CHAPTER 1: Responsive Bragg Reflectors

Multilayers have been a common subject of study of materials and optical scientists for many decades. The possibility to attain color from the stacking of films of transparent materials and, furthermore, the fine control over light transmission and reflection they offer, have attracted the attention of both scientists and technologists. Indeed, the industrial development of these materials has led to the realization of a myriad of passive optical elements that are commonly found in all kind of spectrophotometers or optical characterization setups. From the manufacturing perspective, most efforts have been put in the preparation of thin films as stable as possible against changes in the surrounding environment. This has been mainly motivated by their use as filters of a range of selected optical frequencies, which would not be constant if their structure varies in the presence of moisture or as a consequence of temperature variations. This feature implied that the constituent layers could not present accessible porosity in which condensation of vapor could take place. Also, unless pore sizes are in the nanoscale range, the presence of voids could easily lead to diffuse scattering that will deteriorate its optical quality.

There is currently a boost in the development of film deposition techniques that permit a strict control to be achieved over porosity at the mesoscale, thus preventing diffuse optical scattering phenomena. While porosity in general endows the film with the potential of hosting guest compounds in the interstitial space, such as potential functional groups or analytes transported from gas or liquid phase, fine tuning of the pore‐size distribution yields command over the kinetics of vapor sorption in the layers or molecular‐size‐selective detection. Actually, many of the porous materials that can be prepared as thin films have already been incorporated in a multilayer structure with the aim of taking advantage of the interplay between the responsive properties that porosity provides. The same aim has been reached by employing a different approach based on the multilayer integration of polymeric films whose thickness and refractive‐index change as a function of the species present in their surroundings. In this chapter we will review the main properties that make all these layers interesting building blocks to build responsive optical materials as well as the main synthetic procedures and representative applications that are being explored in this emerging field.

The optical thickness of a film is defined as the product of its geometrical thickness times its refractive index. This parameter determines the range of wavelengths for which optical interference effects are observed when a white light beam impinges on the slab surface. Both transmitted and reflected light will present spectral intensity fluctuations whose frequency will depend on the value of the optical thickness relative to the incident wavelength. For a dielectric film, reflectance maxima are expected when half an integer number of wavelengths, respectively, “fit” in the optical thickness of the film. The intensity of these maxima depends on the dielectric constant contrast between the film and the surrounding media, which typically are the air above the film and the substrate supporting it. Optical interferometry of dense thin films is commonly put into practice to prepare antireflection coatings to reduce light insertion losses in sunglasses or devices such as solar cells. For the case of porous films, the possibility was soon realized of making use of the sensitivity of the pattern of lobes observed in transmittance and reflectance spectra to the refractive index of the film for detection and recognition of specific targeted compounds, provided adequate functionalization of the pore walls was achieved. In fact, the first optically responsive films were developed by anchoring antigens to the inner walls of porous silicon films and exposing them to the corresponding antibodies, which gave rise to an increase of the average refractive index of the film that resulted in a redshift of the monitored optical features. The group of Sailor largely contributed in the 1990s and afterwards to the development of porous silicon structures for sensing of different sorts of species based on this approach. An example of this responsive behavior of a porous silicon film is shown in Figure 1.1. Today, there exist many different types of materials that could be shaped as porous films and thus employed as the basis for a responsive interferometric sensing device.

In the last decade, the possibility to stack porous films of different composition and structure preserving the accessibility of the network of interstices, i.e. achieving continuity of the void space present in the different slabs, has been thoroughly explored. If a rational design of the stack is followed, multilayers in which very intense reflectance peaks (or transmittance dips) are observed as a result of the interference of beams reflected and refracted at each interface. An alternative approach to the construction of responsive optical multilayers without employing porous materials is based on the utilization of block copolymers or hydrogel films as building blocks. These materials may allow the diffusion of certain species through them when put into contact with a solution or vapor containing them. The optical thickness is in this case varied both as a result of swelling, which occurs without loss of the mechanical stability of the films, and refractive‐index change. The group of Thomas has greatly contributed with the integration of such thin polymeric coatings in different sorts of photonic multilayered structures.

In what follows we will describe the main optical features of multilayered systems, providing a guide to easily predict their main reflection and transmission properties as well as to understand the possibilities offered by resonant optical modes designed within the structure as far as the responsive character of the material is concerned.

The main optical feature of periodic multilayers is their capability to reflect, and consequently transmit, light of selected wavelength ranges. At any given incident direction, for those wavelengths for which the beams reflected at each interface present in the stack interfere constructively, an intense specular reflectance peak will be attained. Some simple equations allow one to predict many of the qualitative, as well as some of the quantitative, changes observed in the optical properties of a responsive Bragg mirror when exposed to changes in its environment. In the case in which we have two different types of films alternately distributed in the stack, of thicknesses t₁ and t₂ and refractive indices n₁ and n₂, respectively, the spectral position of the specular reflectance maxima, λ_B(θ), at any given incident angle with respect to the surface normal, θ, can be anticipated by the formula:

where d=t₁+t₂ is the unit cell size and n is the average refractive index of the multilayer, which is in turn given by:

The unit cell of a periodic multilayer is defined as the structural unit that repeats itself along the direction perpendicular to the substrate. Expression (1.1) results from the combination of Snell's and Bragg's laws. In fact, periodic multilayers displaying strong optical reflections are known as Bragg reflectors, Bragg stacks, distributed Bragg mirrors, although they can also labeled as interference filters or rugate filters. For some specific cases, relevant features such as the reflectance peak intensity, R, and spectral width, Δλ₀, can be approximated by relatively simple formulas. In the case in which the layers are designed so that n₁t₁=n₂t₂=λ_B/4, reflectance is given by:¹ 

where n₀ and n_s are the refractive indices of the incoming and outgoing media and N is the total number of periods in the stack. In all cases, the spectral width of the reflectance peak is given by:

For the case in which n₂≈n₁, as it occurs for polymeric multilayers, eqn (1.4) becomes:

where Δn=n₂−n₁ and =(n₂+n₁)/2.

If a more detailed analysis of the interplay between the externally induced changes of optical thickness and the performance of the Bragg mirror is pursued, then a simulation and fitting of the full spectrum obtained experimentally is required. This can be done by employing a vector wave calculation based on a transfer matrix approach. A full description of this method can be found elsewhere.¹  In Figure 1.2a, we plot the evolution of the reflectance spectrum of a multilayer as the number of unit cells increases. In this case the unit cell is made of a layer of thickness t₁=120 nm and refractive index n₁=1.23 and another one of t₂=1.70 and n₂=90 nm. These are typical refractive index values of porous TiO₂ and SiO₂, respectively. As explained above, the primary maximum results from the interference of beams partially reflected at each interface present in the multilayer, while the secondary lobes arise from the interference of beams reflected at the top and bottom faces of the structure. In Figure 1.2(b) we show the variation of the reflectance as the refractive index of one of these layers is gradually increased from n_1,i=1.71 to n_1,f=2.00. Also, in Figure 1.2(c), we plot the reflectance spectra for a multilayer with a low refractive‐index contrast, as it is typical of polymeric Bragg mirrors, and its evolution as one of the layers changes its width from t_1,i=80 nm to t_1,f=280 nm. These shifts exemplify well the sort of changes expected when a layer sequentially incorporates a guest compound, be it by infiltration of its void network (Figure 1.2(b)) or by swelling (Figure 1.2(c)). Sensitivity (how much the optical properties change when a variation of the environment, such as the concentration of a targeted species, occurs) and resolution (minimum external change that gives rise to a distinguishable change in the optical properties) of a responsive Bragg mirror can then be tailored by choosing the right thickness and refractive index of the constituent layers. In this sense, a compromise must be found, since the observation of finer peaks implies the realization of a low refractive‐index contrast in the multilayer, as it can be readily inferred from eqn (1.4), what diminishes their intensity according to eqn (1.3).

The particular way in which field intensity is distributed within a multilayer can also be taken advantage of to enhance the performance of responsive Bragg mirrors. In this section we analyze the different sorts of resonant photon modes that can be found inside the stack by means of the method of transfer matrix. In Figure 1.3 we plot the reflectance and transmittance spectra of two types of multilayered structures, one periodic and another one in which the periodicity is intentionally disrupted by a thicker middle layer. Also, we draw the spatial distribution of the squared electric field within the stack in Figures 1.3(c) and 1.3(d), in which resonances can be identified as bright spots. Regions in which the field intensity is strongly depleted can also be easily spotted. These images illustrate that a designer field intensity pattern can be attained by adequate choice of the layers’ refractive index and thickness. This allows in turn tailoring the light emission and absorption from imbibed species. It is well known that an increase of the local density of states gives rise to faster emission rates and luminescence intensity. For this effect to occur, the physical volume occupied by the resonant photon modes must be of the order of their wavelength. However, in the case of Bragg mirrors, since light is confined in only one dimension and due to the extended character of the multilayer, the cavity volume is always larger than the resonant wavelengths. Nevertheless, the angular distribution of the output power is largely modified and depends strongly on the optical parameters of the structure. Strong directional reinforcement or depletion of luminescence can thus be observed. Regarding absorption, its magnitude will also depend on light–matter interaction, which will be much stronger for resonant wavelengths within the multilayer. Hence, by locating nanomaterials or molecules at positions for which a reinforcement of the optical field is devised, and with absorption bands that overlap the spectral position of those resonances, it is possible to tune the resulting absorption spectrum with great precision. The strong dependence of the resonant modes that originate such directional enhancement or suppression of light emission or absorption on the refractive index of the layers provides an excellent means to obtain a fast and abrupt optical response to the presence of a guest compound inside them. Different examples illustrating this point are given in the last section of this chapter.

Both top‐down and bottom‐up strategies have been employed to achieve a controlled spatial modulation of the refractive index. These preparation routes will determine not only the microstructure, but also the physicochemical characteristics of the layers. Top‐down techniques lead to porous Bragg mirrors by engraving a reactive substrate through a strict control of the porosity at the tens of nanometers length scale. Hitherto, only porous Bragg mirrors obtained from silicon wafers and aluminum films have been realized by a top‐down approach, in both cases based on the electrochemical etching in highly acidic media. Bottom‐up strategies are based on the alternating deposition of layers with different refractive index. These types of deposition are carried out by employing a wide diversity of techniques, such as physical vapor deposition, spin coating, dip coating, etc. More specifically, since a large number of materials can be processed in liquid media (such as metal and metal‐oxide colloidal particles, or polymers), wet deposition methods are preferred over those that make use of condensation from the gas phase.

In what follows, the materials chemistry aspects (preparation methods, structure) of the main different types of multilayers, in which responsive Bragg mirrors properties have been reported, are described.

The term reactive substrate herein refers to a wafer made of a material through which an electrical current can be applied to diminish its free enthalpy, while a chemical agent etches its surface. Aluminum, doped silicon and, more recently, titanium²  seem to be the most suitable materials that can be treated using this methodology, leading to nanometer tubular‐shaped pores of the corresponding metal oxide that grow perpendicular to the substrate.

Silicon was the first material shaped as a porous 1DPC. Its development was in part possible due to the knowledge acquired in the late 1950s when it was demonstrated that crystalline silicon wafers doped n or p could be made porous by passing an anodic current through them in the presence of a hydrofluoric acid solution.^3,4  Although the full mechanism of oxidation has not been totally elucidated yet, it is well established that it involves four electrons and the coordination of a fluoride ion to a silicon atom, located in the surface and that has previously lost a proton. The hydrolysis of the fluoride‐silicon coordinated structure produces a tetravalent complex of silicon from the bulk. Typical layer porosity achieved with these methods ranges between 40% and 80%. The periodic modulation of the refractive index along one direction is in this case achieved by controlled variation of the current during the process of biased etching described above. Since no change in the morphology of the pores occurs when the current is modified, continuous silicon columns are obtained at the end of the process, providing pore connectivity (at least) in the etching direction. Pore size can be tuned from 1 nanometer to a few micrometers by changing the current intensity, the fluoride concentration and the doping level of the active substrate.^5–7  In Figure 1.4(a) we show an image of the cross section of a porous silicon 1DPC, where the periodic modulation of porosity can be readily observed. The preferential pore growth direction is that perpendicular to the substrate, which favors their tubular shape. The group of Sailor has pioneered the research with this type of porous lattices and has made significant advances in the control of the photonic properties of these stacks.^8,9 

In the case of aluminum, in the middle of the last decade it was demonstrated that long pores could be generated in alumina from a mirror polished aluminum foil using hard anodization techniques.¹⁰  Two steps are applied to generate the array of pores. The first step generates the stem pores at a desired pore density, which is inversely proportional to the square of the anodizing potential in the equilibrium condition. The second step generates the columns from the stem pores. The value of voltage applied (in the range of tens of volts) and the nature of the acid determine the pore size of the Al₂O₃ tubes, while the individual slab thickness is related to the duration of these steps. As in the case of silicon, 1DPCs made in this way present a homogeneous composition and the one‐dimensional modulation of the refractive index is obtained through the controlled variation of the anodic current.^11,12  Porosities obtained are typically controlled on the order of a few tens of per cent, thus leading to low refractive‐index contrast between adjacent layers. Due to this, and in order to attain intense Bragg peaks, a large number of unit cells (more than 30) is needed, which implies that high aspect ratio alumina pores are generated.

Nanoparticles can also be used to attain porous 1DPC with responsive properties. In this case, the mesoporosity of the layers arises as a result of the incomplete space filling attained when colloidal size particles are packed. Different aggregation states may lead to different pore‐size distributions and overall porosity, and in consequence different refractive indices. Hence, it is possible to create Bragg mirrors by alternating layers of different refractive index made of particles of the same composition, which has been shown to add functionalities to the optical material.¹³  However, the most common procedure is the alternate deposition of layers of different nanoparticles. In principle, all types of nanoparticles that can be suspended to form a colloid may be integrated in a Bragg stack by this simple method. Wet deposition methods are inexpensive and give rise to uniform coating of substrates with areas about a few tens of square centimeters. Control over the thickness of the layers is achieved through the variation of the parameters that determine the deposition dynamics, which strongly depends on the method of choice. Layer‐by‐layer, for instance, in which electrostatic interactions between particles with different surface charge favors the assembly the whole structure and provides mechanical stability to the ensemble. This approach, developed by the groups of Rubner and Cohen, yields Bragg mirrors made of layers of nanoparticles of SiO₂ and TiO₂ combined with polyanions and polycations, respectively, which allows the surface charge of the layers to be controlled.¹⁴  Once the polymers are removed by thermal treatment, the average porosity of these systems is around 45%. In many cases, the attraction of the particles deposited in a film is greater than the solvation interactions that occur when dispersed in a liquid medium. The origin of this attraction is not well understood yet, and it may be a combination of Van der Waals and hydration forces, the latter resulting from the presence of hydrogen‐bonded water layers surrounding the nanoparticle network. This opens the door to stacking colloidal particles of the same surface charge using similar solvents, as has been repeatedly demonstrated by spin‐ or dip‐coating techniques. As in the previous example, SiO₂ and TiO₂ have been preferred over other materials because of their high refractive‐index contrast, but particles of very different composition, such as SnO₂, ZrO₂, In₂O₃, lanthanide fluorides or metals have been integrated in porous Bragg mirrors to take advantage of other optical functionalities, such as, for example, the possibility to absorb or emit light. Figure 1.4(b) displays a cross section of a porous SiO₂/TiO₂ 1DPC in which a monolayer of gold nanoparticles (bright circular spots in the SEM image) has been precisely located in the center of an optical resonator.¹⁵  In this particular case, advantage was taken of the effect of the interplay between the absorption caused by localized surface plasmons in the metal and the responsive resonant mode of the porous cavity to devise a multilayer that shows abrupt changes of its absorptance spectrum when infiltrated with different liquids.

Another way to produce responsive Bragg mirrors is the alternated deposition of mesoporous SiO₂ and TiO₂ films templated by a block copolymer. The added value of these two‐scale ordered systems is the opportunity that they present to control the geometry and the distribution of the pores in each layer. In this case, a subwavelength order is a consequence of the self‐assembly of a block copolymer included in the same liquid media where a soluble metal oxide precursor is included. Careful control of the hydrolysis and condensation reactions of the metal‐oxide precursor accompanied by the layer deposition conditions leads to the formation of an inorganic network of well‐defined geometry, since it is directed by the block copolymer assembly. The removal of the block copolymer can be made by extraction or by thermal treatment, the latter providing also the crystallization of the inorganic walls. The stacking of meso‐ordered layers is made using the same wet methods described above for nanoparticles. Consolidation of each hybrid inorganic–organic layer without removing the block copolymer allows the deposition of a new layer on top while preventing the infiltration of previously formed layers. Once the final number of layers in the stack is reached, the polymer is removed at once and a porous Bragg stack is developed. The resulting narrow pore‐size distribution brings the possibility to use them as base materials for optical sensing in which the probe will induce a change in the optical response depending on its size.¹⁶  In addition, different types of radicals can be anchored to the metal‐oxide walls of these porous 1DPC, which provides added functionality to these versatile materials. On the other hand, these materials present the capability to be integrated with dense metal‐oxide layers. This characteristic is very desirable when it comes to building different architectures where porous layer is located at a desired position.¹⁷  In Figure 1.4(c), an image of a cross section of a porous mesostructured optical resonator built within a dense 1DPC is shown.

Glancing‐angle deposition (GLAD) combines the traditional thin‐film vacuum deposition with a particular geometry in which the substrate is tilted with respect to the line connecting the target and the substrate.¹⁸  In this way, the vapor‐phase compound arrives obliquely to the substrate onto which it will be deposited. Due to this particular geometry, and the lack of surface diffusion of the deposited species, the microstructure of the deposited material is that of tilted pillars. The ability to control the column orientation leads to interesting applications due to the highly accessible and tunable interconnected pore network of the entire structure. The versatility of GLAD to create photonic crystal structures in different dimensions and the precision it offers to control different types of columnar structures have been thoroughly studied by the group of Brett, who pioneered both the technique and the development of the first photonic structures based on them.¹⁹  One of the main advantages of GLAD is that it allows uniform porous layers with homogeneous optical properties over large areas to be obtained, which makes it compatible with industrial processes. Since GLAD allows control of the porosity of the layers and thus refractive index by means of the angle of deposition, multilayers made of a single material can be prepared by changing, periodically, the tilt angle between the material source (the so‐called target) and the substrate. The aim of using only one material is to preserve its intensive bulk properties, bringing different functionalities together.²⁰  In Figure 1.4(d) we show a cross section of a columnar TiO₂/SiO₂ photonic crystal prepared by GLAD in the labs of the group of González‐Elipe.²¹ 

Alternate stacking of layers of different polymers also gives rise to a spatial modulation of the refractive index to construct a one‐dimensional photonic crystal. In this case, the higher refractive‐index contrast that can be achieved is lower than for the case of inorganic multilayers. In consequence, a high number of layers (more than 10 cell units) is required to reach a significant peak reflectance intensity, although it should be mentioned that, very recently, high dielectric contrast has been achieved in multilayers prepared by vacuum deposition of 4,4′‐Bis[4‐(diphenylamino)styryl]biphenyl (BDAVBi) and 2‐(4‐biphenyl)‐5‐(4‐tert‐butylphenyl)‐1,3,4‐oxadiazole (PBD) polymers.²²  A priori, polymeric Bragg structures do not present an open and interconnected porosity. Therefore, their responsive optical behavior is related to the capability of the layers to swell under the presence of certain solvents or vapours. Polymer layers are commonly deposited by spin coating from liquid solution. Crosslinking or total swelling of the recently deposited polymer layer is needed in order to prevent the dissolution of the whole structure when a drop of fresh polymer solution takes contact with the previously deposited film.²³  As a consequence, it is difficult to build responsive polymeric structures only with polymers. Zhai and coworkers have found a way to overcome this limitation by using polyelectrolyte layers that provide both porosity and swelling capability to the total ensemble.²⁴ 

Diblock copolymers can also be used to create all‐polymeric responsive Bragg mirrors. These dual compounds can self‐assemble spontaneously under certain conditions to produce periodic refractive index structures in 1, 2 and 3 dimensions.²⁵  The lamellar phase of these self‐organized materials gives rise to multilayers with 1DPC properties. The tuning of the Bragg peak in the visible implies that the thickness of the unit cells must be in the range of a few hundred nanometers, if a refractive index of around 1.5 is considered. This spacing is achievable by self‐assembly of high molecular weight copolymers or by a blend with their respective homopolymers, as Thomas and coworkers demonstrated by using a poly(styrene‐b‐isoprene) symmetric di‐block copolymer.²⁶  Layers of 100 nm of each block are stacked forming a multilayer. In 2007, the same group reported the first responsive structure based on this block‐copolymer self‐assembly approach using a hydrophobic–hydrophilic polyelectrolyte block polymer.²⁷  The responsiveness of this photonic structure is based on the uniaxial expansion of the polyelectrolyte layer when the system is put into contact with different salt solutions. This type of structure is also referred to as a photonic hydrogel, due to its capability to incorporate water into the structure. The structure can be frozen at a desirable thickness by the incorporation of inorganic compound.²⁸  From a different synthetic approach, block copolymers also offer the possibility to obtain highly ultraviolet‐reflecting porous periodic multilayers.²⁹  In this latter case, a combination of thermally driven self‐organization involving phase separation, selective UV degradation and collective osmotic shock, yields a one‐dimensional photonic crystal with an interconnected open‐pore structure. Figures 1.4(e) and 1.4(f) display cross sections of a swellable polymeric multilayer obtained by spin coating and an ordered porous polystyrene film prepared by collective osmotic shock, respectively.

Optical multilayers can also be developed by combining films of very diverse composition and structures, such as polymers, metal oxides, clays, etc. Bragg stacks made of organic polymer layers mixed with nanoparticles,³⁰  or alternated with porous metal oxide layers,^31–33  are examples of hybrid multilayers that display intense responsive optical properties. In these, swelling and pore infiltration occurs simultaneously in the different constituent layers, providing (and preserving after infiltration) enough refractive‐index contrast so as to achieve strong reflections with 10 periods.

Other types of compounds that are well integrated into Bragg reflectors are clays. Ozin's group developed a clay Bragg stack based on the alternating layers of laponite (a synthetic philosilicate clay of empirical formula Na_0.7[(Si₈Mg_5.5Li_0.3)O₂₀(OH)₄]) and metal‐oxide porous layers.³⁴  Laponite layers were successfully deposited from water‐based precursor dispersions and templated with polystyrene spheres to allow flowing liquids and gases through them. The importance of the use of clay films as building blocks is the capability of these layered silicates to intercalate, adsorb, and exchange ions within its structure. All these processes modify the optical thickness of clay layers, thus changing the optical properties of the whole ensemble.

The main common effects observed in the response of a Bragg reflector against changes in the environment are described in the first part of this section. As the optical response of layered materials is strongly dependent on the individual response of the constituent layers, a deeper description of the phenomena occurring during infiltration, as well as of the change of the optical parameters it gives rise to, is provided. Also, some representative examples, chosen to illustrate the various flavors of porous and/or swellable Bragg reflectors available and the main features of their response, are presented in the last part of this section.

The intense optical effects observed in Bragg mirrors are highly sensitive to the optical thickness of the individual layers present in the stack. In the case of the responsive Bragg mirrors herein described, such optical thickness can be modified either by infiltration of guest compounds in the pore network, which would result in an increase of the refractive index, or by diffusion of species in the polymeric layer, which would cause both swelling, and thus modification of the geometrical thickness, and variation of the refractive index. It is precisely this dependence that is behind the use of these multilayered materials as responsive optical mirrors. The magnitude and specificity of the changes observed will depend, in the former case, on the sorption properties of the pore network, which will in turn be a function of the pore‐size distribution and the chemical nature of the pore walls, or in the capability to admit targeted species within the polymeric network for the latter.

From the formulas (1.1)–(1.4), some of the main properties of responsive Bragg mirrors can be readily derived. First, incorporation of a compound into the full structure will cause a spectral redshift of the reflectance peak and the magnitude of this displacement will be directly proportional to the infiltrated amount of such compound. This will be the case no matter whether the effect of the guest compound was to increase the average refractive index or the film thickness. Also, stacks with a larger number of layers will present a higher reflectance and thus a higher signal‐to‐noise ratio, which favors readability. Peak intensity and width will increase as the refractive‐index contrast between the two types of constituent layers does, although the growth of the latter will stabilize as a consequence of the compensation effect of the rising average refractive value, as can be deduced from eqn (1.4). So, a compromise must be found between resolution, which is affected by peak width, and sensibility, which depends on the magnitude of the reflectance peak.

However, if the infiltration does not take place simultaneously in the whole structure, information from the optical response can only be extracted from the full detailed analysis of the reflectance or transmittance spectra. This is actually the case in most multilayered structures, in which films of different pore‐size distribution and composition are alternated. Several examples demonstrate that a complex dynamics of incorporation of guest compounds occurs, which makes the fitting of the full optical spectra necessary.

In the case of porous films, n₁ and n₂ are the result of averaging the refractive index of the walls and that of the pores, which might be empty or partially filled. In the most general case in which pore filling is not complete, the average refractive index of the ith layer, n_i, can be obtained from the equation derived by Bruggeman for a three‐component dielectric medium,³⁵  which is based on an effective medium theory:³⁶ 

which is derived considering that our inhomogeneous film as composed by the material of which the pore walls are made of, with refractive index n_wall, and the adsorbed species present in the pores, n_ads, embedded in an otherwise homogeneous background of n_bkg=1. Here f_wall, f_ads and f_bkg are the volume fractions of the material composing the pore walls, the adsorbed species and the surrounding medium, respectively. Knowing n_wall and n_ads, and extracting the effective refractive index of the film n_i from the fittings of the specular reflectance of a multilayer measured from the empty sample (f_ads=0) and by means of eqn (1.3), we can estimate f_wall and thus the total pore volume (f_medium=f_pore=1−f_wall) of the starting material. Then, from the effective refractive index of the film obtained at different environmental conditions and thus degrees of filling, we can estimate the volume fraction occupied by the adsorbed, and eventually condensed, species, f_ads, since we can write f_medium=1−f_wall−f_ads, leaving f_ads as the only unknown parameter. The ratio f_ads/f_pore is the ratio between the volume occupied by the infiltrated species, V_ads, and the originally free pore volume, V_pore. The specific spectral and temporal response to a particular event (i.e. gradual raise of gas pressure or increase of concentration of a target compound in solution) will be determined by the amount and rate of incorporation of the adsorbed species in the Bragg mirrors. Some examples are provided in Section 1.4.2. It should be noticed that, conversely, this tool has been used to analyze the pore‐size distribution of mesostructured films by relating the changes of adsorbed vapour volume with the size of the pore employing the Kelvin equation.

For the case of swelling films, such as those made of hydrogel, the materials can be considered homogeneous and eqn (1.3) does not apply any longer, but the effect of the concomitant change in the thickness of the constituent slabs must be taken into consideration.

The specificity of the response of Bragg reflectors to the presence of targeted compounds, as well as its magnitude, speed, etc. depend on the physical or chemical mechanisms involved (diffusion, adsorption, condensation, swelling, etc.), the nature of the building blocks and the presence of functional groups in the structure. An exhaustive enumeration and description of all responsive layered optical materials would be too long and beyond the scope of this chapter. The sort of effects observed in the reflectance, transmittance, or, in the case of the integration of optically active materials, luminescence spectra of responsive Bragg reflectors are herein illustrated with a few representative cases.

As was pointed out above, porous mesostructured materials are susceptible of being used as building blocks of responsive Bragg reflectors for their capability to adsorb and eventually condense molecules from their environment. This is a phenomenon that depends on the vapor pressure and therefore, a gradual change of the optical response will occur as this parameter is varied. Several groups have reported this effect, and make use of it to show that these materials can be the base of gas sensors. In Figure 1.5(a), the response of a porous alumina optical resonator, developed by Brett and coworkers using GLAD, to varying humidity conditions is displayed.¹⁹  Large redshifts of the cavity resonance can be observed in the transmittance spectra. In Figure 1.5(b), we plot the reflectance spectra of resonators built by sandwiching mesostructured layers prepared by supramolecular templating between two dense 1DPC as the vapor pressure of different alcohols is varied. From top to bottom, the solvent vaporized in the chamber is methanol, ethanol, isopropanol and butanol. Strict control over pore‐size distribution yields layered media capable of responding only when the size of the molecules is such as to allow them to flow through the pore network of the optical cavity, thus adsorption and condensation takes place and, consequently, gives rise to the redshift of the resonance. This latter example shows the added value brought by controlled porosity, since it may allow selective detection depending on the molecule size. The integration of mesostructured layers of this sort in different layered configurations has been demonstrated to give rise to responsive optical materials in which a rich interplay between diffusion, adsorption and condensation phenomena takes place.³⁷ 

Responsive Bragg reflectors have also shown a very clear response to the concentration of specific species in solution. One relevant example of this behavior is provided by the different lamellar Bragg reflectors prepared with self‐organized block copolymers. In Figure 1.6(a) the absorbance spectra of a polystyrene‐block‐quaternium poly2vynilpyridine (PS‐b‐QP2VP) Bragg mirror swollen by contact with different concentrations of NH₄Cl aqueous solution (concentration in mol dm⁻³ is noted between brackets) are plotted. The numbers above the peaks indicate the diffraction order. Please notice that the initially swollen structure decreases its thickness as the concentration of salts in the medium increases. Each one of the swollen states of these Bragg mirrors can be frozen by introduction of SiO₂ particles, which allows removal of the sample from the solution without altering its thickness and thus preserving its color. A series of pictures of PS‐b‐QP2VP Bragg mirrors treated in this way is shown in Figure 1.6(b). Similar effects have also been observed in hybrid structures combining inorganic layers and block polymers. An example of the spectral shift of the Bragg peak measured from a TiO₂/polydimethylaminoethyl methacrylate‐co‐ethyleneglycol dimethacrylate (PDMAEMA‐co‐PEGDMA) Bragg mirror at different concentrations of isothiocyanate (SCN⁻) groups, as well as pictures showing the observed color change, are displayed in Figures 1.6(c) and 1.6(d).

As has been mentioned before, the intrinsically accessible nature of responsive optical layered media allows both the integration of optically active molecules or nanomaterials inside them, and tailoring of the emission or absorption properties of such guest compounds through the interaction with the confined electromagnetic field. The luminescence of a layer of rare‐earth‐based nanophosphors (europium‐doped yttrium fluoride nanoparticles) integrated in a porous nanoparticle based optical resonator exemplifies well this type of effect.³⁸  Emission (blue lines) and reflectance (black lines) spectra obtained from such a structure when exposed to different pressure of isopropanol are plotted in Figure 1.7(a), while Figure 1.7(b) displays the changes in the emission intensity of the selected line (λ=708 nm) as the vapor pressure increases. This same structure shows an abrupt change in the emission properties when it is soaked in tetrahydrofurane, as can be seen in Figure 1.7(c). The Bragg reflector is herein causing the directional reinforcement or suppression of selected emission lines, largely modifying the standard luminescence spectrum of these nanophosphors (all measurements were taken at normal incidence and collection). At the same time, the pore network of the photonic matrix provides the path for fluids to infiltrate the material and give rise to the spectral and intensity changes observed in the emitted light.

Responsive Bragg reflectors present a great potential for the development of materials that could serve to build new types of nanostructured optical sensors as well as devices in which the emission and absorption of selected infiltrated species could be tailored to measure. Research activity in this emerging field is currently devoted to the exploration of new types of responsive films that could be used as building blocks, their functionalization, the improvement of its optical quality and device integration.

The research leading to the author*s results has received funding from the European Research Council under the European Union*s Seventh Framework Programme (FP7/2007‐2013)/ERC grant agreement n° 307081 (POLIGHT), the Spanish Ministry of Economy and Competitiveness under grants MAT2011‐23593 and CONSOLIDER HOPE CSD2007‐00007, and the Junta de Andalucía under grants FQM3579 and FQM5247.