In this work, a new approach based on the use of a one-dimensional photonic crystal (1DPC) made of dielectric layers with alternating refractive indexes deposited inside a photonic crystal fiber (PCF) is proposed as a suitable platform for the excitation of Bloch surface waves (BSWs). The presence of an additional dielectric layer on the 1DPC modifies the local effective refractive index, enabling a direct manipulation of the BSWs. In particular, we investigate BSW resonance conditions in a 1DPC of alternating layers of TiO2 and SiO2 deposited inside a three-hole suspended-core PCF to design an ultra-wide range refractive index sensor in the near infrared. The obtained simulation results indicate that BSW sensors based on PCF could be an alternative to surface plasmon resonance (SPR) sensors, with a ultrahigh sensing figure-of-merit, which might facilitate applications in high-resolution refractive index sensing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Electromagnetic surface waves (ESWs) are a specific type of wave that are confined at the interface between two different media and decay exponentially into the neighboring media . Among them are the surface plasmon polaritons (SPPs) which are excited at the boundary of metallic and dielectric media. SPP waves are characterized by their short propagation length as a consequence of the strong absorption of the metallic layer , therefore, there is a great interest in the excitation of ESWs between two dielectric media, since they can propagate at the interface with very low losses . Bloch surface waves (BSWs) are waves that propagate at the interface between two dielectric media, where, in the simplest case, at least one of them is a dielectric multilayer stack, also called one-dimensional photonic crystal (1DPC)  or Bragg reflector, and the propagating modes are established by breaking the structure periodicity with an additional layer of appropriate thickness deposited on top of the 1DPC . Although they are more complicated than metallic systems, 1DPC-based devices are highly customizable and do not suffer from absorption losses that affect metallic structures . In general, a 1DPC can sustain BSW modes if the dispersion curves of the BSWs are located within the photonic crystal forbidden bands  and below the light line of the surrounding medium .
BSWs were first theoretically reported  and followed by experimental demonstration in 1978 . However, recent advances in thin film deposition allowed to increase the design possibilities and renovate the interest in ESWs in dielectric interfaces. BSW excitation using the prism-based Kretschmann-Raether configuration has been used in applications such as BSW-based sensors [1, 7], guided optical applications based on BSW [5, 10–12], and BSW-controlled fluorescence [13, 14]. Some of the dielectric media used to build the 1DPC are bilayers of TiO2/SiO2 [7, 15], Si/SiO2 [5, 16], and plasma composed of a mixture of SiH4 and NH3 in different concentrations [4, 11, 17]. A direct comparison between SPP and BSW sensors in prism-based optical systems showed that BSWs have considerably narrower reflectance curves than SPPs, as a consequence of the reduced loss of dielectric materials . Current studies in conventional optical fibers have been reported where BSWs are analyzed by using methods based on the operating principle of the Kretschmann-Raether configurations in which multilayer structures have been deposited at the tip of a single-mode fiber , the flat surface of a D-shaped single-mode fiber , and an omnidirectional one-dimensional multi-mode optical fiber .
BSW based sensing scheme can be more functional with the use of suitable optical platform. Photonic crystal fiber (PCF) offers several advantages over the conventional fiber [20, 21]. The design flexibility of PCF enable it to support a number of applications over conventional fiber [22–25]. EWS resonance devices and sensors based on PCF attract the most research interest because of their flexible design of microstructure, with SPPs the most widely studied type of EWS .
In this paper, we present a theoretical investigation to demonstrate excitation of TM- and TE-polarized BSWs in a PCF. We design a 1DPC structure deposited inside a PCF, where BSWs are excited by the evanescent field of the fundamental core-guided mode. Numerical simulations were carried out by using the finite element method (FEM) taking into account multi-BSW excitations, thickness variations of the additional top layer, and analyte refractive index changes. We present what we believe is the first design of a fiber optic sensor based on BSW resonance in the near infrared that can operate in an ultra-wide range of refractive indices, from 1.0 to 1.4. The designed sensor has potential applications in the sensing of gases, bio-analytes, and liquids of high-refractive index, where it can reach sensitivities up to 2575 nm/RIU and a ultrahigh 669 RIU−1 sensing figure-of-merit.
2. Structure and numerical modeling
2.1. 1D photonic crystal
We consider a planar 1DPC because the principal region of BSW excitation is the central region of a PCF, which can be approximated as a planar section of the fiber. In this work, the dielectric multilayer structure was designed to sustain BSW modes in the near infrared, which is the common range of operating wavelengths in fiber-optic communication components. The designed 1DPC is shown in Fig. 1(a) where SiO2 is used as a substrate. The 1DPC consists of a 4-period stack made of TiO2 (high-refractive index) and SiO2 (low-refractive index) layers whose thickness are dh = 250 nm and dl = 600 nm, respectively, and period Λ = dh + dl. As it was mentioned above, the top layer, which will be in contact with the external environment, breaks the 1DPC periodicity, for which a TiO2 layer of d = 160 nm thick was initially considered.
Figures 1(b) and 1(c) show the band diagrams of the periodic TiO2/SiO2 dielectric structure for the TM- and TE-polarized modes, respectively. The numerical simulations were carried out by means of the transfer matrix method . The diagram’s white regions represent the 1DPC forbidden bands, while the dashed lines are the dispersion relations for light propagating in air; f = βc/2π, where β is the propagation constant and c is the speed of light in vacuum. Dispersion curves for the TM- and TE-polarized BSWs are the green and red lines, respectively, which were calculated by computing the fundamental BSW1, as it will be shown later. As expected, the dispersion curves of the BSW modes are located inside the 1DPC forbidden bands (white regions) and below the analyte light line. The band diagrams show that TE- and TM-polarized BSWs can be excited at near-infrared wavelengths (see the highlighted spectral region in Fig. 1). However, it is worth mentioning that the dielectric 1DPC can be designed appropriately so that it is possible to excite BSWs at any designable wavelength.
2.2. Photonic crystal fiber
We consider a Ge-doped suspended-core three-hole silica PCF, which has been successfully fabricated using the stack and draw technique . This PCF can have exposed regions of the fiber core—often referred to as side-opened suspended-core PCF— to accelerate the fluid filling and access the fiber core and thus achieve real-time sensing . Additionally, using this PCF is possible to design a multi-analyte sensor , a topic that will be addressed in subsequent investigations. The dielectric layers of the designed 1DPC can be deposited on the inner surface of one (or more) hole of the PCF by using high-pressure chemical vapor deposition (HPCVD). Uniform dielectric thin films have been reported inside PCF holes using HPCVD technology, with barely 2% thickness variation . Figure 2 shows the cross-section of the PCF and the inset is a zoom of the fiber central region, where it can be identified that the 1DPC is only deposited inside channel 1 (CH1). As we can see in this figure, CH1 is considered to contain analyte, while channels CH2 and CH3 are filled with air. The bridge thickness is a = 2 µm, the core diameter is 2 µm, the minimum distance between the core and the holes is b = 2 µm, and the bridge curvature radius is r = 11.93 µm.
In order to calculate the propagating modes in the structure, the vector wave equation was solved using COMSOL Multiphysics finite element software, where a perfectly matched layer (PML) was added to avoid reflections at the boundaries. Silica and titanium oxide refractive indexes were calculated using Sellmeier equation with coefficients reported in , and the fiber core refractive index was calculated using coefficients reported in  for 4% Ge-doped silica.
It has been theoretically and experimentally demonstrated that surface waves, such as SPPs, can be excited and coupled from the fiber core modes . The guided light in the core generates an evanescent field that can excite an SPP wave at the resonant wavelength. The same analysis can be applied for the case of resonance between a core-guided mode and a Bloch wave in the dielectric 1DPC. Now, the evanescent field of the y-polarized core mode excites the TM-polarized BSW modes while the evanescent field of the x-polarized core mode excites the TE-polarized BSW modes. Figure 3 shows the electric field distributions of the core-guided mode and the fundamental TM- and TE-polarized surface modes. The insets present the electric-field distributions of surface waves along the 1DPC in the fiber central region (white dashed line), which, as expected, the BSW field decays exponentially in the 1DPC and in the homogeneous external medium due to Bragg reflection and total internal reflection (TIR), respectively [8, 33].
3. BSW excitation
The resonance excitation of BSWs can be studied by analyzing the dispersion curves of the propagating modes in the structure of the PCF, represented by the dotted curves in Fig. 4 for the TM- and TE-polarized BSWs. Resonance is characterized by a peak loss in the transmission spectrum of the core-guided mode, which indicates the largest energy transfer from the core-guided mode to the BSW mode at a particular wavelength, where the effective refractive indexes (neff) of the core-guided mode and the BSW mode coincide. As expected from the band diagrams of the 1DPC structure in Fig. 1, the polarization state of the light has a significant effect on the excitation spectrum of the Bloch waves. For instance, in this case for each state of light polarization, four BSW modes supported by the 1DPC are involved in the coupling properties of the designed PCF. In general, the phase-matching conditions for the excitation of the BSWs by the fundamental core-guided mode indicate that the resonance wavelength of a BSW mode of lower order occurs at a longer wavelength than a BSW mode of high order. It can also be seen that the resonance wavelengths of the TM-polarized BSWs are closer to each other than those observed for the TE-polarized BSWs, which has a significant effect on the structure of the attenuation bands in the transmission spectrum of the core-guided mode, as shown later. The insets in Fig. 4 show the electric field distributions of the BSW modes that indicate the nature of the coupling and the transfer of energy from the fundamental core-guided mode to the BSW modes.
Because the confinement losses are very small, the transmission spectra in Fig. 4 were calculated using coupled mode theory (CMT) , assuming an analyte medium of nA = 1.33 and a 1DPC length of 1.0 mm and 0.7 mm for the TM- and TE-polarized BSWs, respectively. As we can see, the computed transmission spectra feature four attenuation bands for the y-polarized core-guided mode in the wavelength range of 1.515–1.560 µm, caused by the Bloch excitations at 1546.4 (BSW1), 1541.6 (BSW2), 1534.8 (BSW3) and 1524.4 nm (BSW4), and four attenuation bands for the x-polarized core-guided mode in the wavelength range of 2.57 – 2.65 µm, caused by the Bloch excitations at 2629.4 (BSW1), 2621.2 (BSW2), 2607.2, (BSW3) and 2585.8 nm (BSW4). As will be shown below, the difference between the amount of light coupled at each resonance peak is due to the fact that the energy transferred from the fiber core to a BSW mode is a function of the length of the structure, which in this case leads to a higher coupling efficiency for the TM-BSW2 and TE-BSW1 modes.
It is important to note that the resonance wavelength depends on the 1DPC design, especially on the properties of the top layer. Considering TiO2 as the top layer, the resonance wavelength can be adjusted by choosing the proper thickness of the 1DPC top layer. As an example, Fig. 5 shows the resonant wavelength as a function of the top layer thickness for the fundamental TM- and TE-polarized BSW modes with nA = 1.33. The insets in this figure show the electric field distribution of the BSW1 for different thickness of the top layer. From this figure it is possible to see, at the lower limit, that the resonant wavelength of the TM-polarized Bloch mode is less sensitive when the thickness of the top layer is below 70 nm, which is explained because the Bloch wave travels inside the stack, so this mode is named as a Bloch sub-surface wave (BSSW) [5, 35]. BSSWs have been used for detection, however it has been shown that if the analyzed substance can not penetrate the multilayer (as the case we are considering) these are less sensitive waves than the BSW . In contrast, the TE-polarized Bloch mode does not show this behavior and it is revealed that as the thickness of the top layer is thinner the BSW mode is more confined and, consequently, the evanescent field component decreases, which it is not favorable for sensing applications.
On the other hand, at the upper limit of Fig. 5, the TE-polarized Bloch mode reaches the maximum possible when the top layer thickness is greater than 200 nm. In this case, the distribution of the electric field shows that the Bloch mode is extended in the stack and the evanescent field component in the external environment is very small, which means that the BSW1 dispersion curve moves towards the edge of the band gap when the top layer becomes thicker, until it is comparable to the TiO2 layers in the stack. In contrast, at this upper limit one can see that the TM-polarized Bloch mode still does not reach the maximum possible.
Figure 5 further shows that for a given value of top layer thickness, TM- and TE-polarized Bloch waves are excited in very different spectral regions. If it is intended to excite both polarization at the same wavelength, then two structures with different top layer thicknesses should be designed. Finally, it can be concluded that by properly selecting the top layer thickness of the multilayer structure, the Bloch waves can be excited in any desired polarization state over a wide range of wavelengths, from visible to infrared.
4. Ultra-wide range refractive index sensor
From our simulation results above, we demonstrated that a TiO2/SiO2 dielectric 1DPC can be designed in 1550 nm telecom band. Figure 5 show that a TE-polarized BSW will be excited when the top layer thickness is 56 nm and a TM-polarized BSW will be excited when the top layer thickness is 160 nm. However, as can be seen in the field distributions in Fig. 5, at 1550 nm the TE-polarized BSW is very confined in the top layer and, therefore, will have a reduced interaction with the analyte in CH1, which is crucial for the operation of a refractive index sensor. Accordingly, the structure with the top layer thickness of 160 nm was chosen as a refractive index sensing structure with the TM-polarized BSW mode excitation.
In order to evaluate the performance of the three-hole suspended-core PCF-based BSW sensor, an extended range of analyte refractive index, from 1.0 to 1.4, was considered, as shown in Fig. 6 for a 1.5-mm-long sensor. In general, the resonance peaks are very sharp. It can be seen that the four most excited loss peaks move towards longer wavelengths, and the loss of the core-guided mode gradually increases as the analyte refractive index increases. With the increase of the resonance wavelength, the effective refractive index decreases significantly, as a result the refractive index contrast between the core-guided mode and the BSW mode is reduced, which leads to stronger coupling between the core-guided mode and the BSW mode. Considering the wavelength sensitivity, the BSW1 resonance peak is more suitable for refractive index sensing (see yellow dots). In this figure it is clear that higher-order BSW modes are excited close to the BSW1 mode, especially the BSW2 mode, as already observed for the TM-polarized modes, which causes the BSW1 resonance peak to have a non-optimized spectral profile, such as it is shown later. Clearly, the designed sensor can detect analyte refractive index changes in the proposed extended range. This implies that with the analyzed structure, it is possible to have an ultra-wide range sensor with which gases, bio-analytes and liquids with high-refractive index can be sensed.
The resonant wavelength shift, with respect to the analyte variation, is shown in Fig. 7(a), and the sensor sensitivity, defined as Sn = ∂λres/∂nA, is shown in Fig. 7(b). It is possible to see that the BSW1 resonant wavelength shift is approximately linear for low values of analyte refractive index (1.0 < nA < 1.15), a trend confirmed by the sensor sensitivity analysis. Nevertheless, for higher analyte refractive index values (1.15 < nA < 1.4), the sensor response and sensibility exhibit a nonlinear feature due, as already explained, to the strong mode coupling between the core-guided mode and the BSW mode. When the analyte refractive index is nA = 1.4, the sensor sensitivity reaches 2575 nm/RIU, which is comparable with most of the PCF-based SPP sensors .
In order to obtain the highest efficiency of the PCF-based BSW sensor, its response can be optimized by calculating the transmission curves for different sensor lengths, in order to find the conditions in which the coupling between the core mode and the surface modes is optimum. As an example, in Fig. 8 an optimization process is carried out, where it was assumed an aqueous analyte refractive index (nA = 1.33). The full-width-at-half-maximum (FWHM) analysis of the optimized systems can be found in Table 1. It is worth mentioning that larger propagation lengths were not considered, given that a longer sensor it will optimize the coupling of higher order modes, and it will not be possible to track the BSW1 resonance peak.
A more comprehensive description of the sensor response can be given by the figure-of-merit (FOM) analysis of the resonance peak in the transmission spectra, define as FOM = Sn/FWHM . The FOM parameter is an important characteristic to evaluate the performance of a resonant sensor. In Table 1, it can be seen that the sensor length plays an important role to define the sensor quality, represented here as the FOM parameter. For short sensor lengths, the BSWs loss peaks overlap due to their band width, however, as the sensor length increases, each of the resonance peaks becomes narrower and can be differentiated. When the sensor length is L ≥ 1.30 mm, the FHWM of the BSW1 loss peak is not affected for higher-order resonances, then the sensor FOM substantially increases, reaching a value of 669 RIU−1 (see Table 1), which is better than a lot of PCF-based SPP sensors [26, 37, 38]. However, as the sensor FOM increases, the depth of the BSW1 loss peak decreases. Then L = 1.70 mm can be considered as the optimized sensor length to detect refractive indexes in the vicinity of nA = 1.33.
In summary, this work proposes a ESW-supporting dielectric multilayer structure deposited inside a PCF, where BSWs can be excited through the evanescent field of the core-guided mode. The presence of an additional dielectric layer on the top of the multilayer enables a direct manipulation of the BSWs. It is shown that the properties of the platform define both the propagation and manipulation properties of the surface modes. To demonstrate the concept of the platform, a refractive index sensor based on BSW resonance in the near infrared is designed that can operate in an ultra-wide range of refractive indexes, from 1.0 to 1.4. The designed PCF sensor achieves a sensitivity comparable to the sensitivity of reported PCF SPR sensors, with an ultrahigh sensing figure-of-merit. The structure of the designed PCF BSW sensor is simple and easy to fabricate. Results are promising for high-resolution refractive index sensing.
The authors would like to thank the support provided to this work by the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS), project FP44842-107-2016, and the Universidad Nacional de Colombia, Hermes code 39312. E.G.V. acknowledges the support of COLCIENCIAS through the Doctoral Scholarship program.
The authors thank E. Reyes-Vera from Instituto Tecnológico Metropolitano for the simulations in COMSOL Multiphysics.
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