites. (a) different silver NP concentrations, (b) different silver NP types.
Fig. 11
Fig. 11 Diffraction efficiency differences. (a) comparisons of theoretical and experimental results under continuous pulsed exposure, (b) comparisons of different Ag doping concentration.
Fig. 12
Fig. 12 Cumulative gratings strength with and without silver NPs under 1.5 μs pulsed exposure.

Tables (1)

Tables Icon

Table 1 Sample with different silver NPs.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

M P Q + M A g + M p r o d u c t + M m a t r i x = 1
U ( x , z , t ) t = ( D ( U ) U + D ( U ) ) ( 2 U ( x , z , t ) x 2 + 2 U ( x , z , t ) z 2 )
G ( x , x ' ) = exp [ ( x x ' ) 2 2 σ ] / 2 π σ
[ P Q ] ( x , t ) t = R D ( 2 [ P Q ] ( x , t ) x 2 R 2 [ A g ] ( x , t ) x 2 ) G ( x , x ' ) F 0 ( x ' , t ) [ P Q ] ( x ' , t ) d x '
[ A g ] ( x , t ) t = R D ( 2 [ A g ] ( x , t ) x 2 R 2 [ P Q ] ( x , t ) x 2 )
[ p r o d u c t ] ( x , t ) = 0 t G ( x , x ' ) F 0 ( x ' , t ' ) [ P Q ] ( x ' , t ' ) d x ' d t '
Δ n ( t ) = C p Δ [ p r o d u c t ] ( x , t ) + C P Q Δ [ P Q ] ( x , t ) exp ( i ϕ ) + C A g Δ [ A g ] ( x , t )
κ = π n 1 λ + j α 1 2
S = j e α 0 d / cos θ e j ε 1 ν sin c ( ν 2 + ε 2 ) , ε = Δ θ k 0 d sin θ , ν = π n 1 d λ cos θ + j α 1 d 2 cos θ
η = exp ( 2 α 0 d cos θ ) { sin 2 [ π d n ( t ) λ cos θ ] + sh 2 ( α ( t ) d 2 cos θ ) }
PQ P 1 Q * P 3 Q * + PMMA / M M A HPQ + R PQ - P M M A
η = sin 2 ( Δ n π d λ cos θ )

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