**1. Introduction**

Sensors are being developed for every possible aspect of modern life, ranging from the detection of air pollutants [1] and food contaminants [2], monitoring health biomarkers [3,4], and even assisting in the detection of extra-terrestrial life [5]. There are many characteristics of an effective sensor, including high sensitivity, selectivity, high signal-to-noise ratio, fast response time, and reliability/stability. Sensors should ideally also be manufacturable at relatively low cost and have a reasonable shelf life that makes them cost-effective to use.

Optical diffraction grating-based sensors respond to an analyte or environmental stressor via a change in their optical properties, namely grating refractive index, *n*, refractive index modulation, Δ*n*, and/or thickness, *d*. In the case of surface relief grating configuration sensors, Δ*n* is the difference in refractive index, *n*, between the surface relief grating material and the surrounding medium. For volume grating configuration sensors, Δ*n* is the difference in the refractive index, *n*, between illuminated and non-illuminated regions inside the grating. In the case of transmission-mode diffraction grating-based sensors illuminated with a probe beam (with incident intensity *Io*), any change in the value of Δ*n* or *d* will vary the phase difference, ϕ, between the beams propagating along the zero (*It*) direction, and the higher orders (*Id*) of diffraction from the grating. For thin gratings operating in the Raman-Nath regime [6], the diffraction efficiency, η, can be related to ϕ via:

$$
\eta = f\_m^2 \left(\frac{\wp}{2}\right) = \frac{I\_d}{I\_o} \tag{1}
$$

where *Jm* is the Bessel function of the order *m*, and ϕ is given by:

$$\varphi = \frac{2\pi\Delta nd}{\lambda\_r \cos\ \theta\_B} \tag{2}$$

where λ*<sup>r</sup>* is the wavelength of the probe beam and θ*<sup>B</sup>* is the Bragg angle. Thus, changes in *n*, Δ*n* and *d* due to analyte exposure can be indirectly measured via the η. Recently, Sabad-e-Gul et al. implemented this approach for the development of a surface relief diffraction grating (SRG)-based sensor for the detection of heavy metal ions in water [7]. The SRG-based sensor, fabricated via the holographic lithography of an acrylate photopolymer surface, which is subsequently functionalized with zeolite nanoparticles, successfully detected low concentrations of copper (Cu2+), Pb2<sup>+</sup> and Ca2<sup>+</sup> cations. It is postulated that the obtained change in η results from the adsorption of the metal ions onto the zeolite nanoparticles on the SRG surface, thereby changing the *n* of the functionalizing component (i.e., the zeolite nanoparticles) and consequently changing Δ*n*.

While this indirect measurement technique is a straightforward and fast method for sensor evaluation and characterization, this approach provides limited information on the underlying sensor operation mechanism, such as the relative contribution of simultaneous and competing changes in grating *n*, Δ*n* and *d* to the overall measured sensor response. Moreover, due to the nature of the Bessel function in Equation (1), it is not readily possible to ascertain from a change in η alone whether ϕ is increasing or decreasing as a result of analyte exposure. Theoretical modelling of the processes can be conducted; however, models require assumptions and a robust model has yet to be reported. It is thus preferable to directly measure the changes in grating *n* and *d* due to analyte exposure. Such measurements will facilitate the direct study of sensor–analyte interactions, which will facilitate the enhanced understanding, design and fabrication of optical sensors.

Here, the use of ellipsometry as a characterization tool to provide further insight into optical sensor operation and zeolite–analyte interactions is presented. Ellipsometry is a highly sensitive optical technique that uses polarized light to measure the dielectric properties, such as refractive index, of a thin film or layer system [8,9]. A beam of light with a known polarization state is transmitted or reflected from the surface of the thin film, causing a change in its polarization state. The modified polarization state can be decomposed into the reflection coefficients, *rp* and *rs*, as derived by Fresnel, of the parallel and normal components of the electric field with respect to the plane of incidence. Ellipsometry measures the ratio of *rp* and *rs* (known as the ellipsometric ratio, ρ), and uses this to calculate the ellipsometric angles, Δ and ψ:

$$\rho = \frac{r\_p}{r\_s} = \tan\,\,\psi \times \epsilon^{i\Lambda} \tag{3}$$

The angle of incidence, θ, of the light beam is selected to be near Brewster angle of the substrate in order to maximize the difference between *rp* and *rs*. Following the measurement of Δ and ψ, a layer model is established for the thin film, which consists of any known optical constants (*n*, *k*) and thicknesses (*d*) of all individual sequential layers within the thin film. Using an iterative approach, the unknown optical constants and/or thicknesses are then varied until the best match for the measured values of Δ and ψ is obtained. For increased accuracy, as much information as possible regarding the layer model should be known in advance.

The advantages of ellipsometry are obvious; it is a non-destructive, non-contact and non-invasive characterization technique that readily achieves sub-nanometer resolution in thickness. Due to this high sensitivity, its principles have even sometimes been used as a sensor transduction mechanism [10,11].

The current study aims at developing a better understanding of the changes to the nanozeolite-doped thin film that result as a consequence of its exposure to a target analyte. In addition, consideration will be given to the advantages and limitations of both the single wavelength and spectroscopic ellipsometry apparatus for this particular study.
