Optically Tunable Diffraction Efﬁciency in Reﬂection Grating Written in Photomobile Polymers

: In this work, we report the fabrication and optical characterization of a one-dimensional reﬂection holographic volume phase grating recorded in a recently developed holographic photomobile composite polymer mixture. The reﬂection grating recorded on the photomobile material was a periodic one-dimensional arrangement of hard polymeric walls and viscous regions. The reﬂection notch was located in the near-infrared region of the electromagnetic spectrum. The transmission efﬁciency of the grating was modulated by an external CW laser light source operating at λ = 532 nm. The transmission efﬁciency increased with the increase in the power of the external laser source, and in the range of the used power values, the phenomenon was completely reversible. At the highest power levels, a 48% increase in the diffraction efﬁciency was achieved. The increase in the diffraction efﬁciency was related to the growth of the refractive-index contrast of the grating. In particular, under illumination, the viscous material escaped from the irradiated area. This feature explains the experimentally observed changes in the values of the grating’s refractive index.


Introduction
Many optical devices are based on thin or thick holographic gratings or intermediate hybrid configurations [1][2][3][4][5][6][7][8][9][10]. Materials play an important role in the fabrication of holographic gratings, and their properties can be used to add functionalities to the recorded or self-assembled structures [11][12][13][14]. All-optically switchable volume holographic gratings have been studied for decades in several configurations and using a large variety of materials [15][16][17][18][19][20][21][22][23][24][25][26][27]. Optical switching can be found in mixtures containing azo dyes sensitive to the polarization state of the incident light. These dyes are mixed with liquid crystal (LC) molecules, and a change in the polarization state of the incident light results in a reorientation of the LC molecules in the system. The final result is a modification of the physical parameters characterizing the optical properties of the recorded periodic structures [28][29][30][31][32][33][34][35][36][37]. All-optical switching of highly nonlinear mixtures has also been exploited to modulate the optical properties of thin gratings when a static electric field is applied [25]. More recently, photomobile crystal polymer hybrid actuators [38] and azobenzene-based photomobile polymer thin films [39] were activated by light to generate and orient ripples on their surfaces. Other kinds of interesting light-actuated devices and sensors can be found in the literature [40][41][42][43][44][45][46][47]. Recently, we reported on the modulation of the optical properties of a transmission phase grating written in a novel holographic photomobile polymer mixture (H-PMP) [48]. H-PMP allows the production of polymer films that are holographic and photomobile at the same time [12,49]. In the present work, we wanted to miniaturize that optical system by realizing the phase grating in a guided configuration. For this reason, we used an H-PMP mixture where a transmission grating working in reflection mode was recorded between two optical fibers. Such a configuration opens many opportunities in the fields of integrated optics and optical communications.

Holographic Mixture Preparation
The mixture was prepared starting with the recipe published in [12], to which we added the epoxide monomer TPMTGE and the photoinitiator CQ. The monomers used were TPMTGE:DPMHPA:NVBL (0.1:2:5, molar ratio); the photoinitiators used were CQ:PTPTM (0.1:0.1 molar ratio) and 4-AP:PbO 2 (1:0.5 molar ratio). The reaction between the PbO 2 , NVBL, and 4-AP was conducted at room temperature for one week under magnetic stirring. After that, the resulting mixture was left to rest in the dark for one week. Separately, acrylate was mixed with liquid TPMTGE and heated at the temperature of 90 • C. The mixture remained under mechanical stirring until a pale yellow color was obtained. The content of the bottle was mixed with the reaction containing NVBL, 4-AP, and PbO2, and the final mixture remained under magnetic stirring for a further 36 h. The initiators were then added to the system. At this stage, the mixture remained under magnetic stirring for a further 24 h. The addition of a synergic two photoinitiator system allowed the polymerization in the visible range at λ = 532 nm. Further details on the mixture preparation can be found in ref. [48].

Recording, Pumping, and Data Acquisition Setups
An optical fiber (OF) with an internal diameter of 100 µm was inserted between two microscope glasses containing the H-PMP mixture. The OF was cut into two parts, and a transmission grating working in reflection mode was recorded between the two fibers using the setup depicted in Figures 1 and 2. With a writing angle θ = 70°and a refractive index of the H-PMP mixture of 1.58, the notch of the recorded grating observed in the reflection mode was at λ > 880 nm. The written hologram was optically characterized by using a large band Xe light source and a real time spectrometer. The external CW pumping light was a DPSS light source at λ = 532 nm, which impinged on the grating at different powers. The light-induced changes in the optical properties of the recorded structure were detected in real time and analyzed. Filters were used to remove any influence on the recorded spectra due to the presence of the external light source.   Figure 3 shows a typical reflection peak recorded in our samples. The diffraction (reflection) efficiency was ≈30 %. The reflection efficiency was relatively low due to the reflection losses connected with the wide recording angle, the light scattering from the edges of the optical fibers, and the impurities inside the samples. Figure 2a shows the real experimental setup. The green arrows represent the writing beams. The insets show the main steps of the sample fabrication. Figure 2b shows the empty cell and the alignment of the optical fibers, and Figure 2c shows the two glasses cell filled with the H-PMP mixture during the irradiation process.  The diffraction efficiency of a one-dimensional reflection phase grating can be written as:

Results and Discusssion
Respectively, the coupling and detuning parameters are defined as: where ∆n is the induced refractive index variation, d is the grating thickness, λ is the reading wavelength in the free space, θ is the angle of incidence, θ B is the Bragg angle, ∆θ = θ − θ B , n is the average refractive index of the medium, and β = 2πn/λ. The parameter ∆θ in Equation (3) describes the dephasing term appearing when λ or θ are varied. Their connection is given by the following equation in which the grating period Λ appears explicitly: Under the Bragg condition ∆θ = 0, the Equation (4) takes the well-known expression: which leads to the following expression for the diffraction efficiency: cos θ 0 (λ) tanh 2 π · ∆n · d λ cos θ 0 (λ) (6) Assuming an absorption coefficient α, independent of the working wavelength λ and intensity of the pumping laser applied to the sample, we can derive from Equation (6) the refractive index deviation δn as a function of the diffraction efficiency at the measured wavelength λ, as follows: Equation (7) is the nonlinear analytical relationship between the diffraction efficiency and the refractive index contrast. It clearly states that the increase in the diffraction efficiency under the pumping illumination is related to the corresponding changes in the refractive index modulation ∆n. The above equation is used to derive the dynamical behavior of the refractive index deviation at different power levels of the external laser source, as shown in Figure 5. After a proper data normalization, which accounted for the grating response at rest without external pumping, the diffraction efficiency was computed and used to derive the refractive index deviation ∆n, according to the Equation (7). Figure 5 shows the behavior of the refractive index modulation ∆n as a function of time when the grating is illuminated for ≈30 s at λ = 532 nm with different power levels ranging from 30 to 240 mW. The irradiated area overlapped the entire grating surface. For the used powers, we always observed a reversible increase in the diffraction efficiency during irradiation.
Reflection holograms are, at time of writing, impossible to record in H-PMP polymer films. To overcome this limitation, different approaches can be used. As an example, in the recent past, we recorded a high-resolution reflection hologram in a well known holographic mixture and successfully attached it to an H-PMP film. The approach used in this work is different, because we recorded the one dimensional hologram in transmission mode and used it in reflection mode. In this guided configuration, regardless of the power used during the irradiation process, the diffraction efficiency increased in time up to a maximum value and relaxed to the initial value when the external laser was switched off. By inverting the growing curve, the resulting curve completely overlapped the shape of the decay curve. This evidenced that the physical phenomenon governing the excitation and relaxation behaviors was the same. In order to explain the detected changes in the diffracted efficiency during irradiation, we recall the photophobic nature of the used compounds [12,50]. During the irradiation process, the doped-NVBL escaped from the irradiated area, and as a consequence, the grating refractive index modulation increased. The reverse occurred when the pump laser was turned off [48,51]. Our hypothesis is that this property plays the main role when considering the dynamic behavior of our grating under light irradiation.

Conclusions
In this work, we reported on the fabrication and optical characterization of a onedimensional reflection holographic volume phase grating written in a PMP mixture. The reflection grating recorded in the photomobile material was a periodic one-dimensional arrangement of hard polymeric walls and low viscous regions and showed a reflection peak located in the near-infrared region of the electromagnetic spectrum. The depth of the reflection peak was modulated by an external DPSS CW laser light source operating at λ = 532 nm. In particular, the transmission efficiency increased with the power of the external laser source. For low power values, the phenomenon was completely reversible. The increase in the diffraction efficiency was related to the changes in the refractive-index modulation of the grating. In particular, under illumination, the low viscous material escaped from the irradiated area, and the index modulation δn increased. The observed nonlinear optical response can be helpful for optical limiting applications [52] and sensing [53,54].