1. Introduction

Formation of spontaneous periodic nanostructures (SPN), (also known as self-organized gratings) in photosensitive thin AgCl waveguide films doped by silver nanoparticles, has been studied and reported for the first time by V.K. Miloslavsky and L.A. Ageev [1] and was then studied widely with their colleagues [2–7]. Abilities of recording the polarization state of the incident light [1, 3–10] and dynamic response of Ag doped AgCl waveguide thin films to the change of the polarization state [3–7], are well studied effects of the AgCl-Ag system. The photosencitive AgCl-Ag thin films are also able to record information about the wavelength [6, 11] and the angle [1, 12] of the incident light, which makes it a proper material for optical storage of data. Dependence of the period of SPNs on the index of refraction of the substrate [1, 14], the induction of dichroism and optical gyrotropy in the irradiated AgCl-Ag thin films [1, 5, 7, 13], provide them as interesting photonic material promising applications like: (i) optical storage of data (polarization state, wavelength [8], angle of incident [1,12] etc.), (ii) a simple method for determination of index of refraction of the substrate’s material (n_s) by measuring the period of the produced SPN and using its relation to the n_s [14]. The AgCl-Ag system could be used as a simple available physical system, which helps for better understanding the scattering of light by metallic clusters and nanostructures embedded in a dielectric matrix [1–5, 13].

The interaction of thin AgCl waveguide films, doped by Ag nanoparticles, with varying monochromatic light results in interesting optical properties, which has been studied [1,6,11,15]. While these studies already suggest that specific irradiation of photosensitive thin films can be used to customize the nano-structuring of these thin films, none of these studies point the manner of nanostructures in the area irradiated by light beam with different wavelength.

In the present article, we examine in detail the impact of irradiation of AgCl-Cl thin films with monochromatic light of varying wavelength. Monitoring the size, shape and structure of the formed silver nanoparticles is essential for the quality of the produced nano-grating (SPN) made by different wavelength and consequently, its optical properties.

2. Formation of self-organized gratings

As was mentioned in [3, 5], a thin AgCl film (h ~50 nm) on a glass substrate coated by a very thin film of Ag (h_Ag ~10 nm) can act as a photosensitive sub-wavelength slab waveguide. Furthermore, a very thin film of noble metals (Ag, Au, and Cu) on a dielectric substrate like AgCl shapes as an island film made of nano-sized granular metal [1]. Irradiation of such system by polarized monochromatic light (like a He- Ne laser beam (λ' = 632.8 nm)) causes scattering of incident light on the present nanoparticles on the surface of the sample or on roughness of the surface (Fig. 1(a)).

 

Fig. 1 A schematic picture of SPN formation mechanism. An AFM image of a SPN, formed under exposure to a linear polarized light (E₀) is shown in the top-right inset of the figure.

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The scattered beams could propagate along the AgCl slab waveguide (TE_n-modes of the waveguide), which interfere with the incident light (Fig. 1(b)). At this stage, the silver nanoparticles start moving to minima of the interference pattern and form the SPN. Ag nanoparticles prefer move to the minima of the interference patter to minimize their total energy [1]. At the same time, the forming SPN could act as an entrance gate for the waveguide film and therefore enhances the intensity of the propagating modes, which increases the intensity gradient between maxima and minima of the interference pattern. This in turn, accelerates the migration of silver nanoparticles toward the minima of the interference pattern leading to the SPN growth (top-right inset of the Fig. 1). The above-mentioned mechanism is called “positive feedback of light”, which is the reason, why sometimes the SPN are called: “self-organized gratings” [1].

The grating vector of the formed grating can be described as:

Equation (2) is obtained from the phase matching condition at cut-off thickness of the slab AgCl waveguide, at normal incident:

Thus, from Eq. (2) we find that for n_s = const. by changing the wavelength (λ), one can produce SPN with different periods. Hence, by tuning the irradiation wavelength continuously [1, 6, 11] fabrication of multiplexer gratings should be possible. But, the present investigation shows that different regime of irradiation result in different products, and the quality of the SPN (i.e. the sizes and shapes of the optical induced nanostructures) does not only depend on exposure time and intensity of irradiation but on the irradiation wavelength, as well. At the same time, the silver nano-clusters are not able to reconcile themselves to the very smooth gradient of wavelength change along the spectrum.

3. Experiments and results

We have carried out our experiments for continuous spectrum of the white light in two regimes: (1) Slow regime: that is, lower intensity of incident light with very long exposure time (order of few hours); (2) Fast regime: that is, high intensity with relative shorter exposure time (order of few 10 minutes). Our findings indicate that extending the exposure time results in worsening the quality of the formed periodic nanostructures. Microscopic investigations show that, the shape and size of the formed silver nanoparticles and coalescences are strongly affected by the irradiation regime. Consequently, the irradiation regime influences on the fineness and general characteristics of the produced SPN. All of the mentioned parameters play essential roles for spectroscopic and optical properties of the samples.

In this connection, SPN are prepared within three different settings: exposure of the samples (i) to red, green and blue diode laser beams, (ii) to the continuous spectrum of a Xenon white lamp and (iii) to the continuous spectrum of a white laser beam. Then their absorption spectra are measured. Structural development of the formed SPN and relative abundance evolution of silver nano-coalescences are also investigated for each case by AFM and SEM techniques. In the second part of the work temporal evolution of the formed SPNs is studied, in addition.

3.1 Sample preparation method

Samples were prepared by vacuum deposition (at p ≈5 × 10⁻⁵ mmHg) of a thin film of AgCl (n_f = 2.06) on a accurately cleaned glass substrate with n_g = 1.515. Then, a very thin layer of silver (h_Ag ~10 nm) was coated on the AgCl film. Such coating leads to formation of a nano-scaled granular layer of silver on the AgCl film, which turns the AgCl-Ag system into a thin photosensitive sub-wavelength slab waveguide film. The thickness of the AgCl waveguide film should be chosen close to the cut-off thickness of the waveguide TE₀ mode. The cut-off thickness (h) could be calculated using the dispersion equation for an asymmetric slab waveguide (Air/AgCl-Ag/Glass system) [2, 16]. For wavelength λ' = 632.8 nm (He-Ne laser beam) we have: h = 49 nm. If one takes the thickness of the AgCl greater than h, higher order TE_n modes of the slab waveguide (TE₁, TE₂, …) would be excited in the film and thus form higher order gratings interfering with each other. That would decrease the diffraction efficiency of the formed structure and, thereby, lower the quality of the produced multiplexer, especially for shorter wavelength of the incident white light. For thicknesses less than the cut-off limit, no TE-mode excitation occurs and subsequently no SPN formation happens. Unfortunately, it turns out to satisfy both conditions at the same time, in our case, for producing SPN with a continuous spectrum between a wavelength of 400 nm and 700 nm. A thickness of the AgCl layer limited by the cut-off thickness calculated from the maximum value of 700 nm automatically allows for higher order modes at the minimum wavelength of 400 nm, which consequently worsens the quality of the SPN at lower wavelength. Finally, all samples should be reserved in a dark and dry place until the time of use in the experiments.

3.2 Exposure of the samples

For producing SPNs with monochromatic light, the samples were exposed to monochromatic light at different wavelengths, produced by a tunable diode laser (Fig. 2(a)) for 1 hour with wavelengths: λ_R = 661 nm, λ_G = 532 nm, and λ_B = 457 nm, with powers of P_R = 10 mW, P_G = 3 mW and P_B = 5.8 mW, respectively. The radius of the laser beam was r = 3 mm, hence the corresponding intensities were: I_R = 353.3 W/m², I_G = 106.0 W/m², I_B = 204.9 W/m². The related AFM images are shown in Figs. 3(a)-3(c).

 

Fig. 2 Experimental setups for producing the SPN under exposure to: (a) monochromatic laser beam at different wavelengths; (b) continuous spectrum of a white laser beam; (c) continuous spectrum of a Xenon lamp. The sample during and after irradiation by spectrum of a Xenon lamp is shown as an inset in top-right of the figure.

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Fig. 3 AFM images of samples irradiated by a tunable diode laser beam at three different wavelengths: (a) λ_R = 661 nm; (b) λ_G = 532 nm; (c) λ_B = 457 nm. Corresponding dichroism spectra are shown below in (d-f).

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The samples also were irradiated by a white laser light in monochromatic mode for 2 hours (Fig. 2(b)) at three wavelengths: λ_R = 680 nm, λ_Y = 580 nm, and λ_G = 530 nm with powers of P_R = 2 mW, P_Y = 1 mW and P_G = 1 mW, respectively. The radius of the white laser beam was r = 1 mm, hence the resultant intensities were: I_R = 636.9 W/m², I_Y = 318.4 W/m², I_G = 318.4 W/m². The corresponding SEM images of the samples irradiated by the mentioned wavelengths are presented in Fig. 4.

 

Fig. 4 SEM images of samples irradiated by a white laser beam in monochromatic mode at wavelengths: (a) λ_G = 530 nm; (b) λ_Y = 580 nm; (c) λ_R = 630 nm; (d) non irradiated sample. Corresponding surface coverage for each case is calculated and shown below of each image.

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As can be seen from Fig. 4, the non-irradiated sample has a chain-like island structure composed of silver nano- coalescences with no preferred orientation. From both Fig. 3 and Fig. 4, it is obvious that irradiation at longer wavelength produces better oriented and finer SPNs. For Fig. 4 we have determined the surface coverage by silver (surface filling factor), for samples irradiated at different wavelengths. The results are shown in the lower inset of Fig. 4. As can be seen, samples irradiated by the blue laser beam have smaller surface coverage by silver coalescences and they are well arranged along the direction of polarization of the linear polarized incident light in comparison with the SPNs formed by longer wavelengths. For the sample irradiated by red laser beam, empty spaces among the chain-like structures are much less than in the case of exposure to the blue laser beam (compare Fig. 3(a) with Fig. 3(c)). But, clearly, the SPN formed at exposure to the green light has the optimum structure in comparison to the former cases.

For the samples exposed to monochromatic light (produced by a tunable diode laser), we measured the relative abundance of silver nanoparticles with different sizes (Fig. 5). The measurement was carried out by numerical analysis of the SEM images done by Gwyddion software [17]. As Fig. 5 implies, irradiation at longer wavelength produces SPN with smaller Ag clusters. Irradiation at red light has produced nanoparticles with average size of ~50 nm, exposure to green light yields particles with a size round about 60 nm and exposure to blue light has generated coalescences with an average size of ~70 nm. At the same time, as already mentioned, smaller nanoparticles in general could be better ordered along the direction of the polarization of the incident light. The chains which are made of smaller and more compact clusters (Fig. 4(c)) have greater absorption (Fig. 6) in comparison to those which are made of larger clusters with less surface coverage (Fig. 4).

 

Fig. 5 Relative abundance of samples irradiated by a tunable diode laser beam at three different wavelengths: (1) λ_R = 661 nm; (2) λ_G = 532 nm; (3) λ_B = 457 nm.

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Fig. 6 The optical densities for samples irradiated at different wavelengths mentioned in caption of Fig. 5

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The samples were also irradiated by a high power super continuum fiber laser beam (NKT photonics Company: model: Super-K VARIA).The wavelength ranges between 400 nm and 840 nm with nominal total power equal to 4.5 W, but we used 400-700 nm range (Fig. 2(b)). The exposure time was 30 minutes (the Fast regime).

The corresponding SEM images of the induced nanostructures along the spectrum for determined wavelengths are shown in top-left inset of Fig. 7.

 

Fig. 7 The produced multiplexer and corresponding SEM images of each region labeled (a-d).Images in the middle-right inset labeled: 1, 2, 3, 4, 5 are showing the diffraction of the multiplexer at different incident angles of the probe white light.

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The spectrum of the used white laser in our experiments had non-uniform intensity distribution along it, which leads to formation of SPNs along the spectrum with different positive feedback of light. In our case, intensity in the blue region was less than that of the red region of the spectrum, which makes better SPN in the longer wavelength. Because of that, as can be seen from the top-left inset in Fig. 7, SPNs formed at shorter wavelengths are similar to the non-irradiated samples in comparison with those SPNs formed at longer wavelengths.

This outcome is not the same as in the case of exposure at the discrete wavelengths (λ_R = 680 nm, λ_Y = 580 nm, and λ_G = 530 nm) of the same laser.

To check the generated structure as an optical multiplexer the produced SPN was washed with photography fixing solution to remove the AgCl layer and then was coated in vacuum by a 50 nm gold layer to increase its reflectance. With this method at the same time the produced structure loses its photosensitivity. Afterward, the exposed region on the sample was framed by a simple black mute paper for better view. Now, if one illuminates it by white light, for a determined angle of view each part of the multiplexer diffracts different wavelength in that direction, because of changing the mean period of the produced grating at that point. An observer thus sees different colors (middle-left inset in Fig. 7). If one changes the incident angle of the white light on the multiplexer (top-right inset in Fig. 7), it seems that colors for each part of the grating changes (middle-right inset in Fig. 7). The reason for changing colors with changing incident angle is obvious. The corresponding nanostructures for the labeled parts (a, b, c, d) of the multiplexer are shown in bottom of Fig. 7.

A series of samples was irradiated by a Xenon white arc lamp (Fig. 2(c)), (P = 300 W, Ozone free, the Newport Company). The spectral range was 200nm-2400nm. In our experiment we utilized the range 450nm-650nm. The samples were irradiated for 22 hours by the Xenon lamp (the slow regime). In this case, the produced nano-clusters differ from the samples exposed to the monochromatic diode laser or the white laser beams. The results of these series of experiments are shown in Fig. 8.

 

Fig. 8 SEM images (a-c) and corresponding dichroism spectra (d-f) of the samples irradiated under the slow regime of irradiation (Xenon lamp) at different wavelengths: red, yellow and green, respectively.

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In Fig. 8(a)–8(c) the SEM images of three different regions of the sample (red, green and blue parts of the spectrum) are shown. The corresponding regions on the sample are indicated in the inset of Fig. 9. As can be seen, there is now clear grating or obvious arrangements along the polarization vector of the incident light (E₀). It should be noticed that, for irradiation with the blue region of the spectrum the formed coalescences are larger and we see more empty spaces between them.

 

Fig. 9 The relative abundance for the samples irradiated under the slow regime of irradiation (Xenon lamp) at different wavelengths: red, yellow and blue, respectively. The three regions on the sample are labeled: 1, 2, 3 on the top-right inset.

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At the same time, relative abundance measurements points to formation of smaller nanoparticles with narrower size distribution at longer wavelength of the incident light (Fig. 9). In other words, in addition to the formation of larger clusters, exposure to blue light (short wavelength) results in a wider size distribution in comparison to the region of the sample, which is irradiated by the red light (long wavelength) in the slow regime.

Disordering in the exposed samples under the slow regime reveals that there is a contest between the directing forces of the interference field for ordering of the nanoparticles according to the interference field and the random and statistical behavior of the nanoparticles, which leads to absence of noticeable SPN generation. But, as the inset of Fig. 9 shows, the information about the wavelength of the incident light is still recorded in the interaction area on the samples. As can be seen from inset of Fig. 9, the area on the sample, which has been exposed to red light (labeled as: 1) have red color, and the areas which have been irradiated by the yellow or blue part of the spectrum (labeled as: 2 and 3 in the inset of Fig. 9, respectively) have yellow or blue colors, respectively. That is, although there is no visible ordering or arrangement of nanoparticles and clusters in the irradiated AgCl-Ag thin films, the information of wavelengths of the incident light is recorded in it. This is unlike the conventional photography materials, where the complementary color is recorded. In other words, exposure to the Xenon lamp results in inducing photoadaptation and hole burning [18, 19] for the silver clusters (Fig. 6 and Fig. 10).

 

Fig. 10 Optical densities for regions 1, 2, 3 of the samples irradiated under the slow regime are shown in Fig. 9.

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3.3 Absorption spectra after irradiation

Another method of investigation, which can help for better understanding the effect of wavelength of the incident light on the formation of the induced nanostructures and clusters in AgCl-Ag thin films, is absorption spectroscopy. As a measure of absorption, we have determined the optical density ($D=-Log\left(I/I_0\right)$, where $I$ is the intensity of the transmitted light from the sample and $I_0$ is the intensity of the probe light) of the samples. In the present study, absorption spectra of our samples are measured for both non-polarized and linear polarized incident lights.

Absorption spectra of the samples, for non-polarized light, which were irradiated by the diode lasers at three different wavelengths, are shown in Fig. 6. There are obvious differences in the spectra of the samples, which are irradiated at different wavelengths. In general, absorptions of the irradiated samples are less than the non-irradiated one. In addition, irradiation at shorter wavelength results in decreasing the absorption. At the same time, in the absorption spectra of the irradiated samples a shoulder appeared around λ = 360 nm (indicated by a red arrow in the Fig. 6). This could be related to the quadrupole excitation in the chain-like complex nanoparticles which cause the interband transition in the formed clusters [19–22]. The formed clusters are coarsening at decreasing wavelength of the incident light (Fig. 5). Coarsening of the silver nanoparticles leads to a weakening of their surface plasmon resonance peak, consequently enhancement of bulk behavior, and an overall reduction of absorption along the whole spectrum (Fig. 6).

At the same time, absorption spectroscopy of these samples using linear polarized light (E) shows that formation of SPN (i.e. the arrangement of silver nanoparticles along the polarization vector of the incident light, E₀) results in differing absorption for the linear polarized probe beam, when E||E₀, D_||, and E⊥E₀, D_⊥, (Figs. 3(d), 3(e), and 3(f)). The quantity ∆D = D_|| - D_⊥ is called dichroism. Better arranged nanostructure exhibits larger dichroism. The peak position and spectral interval of induced dichroism is proportional to the size of the clusters and coalescences forming the SPN. Anyhow, appearance of dichroism after irradiation means recording of polarization state of the incident light has happened, but its amount depends on the wavelength of the incident light.

As it can be seen from Figs. 3(d)-3(f), irradiation with red light induces dichroism in the blue region; conversely, illumination with green light causes dichroism in the red region (Figs. 3(d) and 3(e)). It means in all cases significant bleaching is observed (see also Fig. 6). In other words, photo-fragmentation and hole burning occur [ ] for the silver clusters, whose size establishes conditions for resonance with the wavelength of the incident beam. Thus, after irradiation with specified wavelength those clusters which were able to absorb the light (with that wavelength) are decomposed to particles and monomers with smaller sizes and vanish. That is, absorption for that wavelength of the incident light reduces. Consequently, the induced dichroism would be stronger in the rest of the spectrum.

The same spectroscopy is done for the samples exposed to the continuous spectrum of the Xenon lamp (Fig. 8). As was mentioned and as we can see from the SEM images of Fig. 8, irradiation at lower intensity with long exposure time (22 hours) makes the statistical behavior dominate the directing forces of the interfering fields which suppresses SPN formation. But, the existence of dichroism at the different wavelengths of the probe beams indicates that information about the polarization of the incident light (E₀) has been recorded in the formed collection of the clusters (Fig. 8).

Decrease in wavelength of the incident light leads to formation of chain-like coalescences with similar width and length of the clusters (Fig. 8(c)), which in general are larger than that formed under exposure at longer wavelengths (Figs. 8(a), 8(b)). As can be seen from Fig. 8(c) and 8(a), dichroism is less in case of exposure at shorter wavelength than at longer wavelength. Furthermore, (Figs. 8(d)-8(f)) reveal that the spectral interval of dichroism for chain-like structures composed of larger clusters with similar length and width is smaller than for longer chains made from finer clusters. That is, in our case, decrease in wavelength of the incident light reduces the ability of the AgCl-Ag system for recording the polarization state of the incident light.

Looking carefully at Fig. 10, especially at curve 2, some hole burning in the absorption spectra depending on the wavelength of the incident light is revealed. This is typical for induction of photoadaptation in the samples, irradiated under slow regime.

3.4 Temporal evolution of the produced nanostructures

As was mentioned in the section 2, the formation of the SPN in the AgCl-Ag thin films is accompanied by a positive feedback mechanism. In order to learn about the impact of the exposure time on the structure of the forming SPN, we have examined the SEM images (Fig. 11) and corresponding absorption spectra (Fig. 12) of the samples, which were irradiated at different exposure times and wavelengths. It is obvious from Fig. 11 (@ λ = 457 nm) that an increase in exposure time, at first, improves the structure of SPN (Figs. 11(a)-11(c)) and then longer exposure results in damaging the formed structure (Fig. 11d). The polarization state of the incident light was linear in this case.

 

Fig. 11 SEM images of samples irradiated by a laser beam at λ = 457 nm and different exposure times: (a) t = 0 min. (b) t = 15 min. (c) t = 30 min. (d) t = 45 min. an enlarged part of each image is shown as an inset in the lower part of each image.

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Fig. 12 Changes of amount and peak positions of dichroism at different exposure times for samples irradiated by: (a) Red; (b) Green; (c) Blue laser beams.

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Measuring the dichroism (∆D) of samples irradiated at different exposure times shows that (Fig. 12) increasing the exposure time results in reducing the dichroism at all wavelengths. Reduction of ∆D means reduction of the regularity induced due to the SPN formation (see Fig. 11(d)).

4. Discussion

As was shown in the previous section, irradiation of the samples under both, the fast and slow regime at different wavelengths, results in different scenarios.

Under the fast irradiation regime better and more regular SPN are formed (Figs. 3, 4, and 7). Under such condition silver nanoparticles rearrange themselves according to the strong interference field and consequently, steeper gradient between maxima and minima of the intensity pattern does not let to the statistical behavior of the nanoparticles and their random agglomeration and aggregation as exothermic processes [23], take place dominantly.

In contrast to the fast regime, irradiation under the slow regime results in forming of SPNs with much less degree of regularity (Fig. 7). The weak field of interference pattern under the slow regime leads to not very steep intensity gradient which makes it incapable to compete with the statistical behavior of the nanoparticles. In both regimes, information about the polarization state of the incident light is recorded by the formed structures and coalescences (the dichroism spectra in Figs. 3, 8, and 12). As it can be seen from the mentioned figures, the observed dichroism is positive only for red light and it is negative for the green and blue lights. It could be explained by considering the fact that, irradiation with red light leads to formation of long chain-like structures made by smaller particles in comparison with the empty space between them. On the other hand, irradiation with longer wavelengths (green and blue) leads to formation of larger coalescences (shorter and wider chain-like structures), whose sizes are comparable to the spacing between them. Such differences in geometry may cause changing the sign of dichroism. This point needs more complete and precise investigations, which could be the next step of the present research.

Our SEM, AFM, and spectroscopic investigations reveal that a decrease in wavelength leads to formation of larger clusters and less regular SPNs (Figs. 3, 4, and 7). But, at the same time samples irradiated under the slow regime have narrower size distribution (Table 1).

Table 1. Comparison of SPR peaks and FWHM of absorption spectra of the samples irradiated by different wavelengths under the two regimes of irradiation: Fast and Slow.

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Analyzing the relative abundance of the produced silver nano-clusters for the irradiated samples under the slow regime leads us to the conclusion that the produced nanoparticles under the slow regime are more homogeneous in size relative to those produced under the fast regime. It could be related to the long exposure time, which lets nanoparticles adopt their size to the wavelength of the incident light at that location in the irradiated area of the sample.

On the other hand, shorter wavelength of the incident light results in smaller surface coverage of the interaction area on the sample in comparison to the areas irradiated by longer wavelength (Fig. 4). Decreasing the surface coverage leads to the overall reduction in absorption of the irradiated samples. At the same time, a shoulder appears in the spectra of the samples (Fig. 6). This is related to the formation of oriented chain-like nanostructures, which results in a quadrupole excitation in the already non-spherical silver clusters [24]. This excitation causes a shoulder in the absorption spectrum, as we mentioned in the right-lower inset of Fig. 6. As the interband levels are very close to each other in comparison to the interval energy between valence and conduction bands [20–23] of the clusters, changing the size of the clusters has no significant influence on the position of the shoulder in the spectra of samples irradiated at different wavelengths (Fig. 6).

At shorter wavelengths (blue region of the spectra) the thickness of the AgCl slab waveguide is larger than the cut-off thickness for the TE₀-mode, which makes more scattering of light within the AgCl thin film, leading to reduction the contrast of the interference pattern, i.e. intensity gradient with mildly slope. Thus, the random and statistical behaviors of the clusters diminish the regularity of the formed structures under shorter wavelengths (Figs. 3, 4, and 7). As we can see from the Figs. 5 and 6, for a constant regime of irradiation (fast regime in this case), with decrease of the wavelength of the incident light, the FWHM of the absorption spectra is widening, which means nanoparticles’ size and its distribution are increasing. Similar results are reported by [25].

Very smooth variation of wavelength (λ) along the continuous spectrum of the white light results in continuous and smooth change in the period of the interference pattern, on the sample, along the spectrum. The period of the forming grating (d) reduces ceaselessly with decrease of the wavelength of the incident light (d = λ / n_s [1, 14], where n_s is the index of refraction of the substrate). Therefore, the few ten-nanometer sized silver clusters could not adapt themselves to the varying interference pattern, properly. That is, in the region of the spectrum with shorter wavelengths the dark fringes, i.e., minima of the interference pattern (where silver nanoparticles prefer to go) become too tight for the migrating clusters. Consequently, the quality of the produced multiplexer reduces in comparison to the quality which we expected from the theory (Fig. 7).

To understand the influence of exposure time on the quality of the produced SPN, it is essential to account for the positive feedback mechanism: As was explained in the introduction the field inhomogeneity resulting from the interference of the incident light with the excited TE-mode in the AgCl thin film, push the silver nanoparticles toward the minima of the interference pattern. The forming SPN opens up the waveguide film for the incident light and consequently increases the intensity of the propagating modes. As it is well-known [26] decrease in difference between intensities of two interfering light beam results in rising the contrast of the produced interference pattern. Thus, the intensity gradient between maxima and minima of the interference pattern increases, which in turn, facilitates better and faster migration of silver nanoparticles from maxima of the interference pattern to the minima, leading to the SPN growth. This cycle repeats over and over. That is to say, the forming grating makes itself better and better. This is why they are named: self-organized gratings or spontaneous periodic nanostructures. But, there are three limitations to the growth of the SPN: (1) limitation of amount of available silver nanoparticles on the sample; (2) spatial restriction because of absence of sufficient space between interference fringes for the clusters which are bigger than the width of the fringes; (3) Gaussian distribution of laser beams which establishes an intensity gradient from the center of the interaction area toward its periphery (in case of laser beam as an incident light, fast regime), leading to damage the produced SPN at long exposures (Fig. 11d). Thus, reduction of dichroism for longer exposure (Fig. 12) is due to the beginning of the SPN damage.

5. Conclusion

The formation of spontaneous periodic nanostructures (SPN) in thin AgCl film, doped by silver nanoparticles, under exposure to incident light at different wavelengths is studied. Two regime of irradiation were applied: (1) Fast regime, few 10 minutes exposure with relative intensive monochromatic laser beams at different wavelengths; (2) Slow regime, many hours (more than 20) exposure at comparatively low intensity of a continuous spectrum of white light. Our results indicate that there are obvious differences for SPNs formed under the conditions of the two regimes. In comparison to the slow regime, SPNs formed under the fast regime have better regularity and consequently exhibit larger dichroism, because of the induced order and arrangement of the silver nanoparticles. In both regimes of irradiation information about the wavelengths of the incident light is memorized in the SPNs grating constant and the cluster sizes. Under the slow irradiation regime noticeable gratings are not formed, but the information about the orientation of the polarization vector of the linear polarized incident light is recorded. The different results for different irradiation regimes can be attributed to the competition between the directing forces caused by the interfering fields and the random statistical behavior of nanoparticles.

Decrease in wavelength of the incident light results in coarsening of forming nano-clusters and at the same time reduces the regularity of the formed SPNs. This is attributed to more scattering and narrower fringes at shorter wavelengths.

In case of irradiation by the laser beams, increase in exposure time leads to, at first, improvement of the SPN, but longer exposure results in damaging the formed SPN, because of general Gaussian gradient across the laser beam which tries to push the silver clusters to the periphery of the interaction area on the sample. Results of our experimental investigations are in good accordance with results of theoretical studies which are reported in [23–25].

On the base of dependent of period of SPN on the wavelength of the incident light, we tried to make an optical multiplexer (Fig. 7), which needs more improvement in the technique to produce a multiplexer with higher diffraction efficiency.