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Phase changes can be grouped into first order or second order transitions and are characterised by changes of thermodynamic properties around that transition, such as order, enthalpy and heat capacity. First order transitions are characterised by a discrete change in order and have an associated latent heat, whereas second order transitions display continuous changes. The melting and evaporation of water and the transition between isotropic and nematic liquid crystal states [13] are first or- der transitions. The change in order of the substances can be expected to have an associated change of refractive index, the property that is measured here.

9.3

Design Considerations

The basic design and fabrication method of the planar sensors is shown in figure 9.1. A UV written waveguide with integrated Bragg grating is written into the sample as described in chapter 3. The overclad directly above the Bragg grating section is removed using an etch process. In this way the waveguide remains in its as-written state whilst the Bragg grating is exposed to atmosphere. The hole in the overcladding is then simply filled using the analyte to be studied. Changes in the analyte refractive index can then easily be monitored by interrogation of the Bragg response.

Whilst the cylindrical symmetry of optical fibre lends itself readily towards modi- fication of the cladding index all around the core, planar geometries are more re- stricted as shown in figure 9.2. Consequently planar sensors of the type presented in this chapter can be expected to have a somewhat lower sensitivity to refractive index changes than their equivalent fibre based designs. For practical reasons the work described here is restricted to modifying the cladding refractive index above the waveguide core whilst leaving the cladding either side and below the core un- changed.

1 2

3

Figure 9.1: From planar waveguide to planar sensor. 1) The waveguide and Bragg grating are defined in the core layer, 2) The overclad above the grating is etched away and 3) replaced by the analyte.

The principles used here to allow a Bragg grating to act as a sensing element ap- ply equally well to Bragg devices produced by any method. For some applications however, there are advantages to using a UV writing approach. A planar waveguide fabricated using standard etch process will not have a truly planar surface. Even when planarisation steps are taken it is very difficult to avoid surface relief above the waveguide core. In UV writing all depositions are performed prior to the waveguide definition and so no surface relief is introduced to the layers. Thus when the upper layer is etched away to uncover the grating, it is a smooth, flat surface that is being etched, allowing the resultant etched surface to also be smooth and flat. This chapter centres on the use of liquid crystal and water overlayers on the exposed grating. It is important, due to reasons discussed in section 9.6, that the surface structure is as ho- mogeneous, clean and smooth as possible to allow the liquid crystal - silica surface interface to act in a controlled predictable way. Any surface structure, such as that over an etched waveguide, will degrade performance. When monitoring the phase changes of water, consideration must be given to the expansion and contraction that is known to occur as water thaws and freezes. A relief grating which by definition has a structured surface, is susceptible to ‘weathering’ by water. Again, the smooth, flat surface allowed by UV writing is an advantage in this case.

Chapter 9 Detection of Phase Transitions

Analyte

Fibre Core with Bragg Grating Fibre Cladding

Waveguide Core with Bragg Grating

Analyte

Figure 9.2: Schematic showing restricted contact of Bragg grating core with analyte in planar relative to fibre geometries

9.4

Device Modelling

To asses the expected sensitivity of Bragg wavelength to variations in overclad re- fractive index the structure shown in figure 9.3 has been modelled according to the method proposed by Marcatili [14]. This technique is used to estimate the effective index of a waveguide with a range of overclad refractive indices, the results of which are shown in the graph of figure 9.3.

Analyte Refractive Index

1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 Ef fe c ti v e In d e x 1.452 1.453 1.454 1.455 1.456 1.457 1.458 Analyte 1.4613 1.4505 1.4434 1.4505 5m 5m Idealised Refractive Index Structure

Figure 9.3: Sensitivity curve for a planar sensor with a refractive index structure as shown.

As previously mentioned in chapter 7, the exact refractive index structure of the UV written waveguides presented here is not known. However, approximate values of the refractive index of the layers can be estimated based on prism coupling and data

from fluence curves. Using experimentally obtained effective index measurements presented later in this chapter, the parameters used in the Marcatili model have been refined such that the modelled results match the experimental data. This was done using the known refractive index of air (n=1.0) and of water (n_≈1.31) [15, 16] at 1550nm. The refractive index profile of the modelled waveguide shown in figure 9.3 is such that the model predicts the correct effective index (the values of which are presented later in this chapter) with overclad refractive indices of 1.0 and 1.31. A superior index structure could be generated using more calibration points closer to the refractive index of the doped silica where the gradient of the sensitivity curve is higher. There are however several assumptions that must be made in order to use this model and as such the use of improved calibration points would be of lim- ited value. In addition to the simplifications inherent to the Marcatili method, the waveguide core has been treated as a symmetrical step index structure with a per- fectly etched overclad.

Recalling that the Bragg wavelength varies linearly with effective index it can be seen that the sensitivity of the sensor to refractive index variation is given by the gradient of the graph, δneff

δnclad. For an overcladding very close to the waveguide core in terms of

refractive index the gradient of the sensitivity curve is high showing that there is a large variation of Bragg wavelength with overclad index. With cladding index above that of the core the structure ceases to act as a waveguide and the sensor no longer functions. As the overclad index drops, the dependence of effective index becomes weaker and thus the sensor is less sensitive.

A modelled sensitivity of unity is achieved with an analyte refractive index of 1.4606 i.e. a change in overclad index causes a change of equal magnitude in the effective index. As figure 9.3 shows this drops rapidly with decreasing analyte index. At the refractive index of water the modelled sensitivity is reduced by a factor of approx- imately 500. Even with this reduced sensitivity, the model predicts that the typical wavelength resolution of a standard optical spectrum analyser (10pm) allows the de- tection of refractive index changes in water of5_×10−3_{or lower despite its relatively}

low refractive index. Specialist grating interrogation equipment with resolutions an order of magnitude higher allow detection of index changes a corresponding order

Chapter 9 Detection of Phase Transitions

of magnitude smaller.

The reduced sensitivity at high analyte refractive index values is due to variation of the penetration of the mode into the analyte. This is shown graphically in fig- ure 9.4 which has been generated using the Marcatili model discussed earlier. The graph shows the variation of the depth to which the electric field penetrates before decaying by 1/e.

Analyte Refractive Index

1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1 /e p e n e tr a ti o n d e p th / m icr o n s 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Figure 9.4: Variation of electric field penetration with analyte refractive index.

It can be seen that with water as an overlayer (n≈1.31) the penetration depth is a few hundred nanometres but increases rapidly with analyte index, explaining the similarly rapid increase in sensitivity.

Figure 9.5 is shown to compare the sensitivity of the planar device presented here with the possible response of a similar fibre based device. The same modelling method described above was used but for the case of the fibre sensor the entire clad- ding surrounding the core was used to vary the effective index. It can be seen that the fibre based design with analyte entirely surrounding the core shows a higher sensitivity as expected, with a wider range of effective indices for the given range of cladding indices.

The relative sensitivities of practical sensor devices will depend significantly on the thickness of cladding layers between the analyte and the waveguide core as well as on the proportion of the core circumference that is exposed to analyte instead of overcladding. As such, the modelling presented here does not provide an exact determination of the sensitivity of the devices described. Rather, it demonstrates how the sensitivity varies with the penetration of the mode into the analyte.

Analyte Refractive Index 1.435 1.440 1.445 1.450 1.455 1.460 1.465 E ff e c ti v e In d e x 1.452 1.454 1.456 1.458 1.460 1.462

Fibre grating sensor Planar grating sensor

Figure 9.5:Comparison of sensitivity curves for fibre Bragg grating and planar Bragg grating sensor designs.

For practical reasons, a fibre grating sensor of this nature is likely to be encapsu- lated in some way to enhance the physical strength. Such pseudo-planarisation will inevitably reduce the sensitivity towards that of the planar device modelled above. It is of course possible, with additional engineering to develop a planar sensor struc- ture with three sides of the waveguide core (making the assumption of a rectangular cross-section guide) in contact with the analyte as shown in figure 9.6. In this case the sensitivity improves towards that of the fully surrounded version possible with fibre based designs. To date this has not been studied experimentally so further dis- cussion is restricted to the case where only variations in overclad refractive index are detected.

Analyte

Waveguide Core with Bragg Grating

Figure 9.6:Schematic of route towards enhanced sensitivity planar sensor.

It is worth commenting that the asymmetry of the waveguiding structure used in these devices causes a high level of birefringence. Whilst such a property would be of concern in, for example, high bit rate telecommunications systems where polari- sation insensitivity is desirable, it is not of significant concern in a sensing device.

Chapter 9 Detection of Phase Transitions