We propose to use radially, azimuthally and circularly polarized Bessel beams as inhomogeneous illuminating system to unambiguously analyze the vectorial optical response of azo-dye polymers. It is shown that the well-known sensitivity of azo-dye molecules to polarization direction gives rise to surface deformations which are proportional to the longitudinal electric-field component. This property opens a large field of applications in the vectorial analysis of light fields, especially for nano-optics/nanophotonics.
©2006 Optical Society of America
It has been shown for more than one decade that azo-polymer films give rise to direct surface modulation when illuminated with visible light in their absorption band [1, 2]. The mechanism of this photoinduced material migration involves repeated photoisomerization cycles of the azobenzene group during light exposure. It is known that the polarization of the incident light beam plays a role in this phenomenon . More recently, radially polarized Bessel beams have been used as test-objects to separate the effects of transverse and longitudinal polarizations in near-field optical imaging process . It has been demonstrated that the commonly used bare fiber-tips play the role of polarization filters as they do not collect the longitudinal electric field component. In this paper, we propose to adapt the technique developed in Ref.  to demonstrate that azo-polymer films also provide a polarization filtering (PF) capability through topographical shaping. Such a behavior has direct applications in the vectorial analysis of the electromagnetic fields around structures used in nano-optics. Our study focuses onto the so-called PMMA-DR1 polymer which consists of azo-chromophore DR1 (dispersed red one) grafted into a polymethyl methacrylate matrix (PMMA).
2. Principle and theory
The proposed technique is divided into two steps. First, the azo-dye polymer layer is illuminated by means of a high aperture angle (θ) Bessel beam in order to write a specific imprint onto its free surface. Second, the topography of the exposed area is recorded by usual shear-force detection technique . Let us recall that Bessel beams are the non-diffracting solutions of Maxwell equations . A large number of studies have been devoted to take benefit of these propagation-invariant confined fields in various domain of physics [6, 7, 8]. In our case, the Bessel beams generate field distributions whose square modulus can be described by simple analytical expressions inside the polymer layer (derived from Ref. ). We have, for the radially polarized Bessel beam:
for the azimuthally polarized Bessel beam:
for the circularly polarized Bessel beam:
ET and EL are respectively the transverse and longitudinal field components inside the polymer layer. ET is parallel to the film interfaces whereas EL is perpendicular to them. In the following, |ET |2 and |EL |2 will be called transverse and longitudinal intensities, respectively. α and C are constants (α = (2π/λ)sinθ) and r gives the radial transverse spatial position (parallel to the interfaces) in polar coordinates. Functions Jm are the m-order Bessel functions of the first kind. The photosensitive layer is modelled through coefficients ts , tpT , tpL . In our model, the polymer layer is limited on one side by a semi-infinite glass substrate and on the other side by a semi-infinite air medium. The Bessel beam is incident into the glass substrate and it is transmitted in air through the layer.
In this study, coefficient of in Eq. (5) is sufficiently small so that the contribution of can be neglected in the expression of |ET|2. Therefore, the radially and circularly polarized Bessel beams lead to 3D fields whose transverse intensities are described by functions and , respectively, and longitudinal intensities are described by functions and , respectively. From Figs. 1(b) and 1(c), it turns out that and are easily identifiable: exhibits a bright central spot whereas shows a central dark spot. Moreover, has maxima around minima of , and conversely, has maxima around minima of (Fig. 1(a)).
Such a complementarity makes easy the study of the vectorial optical response of azo-dye polymers. First, these two polarizations fulfill the condition for the generation of deep surface relief patterns. This is due to the fact that circularly and radially polarized Bessel beams can be expanded in circularly and p polarized waves which are known to induce pronounced surface deformations [1, 2, 3]. Second, the discrimination between |ET |2 and |EL |2 in the surface imprint becomes possible and it will be obvious whether the azo-dye polymer exhibits a PF phenomenon. In that case, the study of the polymer response with two complementary excitations is determinant to undoubtedly validate the fact that the surface deformation process records faithfully |EL |2 or |ET |2. Another comparison with the pure 2D-transverse field distribution given by the azimuthally polarized Bessel beam will confirm our conclusions.
Because the argument of the Bessel functions involved in Eqs. (1)-(6) is z non-dependent (α is constant), the light distributions do not spread inside the film. Figure 2 reports the longitudinal cross section of the intensities I = |ET |2 + |EL |2 simulated from Eqs. (1),(2) in radial polarization (Fig. 2(a)), from Eqs. (5),(6) in circular polarization (Fig. 2(b)) and from Eqs. (3),(4) in azimuthal polarization (Fig. 2(c)). Here, the film thickness is equal to 100 nm, θ = 26.5°, λ=514 nm and the refractive index of PMMA-DR1 is assumed to be equal to 1.6 . The non-diffracting behavior of the beam inside the film is here clearly shown. Such a property makes the proposed illumination technique much less sensitive to sample thickness than conventional focused beam techniques for which the spot size in the focal region depends strongly on the longitudinal z-coordinate. Thus, the study of PF in relatively thick samples as well as the study of the relationship between polymer thickness and PF is possible with Bessel beams. Although being non diverging, the intensity distributions do not keep unchanged over the film thickness (Fig. 2). This is explained by the fact that coefficients ts , tpT , tpL are functions of the longitudinal z-coordinate (the polymer layer acts as a longitudinal optical cavity). Therefore, the relative weights of and in the intensity expressions are z dependent. This gives rise to possible contrast variations over the film thickness (Fig. 2(a)).
The experimental setup is depicted in Fig. 3. The experimental parameters are the same as the ones used in Fig. 2. A 100-nanometer-thick PMMA-DR1 layer is deposited by spin-coating onto a microscope cover-glass. The excitation source is an argon laser light beam (λ= 514 nm) which fits the peak absorption wavelength of PMMA-DR1 (around 488 nm ).
The Bessel beams are created by projecting a collimated laser beam onto an axicon-based converging system  (Fig. 3(a)). The incident radially and azimuthally polarized beams have have been generated through the optical fiber system described in Ref. . The so-generated Bessel beams have an aperture angle in air slightly smaller than 45°. In this case, they provide longitudinally-invariant submicron light confinements over a distance larger than 1 mm. The exceptionally long depth of field of the axicon is an advantage both to study thick samples and to perform an easy positioning of the photosensitive layer into the beam. There is no necessity to set the film in a given plane as it is the case with focusing objectives. The transverse intensity of the Bessel beam is experimentally mapped by scanning the beam with a common bare fiber local probe, as shown in Fig. 3(a) . The probe is realized by usual heating-pulling technique of a monomode optical fiber.
The exposure setup is reported in Fig. 3(b). The average power-density of the Bessel beams has been set to 32 mW.cm-2. In that case, the maximum intensity inside the polymer film (Fig. 2(a)) has been calculated to a value slightly higher than 40 W.cm-2 with radial polarization (calculations not detailed here). We can expect that the two other polarizations give maximum intensities close to this value. The illumination durations have been limited to 0.5 seconds giving rise to a maximum photon dose of 20 J.cm-2.
4. Results and discussion
For each radially, circularly and azimuthally polarized Bessel beam, the experimental transverse intensities are reported in Figs. 4(a), 4(e), 4(i), respectively, whereas the longitudinal intensities are simulated in the radial and circular cases (Figs. 4(b), 4(f), respectively). Topography acquisitions are reported in Figs. 4(c), 4(g), 4(j).
We see from Figs. 4(b), 4(c) and 4(f), 4(g) an obvious relationship between the surface deformations and the longitudinal intensity of the illuminating Bessel beams. In radial polarization, the simulated longitudinal intensity (Fig. 4(b)) and the experimentally measured topography (Fig. 4(c)) exhibit a central maximum whereas the experimental transverse intensity provides a central dark spot (Fig. 4(a)). Moreover, the central bump displayed in Fig. 4(c) is of the same size as the central spot of Fig. 4(b). Figure 4(d) confirms the clear similarity between the simulation of |ET |2 (top dashed profile) and the experimental optical inspection (top solid profile) and between the simulation of |EL |2 (bottom dashed profile) and the photoinduced surface deformation (bottom solid profile). In circular polarization, the simulation of |EL |2 (Fig. 4(f)) and the experimental topography acquisition (Fig. 4(g)) exhibit a central minimum whereas |ET |2 presents a central bright spot (Fig. 4(e)). The central relief does not reflect exactly the highly symmetrical annular shape of |EL |2 surrounding the central dark spot (Fig. 4(f)). This can be explained by a slight non-linearity of the polymer layer with respect to the illumination parameters. Nevertheless, as for radial polarization, Fig. 4(h) displays a quasi overlap between the profiles of the experimental optical image (top solid curve) and the simulation of |ET |2 (top dashed curve) as well as between the profiles of |EL |2 simulation (bottom dashed curve) and topography acquisition (bottom solid curve, profile along the direction perpendicular to the central node line).
Figures 4(i)–4(k) depict the case of the azimuthally polarized Bessel beam exhibiting a null |EL |2. Figures 4(j) and 4(k) show that the visibility of the imprint written by the lateral fringes of the Bessel beam does not exceed the noise level of our topography sensing device. It means that the maximum amplitude of the surface deformation is limited to a few nanometers. It is much lower than the one obtained with the two other polarizations since the topography acquisitions exhibit in these cases much higher signal-to-noise ratios (see Figs. 4(c), 4(d) and 4(g), 4(h)).
From these results, we can assert first that the concentrations of matter are mainly located in the maxima of |EL |2 and second that the surface modulation is proportional to the longitudinal intensity (a PF phenomenon is observed). In the following, that will be our first and second conclusions.
Our interpretation does not explain the photochemical mechanisms which originate the surface deformation. However, several models have proposed some ways to describe the process [15, 16]. These models use Fresnel diffraction theory to calculate the optical fields. This implies that EL is not taken into account in the interpretation of the photochemical process. Such an approximation is disputable in the description of a polarization sensitive process even whether the study is made in paraxial regime. In our case, it can explain the difference between our experimental surface imprint and the surface relief predicted in Ref.  (Fig. 4(l)). Although the maxima of the two curves coincide, which confirms our first conclusion, the modulations do not overlap.
More generally, complete vectorial theory of electromagnetism points out that |ET |2 and |EL |2 exhibit two distributions which do not overlap. For example, the interfering beams used to generate surface relief gratings carry two interference patterns. They are described by complementary square sinusoidal functions exhibiting a π-phase difference to each other. Therefore, the fact that the polymer moves toward the maxima of |EL |2 is consistent with experimental observations of the surface relief grating formation . It gives an alternative explanation to the π-phase difference between |ET |2 and the surface deformation. Here, the azo polymer records faithfully |EL |2, which confirms our second conclusion. The linearly polarized focused fields, described in Ref. , exhibit |EL |2 distributions in a two side-lobe structure around the central spot carried by |ET |2. The surface relief patterns generated by such beams show a two-bump structure around a central hollow . From this result, the polymer appears to leave |ET |2 in order to concentrate into the longitudinal intensity maxima. The polymer relief roughly reproduces |EL |2 despite the fact that we observe a strong non-linearity in the center.
Let us stress that care must be taken to avoid the shortcuts between |ET |2 and the total intensity, as suggested by Fresnel theory. For example, it is assumed in Ref.  that the material is concentrated in the minima of the light intensity. This is not confirmed in Fig. 5 which displays the surface deformation obtained with a radially polarized highly-convergent Bessel beam (the numerical aperture of the Bessel beam generator is equal to one, λ = 488 nm, the index of refraction of the azo-polymer is equal to 1.55  and the maximum photon dose inside the polymer layer is calculated from experimental parameters to 550 J.cm-2). Topography acquisition has been performed with the usual shear-force detection technique . In that case, the maximum of the light intensity over the film thickness (which corresponds to the maximum of |EL |2) gives rise to the maximum of the surface relief pattern. Figures. 4(j) and 4(k) also show that matter does not move in the minima of the total light intensity.
Our approach has two consequences in the study of azo-dye polymers. First, the models describing the microscopic photochemical reaction must take EL into account. The sensitivity of azobenzene molecules to EL can explain the surface deformation process. Second, our conclusions can be enlarged to any illuminating objects whatever their nature (diffractive objects, fluorescent elements, etc).
In this paper, we have shown that azo-dye polymers (PMMA-DR1) have remarkable optical properties as their surface deformation reproduces the longitudinal intensity of the illuminating light field. Such a property makes azo polymer layers opening a wide field of applications in which they can play the role of longitudinal electric-field probe. This new kind of polarization sensitive sensors will offer new possibilities in the vectorial characterization of electromagnetic fields, in particular for nano-optics. Its dielectric nature limiting the risks of probe-to-sample coupling, it can probe either dielectric or metallic nano-objects [19, 20], providing the complementary information missing with usual dielectric bare tips (transverse intensity sensors).
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