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We investigated the contribution of the absorption and phase gratings to the total diffraction efficiency of volume holographic gratings written in glass-like polymer recording materials based on poly(methyl methacrylate) and its thermostable derivative (copolymer with acrylic acid) with distributed phenanthrenequinone. The typical maximal diffraction efficiency was 0.5%–2.0% for the absorption grating and 22–32% for the phase grating. The modulation of the absorption coefficient varied between 10cm-1 and 100cm-1 and the modulation of the refractive index was about 10-4-10-3.
©2008 Optical Society of America
1. Introduction
The polymer medium based on poly(methyl methacrylate) PMMA with distributed phenanthrenequinone (PQ) is known as an effective holographic recording material [1–5]. Two holograms, phase-shifted by π to approximately cancel each other out, are created during exposure. One of these holograms is based on the migration of PQ molecules that are free from the long-chain PMMA molecules, while the other is based on the PQ becoming attached to the PMMA. Over time, or when illuminated to enough heat, the free molecules diffuse through the material, destroying the grating of which they had been apart. This has the effect of increasing the diffraction efficiency (DE) of the other grating with its molecules anchored to the PMMA such that they cannot move [1,6,7]. Detailed description of the chemical and optical properties of the PMMA+PQ recording medium is published e.g. in [1,6–13].
Because of good photorefractive properties the glass-like polymer recording materials can be used for Head-Up-Displays in vehicles as a holographic screen. The holographic screen is located between glass plates in windshields and should be stable to temperatures up to 160 °C defined by the manufacturing process of the windshields. The thermal stability of the holograms written in PMMA+PQ is limited by the melting point of the PMMA at 105°C. Recently we have modified the PMMA+PQ recording medium by including of molecules of acrylic acid (AA) in order to get higher thermal stability. The thermal stability of the holograms in the obtained PMMA+AA+PQ recording medium can be observed up to 200°C [14]. During our experiments with PMMA+AA+PQ as well as PMMA+PQ we have noticed that absorption of both materials can be changed by illumination or heating. Spatial periodical modulation of the absorption coefficient leads to generation of an absorption grating along with phase grating. Considering the possible application of the developed recording material in Head-Up-Displays, where the spatially modulated absorption as well as general transparency of the material are strongly regulated by utilization purposes, investigation of the role of the induced absorption grating is of great interest. In this paper we continue our recently published investigations of the PMMA+PQ recording medium as well as its thermostable derivative PMMA+AA+PQ [14] and estimate to our knowledge for the first time the contribution of the DE of the absorption grating to the total DE of holographic gratings in PMMA+PQ and PMMA+AA+PQ recording media.
2. Induced absorption in PMMA and PMMA+AA
Figures 1 and 2 show the spectral dependences of the internal absorption of the recording media based on PMMA and PMMA+AA in the VIS range during illumination and after illumination during heating, respectively. The absorption factor is determined by the ratio between the input Jin and transmitted Jout intensities. The offset depends on the background illumination. There are average curves of at least 10 independent samples. The experimental error amounts about 8%.
Fig. 1. Spectral dependences of the internal absorption factor A of the recording media based on PMMA a) during illumination and b) after illumination during heating (120°C). The polymer was illuminated at 514 nm with the intensity of 60 mW/cm2.
The recording media were illuminated by an Ar-laser (514 nm) with the intensity of 60 mW/cm2. Figures 1(a) and 2(a) show the change of the absorption spectrum of the PMMA and PMMA+AA correspondingly in dependence on the exposure time. Here and further we designate the “recording media based on PMMA (PMMA+AA)” briefly by only “PMMA (PMMA+AA)”. The initial spectra as well as the tendency towards clarity were in general similar for both polymers. However the absorption of the PMMA decreased quicker than of the PMMA+AA. After an illumination of about 5min the PMMA was clear almost completely. The absorption of the PMMA+AA decreased slowly and amounted about 50% in a saturation state (about 7min) of the initial value. This can be explained by the total utilization of the PQ in the PMMA and only partial utilization of the PQ in the PMMA+AA. In general the final change of the absorption in saturation state does not depend on the beam intensity. The intensity influences only the temporal behaviour of the absorption. By the heating of the pre-illuminated photopolymers (over 5min, PMMA; over 7min, PMMA+AA) in an oven at 120°C (Fig. 1(b) and 2(b)) the absorption of the illuminated areas increased and reached the values that were even higher than the initial ones. The samples were put into the oven, after it was warmed up to the constant 120°C.
Fig. 2. Spectral dependences of the internal absorption factor A of the recording media based on PMMA+AA a) during illumination and b) after illumination during heating (120°C). The polymer was illuminated by 514 nm with the intensity of 60 mW/cm2.
Figure 3 shows the spectral dependences of the absorption of the PMMA and PMMA+AA in the VIS range due to heating without illumination. There are no appreciable changes of the absorption of the recording media during more than 14 hours of heating.
Considering Figs. 1, 2, and 3 we can conclude that, first, only the photoproduct is sensible to the change of the temperature and, second, an absorption (amplitude) grating is generated in the photopolymer along with the phase grating. The second statement is proved also by the observation of the dark and bright regions on the holographic gratings with microscope. If the grating is written by two-wave-mixing, the frequency of the change of the dark and bright regions corresponds to the grating period. We have noticed that the photopolymer becomes sensible to external illumination after heating. The change of the spectrum of the absorption during illumination correlates with the spectral characteristics of the PQ (up to about 525nm), whereas the increasing of the absorption during heating is observed also above 525nm.
3. Contribution of the absorption grating in PMMA and PMMA+AA
In order to estimate the contribution of the absorption grating to the total DE along with the phase grating for two-wave-mixing experiments we apply the theory of Kogelnik [15]. Knowing the absorption modulation between the illuminated and non-illuminated areas one can get the DE of the absorption grating. Based on this DE the corresponding DE of the phase grating can be found from the total DE. The DE of the phase grating yields the modulation of the refractive index.
The principal scheme for the recording and reconstruction of holographic gratings is shown in Fig. 4. The geometric size of the samples was 10 mm×15 mm, whereas two gratings were recorded on each sample and tested afterwards under the same conditions in order to have two independent comparable results for each measured value. The aperture of the gratings amounted to 5 mm. The thickness of the photopolymer layers was 90 µm.
An Ar-laser was used as a monochromatic light source (514 nm) with a coherence length of about 30 cm. The temporal and spatial coherence of the source were proven with a Michelson- and a Young-Interferometer, respectively. The output laser beam was expanded up to a diameter of 20 mm by a telescope of two lenses with a pinhole in their common focal point and cut off to 5 mm by a pinhole in the screen in front of the sample. The angle between the interfering beams was 64° (=2θ) in the sample, what corresponds to a grating period of 323 nm. The input beam intensities were chosen to be 30 mW/cm2 and 30 mW/cm2. These intensities were enough for rapid generation of the absorption grating, whereas the absorption grating reaches its saturation before the total DE reaches its maximum (Fig. 1, 2, 5).
Fig. 3. Spectral dependences of the internal absorption factor A of the recording media based on a) PMMA and b) PMMA+AA without illumination during heating (120°C).
Fig. 4. Schematic for a) recording and b) reconstruction of the grating in the polymer film layer. The Bragg angle θ is considered in the material. θ=32° for λ=514nm and θ=41° for λ=633nm.
The temporal development of the grating was controlled by a detector at 514 nm, whereas one beam was blocked for a while and the detector took the diffracted part of the second beam (Fig. 4). The DE η was measured as a ratio of the intensity of the diffracted part of the beam Iout to the intensity of the input beam Iin
The measurements of the DE during recording were also done with a He-Ne-Laser at 633nm (Fig. 5). The pure intensities in the bulk material were taken: Fresnel reflection on surface borders was considered in (1).
For investigation of the gratings by heating, the gratings were recorded till they achieved the maximal value of the DE. The DE of the gratings was measured with a He-Ne laser (633 nm, 6.5 mW/cm2) before and after heating. These experiments were not carried out with the Ar-laser, since the photopolymer is photosensitive at 514nm and the gratings could be destroyed.
3.1 Recording
From the relationships (40) and (67) in [15] we can derive the DE of the absorption grating
where
with the absolute absorption coefficient α, the modulation of the absorption coefficient α1, the thickness of the reflection grating d, and the Bragg angle θ. The absolute absorption coefficients and their modulations are taken from Fig. 1a and 2a. Here and further the absorption coefficient α is derived though the relationship , where A is the absorption factor in Fig. 1, 2, and 3. The modulation of the absorption coefficient α1 is taken as the difference of the absorption coefficient before illumination and after illumination in saturation state. Table 1 shows the values of the DE of the absorption grating ηA calculated from the experimental values in saturation. The Bragg angle is taken within the photopolymer.
Fig. 5. DE of the grating in recording media based on a) PMMA and b) PMMA+AA in dependence on the recording time. The grating is written with an Ar-laser (514nm) and read out by the Ar-laser (514nm, squares) and by a He-Ne-Laser (633nm, triangles)
Table 1. Recording. Experimental values of the thickness of the grating d, the Bragg angle θ, the absolute absorption coefficient α (saturation), the modulation of the absorption coefficient α1 (saturation); calculated values of the auxiliary parameters D0, D1; and calculated values of the DE of the absorption grating ηA. Wavelength 514nm.
The DE of the phase grating ηPh is given as difference between the total DE η and the DE of the absorption grating ηA.
From the relationship (59) in [15] one can obtain the modulation of the refractive index n1
with the wavelength λ.
We calculated the values of the DE of the phase grating and the modulation of the refractive index both for the maximal (max) and the saturated (sat) total DE (Fig. 5). The obtained results are shown in Table 2.
Table 2. Recording. Experimental values of the maximal total DE η(max) and saturated total DE η(sat); calculated values of the DE of the absorption grating ηA, of the DE of the phase grating in maximum ηPh(max) and in saturation ηPh(max), and calculated values of the refrative index modulation for maximum n1(max) and for saturation n1(sat)
The DE of the absorption grating is weaker than the DE of the phase grating. However it can consist about 6–7% of the total DE, especially in the case of PMMA+AA. The DE measured with the He-Ne-laser (Fig. 5) is weaker than the DE at 514nm. According to Fig. 1 and 2 there is no absorption change of the recording media at 633nm during illumination, so that no absorption grating is generated. Figure 5a proves experimentally both the existence of the absorption grating at 514nm and its absence at 633nm at least in PMMA. The DE at 514nm was about 0.5–0.6% after 600s, but no diffraction was observed at 633nm. Thus, the phase grating (that can be observed at 514nm and 633nm) was destroyed, whereas the absorption grating (that can be observed only at 514nm) was stable.
3.2 Heating
The temporal development of the diffraction efficiencies of the absorption and phase gratings by heating of the samples in an oven at 120°C can be seen in Fig. 1b, 2b and 6. The absorption of the pre-illuminated areas increased by heating and reached saturation after about 15min for PMMA and after about 240min for PMMA+AA. On the other hand, the temporal dependences of the diffraction efficiencies of the recording media had also local extrema at about 15min and about 240min for PMMA and PMMA+AA, respectively. Although it is difficult to claim a determined microscopic behaviour of the materials just from the change of the macroscopic optical parameters, the coincidence of the development of the absorption coefficient and the DE let us suggest that the spatial movements of the free PQ molecules were stopped after 15min for PMMA or 240min for PMMA+AA. The further variation of the DE happens because of the partial mechanical decay of the gratings. This can be indirectly proved by the fact that the decay of the gratings in PMMA is much more advanced than in the PMMA+AA, which is easily explained by the higher thermal stability of the PMMA+AA [14]. After about 1000min heating no changes of the optical parameters of the photopolymers were observed.
In order to determine the contribution of the absorption grating to the total DE during heating we apply the same mathematical derivations as in the paragraph recording. Table 3 shows the obtained experimental and calculated values. The total DE was measured with a He-Ne laser at 633nm. The Bragg angle as well as the thickness of the grating were recalculated for 633nm.
Fig. 6. Normalized diffraction efficiency in dependence on heating time at 120°C: a) PMMA (value 1 corresponds to 16%), b) PMMA+AA (value 1 corresponds to 24%). The measurements were made with an accuracy of 5%.
Table 3. Heating. Experimental values of the thickness of the grating d, the Bragg angle θ, the absolute absorption coefficient α (saturation), the modulation of the absorption coefficient α1 (saturation); calculated values of the auxiliary parameters D0, D1; and calculated values of the DE of the absorption grating ηA.
The total DE in saturation is about 10% for PMMA as well as for PMMA+AA after the heating. Since the contribution of the absorption grating in PMMA+AA is weak, the DE of the phase grating amounts to the total DE of 10%, while the DE of the phase grating for PMMA is about 6%. The calculated value of modulation of the refractive index for both polymers lays at about 5·10-4.
4. Conclusion
Glass-like polymer recording media based on PMMA and PMMA+AA were investigated with regard to their application as storage materials for holographic gratings. We had estimated to our knowledge for the first time the contribution of the absorption gratings to the total DE of holographic gratings in these materials. Absorption of the recording media decreased under illumination and increased by heating. The maximal DE was 2% (0.5%) for the absorption grating and 32% (22.5%) for the phase grating in PMMA+AA (PMMA). The refractive index modulation covered the range of 10-4-10-3 during recording. During heating the DE of the absorption grating could reach 4% for PMMA, while the absorption grating in PMMA+AA was not essential. The total DE in saturation was about 10% for both polymers.
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