Received 26th December 2013Accepted 4th February 2014
DOI: 10.1039/c3ra47984f
www.rsc.org/advances
10454 | RSC Adv., 2014, 4, 10454–1046
Computational modelling and characterisation ofnanoparticle-based tuneable photonic crystalsensors†
Constantinos P. Tsangarides,‡a Ali K. Yetisen,‡b Fernando da Cruz Vasconcellos,b
Yunuen Montelongo,a Malik M. Qasim,a Timothy D. Wilkinson,a Christopher R. Loweb
and Haider Butt*c
Photonic crystals are materials that are used to control or manipulate the propagation of light through a
medium for a desired application. Common fabrication methods to prepare photonic crystals are both
costly and intricate. However, through a cost-effective laser-induced photochemical patterning, one-
dimensional responsive and tuneable photonic crystals can easily be fabricated. These structures act as
optical transducers and respond to external stimuli. These photonic crystals are generally made of a
responsive hydrogel that can host metallic nanoparticles in the form of arrays. The hydrogel-based
photonic crystal has the capability to alter its periodicity in situ but also recover its initial geometrical
dimensions, thereby rendering it fully reversible and reusable. Such responsive photonic crystals have
applications in various responsive and tuneable optical devices. In this study, we fabricated a pH-
sensitive photonic crystal sensor through photochemical patterning and demonstrated computational
simulations of the sensor through a finite element modelling technique in order to analyse its optical
properties on varying the pattern and characteristics of the nanoparticle arrays within the responsive
hydrogel matrix. Both simulations and experimental results show the wavelength tuneability of the
sensor with good agreement. Various factors, including nanoparticle size and distribution within the
hydrogel-based responsive matrices that directly affect the performance of the sensors, are also studied
computationally.
Introduction
Photonic crystals (PC) have applications in a myriad of appli-cations such as optical devices, sensing materials and displaytechnologies.1 We studied the optical tuneability of one-dimensional (1D) photonic crystals, also known as Braggmirrors. The mechanism behind the operation of photoniccrystals is governed by the periodicity of their lattice anatomy,which can directly affect the propagation of photons. Periodicityin lattices represents an alternating pattern of macroscopicdielectric media along a specic direction.2,3 If the absorption oflight by the entire structure is minimal, and there is a large
of Engineering, University of Cambridge,
Biotechnology, University of Cambridge,
K
y of Birmingham, Edgbaston, Birmingham
(ESI) available: It contains informationpling, synthesis of poly(HEMA) lms,lms with silver halide chemistry. See
1
contrast between the dielectric strength of the alternatingmedia, some frequencies are ltered out as they pass throughthe media. The excluded group of frequencies is called thephotonic band gap (PBG). A wide array of optical applicationshave been devised, which utilise the band gaps of photoniccrystals, such as Fabry–Perot lters, distributed feedback lasers(DFBs),4 reective coatings for sunglasses or aircra windowsand anti-reective coatings for light-emitting diode (LED)enhancement of output efficiency.5 Photonic crystals can also beused as waveguides,6,7 wavelength multiplexers8 and colourlters.9 All of these devices have a wide range of commercialapplications from telecommunications based on optical bresand routing to medical elds for sensing and quantitativeanalyses.10
Photonic crystal-based dynamic structural coloration innature is rare. Notable examples include sh (e.g. Paracheirodoninnesi),11,12 cephalopods13 and beetles (e.g. Tmesisternus isa-bellae).14,15 The diversity of photonic structures might providecamouage, warning colouration, superiority in reproductivebehaviour, signal communication, thermoregulation andconspecic recognition. The dynamic coloration is generallyachieved by altering the dielectric structure either by changingthe thickness of the multilayers or the refractive index of
Fig. 1 A simulated geometry of a photonic crystal (a) model geometryshowing silver nanoparticle stacks within a hydrogel medium. (b)Meshing of the silver nanoparticle pattern.
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individual layers through chemical reactions. The operationalmechanism for these naturally occurring tuneable photoniccrystals may seem quite simple, but difficulties arise in thefabrication of such structures in the laboratory. A photoniccrystal is constructed according to the frequency range that thePBG must fall in. If infrared frequencies are required, microndimensions must be used for a given geometry.4 The higher thefrequency band the smaller must be the photonic crystalstructure. Hence, for the visible region, which is the maininterest of this study, the fabrication is challenging and costly.Most typical strategies to fabricate a 1D geometry photoniccrystal are based on either molecular beam epitaxy (MBE)16 orchemical vapour deposition (CVD).17 However, MBE is a slowand expensive process, while CVD lacks positional precisionand compatibility with several notable materials.18–24 Conse-quently, they do not fulll the desired attributes for massproduction capability and practical applications via low cost,and material and process exibility.
A rapid, low-cost and efficient approach is to develop a PBGstructure through creating a periodic structure via laser light.25
It has been demonstrated recently that the light-directedfabrication of 1D photonic crystal structures in functionalisedmedia allow tuning their PBG in response to external stimuli.25
The photonic crystals therefore act as chemical sensors. Thematerials used to construct these photonic crystals werecomposed of a functionalised hydrogel and metallic silvernanoparticles; the resulting polymer was both transparent andelastic. The silver nanoparticles were organised within thehydrogel in particular formations (via laser photochemicalpatterning) such that it produces a periodicity through thethickness of the hydrogel (see ESI† for electron micrographs).
The nanoparticle-based multilayered structure that wasformed within the hydrogel acts as a 1D photonic crystal, whichdiffracts the frequencies of electromagnetic radiation that fallwithin the band gap region. When the band gap region shis itsposition to higher or lower frequencies, different frequenciesare back scattered. The functionalised hydrogels used as themedium for the multilayered structures have the ability to varytheir thickness in response to chemical stimuli. For example,this may be achieved via protonation and deprotonation ofcarboxyl groups in pH-sensitive hydrogels. Altering the thick-ness of the hydrogel directly changes the lattice constant of thephotonic crystal periodicity and therefore induces a band gapshi.
Here we demonstrate a theoretical and experimental study ofa 1D photonic crystal-based tuneable sensor. A photonic crystalsensor sensitive to pH changes was fabricated using laser-directed photochemical patterning. Computational simulationsare utilized to analyze the tuneability and optical characteristicsof the photonic sensor to achieve further improvements in thefabrication procedure.
Modelling of photonic crystal sensor
To present the working principle of the PC sensor, we used anite element method based computational soware, COMSOLMultiphysics®.26 The photonic crystal consisted of periodic
layers of nanoparticles in a hydrogel medium. The photoniccrystal patterns consisting of stacks of randomly sized nano-particles were generated using a MATLAB code. Since thehydrogel medium has a refractive index of 1.512, and the laserwavelength used for photochemical patterning was l ¼ 532 nm,then l/2n would give a lattice constant of l ¼ 176 nm to thenanoparticle-based multilayered structure. As shown in Fig. 1,the 1D periodic array of stacks consisted of nanoparticlesdesigned as nanospheres with different radii.
As a starting point, the number of nanospheres tested perstack was �60, with 6 stacks in total. Along the vertical axis ofeach stack, the nanospheres were uniformly distributed, whilstin the horizontal axis, the nanospheres were distributed withinthe layers dened by the laser-induced photochemicalpatterning. To achieve this, a normal random distribution wasperformed with the mean positions of the stacks set with adistance equal to the lattice constant. Additionally, to renderthe photonic pattern more realistic in terms of representing afabricated photonic multilayer system, a normal randomdistribution was also used to dene the radii of the nano-spheres. Themean value of the radii was set within a range from4–24 nm, s ¼ 5 nm.
Aer generating the nanoparticle patterns in MATLAB, theywere imported into COMSOL for two-dimensional (2D) model-ling. The pattern of nanospheres was then surrounded with asquare domain of a medium that mirrored the material of thehydrogel to have a refractive index of 1.512. The remainingsubdomains (i.e. nanospheres) were set to have an electricalconductivity of silver (61.6 mS m�1). Since there is an absorp-tion of electromagnetic radiation by the silver nanoparticles, acomplex refractive index was required. This absorption shouldnot affect signicantly the propagation of light when taking intoaccount a small number of stacks. However, the absorption canreduce the efficiency of diffracted light when consideringphotonic crystals that have a high number of stacks. Fig. 1shows how the photonic crystal was represented when fullyconstructed in the COMSOL Multiphysics® soware. The elec-tromagnetic waves were incident on the photonic crystal fromthe le and propagated from le to right along the array of
nanoparticle stacks. The le boundary of the cell was set to ascattering boundary condition. The light source was dened asa plane wave of varying wavelengths obeying by the followingequation:26
n � (V � Hz) � jkHz ¼ �jk(1 � k$n)Hoz exp(�jkr) (1)
where, n is the complex refractive index, Hz is the magnetic eldstrength at position r, k is the propagation constant and Hoz isthe initial magnetic eld strength. Meshing was performed withthe smallest nite element size of �2 nm to resolve eachnanoparticle. Once meshing was established, a computationwas performed via a parametric sweep, providing the ability tosolve for a range of wavelengths in a single simulation run. Thewavelength parameter values set covered a range from 400 nmto 900 nm within the entire visible spectrum. Finally, using“power outow and time average” boundary integration, therelevant data of transmission of the waves was collected. Byanalysing the results, the amount of radiation reaching theopposite end of the photonic crystal can be estimated.
Fig. 2 Model geometries and wave propagation results for the Braggdiffracted waves for photonic multilayer structures with latticeconstants of (a) 176 nm, (b) 215 nm and (c) 270 nm. (d) The simulatedtransmission spectra for different photonic crystal lattices. A red shift inthe reflection bands was observed with the increase in latticeconstants.
Simulation results
Fig. 2 shows the simulated optical transmission results for thephotonic crystal. Fig. 2(d) illustrates the transmission spectrumfor the PC. The spectrum shows peak reectivity at �532 nm,corresponding to the wave propagation for a lattice spacing of176 nm, shown in Fig. 2(a). This is the wavelength thatundergoes lowest transmission due to Bragg diffraction, whichdenes the green diffracted colour of the photonic crystalsystem. This demonstrates that the colour of the photonicmultilayer device is dictated by the spacing between the nano-particle stacks.
Additional simulations were performed to analyse the effectof expanding the nanoparticle lattice on the reection bandgaps. Here, the photonic multilayer structure was expanded,while keeping the number and dimensions of the nanoparticlesconstant, simulating the tuneable nature of a hydrogel-basedphotonic crystal device. Tuneable hydrogel-based systems arefunctionalised and tailored to respond to an external stimulus,such as a pH change. This response results in a correspondingshrinkage or expansion of the hydrogel, and hence, of themultilayered lattice within it. As shown in Fig. 2(b) and (c), thelateral expansion of the photonic crystal system results in anincrease in the effective-stack spacing, stack size and a reduc-tion in the concentration of nanoparticles per stack. The overalleffect of these changes on the wave propagation was clearlyobserved in the simulated transmission results. The trans-mission spectra (Fig. 2(d)) show a red shi in the reectionbands with an increasing stack spacing. The expanding multi-layer structure displayed a changing colour (reection band)varying across the visible spectrum from approximately 532 nmto 815 nm. It was also observed that with an increase in stackspacing, the efficiency of the multilayer structure decreases,shown by the decrease in the intensity of the reection band.This could be due to the decrease in the concentration ofnanoparticles present in each stack, which reduces the effective
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index contrast between the nanoparticle stacks and thesurrounding medium.
PC sensor fabrication
Based on the working principle of a tuneable 1D PC (asdemonstrated in the simulated results), a pH-sensitive photoniccrystal sensor was fabricated. The PC sensor consisted of apoly(2-hydroxyethyl methacrylate) (pHEMA) lm (�10 mm thick)on a glass substrate. First, the glass substrate was treated with3-(trimethoxysilyl)propyl methacrylate in acetone 1 : 50 (v/v)to promote adhesion of the methacrylate polymer to thesubstrate (Fig. 3(a)). A monomer solution (200 ml) consisting of
Fig. 3 Fabrication of a photonic crystal sensor via silver halidechemistry. (a) A glass slide was functionalised with silane chemistry; (b)the monomer mixture was polymerised on the glass slide; (c) theresulting system was rinsed with ethanol; (d) a AgClO4 solution wasallowed to diffuse into the polymer; (e) the excess AgClO4 solutionwasremoved and the system was dried; (f) silver halide grains were formedin the pHEMA film; (g) the system was rinsed with DI water; (h) thesystem was exposed to a single pulse of a laser-light at 5�; (i) the latentimage was developed to metallic silver; (j) the system was neutralised;(k) undeveloped silver halide grains were removed from the system;and (l) the system was rinsed with ethanol solution in order to removethe cyanine dye from the hydrogel matrix.
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2-hydroxyethyl methacrylate (HEMA) (91.5 mol%), ethylenedimethacrylate (EDMA) (2.5 mol%), and methacrylic acid (MAA)(6 mol%) was prepared. The solution was mixed by 1 : 1 (v/v)with 2% (w/v) 2-dimethoxy-2-phenylacetophenone (DMPA) inpropan-2-ol and the resulting solution was polymerised on thesilanised glass substrate using UV light-induced free radicalpolymerisation for an hour (Fig. 3(b)). The resulting pHEMAand glass substrate system was rinsed with ethanol (100%) inorder to remove unreacted compounds (Fig. 3(c)).
Under red safe lighting, an AgClO4 solution (200 ml, 0.3 M)dissolved in propan-2-ol and DI water (1 : 1, v/v) was allowed toperfuse into the polymer layer for 3 min (Fig. 3(d)). The excessAgClO4 solution was removed with a squeegee and the lm wasdried under a tepid air current for 5 s (Fig. 3(e)). For 30 s, thepHEMA–glass system was submerged into a photosensitisingbath, which consisted of lithium bromide (0.3 M, 40 ml) in 3 : 2(v/v) methanol : H2O and 1,10-diethyl-2,20-cyanine iodide(1 : 500, w/v, 1 ml) in methanol (Fig. 3(f)). The slide was washedthoroughly with deionised (DI) water (Fig. 3(g)).
Once the photosensitisation was achieved, the system wasexposed to laser light and developed. A levelled Petri dish, with amirror placed on the bottom surface, was lled with unbufferedascorbic acid (2%, w/v) (pH 2.66). Polymer side facing down, theslide was immersed in the bath with an inclination of 5�. Thepolymer lm was equilibrated in the bath for 15 min. Next, thelm was exposed to a single 6 ns pulse by Nd–yttrium–
aluminum–garnet (Nd:YAG) laser (350 mJ) with a spot sizelarger than the pHEMA–glass system (Fig. 3(h)). A photographicdeveloper (pH 13.0) comprising of 4-methylaminophenolsulphate (0.3%, w/v), ascorbic acid (2%, w/v), sodium carbonate(5%, w/v) and sodium hydroxide (1.5%, w/v) was dissolved in DIwater. The lm was submerged in the developer until no moredarkening was seen (Fig. 3(i)). The lm was washed thoroughly
with DI water and immersed in acetic acid (5%, v/v) solution toneutralise the developer (Fig. 3(j)). The lm was rinsed with DIwater and immersed in 10% (w/v) sodium thiosulphate mixedwith ethanol 1 : 1 (v/v) for 15 min to remove the undevelopedlithium bromide grains (Fig. 3(k)). Finally, the lm wassubmerged in an ethanol–water (50% v/v) solution for 15 min toremove the cyanine dye from the polymer matrix and thisprocess was repeated three times (Fig. 3(l)). The result is a 1Dphotonic crystal consisting of silver nanoparticles layers withina dynamic hydrogel medium. Similar multilayer structures havealso been reported earlier using this method (see ESI†).
Optical measurements were performed on the fabricated pH-sensitive photonic crystal sensors. Buffer solutions (150 mM)consisting of Na2HPO4–citric acid (pH 3.00–8.00), Na2HPO4–
HCl (pH 9.00), Na2HPO4–NaOH (pH 10.00) were prepared toobtain the desired pH values. The sensor (0.5 cm � 2.5 cm) wasrst submerged into a cuvette and buffers in the range of pH3.00–10.00 were dispensed into the reservoir. The cuvette wascentred in a goniometer setup having a white light source andspectrometer. The reection spectra from the PC sensor weremeasured using the spectrometer. A bifurcated cable was usedto feed the spectral data into a camera as well to capture imagescorresponding to the spectrometer measurements. Fig. 4(a)shows the measurements of reection spectra of the pH-sensi-tive photonic crystal sensor. With the increase in pH, thehydrogel expands, which consequently increases the latticespacing between the silver nanoparticle layers. The reectionspectra was red shied by�280 nm, which was predicted by thesimulation results. An increase in lattice spacing consequentlyreduced the effective index contrast, hence the efficiency of themultilayer structure decreased, also predicted by the simula-tions. The tunable wavelength shi as a function of pH is shownin Fig. 4(b) Aer every reading, the pH buffer was removed andthe cuvette ushed consecutively three times for each newbuffer point. A standard error bar in the Fig. 4(b) representsthree replicates of the same sensor. Standard error bars in pHwere approximated using linear interpolation based on thecalibration curve. The apparent pKa value was calculated as 6.08using the Henderson–Hasselbalch equation. Fig. 4(c) shows thecamera images (colour readouts) for the PC sensor showingdifferent colours diffracted in the presence of different pHvalues. The sensors operated within the visible spectrum as wellin the near infrared. The spectrophotometer has a resolution of0.5 nm wavelength shi, which corresponds to a minimumfringe swelling distance of 0.18 nm, which obeys the Bragg's law(lpeak ¼ 2nd cos(q)), where lpeak is the wavelength of the rstorder diffracted light at maximum intensity, n is the averageeffective refractive index, d is the lattice spacing between thetwo consecutive layers, and q is the angle of incidence of theincoming illumination. Since a �10 mm thick hydrogel wasfabricated in this study, it can theoretically accommodate �55fringes. In order to cause a resolvable spectral shi, thehydrogel needs to swell a minimum of �9.7 nm.
Fig. 4 (a) Visible-near-infrared diffraction spectra of a photonic crystal sensor swollen by different pH solutions using phosphate buffers. (b) Thesensor response over three trials. The measured wavelength shifts in the reflection spectra. (c) Colorimetric readouts of the photonic crystalsensor at various pH, taken using a CCD camera.
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The pH-sensing range and the sensitivity of the sensor can becontrolled through variation of the nature of the ionisable co-monomer in the polymer matrix and its concentration.27 Thesensor can also be synthesised to respond to other analytes suchas glucose,28 metal ions29 and hormones.30
Simulations of other parameters
Further simulations were also carried out to study differentparameters that could inuence the performance of the pre-sented PC sensor. This analysis will be helpful to optimise thefabrication of the current photonic crystal structures.
Fig. 5 Simulated transmission for a variety of patterns consisted ofsilver nanoparticles of lattice constant 176 nm but different meanradius size. Large nanoparticle mean radius sizes lead to broader stopbands centered at longer wavelengths.
Effect of mean nanoparticle size
The effect of varying nanoparticle radii on the performance ofthe photonic crystal was evaluated. Nine different geometrieswere generated with a range of mean nanoparticle radii from 6nm to 22 nm. The number of nanoparticles per stack was keptconstant at 60. The transmission plots in Fig. 5 show that as thenanoparticle size increases, so does the intensity of the reec-tion band, which can be attributed to the area that theserespective nanoparticles with varying sizes cover. It was statedin the previous simulation run that a higher effective refractiveindex of the stack will give a stronger reection. Therefore, if allthese congurations have the same number of particles, thenthose with larger particles will cover more area within thehydrogel medium, thus resulting in a higher effective refractiveindex. The disadvantage, however, of having a photonic struc-ture with very large nanoparticles, is that these particles inducea very broad bandwidth and a redshi on their reectionband gap.
The broad bandwidth can be explained by the unevenuniformity in the width of the stacks in a photonic crystalpattern. For example, for r ¼ 22 nm, not all ve stacks have thesame width, because MATLAB attempted to generate a patternwhere the nanoparticles were evenly spaced inside a stack andhence placed them with a modest degree of uniformity alongthe horizontal direction. The red shi can also be explained by
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the surface plasmonic resonances of the silver nanoparticles.31
The excitation of surface plasmons arises from the excitation ofa collective electron oscillation within the nanostructureinduced by the incident light. This leads to a large optical local-eld enhancement and a dramatic wavelength-selective photonscattering and localisation at the nanoscale. The plasmonicresonances are highly affected by the size, shape and themedium of silver nanoparticles. The reected light/band gapsdisplayed by the PC sensor were highly inuenced by the plas-monic resonance of the silver nanoparticles. As the averagenanoparticle size increased, the peak plasmonic resonanceunderwent a red shi. Therefore, the band gaps broadened asthey represent an effective reection, which occurred due to theperiodicity of the stacks and the surface plasmon resonances ofthe large silver particles.
The ideal radius size should be between 8 nm and 10 nmeven if they seem to give weaker reections than the larger sizeparticles. In this range, the surface plasmon resonance and the
lattice constant dictated band gaps seem to coincide. Thereection intensity can also be improved by increasing theconcentration of the particles as discussed later.
Effect of number of nanoparticle stacks
The effect of changing the number of nanoparticle stacks wasalso studied. As shown in Fig. 6(a)–(c), three congurations weresimulated, with all consisting of 60 nanospheres per stack witha mean radius of 10 nm and a lattice constant of 182 nm.Fig. 6(d) shows the transmission plots respectively for allcongurations. All curves show a transmission dip at 550 nm.This shows that the reection band does not change position byadding or removing stacks of silver nanoparticles with the sameperiodicity. By looking at the depth of each trough it can beclearly seen that, as the number of stacks increases, so does theintensity of the reected diffraction. For 6 stacks, there is a 60%reection (0.4 normalised transmission), for 5 stacks there is a48% reection and for 4 stacks a 40% reection. Therefore, at 6stacks the reection seems to be stronger than other two. It isalso observed that the lower the reection, the wider the troughappears to be. The full width at half maximum (FWHM) of the 4stacks curve is 160 nm, whereas in a 6 stack it is 110 nm.Consequently, the greater the number of nanoparticle stacks,
Fig. 6 Simulations were performed with (a) 4 stacks, (b) 5 stacks and(c) 6 stacks of silver nanoparticles, with a lattice constant of 182 nm.The wave propagation results are shown for the wavelength of 550 nmin each case. (d) Each curve represents the transmission along thepatterns with the corresponding number of stacks. All of them show astop band centered at 550 nm, however with varying depth.
the deeper the PBG trough and narrower the bandwidthbecome.
Effect of the number of nanoparticles per stack
Four different congurations were used with varying numbers ofnanoparticles per stack, ranging from 20 to 80 nanoparticles perstack (Fig. 7). Comparing the model geometries, we can observethat as the number of nanoparticles per stack increases, thestacks become more uniform; like a continuous medium withfewer voids. This means that the effective refractive index of thestacks is different in each case. As shown in the spectral results(Fig. 7), the case with 20 particles per stack gives very weakreection. With an increasing number of particles the reectionband becomes stronger, with the deepest one reaching 65% ofreection for 80 particles per fringe. Increasing the number ofparticles increases the index contrast between the layerswith andwithout the nanoparticles, thus resulting in lower reection. Alsowith the increase in the number of nanoparticles the netabsorption increases leading to effectively lower transmission. Bycarefully observing the position of the trough it seems that itundergoes a red shiwith the increase inparticles per stack. At 20particles per stack, the minimum point of the curves are locatednear 530 nm, but for the other two concentrations the minimumpoint is located at about 555 nm. This shi could be due to theoverall increases in the size of the nanoparticles stacks and alsodue to a shi in the surface plasmon resonances caused by theclose proximity of nanoparticles. Therefore, an increase inparticle concentration per stack will result in a correspondingincrease in the contrast characteristic of the photonic crystals.
Fig. 7 Simulations were performed with (a) 20 particles, (b) 40 parti-cles, (c) 60 particles and (d) 80 nanoparticles per stack. (e) Thetransmission spectra corresponding to above concentrations ofparticles per stack.
Effect of anomalies in the photonic multilayered pattern
The effect of anomalies in the photonic multi-layered patternwas evaluated by simulating four new pattern congurations, inwhich the mean sizes of the nanoparticles increases whilemoving from the rst to the last stack (Fig. 8). Such distortionsare normally present in optically fabricated photonic crystalsensors, since the metallic nanoparticles are introduced intothe polymeric matrices through a diffusion and reductionprocess, leading to inhomogeneous distribution of nanoparticleconcentrations dispersed within the matrix. The simulatedgeometries contained six stacks and all begin with the rst stackof nanoparticle mean radius of 10 nm. For example, Fig. 8(a)shows a pattern with nanoparticle mean radius that increasesby 2 nm per stack, so the rst stack has a mean radius of 10 nmand last stack a mean radius size of 20 nm.
The reason of performing these simulations is to evaluatehow possible errors during the fabrication process, such asinhomogeneous nanoparticle distribution through the hydrogelcan affect the optical properties of the photonic crystal. Thetransmission plots in Fig. 8 show a reference curve for whichthere is a constant mean radius along all the stacks with theremaining curves representing a gradient change ofmean radiussize. In the worst-case scenario of an increase of 2 nm per stack,the curve shows a trough being much wider and centred on anew central wavelength of about 585 nm, rather than 550 nm.
The lattice constant of the reference curve differs from theworst-case scenario, as the latter has a much smaller effective
Fig. 8 Four different patterns with the nanoparticle mean radiusincreasing by (a) 0.5 nm, (b) 1.0 nm, (c) 1.5 nm and (d) 2.0 nm per stackalong the horizontal direction of geometry. (e) Transmission spectra ofthese four patterns compared to a patternof constantmean radius size.
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lattice constant. In Fig. 8(d), it can be observed that the distancebetween last two stacks is very small, almost unrecognizable;hence, the total effective lattice constant is smaller. Also, thespacing between each pair of stacks is non-uniform, which leadsto several band gaps overlapping each other and effectivelyleading to a wide bandwidth. This may give a strong reection,hence highly intense optical reection from the photonic crystal,but poor selectivity (broadband response) in terms of an opticaldevice that needs to display narrow peak diffraction.
Conclusions
Wehave fabricated anoptical photonicmultilayer structure basedon a stack of nanoparticle layers within a hydrogel-based system(1D photonic crystal) and computationally studied differentparameters affecting its performance. The wavelength tuneabilitywas studied both computationally and experimentally with goodagreement. Further simulation results also showed that thedegreeofdiffraction andbandwidthof the photonic crystal canbealtered to the desired level bymodifying somebasic parameters ofthe geometrical structure. We have demonstrated that thereection band increases in strength with an increasing numberof nanoparticle stacks. The change in the reection was dramat-ically increased, alongwith a narrowing of the bandwidth, evenbythe addition of two extra nanoparticle stacks. It was also foundthat an increase in the number of nanoparticles is proportional toboth the depth and width of the bandwidth. Therefore, by ratio-nally fabricating photonic crystals with high control over theentire system, including the size and distribution of the nano-particles within the tuneablemedium, one can avoid undesirableeffects like red-shied reection and wider band gaps, andsuccessfully obtain highly precise tuneable optical devices. Manyfurther applications can follow from these results ranging fromprintable photonic crystal devices for biomolecular sensing todisplay and security applications, where specic photonic crystalpatterns can lead to unique light transmission spectra.
Author contributions
The manuscript was written through contributions of allauthors. All authors have given approval to the nal version ofthe manuscript.
Conflict of interest
The authors declare no competing interests.
Acknowledgements
F.C.V thanks Fellowships from FAPESP (Grant no. 2011/06906-6) and CNPq INCTBio (Grant no. 209869/2013-5). H.B. thanksthe Leverhulme Trust for the research grant.
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