Formation of colorimetric fingerprints on nano-patterned deterministic aperiodic surfaces

Periodic gratings and photonic bandgap structures have been studied for decades in optical technologies. The translational invariance of periodic gratings gives rise to well-known angular and frequency filtering of the incident radiation resulting in well-defined scattered colors in response to broadband illumination. Here, we demonstrate the formation of highly complex structural color patterns, or colorimetric fingerprints, in twodimensional (2D) deterministic aperiodic gratings using dark field scattering microscopy. The origin of colorimetric fingerprints is explained by rigorous full-wave numerical simulations based on the generalized Mie theory. We show that unlike periodic gratings, aperiodic nanopatterned surfaces feature a broadband frequency response with wide angular intensity distributions governed by the distinctive Fourier properties of the aperiodic structures. Finally, we will discuss a range of potential applications of colorimetric fingerprints for optical sensing and spectroscopy. ©2010 Optical Society of America OCIS codes: (050.2770) Gratings; (160.5298) Photonic crystals; (290.4210) Multiple scattering; (130.6010) Sensors. References and links 1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). 2. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton Univ Pr, 2008). 3. A. David, “High efficiency GaN-based LEDs: light extraction by photonic crystals,” Ann. Phys. Fr. 31(6), 1–235 (2006). 4. N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nat. Nanotechnol. 2(8), 515–520 (2007). 5. B. Cunningham, P. Li, B. Lin, and J. 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Introduction
Scattering of photons by periodic photonic structures gives rise to a variety of interesting physical effects including manipulation of spontaneous emission [1], formation of forbidden photonic gaps [2], enhanced resonant light extraction [3,4], and resonant narrow-band backscattering [5].Recent theoretical and experimental studies revealed that these effects can also be observed in more complex structures with deterministic aperiodic morphologies (e.g., quasi-crystals, pseudo-random structures) that do not possess translational periodicity despite their long range order.In particular, photonic bandgaps (including complete bandgaps) have been observed in aperiodic photonic structures [6][7][8][9][10], lasing in defect-free photonic quasicrystals has been demonstrated [11], and enhanced light extraction and beam shaping have been obtained with aperiodic nanopatterned photonic surfaces [12][13][14].Furthermore, phenomena inherent to random media, such as light localization, have been demonstrated in aperiodic photonic structures with high degrees of structural complexity [6].
Deterministic aperiodic structures lack translational invariance inherent to periodic media, yet may feature global and/or local rotational symmetries that are forbidden in periodic lattices (i.e non-crystallographic symmetries).Aperiodic lattices range from incommensurately-modulated periodic patterns and incommensurate composite structures [15] to quasiperiodic patterns such as the well-known Fibonacci [16,17] and Penrose lattices [9,11,18] and to pseudo-random geometries with properties similar to those of random media [6,17].Unlike random media, however, aperiodic structures are generated by well-defined deterministic algorithms based on symbolical dynamics and number theory [19], and are amenable to rigorous engineering and optimization.Furthermore, aperiodic photonic structures offer a broader and more flexible design space than their periodic counterparts, enabling larger control over the degree of anisotropy in their angular and spectral optical responses.
The optical properties of photonic gratings are governed by the Fourier spectra of the associated geometrical lattices, which range from truly discrete spectra in the case of periodic and quasiperiodic structures to singular-continuous and absolutely-continuous (flat) spectra for structures with higher degrees of the structural disorder such as Thue-Morse and Rudin-Shapiro lattices [6,17,19].The discrete set of Bragg peaks in the Fourier transforms of simply periodic lattices corresponds to a discrete set of wave vectors k in their diffraction diagrams, and results in the appearance of well-defined grating orders in optical scattering [20].The Fourier spectrum of photonic quasicrystals is generally dense, and usually features one or several subsets of main reflections (brighter Bragg peaks) over-imposed to a diffused background of weaker satellites [Fig.1(a This feature of aperiodic gratings has already been used to efficiently extract light from semiconductor light-emitting diodes (LEDs) and to shape the light emission profile [12].Here, we demonstrate how multiple light scattering in nano-patterned deterministic aperiodic surfaces, which occurs over a broad spectral-angular range, leads to the formation of highly complex structural color patterns, or colorimetric fingerprints, in both the near and the farfield zones.We also discuss the new opportunities in the field of bio-chemical sensing that are offered by the spatial and spectral modifications of these colorimetric fingerprints induced by small refractive index perturbations on aperiodic surfaces.[21] and their corresponding 2D Fourier transforms (b,e).Simulated far-field multi-color scattered intensity maps of the Gaussian prime (c) and Rudin-Shapiro (f) arrays of 200nm-diameter nano-spheres with the refractive index of 1.5 and minimum center-to-center separations of 300 nm (c) and 400 nm (f).The RGB images shown in (c) and (f) are obtained by overlapping the forward-scattered field intensity distributions corresponding to the arrays illumination by a plane wave at three wavelengths in the red, green and blue parts of the optical spectrum: λB = 470 nm (blue), λG = 520 nm (green), λR = 630 nm (red).

Colorimetric fingerprints of periodic and aperiodic gratings
In order to better understand the distinctive scattering behavior of aperiodic nano-patterned surfaces, we will first briefly review the scattering properties of regular periodic gratings.We fabricated two-dimensional air-holes periodic gratings on quartz substrates by using standard electron-beam lithography (EBL).Several representative arrays of 100nm-radius and 70nmdeep cylindrical indentations with the grating period (center-to-center separation between neighboring indentations) ranging from 500nm to 800nm are shown in Fig. 2(a).The arrays were illuminated by a white light from a glass optical fiber bundle with 1.6mm bundle diameter at an approximately 15° grazing angle to the array surface using a dark field scattering setup shown in Fig. 2(b).The light reflected normally from the array plane is collected with a 5X microscope objective and imaged using a CCD digital camera (Media Cybernetics Evolution VF).The acquired images are shown in Fig. 2(c) and demonstrate the typical single-color scattering response of periodic arrays.It can be seen in Fig. 2(c) that the increase of the array grating period results in the red-shift of its scattering response.The observed red-shift is a well-known phenomenon that can be qualitatively described with classical scalar diffraction theory of periodic gratings as follows: ( ) where Λ is the grating period, λ is the wavelengths of the incident light, θ inc and θ sc are the incident and scattered angles (measured with respect to the normal to the grating surface), m is the diffraction order and n 1 and n 2 are the refractive indices of the ambient medium and the grating, respectively.The scattered wavelengths corresponding to the first four diffraction orders of a periodic grating with the 400 nm period calculated by using Eq. ( 1) are shown in Fig. 2(d) as a function of the scattering angle.In the experimental setup used, the angular distribution of the collected light is restricted by the objective collection cone (NA = 0.15), and the frequency spectrum is limited to the visible wavelength range.The range of the angular and spectral distribution of the collected light is shown in Fig. 2(d) by the dark shaded area, which is formed by the intersection of the light-shaded strips indicating the spectral and spatial collection limits, respectively.It can be seen in Fig. 2(d) that only one grating order crosses the dark-shaded area (meaning that it can be collected by the microscope), resulting in the observed single-color response of periodic gratings.The diffraction theory of periodic gratings predicts that the increase of the grating period results in the angular shifts of all the diffraction orders, giving rise to a red-shift of the scattered radiation that can be collected by the objective, in perfect agreement with the experimental data.The observed angular response of periodic gratings is sensitive to the ambient refractive index variations and thus has been used to design biochemical sensors [5,20] and optofluidic switches [22].In particular, the wavelength shift of the collected light caused by the change in the ambient refractive index or by the adsorption of molecules on the periodic nanopatterned surface is used as a transduction signal in grating-based optical sensors [5,20].3(g)] lattices were fabricated on quartz substrates by using the same standard EBL process as for periodic gratings.Since aperiodic structures lack translational periodicity, they cannot be assigned a single lattice parameter such as the grating period, but are simply characterized by defining the minimum center-to-center interparticle separation in the array.All the other, generally incommensurate, length scales present in a particular aperiodic structure can be exactly calculated from the particular deterministic inflation rule used to generate the lattice.The aperiodic arrays shown in Fig. 3 have the minimum center-to-center interparticle separations in the 300 nm to 400 nm range.In contrast to the dark-field scattering images of periodic gratings shown in Fig. 2(c), the images of aperiodic arrays collected with the experimental setup described in Fig. 2(b) feature highly organized colorimetric fingerprints, as demonstrated in Fig. 3(b), 3(d), 3(g), 3(h).Color spatial localization in different parts of the nanopatterned aperiodic surfaces can clearly be observed.We have also fabricated aperiodic arrays with different minimum centerto-center separations ranging from 250 nm to 700 nm.The colorimetric fingerprints of these structures are shown in Fig. 4. The spatial localization of the different chromatic components on the nano-patterned surfaces is evident for all the inter-particle separations within the visible spectral range.We have also studied the role of the grating material on the formation of colorimetric fingerprints.Aperiodic nanostructures have been fabricated in various material platforms, including low-index dielectrics (such as quartz and organic polymers), higher-index dielectrics (silicon nitride (SiN)) and metals (chromium and gold).The collected dark-field images of Rudin-Shapiro arrays composed of indentations in the quartz substrate, of SiN and gold nano-disks deposited on quartz substrates are compared in Fig. 5. Clearly, all the three colorimetric signatures shown in Fig. 5 feature spatial localization of various spectral components of scattered light, while the relative intensities of different spectral components depend on the specific material platform used.We can conclude that the observation of structural color localization and the formation of colorimetric fingerprints under white light illumination is a general feature of the aperiodic arrangement of nano-scale elements with separations on the order of the wavelength of light.The particular spatial distribution of the localized colors is uniquely governed by the geometrical configurations of the aperiodic structures, while the resonant scattering response of individual scattering elements contributes to the intensity distribution of various spectral components in the colorimetric fingerprint.

Formation mechanism of colorimetric fingerprints
To get a physical insight into the mechanism governing the experimentally observed colorimetric response of periodic and aperiodic gratings, we simulate the light scattering process by modeling 2D gratings of dielectric microspheres in free space.In the simulations, the gratings are illuminated by a plane wave incident at a grazing angle (15 degrees) to the array plane similarly to the experimental geometry.Far-field scattering characteristics and near-field intensity distributions of the electric field scattered by both periodic and aperiodic gratings were calculated by using rigorous full-wave generalized multi-particle Mie theory (GMT) [17,23].GMT algorithm provides an exact analytical solution to Maxwell's equations for a cluster of spheres of an arbitrary spatial configuration and enables understanding the role of the array morphology on its angular and spectral scattering characteristics.The scattering responses of finite-size periodic and aperiodic gratings were simulated and compared, including the periodic grating composed of 486 spheres with 400 nm grating period, a Gaussian prime aperiodic array of 412 spheres with 300 nm minimum separation, and a Rudin-Shapiro array of 512 spheres with 400 nm minimum separation.The spatial intensity distributions in Fig. 6 were calculated for the scattered fields at three different wavelengths in the blue, green, and red parts of the visible spectrum.The single-color intensity patterns in the plane above the array were super-imposed to produce multi-colored Red-Green-Blue (RGB) images, which well approximate the intensity distribution experimentally collected by the microscope objective.
By observing the images in Fig. 6 and the corresponding movies (Media 1, Media 2, Media 3), it can be seen that although for both periodic and aperiodic gratings most of the light intensity is scattered into the zero-th diffraction order, they feature drastically different angular distributions of scattered light.In particular, periodic gratings scatter light anisotropically, redirecting it along well-defined directions corresponding to angularly distinct grating orders [Fig.6(a)-6(c)].This frequency-dependent anisotropy in the angular intensity distribution leads to the angular color filtering observed in the experiments under the limitation of a finite collection efficiency [Fig.6(d)] and results in the single-color responses of periodic gratings (see Fig. 1).In turn, scattering from aperiodic arrays results in the appearance of multiple diffractive orders covering a much wider angular and spectral range [Fig.6(e), 6(g), 6(i), 6(k)].Therefore, even if the light is collected within a limited collection cone (or numerical aperture), multiple spectral components always reach the detector.The collected spectral components are then combined to re-create multi-color colorimetric fingerprints that form on aperiodically nanopatterned surfaces due to multiple light scattering at various incommensurate length scales.

Sensitivity of fingerprints: implications for optical sensing
The refractive index sensitivity of the spatial distribution of the field intensity scattered by an aperiodic nanopatterned surface can be used as a novel transduction mechanism for label-free bio-chemical sensing.For a fixed wavelength of the incident light, the changes in the aperiodic array geometry and/or refractive index contrast caused by the presence of target molecules near the nanopatterned surface will modify the resonant conditions for the multiple light scattering at multiple frequencies in the array plane.As a result, a single-wavelength colorimetric fingerprint of the array will be significantly perturbed by the local modifications of the surface structure.This effect is illustrated in Fig. 8, which shows a single-color fingerprint of the Gaussian prime array of 100 nm-radius nanospheres before and after the incorporation of a 10 nm-thick index-matching dielectric layer that uniformly covers all the nanoparticles.The modifications in the spatial intensity profile are clearly observed.These changes can be quantified and compared by using the well-developed mathematical framework of correlation-function analysis [24][25][26].We finally remark that the sensitivity of the proposed aperiodic structures can be further improved by proper size scaling of the arrays.In fact, due to the aperiodicity of these systems, their scattering peaks become sharper and denser (the density of surface spatial frequencies increases) by increasing the systems size and, in stark contrast with the behavior of regular periodic lattices, the intensity of their Bragg peaks does not decrease significantly far from the center of the diffraction patterns [27].This provides additional degrees of freedom with respect to periodic systems for performance optimization, and offers the opportunity to tailor multiple scattering effects in deterministic aperiodic structures by proper size scaling.We are currently exploring the proposed sensing approach to detect the presence of thin low-index molecular layers accumulating on aperiodic nanopatterned surfaces [28].

Conclusions
We have investigated both experimentally and theoretically the scattering characteristics of periodic and deterministic aperiodic photonic gratings illuminated by the white light.In sharp contrast to the well-known single-color scattering response of periodic gratings, aperiodically nanopatterned surfaces feature highly complex spatial intensity patterns uniquely associated to the spectral properties of the scattering surfaces.The experimentally observed colorimetric fingerprints of aperiodic gratings result from the resonant multiple scattering of various spectral components of light interacting with the nanostructured surfaces in combination with broadband angular scattering distribution observed in aperiodic systems.These unique scattering characteristics of deterministic aperiodic scattering systems and the sensitivity of the associated colorimetric fingerprints to morphological and refractive index surface variations make them very appealing for the engineering of novel sensing platforms for labelfree optical detection of thin molecular layers.
), 1(b)].On the other hand, no point-like Bragg peaks appear in the continuous Fourier spectra of pseudo-random structures such as Rudin Shapiro lattices [Fig.1(d), 2(e)].The scattering intensity distribution in the far-field zone of aperiodic photonic gratings follows the corresponding Fourier transforms of the geometrical lattices [see Fig. 1(c), 1(f)] and can be flexibly engineered by changing the aperiodic array morphology.

Fig. 1 .
Fig. 1. 2D aperiodic lattices arranged according to the Gaussian prime (a) and Rudin-Shapiro (d) inflation rules[21] and their corresponding 2D Fourier transforms (b,e).Simulated far-field multi-color scattered intensity maps of the Gaussian prime (c) and Rudin-Shapiro (f) arrays of 200nm-diameter nano-spheres with the refractive index of 1.5 and minimum center-to-center separations of 300 nm (c) and 400 nm (f).The RGB images shown in (c) and (f) are obtained by overlapping the forward-scattered field intensity distributions corresponding to the arrays illumination by a plane wave at three wavelengths in the red, green and blue parts of the optical spectrum: λB = 470 nm (blue), λG = 520 nm (green), λR = 630 nm (red).

Fig. 2 .
Fig. 2. Colorimetric signatures of 2D periodic gratings.(a) Scanning electron microscopy (SEM) images of 2D periodic arrays of 100-radius and 70nm-deep cylindrical indentations nano-patterned on a quartz substrate.The center-to-center lattice constants of different arrays are: 500 nm (top left), 600 nm (top right), 700 nm (bottom right), and 800 nm (bottom left).(b) A schematic of the dark field scattering setup used in the measurements.(c) Images of periodic arrays illuminated at a grazing incidence with white light from a single fiber.(d) Wavelength versus the scattering angle for the first four diffractive orders of the periodic grating with 400 nm period.

Fig. 3 .
Fig. 3. SEM images and colorimetric fingerprints of 2D aperiodic gratings.Nanopatterned aperiodic arrays of 100-radius and 70nm-deep cylindrical indentations on a quartz substrate.(a) Thue-Morse lattice (nearest center-to-center separation d = 400 nm), (c) Rudin-Shapiro lattice (d = 400 nm), (e) Penrose lattice (d = 400 nm), and (g) Gaussian prime lattice (d = 300 nm).(b,d,g,h) Dark-field microscopy images of corresponding aperiodic gratings.Next we will focus on the distinctive scattering behavior of deterministic aperiodic gratings.Four types of aperiodic gratings with Thue-Morse [Fig.3(a)], Rudin-Shapiro [Fig.3(c)], Penrose [Fig.3(e)], and Gaussian prime [Fig.3(g)]lattices were fabricated on quartz substrates by using the same standard EBL process as for periodic gratings.Since aperiodic structures lack translational periodicity, they cannot be assigned a single lattice parameter such as the grating period, but are simply characterized by defining the minimum center-to-center interparticle separation in the array.All the other, generally incommensurate, length scales present in a particular aperiodic structure can be exactly calculated from the particular deterministic inflation rule used to generate the lattice.The aperiodic arrays shown in Fig.3have the minimum center-to-center interparticle separations in the 300 nm to 400 nm range.In contrast to the dark-field scattering images of periodic gratings shown in Fig.2(c), the images of aperiodic arrays collected with the experimental setup described in Fig.2(b) feature highly organized colorimetric fingerprints, as demonstrated in Fig.3(b), 3(d), 3(g), 3(h).Color spatial localization in different parts of the nanopatterned aperiodic surfaces can clearly be observed.We have also fabricated aperiodic arrays with different minimum centerto-center separations ranging from 250 nm to 700 nm.The colorimetric fingerprints of these structures are shown in Fig.4.The spatial localization of the different chromatic components on the nano-patterned surfaces is evident for all the inter-particle separations within the visible spectral range.

Fig. 5 .
Fig. 5. Experimentally measured colorimetric fingerprints of Rudin-Shapiro arrays with 400nm center-to-center nearest separation on quartz substrates with array nanoelements made of different materials: (a) 100nm-deep air indentations, (b) 80nm-high silicon nitride disks, and (c) 30nm-high gold disks under white light illumination and dark-field scattering microscopy.

Fig. 6 .
Fig. 6.Angular profiles of light scattered by periodic and aperiodic gratings.Spatial field distributions (side view) of the light scattered by a periodic array of 100nm-radius nanospheres with refractive index n = 1.5 and 400 nm grating period illuminated by a plane wave at θinc = 75° and (a) λ = 470 nm (blue), (b) λ = 520 nm (green), (c) λ = 630 nm (red).The direction of the incident field is indicated with a white arrow (see also Media 1).(d) Multiwavelength scattered field distribution (top view) at 100 µm above the periodic grating within the collection cone ( ± 30°) of the microscope objective with N.A. = 0.5.(e-l) Same as (a-d) but for a Gaussian prime array with 300 nm nearest center-to-center separation and a Rudin-Shapiro array with 400 nm nearest center-to-center separation, respectively (see also Media 2 and Media 3).To directly compare with the conditions of the dark-field scattering experiments, we plot only the spatial distribution of the calculated scattered field intensity in the plane perpendicular to the array [side view, Figs.6(a)-6(c), 6(e)-6(g), 6(i)-6(k)] and in the plane parallel to the array [top-view, Figs.6(d), 6(h), 6(l)] located above the array surface (100 µm).The scattering responses of finite-size periodic and aperiodic gratings were simulated and compared, including the periodic grating composed of 486 spheres with 400 nm grating period, a Gaussian prime aperiodic array of 412 spheres with 300 nm minimum separation, and a Rudin-Shapiro array of 512 spheres with 400 nm minimum separation.The spatial intensity distributions in Fig.6were calculated for the scattered fields at three different wavelengths in the blue, green, and red parts of the visible spectrum.The single-color

Fig. 7 .
Fig. 7. Colorimetric fingerprint formation in the plane of aperiodic arrays.Calculated spatial field distributions (top view) of the scattered light in the plane of a Gaussian prime array of nanospheres with n = 1.5 and 300 nm nearest center-to-center separation at (a) λ = 470 nm (blue), (b) λ = 520 nm (green), (c) λ = 630 nm (red), and a combined RGB image.The calculated intensity distribution of the scattered light in the plane of the Gaussian prime array illuminated by a plane wave at several visible wavelengths is plotted in Fig. 7(a)-7(c).Because the incident fields of different wavelengths resonantly interact with different length scales encoded in the aperiodic surface, the resulting monochromatic scattering intensity patterns show different distribution of intensity maxima in the array plane.The colorimetric patterns of the RGB principal frequency components are mixed together in Fig. 7(d).It can be seen that the single-color images do not overlap completely, resulting in the formation of complex colorimetric fingerprints characteristic of the Gaussian prime array surface morphology [compare to Fig. 3(h)].

Fig. 8 .
Fig. 8. (a) Calculated spatial field distributions (top view) of the scattered light in the plane of a Gaussian prime array of nanospheres with n = 1.5 and 300 nm minimum interparticle separation at λ = 530 nm.(b) Same in the presence of a 10-nm thick index-matching layer covering the particles.