A planar optical sensor consisting of a diffraction grating and a onedimensional photonic crystal based on Bloch surface wave excitation effect is proposed. The obtained results can find application in the design of novel onchip refractive index sensors.
Nowadays, resonant optical sensors based on the excitation of surface electromagnetic
waves (surface plasmon polaritons (SPP) or Bloch surface waves (BSW)) are widely
used for refractive index measurement and for detection of various micro-objects.
SPPbased sensors [
Fig. 1 shows the geometry of the investigated sensor. The structure comprises a diffraction grating with one-dimensional periodicity and a one-dimensional photonic crystal (PC). The PC consists of N periods (N pairs of plane-parallel layers with alternating thicknesses and dielectric permittivities). Let us consider an example with the following parameters: PC layer thicknesses h1 96 nm and h2 140 nm , dielectric permittivities 1 4.511.7 103 i (corresponds to TiO2 at 0 550 nm ) and 2 2.05 6 104 i (corresponds to SiO 2 at 0 550 nm ). At the upper surface of the PC, an additional layer with the thickness h and the dielectric permittivity is located. In the considered example, we set 1 and h h1 hc , where hc 63.8 nm . The studied structure is intended for the measurement of the refractive index of the superstrate (the medium over the PC with the unknown refractive index nsup ). The working refractive index range in the considered example is 1.33–1.34 (distilled water and weak NaCl solutions). At the lower surface of the PC, a onedimensional diffraction grating with the period dgr , ridge height hgr , ridge width lgr and dielectric permittivity gr (in the present example, gr 1 ) is located. The values of the parameters dgr , hgr , lgr are chosen so that BSW are excited by a prescribed diffraction order (orders) of the grating.
z s d o i r e p N x nsup h’ ’ h2 2 h1 1 The operating principle of the sensor consists in the measurement of the reflection coefficient at different (gradually varying) values of the incident angle or the incident wavelength. In the vicinity of the resonance that occurs at certain combinations of parameters (e.g., the refractive index of the superstrate and the angle of incidence), BSW is excited at the interface between the PC and the superstrate, which leads to a pronounced dip in the reflectance spectrum.
To evaluate the sensor performance, we use the following conventional figure of merit
[
Let us note that the FoM values given below were obtained on the basis of a rigorous
solution of the Maxwell’s equations using the Fourier modal method [
The sensing performance of the considered structure was investigated for the following superstrate media: double-distilled water and 1%, 2% and 3% NaCl solutions with the refractive indices equal to 1.3330, 1.3347, 1.3364, and 1.3381, respectively. The values of the diffraction grating parameters dgr 453.2 nm , hgr 563.7 nm , lgr 0.59dgr were found using an optimization procedure from the condition of BSW excitation by the first diffraction order at the incidence angle of 10º and the superstrate refractive index of 1.335.
Fig. 2 shows the absolute value of the reflection coefficient vs. the incidence angle for
the four measured media. According to Fig. 2, the resonance (the reflection dip) is
present for all considered media. Let us note that the angular position of the reflectance
dip changes continuously and monotonically with the change in the refractive index of
the measured medium. The performance of the grating-based sensor and the sensor
based on the Kretschmann geometry is compared in Table 1. It follows from Table 1
that the FoM values for the sensor with a diffraction grating are slightly lower than the
values for the sensor based on the Kretschmann configuration. At the same time, these
values are significantly (by almost 5 times) greater than the theoretical limit for
SPPbased sensors with a gold film ( FoM 108RIU-1 ) [
Let us now study the performance of the considered sensors in the case of varying wavelength.
As in the previous case, the grating parameters dgr 396.8 nm , hgr 805.5 nm , lgr 0.72dgr were found using an optimization procedure. In the present example, two counter-propagating BSW were excited by ±1st diffraction orders at normal incidence of the wave with 0 550 nm at nsup 1.335 .
Similarly to Fig. 2, it is evident from Fig. 3 that the reflection dip is present for all measured media. The comparison of the proposed sensor with the sensor in the Kretschmann configuration is given in Table 2. It follows from Table 2 that in the case of varying wavelength, the grating-based sensor provides better average FoM value.
ddH2O NaCl NaCl 1% 2 %
Sv, nm/RIU 773.5 786.9 801.0
Sv, nm/RIU 163.9 165.2 166.5 In the present work, a planar configuration of an optical refractive index sensor was proposed and numerically investigated. The sensor contains a diffraction grating with one-dimensional periodicity and a one-dimensional photonic crystal. The working principle of the sensor is based on the excitation of Bloch surface waves. As a varying parameter, the angle of incidence or the wavelength can be used. The proposed sensor is compared with the conventional sensor based on the Kretschmann configuration in the case of four measured media: double-distilled water and 1%, 2% and 3% NaCl solutions. It is shown that two sensor configurations have comparable performance, which significantly exceeds the theoretical limit for SPP-based sensors with gold films. The obtained results may find application in the design of novel on-chip refractive index sensors.
This work was funded by the Russian Science Foundation grant № 14-31-00014.