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Averaging and shifting the refractive index profiles of quasiperiodic structure reveals the formation of several localized modes in the reflectivity spectrum and were used to generate different spectral barcodes. By associating the depth and wavelength of the observed resonant modes to the thickness and position of blackbars, respectively, the possibility to generate multiple codes has been shown. An experimental verification was carried out with multilayered dielectric porous silicon structures with reflectivity spectra revealing unique photonic fingerprints.
© 2015 Optical Society of America
1. Introduction
Due to the fact that porous silicon (PS) is relatively easy to fabricate, economically viable and compatible with electronic industry, it has been intensively explored for fabricating different types of one dimensional photonic crystals like rugate filters [1], Bragg reflectors [2], microcavities (MCs) [3], quasi periodic structures [4], which have been applied in the field of chemical and biosensors [5], optical filters [6], etc. Detection of organic molecules such as antibodies, enzymes or proteins, has been performed using PS templates by monitoring the shift of the optical reflectivity spectrum [7–10]. However, when there are many different binding reactions with different events occurring in a single sample, distinguishing between them becomes crucial to identify a specific component. Hence, there is a requirement to fabricate devices with spectral barcode response facilitating the search and identification of different molecules/nanomaterials [11–13]. So, apart from the standard systems mentioned above, many other structures have been proposed, e.g., Chan et al. showed the formation of multiple peak/dips microcavity resonator as a possible biosensor [14], where the number of reflectivity dips was controlled by increasing the thickness of the defect layer (IDL). Chen et al., showed the formation of composite barcode structures by simple summation of up to 20 different cosine waveforms in the 500–1000 nm wavelength range [15]. The information capacity was compared with the composite step method consisting of stacking 4 different Fabry-Pérot layers and analyzing their corresponding FFT spectra. Moreover, in order to obtain a multiple-peak optical response from the same photonic structure, the fabrication of composite structures has been studied through sequential (SQ) [16–18] and superposition (SP) addition [19–21] of refractive index profile functions. Composite rugate type structures have been tested as sensors and found to demonstrate relatively high sensitivity and quick response as compared to sequenced rugate filters [22]. Additionally, Ramiro-Manzano et al. reported the photoluminescence based barcode structure with colloidal porous silicon [13]. Recently our group demonstrated the tunability of the optical response of superposition/sequential addition of refractive index profile functions to obtain better quality resonant modes [16]. In this work, multiple barcodes have been systematically designed by combining the averaging [19], shifting [16], and IDL effects [14], to fabricate a multi-peak spectral response structure based on nanostructured porous silicon dielectric multilayers.
2. Theoretical overview
To model the propagation of light in these systems transfer matrix method reported in [6, 16] was used. Briefly, if an electromagnetic polarized wave propagating in a one dimensional multilayered dielectric structure is considered, the reflectance can be written as
where is the amplitud reflection coefficient and where ε0 is the vacuum permittivity, μ0 is the vacuum permeability, and nj is the refractive index of the j-th layer. The matrix elements mαβ of Eq. (2) corresponds to the resultant multiplication of individual matrices of the form where N is the number of the layers, s is the substrate, k0 is the wavevector magnitud, hl is the optical thickness of the l-th layer, and .In order to show the optical properties of the composite multilayers, and modulation effect under addition and shift, the averaging technique of the superposed structures is proposed as follows:
where ni(x) is the refractive index profile of the ith functions, x is the optical thickness, and p is the number of averaged functions. The information regarding the physical thickness di and the corresponding refractive index ni is encoded in the composite averaged function nave(x) which in turn is used to obtain the reflectance spectrum.In this article, we study the reflectivity response of averaging refractive index MC functions which have been added starting from different initial position (i.e., shift), to generate localized modes and show their application as barcodes.
3. Experimental details
Some of the simulated photonic structures were fabricated through anodic etching of a (100) oriented, p-type crystalline Si wafer (resistivity 0.002–0.005 Ω·cm), under galvanostatic conditions [23]. The electrochemical anodization process was performed at room temperature, with an electrolyte mixture of aqueous HF (concentration: 48 % of wt), glycerol (purity: 99.8 % of wt), and ethanol (purity: 99.9 % of wt) in 3:7:1 proportion of volume, respectively. The current density and the duration of the etching time of each layer was controlled by a computer interfaced electronic circuit, where the current density was varied from 1.1 to 70.4 mA/cm2, corresponding to the refractive indices of 2.05 and 1.1, respectively. After the anodization process, the samples were rinsed with ethanol (purity: 99.9 % of wt) and dried with n-pentane (purity: 99.6 % of wt). The reflectivity measurements were carried out with a Perkin Elmer Lambda 950 UV-vis-NIR spectrophotometer. The refractive indices of the samples used in this work were calculated by interferometric method at 1500 nm.
4. Results and discussion
In Fig. 1, we show theoretical modelling results of the effect of averaging and shifting two MC quasiperiodic structures. Two ”close” MCs have been designed at λ1 = 0.84 μm and λ2 = 1.0 μm with a Bragg-periodicity of 12 periods and high/low refractive index values of 2.05/1.15. Figs 1(a) and 1(c) show the schematics of the refractive indices against optical thickness of MCs designed for λ1 and λ2, respectively. Fig. 1(e) shows the composite refractive index as obtained by averaging Figs. 1(a) and 1(b). Fig 1(g) corresponds the averaged and shifted structures with a relative shift of 1.5%. Figs 1(b), 1(d), 1(f), and 1(h), exhibit the corresponding reflectivity spectra of Figs. 1(a), 1(c), 1(e), and 1(g), respectively.
Fig. 1 Refractive index profiles of MC mirrors designed for (a) λ1 = 0.84 and (c) λ2 = 1.0 μm, (e) averaged resultant structure (obtained combining MCs of Figs. 1(a) and 1(c)), and (g) averaged and shifted resultant structure (obtained combining MCs of Figs. 1(a) and 1(c)). The corresponding theoretical modelling results of reflectivity spectra are shown in (b), (d), (f), and (h). The high/low refractive index nH/nL = 2.0/1.15.
The single microcavities designed at λ1 and λ2 present a clear localized mode with a quality factor (Q = λ/Δλ) of 4200 and 5000, respectively. The averaged structure is observed to inherit the two modes localized at the same wavelength as the single structures as reported in [19, 22] (for rugate structures). Moreover, the averaging plus shifting effect (Fig. 1(h)) also inherit the single modes and additionally generate a new one localized at 0.92 μm (as observed in a previous study [16]). However, the quality factor is reduced to 603 (for λ1), 424 (for λnew), 445 (for λ2) as compared to the single structures. The diminution of the quality factor can be attributed to the effect of averaging. It has also been observed that the quality factor of the composite structure depends upon the relative overlapping and shifting among the constituent structures. This point will further be elaborated in the latter sections. Hence, averaging MC refractive index functions generates a structure with the optical properties of each individual structure, while shifting effect provokes the emerge of new localized modes. The advantage of this averaging method is to obtain several localized modes with a reduced physical thickness structure as compared to the sequentially added substructures, for example, in the case reported in [18].
On the other hand, Fig. 2 shows theoretical modelling results of the generation of many microcavity modes by increasing the defect layer (IDL) thickness. In this case, microcavity mode was designed at λ3 = 0.74 μm using the same refractive high/low index values as Fig. 1. Figs 2(a) and 2(b) show the typical microcavity reflective index profile and the reflectivity response, respectively, with λ3/2 defect layer size. As the defect layer is gradually increased (Figs. 2(c) and 2(e)), more microcavity modes appears as can be observed in their corresponding right hand side spectra (Figs. 2(d) and 2(f)), however, to remain the designed mode (at 0.74 μm) the thickness must be an integer multiple of λ3/2. Similar results have already been discussed in [14, 17].
Fig. 2 Refractive index profiles of MC mirrors designed for λ = 0.74 μm with the cavity optical thickness of (a) λ/2, (c) 6.5λ, and (e) 13λ. The corresponding theoretical modelling results of reflectivity spectra are shown in (b), (d), and (f). The refractive indices are taken as nH = 2.0 and nl = 1.15.
Combining the averaging, shifting and IDL effects, a composite photonic structures with multi-peak optical response, was obtained (Fig. 3). Additionally, the implementation of multimode microcavities as barcode is illustrated. The composite multimode structures have been obtained by averaging two close nearby multi-MC structures designed at wavelengths λ4 = 0.74 μm and λ5 = 0.76 μm. The defect layer has been increased sufficiently to incorporate 7 microcavities in each substructure. The upper part of each panel in Fig. 3 represents an schematic of the resultant refractive index profile with the three mentioned effects (averaging, shifting, and IDL); middle part corresponds to the reflectivity response and the lower part is the barcode image of the experimental spectra. Figures 3(a)–3(d) correspond to 10, 30, 40, and 60 % of shift, respectively. Depending on the percentage shift and averaging, microcavities are highly tunable in terms number of localized modes, position, and depth, obtaining up to 14 MC peaks (Fig. 3(c)). This information has been used to represent the composite microcavities as barcodes. Each bar has been initially drawn at the position of each microcavity peak and the thickness of the bar has been scaled to the subsequent depth of the corresponding microcavity, normalized to the distance between its corresponding peak. Unique barcode structure for each shift value is revealed. In order to verify the theoretical assertions, optical response of experimentally fabricated PS based barcode structures is also presented as a black line along with the corresponding simulated response (gray line). Although there are differences in the quality factor/depth of the resonant modes of the microcavities, the experimental data is in close agreement with the corresponding theoretical simulation. The reduction of the quality factor and the width of the photonic band in the experimental data can be attributed to the dispersion at the interfaces, experimental errors in the measured refractive indices, physical thicknesses and the resolution of the equipment.
Fig. 3 Schematics of the refractive index profile (upper part of each panel), simulated (gray line) and experimental (black line) reflectance spectra (central part of each panel), and the corresponding barcode image (lower part of each panel) of the experimental spectra, for averaged and shifted structures with (a) 10, (b) 30, (c) 40 and (d) 60 % of shift.
The cross sectional field emission scanning electron microscopy (FESEM) images of PS based barcode structures corresponding to the optical response analyzed in Fig. 3, are shown in Fig. 4. Variation of porosity can be seen in the form of layered structure.
Fig. 4 FESEM cross section of multi-peak response structures obtained by averaging two multi-MCs designed at λ1 = 0.74 μm and λ2 = 0.76 μm with (a) 10%, (b) 30%, and (c) 40% shift. The dark and clear zones correspond to the high (low) and low (high) porosity (refractive index) layers, respectively. Left hand side of each image shows the corresponding schematic of the refractive index profile along the depth.
To understand the complete range of tunability of the resultant structure, a contour plot of the reflectivity response as function of the percentage shift and wavelength is shown in Fig. 5. The effect of shifting in the microcavity modes can be observed as slanted wavy lines which correspond to localized modes when obseved vertically for a specific shift value. The position in terms of wavelength and the depth of the microcavity can be tuned with an appropriate shift value. The number of microcavity modes at 0 % shift is lower than in the central part (e.g. in 50 %), however, the depth of the modes is reduced with an increase in % shift. Moreover, at the far end when shift is 100 %, modes almost disappear. Hence, multiple combinations of barcodes can be generated by choosing the various intermediate shifting values. There are in principle infinite combinations of barcodes due to the continuous nature of the superposition addition technique; however, in practice the number of possible codes is restricted by the resolution of the measured spectrum.
Fig. 5 Contour plot of the reflectivity spectrum, as a function of wavelength and the percentage of relative shift for two composite microcavities under averaging. The color scale indicates the percentage of reflectivity.
5. Conclusion
The design and fabrication of spectral barcodes has been theoretically and experimentally demonstrated, by averaging and shifting the refractive index profiles of multi-peak microcavity substructures. Apart from the inheritance of the localized modes corresponding to the individual peaks of each single microcavity, combining the three effects (averaging, shifting, and IDL), the emergence of upto 14 localized modes could be obtained, with the advantage of a reduced physical thickness and higher number of MC modes as compared to sequentially added substructures. A unique spectral barcode codification was shown by associating the position and depth of each peak of the spectrum, to a set of black bars.
Acknowledgments
The authors acknowledge M. José Campos (IER-UNAM) for FESEM imaging. The work is financially supported by CONACyT ( CIAM 188657).
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