1. Introduction

Optical engineering of the photonic properties of polymer films provides efficient and convenient ways to store information within photo-sensitive materials. Recent demonstrations have shown the possibility to induce dichroism, birefringence [1, 2] or polarization gratings [3] by optical excitation in a polymer matrix containing active chromophores exhibiting a linear anisotropy. The grating formation is based on the reorientation of such chromophores perpendicularly to the optical excitation polarization, driven by photoizomerization cycles.

Such orientation techniques have been extended to the non-centrosymmetric alignment of nonlinear and photoizomerizable chromophores using a combination of resonant one and two photon excitations [4]. This multiphoton poling process is based on the non-centrosymmetric component of the angularly selective absorption cross-section of the molecules, due to the coherent superposition of a fundamental beam at the frequency ω and its harmonic at 2ω. Breaking the centrosymmetry inherent to the polymeric solid state solution promotes nonlinear quadratic optical properties in the material, which cannot arise from a single one-photon excitation.

One of the main specificities of this all-optical technique is the possibility to engineer the symmetry of the induced χ ⁽²⁾ nonlinear quadratic tensor by the control of the ω and 2ω fields polarizations, which govern the angular photoselection and thus the angular redistribution of the molecules. In the poling process, the nonlinear molecule-fields interactions induce a perturbation of the molecular orientation distribution up to the fourth order parameter, and thus allows the control of the spherical components of the macroscopic polarizability tensors up to J=4, namely ${\chi }^{{\left(1\right)}^{J=0,2}}$, ${\chi }^{{\left(2\right)}^{J=1,3}}$ and ${\chi }^{{\left(3\right)}^{J=0,2,4}}$. In this work, we focus on the specific non-centrosymmetric coupling involving the χ ⁽²⁾ tensor and therefore on the engineering of the J=1 and J=3 orders of the molecular orientational distribution.

The application of this technique to imprint second harmonic generation (SHG) spatial images within organic thin films has been demonstrated recently [6, 7]. In this work, we address the potential of this all-optical orientation as a new nonlinear optical storage scheme. In particular, we demonstrate the local imprinting of multipolar quadratic nonlinear properties in polymer films using a polarization resolved nonlinear microscopy set-up. The spatial reduction of the optical processes down to the micrometric scale is shown to be beneficial for both the patterning of the polymer film and the parallel SHG read-out resolution. In addition, we demonstrate that this nonlinear polarization encoding is not readable by linear imaging techniques based on traditional holography.

2. Principle of optical poling and experimental setup

Following mutually coherent one- and two-photon excitations by two optical frequencies ω and 2ω, the induced molecular orientational distribution, f(Ω), can be expressed as f(Ω)∝ 1-P _0→1(Ω), with Ω standing for the Euler set of angles defining the molecular 3D orientation and P _0→1(Ω) the absorption probability of the molecules between the ground and excited states. This probability contains linear- and non-linear coupling terms between the molecular susceptibilities and corresponding coherent combinations of the excitation fields. Among these terms, the non-centrosymmetric contribution can be expressed as a coupling between the third rank molecular β tensor and the third rank multipolar field tensor E=(E2 ^ω *⊗E ^ω ⊗E ^ω ) [5]. The resulting angular photoselection $P_{0\to 1}^{2\omega ,\omega }$(Ω)=Im(β(-2ω,ω,ω))• E is then non-centrosymmetric. It has been shown that using a spherical decomposition of the β and E tensors, the resulting non-centrosymmetric J=1,3 contributions to f(Ω) can be simply expressed as functions of the E ^J=1,3 and β ^J=1,3 spherical components. These components can be tailored by a proper engineering of the molecular symmetry or of the incoming fields polarizations. In particular, contra-circular ω and 2ω polarizations lead to a pure E ^J=3 contribution [5], whereas β ^J=1 and β ^J=3 are respectively dominant in dipolar and octupolar molecular structures [8].

The resulting macroscopic hyperpolarizability is inferred by averaging the molecular β tensors on the orientational distribution: χ ⁽²⁾=𝓝∫β(Ω)f(Ω)dΩ where 𝓝 is the molecular density. The spherical components of this tensor can thus be expressed as ${\chi }^{{\left(2\right)}^J}\propto 𝓝{\parallel {\beta }^J\parallel }^2{E}^J⁄\left(2J+1\right)$ with a scaling factor accounting for dispersion coefficients, relative phase factors and the reorientation quantum yield [5]. In this work, we use the resulting SHG polarization response as a signature of the χ ⁽²⁾ symmetry, represented by the ${\chi }^{{\left(2\right)}^{J=1}}$ and ${\chi }^{{\left(2\right)}^{J=3}}$ contributions.

The all-optical poling technique consists in two steps, the poling and the reading processes, which are both performed at room temperature. The fundamental ω poling and reading field is provided by the same laser which is a transverse and longitudinal single-mode Nd ³⁺:YAG laser at 1.064µm with 22-ps pulse duration at a 10-Hz repetition rate. The 2ω harmonic poling field is generated by frequency doubling in a phase-matched type II KDP crystal. A Glan polarizer and quarter-wave plates enable the control of the polarizations of the E ^2ω and E ^ω fields. The reading process consists in monitoring the induced SHG polarization response in the locally poled areas using an incident ω infrared rotating polarization.

In order to reduce the optical poling process down to the micrometric scale, the one- and two-photon excitations are brought through a nonlinear microscopy setup using a low-aperture objective (×10, NA=0.25) as shown on Fig. 1-a. Due to the chromatic aberrations of the microscope objective, the focal points of the ω and 2ω fields are different and reducing the size of the poled areas implies optimizing the focalization of one of these two fields. Experimentally we chose to focus the 2ω beam on the sample while keeping a diameter of the ω excitation of the order of 20µm. The size of the poled area is thus limited to the spatial overlap of the ω and 2ω beams. The sample patterning is ensured by translating the sample in its (X,Y) plane using computer controlled picomotors. This scheme allows the reading process to be implemented with the same focusing objective at the same position, providing a ~(20µm)×(20µm) image of the sample excited with the fundamental reading ω field. The SHG information is then imaged on a thermo-electrically cooled CCD camera using a (×20, NA=0.35) objective and a f=150mm tube lens, as shown on Fig. 1-b. Accounting for the characteristics of the objective and of the tube lens, the magnifying power of this imaging set-up is estimated to be ×18.75. The SHG polarization response is analyzed by rotating the incident polarization between 0° and 180° by 10° steps, while recording an image per polarization step. In this configuration, the fundamental energy ranges from 1 to 3J/cm² and the harmonic energy is kept lower than 2mJ/cm ². Similar experiments have demonstrated induced nonlinear efficiencies in polymers up to 76pm/V [4]. The poling time is typically several minutes per poled area, which ensures a sufficient SHG response stability over the duration of the subsequent polarization analysis. Long-term SHG stability can be reached by increasing the poling time to 30 minutes [4].

The samples are polymeric solutions spin-coated on 1mm thick glass substrates. The solutions are either polymethyl-metacrylate doped with Disperse Red 1 (λ _max =490nm in the polymer) with a 5% weight to weight ratio (DR1(5%)/PMMA) or polycarbonate doped with DCM (4-(dicyano methylene)-2-methyl-6-(p-dimethyl aminostyril)-4H-pyran) (λ _max =470nm in the polymer) 5% w/w (DCM(5%)/PC). The optical density of these samples at 532nm are respectively 0.55 and 0.41. These two dyes have similar non-linear efficiencies (${\beta }_0^{\mathit{\text{DR}}1}$=69 10^-30 esu [10] and ${\beta }_0^{\mathit{\text{DCM}}}$=63 10^-30 esu [11]) and photoisomerization quantum yields (${\varphi }_{\mathit{\text{iso}}}^{\mathit{\text{DR}}1}$ =0.11 [12] and ${\varphi }_{\mathit{\text{iso}}}^{\mathit{\text{DCM}}}$ =0.15 [13]). These molecular systems have been previously used in all-optical poling experiments and are known to be simple rod-like structures exhibiting a reasonable balance between dipolar β ^J=1 and octupolar β ^J=3 molecular components (‖β ^J=3‖/‖β ^J=1‖=0.6 for DR1 [5] and 0.9 [9] for DCM). In addition to nonlinear properties, the laser dye DCM exhibits a non-negligible two-photon fluorescence efficiency which enables us to estimate the size of the read-out area excited by the fundamental beam (in this case the emission filter is a high pass 550nm filter which allows two-photon fluorescence imaging).

 

Fig. 1. a): Experimental setup for the poling step (G: glan polarizer, S: sample). b): Experimental set-up for the SHG read-out step (F ₁: high pass infrared filter, F ₂: band pass visible filter, F ₃: 530nm interferential filter, L: 150mm lens).

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Figure 2-a depicts six poled areas on a DR1(5%)/PMMA film imaged by SHG. The six areas are poled using the same linearly polarized parallel exciting fields and the read-out polarization is parallel to this common direction. A gaussian fit of the SHG profiles gives an average diameter of the poled areas of 1.94µm±0.07µm. This diameter is smaller than the 2.6µm diffraction limit of the system at 532nm, which is due to the non-linear behavior of the poling process.

 

Fig. 2. a): Image of the SH generated by six poled areas on a DR1 film with parallel linear polarized fields (I^ω =1.5J/cm ²) during 2min (integration time: 15s). b): Gaussian fit (line) of the SHG intensity distribution (dots) on the diagonal of a poled area.

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3. SHG polarization encoding using different poling polarization configurations

As mentioned previously, it is possible to tailor the symmetry of the induced quadratic nonlinearity χ ⁽²⁾ by controlling the polarizations of the ω and 2ω poling fields (i.e. the E ^J spherical components). Specific poled areas which have been generated using different poling polarization configurations are thus expected to exhibit different SHG polarization responses, providing non ambiguously distinct optical information. Figure 3-a illustrates this effect on four different poled areas that have been imprinted using four different configurations of linear parallel poling polarizations, namely E ^2ω‖E ^ω , directed along four different directions: 0°, 45°, 90° and 135° (with respect to the X axis of Fig. 1). Figure 3-b shows that a 90° read-out polarization of such a SHG image exhibits clearly three active areas while almost completely cancelling the fourth one, in which molecules have been oriented at 0°. The four insets, which represent the polarization responses of each poled area when rotating the read-out polarization in the sample plane, show a good agreement with their expected theoretical behavior obtained from the E^J and β^J respective spherical components given in reference [5]. As expected, the four different areas present similar SHG polarization responses rotated by 45°.

 

Fig. 3. a): SH generated by four poled areas on a DR1 film with linear parallel polarized fields (I^ω =1.5J/cm ² during 2min, integration time: 5s, excitations directed respectively along the 0°, 45°, 90° and 135° directions with respect to the X axis). One image is depicted per read-out polarization direction step, rotating in the sample plane as represented by the red line in the inset. b): Image of the SHG intensity of the four poled areas with the read-out polarization parallel to the 90° axis. Insets: SHG polarization responses of each poled area (open circles) and predicted theoretical behavior (lines) in the X,Y plane. [Media 1]

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These experimental results illustrate the possibility to control the imprinted nonlinear information in a polymer film. However, in order to achieve a high density of encoded nonlinear optical information, a large diversity of SHG polarization response patterns are required. This can be provided by more complex combinations of the ω and 2ω field polarizations. Recent demonstrations have shown that a continuous variation of the ratio E ^J=3/E ^J=1 could be reached using either linear ω and 2ω polarizations with a varying angle between them, or elliptic polarizations [5]. To illustrate the effect of more complex poling field configurations on the SHG polarization response, Fig. 4 depicts the nonlinear responses of poled areas on a DCM sample with linear perpendicular (a) and contra-circular (b) exciting fields polarizations. The experimental data are in agreement with the behavior predicted by the spherical decomposition of both fields and susceptibility tensors. The visible background level is higher than in Fig. 3 because of the two-photon fluorescence emission from the DCM molecules which slightly overlaps with the second harmonic 532nm emission wavelength. The demonstration of this technique on the DCM fluorophore shows that the nonlinear SHG emission can be advantageously combined with other optical properties such as luminescence for multi-functional applications [9].

The nonlinear holography technique described in this work provides furthermore an interesting scheme towards data encryption, due to its transparency for other linear holographic techniques such as the more traditional birefringence or dichroism measurements. This property is due to the fact that linear read-out processes related to the χ(1) tensor are only sensitive to the J=0,2 order parameters of the f(Ω) distribution, whereas the present information encoding relies on the J=1,3 orders. A simulation of the expected linear and nonlinear polarization responses is shown in Fig. 5 in the case of different poling polarizations. The calculations account for the J=0,2 contributions of the even-order angular photo-selections: $P_{0\to 1}^{2\omega }$(Ω)=Im(α(-2ω,2ω))∙(E ^2ω*⊗E ^2ω) and $P_{0\to 1}^{\omega }$(Ω)=Im(γ(-ω,-ω,ω,ω))∙(E ^ω*⊗E ^ω*⊗E ^ω⊗E ^ω ) [9]. As can be observed in Fig. 5, the polarization dependence of the linear information is poorly resolved for two different poling polarization cases, whereas the nonlinear SHG read-out is able to provide accurate information on the poling polarization conditions. These results confirm that studying the induced birefringence or dichroism in a poled sample is not sufficient to read-out an all-optically encoded quadratic non-linear information.

 

Fig. 4. SHG polarization responses of a poled area on a DCM sample (open circles) compared to the theory (lines) with linear perpendicular (a) and contra-circular (b) exciting fields polarizations (a): I^ω =2J/cm ² during 2min and b): I^ω =2.5J/cm ² during 5min. Insets: SHG intensity imaged on the poled sample with 0°, 40° and 90° read-out polarizations. Integration time: 10 s.

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Fig. 5. Simulation of the polarization responses of the one-photon absorption (a,c) and SHG (b,d) in a poled polymer film with linear parallel (a,b) and perpendicular (c,d) ω and 2ω fields polarizations. The ω and 2ω intensities are chosen so that the one-photon absorption probability is four times lower than the two-photon one, which corresponds to usual experimental conditions.

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4. Conclusion

The one- and two-photon all-optical poling procedure, which has been developed for the last ten years, has been implemented in a polarization resolved nonlinear microscopy setup in order to exploit its potential for encoding optical information in polymer films. This technique furthermore offers a high order excitation process that should lead to a far-field poling process below the diffraction limit. The resolution is limited to 2µm in this work, however the use of high numerical aperture optical systems should enable the achievement of diffraction limited 300nm lateral and 500nm axial scales with respect to the fields propagation direction. Moreover the interferential nature of this process is compatible with an holographic writing procedure and allows parallel nonlinear polarization multiplexing. In addition to the rich variety of imprinted nonlinear polarization patterns that can be provided in order to reach a high density of stored information, this novel nonlinear encryption scheme allows for protection against standard linear read-out procedures.