From Bloch surface waves to cavity-mode resonances reaching an ultrahigh sensitivity and a figure of merit

We report on a new sensing concept based on resonances supported by a one-dimensional photonic crystal (1DPhC) microcavity resonator in the Kretschmann configuration. For a 1DPhC comprising six bilayers of TiO2/SiO2 with a termination layer of TiO2 employed to form a microcavity, we show that when the angle of incidence is changed, the Bloch surface waves (BSWs) can be transformed into cavity-mode resonances exhibiting an ultrahigh sensitivity and a figure of merit. Using wavelength interrogation, we demonstrate that Bloch surface TE wave excitation shows up as a sharp dip in the reflectance spectrum with a sensitivity and a figure of merit (FOM) of 70 nm per refractive index unit (RIU) and 19.5 RIU-1, respectively. When the angle of incidence decreases, cavity-mode resonances for both TE and TM waves are resolved for RI in a range of 1.0001-1.0005. The sensitivity and FOM can reach 52,300 nm/RIU and 402,300 RIU-1 for the TE wave, and 14,000 nm/RIU and 2154 RIU-1 for the TM wave, respectively. In addition, resonances are confirmed experimentally for a humid air with a sensitivity of 0.073 nm per percent of the relative humidity (%RH) for BSW resonance and is enhanced to 1.367 nm/%RH for the TM cavity-mode resonance. This research, to the best of the authors' knowledge, is the first demonstration of a new BSW-like response that can be utilized in a simple sensing of a wide range of gaseous analytes.

Sensing based on Bloch surface wave and self-referenced guided mode resonances employing a one-dimensional photonic crystal

Sensing abilities of a one-dimensional photonic crystal (1DPhC) represented by a multilayer dielectric structure are analyzed theoretically and experimentally, using a new wavelength interrogation interference method. The structure comprising a glass substrate and six bilayers of TiO₂/SiO₂ with a termination layer of TiO₂ is employed in both gas sensing based on the Bloch surface wave (BSW) resonance and liquid analyte sensing based on a self-referenced guide-mode resonance (GMR). We model the spectral interference reflectance responses in the Kretschmann configuration with a coupling prism made of BK7 glass and show that a sharp dip with maximum depth associated with the BSW excitation is red-shifted as the refractive index (RI) changes in a range of 1-1.005. Thus, a sensitivity of 1456 nm per RI unit (RIU) and figure of merit (FOM) of 91 RIU^-1 are reached. Similarly, we model the responses for aqueous solutions of ethanol to show that dips of maximum depth are associated with the GMRs, and the highest sensitivity and FOM reached are 751 nm/RIU and 25 RIU^-1, respectively. Moreover, we show that one of the dips is with the smallest shift as the RI changes, and hence it can be used as a reference. The theoretical results are confirmed by the experimental ones when the BSW resonance is used in sensing of humid air with a sensitivity of 0.027 nm/%relative humidity (RH) and FOM of 1.4×10^-3 %RH^-1. Similarly, the GMR is used in sensing of aqueous solutions of ethanol, and the highest sensitivity and FOM reached 682 nm/RIU and 23 RIU^-1, respectively. The reference dip is also resolved and this self-reference makes the measurement more accurate and repeatable, and less sensitive to optomechanical drifts.

Guided-mode resonance based humidity sensing using a multilayer dielectric structure

We report on a highly sensitive measurement of the relative humidity of air, which utilizes a guided-mode resonance (GMR) of a multilayer dielectric structure (MDS) and the spectral interference of s- and p-polarized waves reflected from the MDS. We employ the MDS represented by four bilayers of TiO₂/SiO₂ with a termination layer of TiO₂ and demonstrate that the GMR shows up as a shallow and asymmetric dip. The GMR enables us to measure the relative humidity (RH) of air with sensitivities of 0.031-0.114 nm/%RH. In addition, by employing a birefringent crystal of mica, which modifies the phase difference between the polarized waves, the GMR is transformed into the resonance with a sharp dip, and the measured sensitivity is enhanced to 0.120 nm/%RH at 81 %RH. We also determined the sensitivity to the refractive index and the figure of merit as high as 8000 nm/refractive index unit (RIU) and 702 RIU^-1, respectively. The results demonstrate that the GMR based sensor employing the MDS and the spectral interference of polarized waves with their phase difference appropriately adjusted enables a highly sensitive, hysteresis-free humidity measurement, characterized by a high FOM. Humidity sensors employing dielectric multilayers thus represent an effective alternative to available sensors, with advantages such as better mechanical and chemical stability.

Bloch Surface Wave Resonance Based Sensors as an Alternative to Surface Plasmon Resonance Sensors

We report on a highly sensitive measurement of the relative humidity (RH) of moist air using both the surface plasmon resonance (SPR) and Bloch surface wave resonance (BSWR). Both resonances are resolved in the Kretschmann configuration when the wavelength interrogation method is utilized. The SPR is revealed for a multilayer plasmonic structure of SF10/Cr/Au, while the BSWR is resolved for a multilayer dielectric structure (MDS) comprising four bilayers of TiO2/SiO2 with a rough termination layer of TiO2. The SPR effect is manifested by a dip in the reflectance of a p-polarized wave, and a shift of the dip with the change in the RH, or equivalently with the change in the refractive index of moist air is revealed, giving a sensitivity in a range of 0.042-0.072 nm/%RH. The BSWR effect is manifested by a dip in the reflectance of the spectral interference of s- and p-polarized waves, which represents an effective approach in resolving the resonance with maximum depth. For the MDS under study, the BSWRs were resolved within two band gaps, and for moist air we obtained sensitivities of 0.021-0.038 nm/%RH and 0.046-0.065 nm/%RH, respectively. We also revealed that the SPR based RH measurement is with the figure of merit (FOM) up to 4.7 × 10-4 %RH-1, while BSWR based measurements have FOMs as high as 3.0 × 10-3 %RH-1 and 1.1 × 10-3 %RH-1, respectively. The obtained spectral interferometry based results demonstrate that the BSWR based sensor employing the available MDS has a similar sensitivity as the SPR based sensor, but outperforms it in the FOM. BSW based sensors employing dielectrics thus represent an effective alternative with a number of advantages, including better mechanical and chemical stability than metal films used in SPR sensing.

Surface Plasmon Resonance-Based Sensing Utilizing Spatial Phase Modulation in an Imaging Interferometer

Spatial phase modulation in an imaging interferometer is utilized in surface plasmon resonance (SPR) based sensing of liquid analytes. In the interferometer, a collimated light beam from a laser diode irradiating at 637.1 nm is passing through a polarizer and is reflected from a plasmonic structure of SF10/Cr/Au attached to a prism in the Kretschmann configuration. The beam passes through a combination of a Wollaston prism, a polarizer and a lens, and forms an interference pattern on a CCD sensor of a color camera. Interference patterns obtained for different liquid analytes are acquired and transferred to the computer for data processing. The sensing concept is based on the detection of a refractive index change, which is transformed via the SPR phenomenon into an interference fringe phase shift. By calculating the phase shift for the plasmonic structure of SF10/Cr/Au of known parameters we demonstrate that this technique can detect different weight concentrations of ethanol diluted in water, or equivalently, different changes in the refractive index. The sensitivity to the refractive index and the detection limit obtained are -278 rad/refractive-index-unit (RIU) and 3.6 × 10 - 6 RIU, respectively. The technique is demonstrated in experiments with the same liquid analytes as in the theory. Applying an original approach in retrieving the fringe phase shift, we revealed good agreement between experiment and theory, and the measured sensitivity to the refractive index and the detection limit reached -226 rad/RIU and 4.4 × 10 - 6 RIU, respectively. These results suggest that the SPR interferometer with the detection of a fringe phase shift is particularly useful in applications that require measuring refractive index changes with high sensitivity.

Sensing concept based on Bloch surface waves and wavelength interrogation

We report on a new, to the best of our knowledge, sensing concept based on Bloch surface waves (BSWs) and wavelength interrogation that utilizes the interference of $ s $s- and $ p $p-polarized waves from a one-dimensional photonic crystal (1DPhC), represented by a multilayer structure comprising a glass substrate and four bilayers of $ {{\rm TiO}_2}/{{\rm SiO}_2} $TiO₂/SiO₂ with a termination layer of $ {{\rm TiO}_2} $TiO₂. We show that when a standard approach based on measurement of the reflectance of a $ p $p- or $ s $s-polarized wave in the Kretschmann configuration fails to confirm the excitation of the BSW, a new approach is successful. We demonstrate that the BSW excitation shows up as a dip with maximum depth, and resonance thus obtained is comparable in magnitude with resonance commonly exhibited by surface plasmon resonance (SPR). The new sensing concept is verified experimentally for ethanol vapors. The BSW resonances are resolved within two band gaps of the 1DPhC with sensitivities of 3272 nm/RIU and 1403 nm/RIU, and figures of merit of $ 43.7 \;{{\rm RIU}^{ - 1}} $43.7RIU^-1 and $ 173.2 \;{{\rm RIU}^{ - 1}} $173.2RIU^-1, respectively. This research, to the best of the authors' knowledge, is the first demonstration of a new SPR-like response that can be utilized in a wide range of sensing applications.

Ultrahigh-sensitive plasmonic sensing of gas using a two-dimensional dielectric grating

We demonstrate an ultrahigh-sensitive plasmonic sensing of gas, employing a two-dimensional (2D) dielectric grating fabricated by laser interference lithography. The 2D grating was designed with the period of 500 nm and prepared in an AZ1505 photoresist layer on a gold film of 20 nm thickness deposited on a fused silica glass substrate. The surface plasmon resonance (SPR) in the Kretschmann configuration with spectral interrogation was utilized to measure the response of the sensor to vapors of aqueous solution of ethanol. Based on measurement of the gas refractive indices with the reference Au/Cr/SF10 sample, the resonance wavelength dependence was obtained. The SPR response of the structure in a spectral range of 1.68-1.85 µm with a sensitivity of 8200-111,000 nm/RIU was revealed. The sensor provides significantly higher sensitivity in comparison to conventional and grating-based SPR sensors.

Absolute phase birefringence dispersion in polarization-maintaining fiber or birefringent crystal retrieved from a channeled spectrum

We report on a simple method for retrieving the wavelength dependence of the phase birefringence in a polarization-maintaining fiber or a birefringent crystal from a channeled spectrum. The method utilizes interference of polarized modes or waves resolved as the channeled spectrum and its processing by a windowed Fourier transform to reconstruct precisely the phase as a function of wavelength. The ambiguity of the phase is removed provided that we know both the approximative function for the birefringence dispersion and the length of the fiber or the thickness of the crystal. The method is used in measuring the wavelength dependence of the phase birefringence in an elliptical-core fiber or in a quartz crystal in a range from 500 to 900 nm. The dependences are compared with those resulting from the available data, and very good agreement is confirmed.

Spectral interferometric technique to measure the ellipsometric phase of a thin-film structure

A two-step white-light spectral interferometric technique is used to retrieve the ellipsometric phase of a thin-film structure from the spectral interferograms recorded in a polarimetry configuration with a birefringent crystal. In the first step, the phase difference between p- and s-polarized waves propagating in the crystal alone is retrieved. In the second step, the additional phase change that the polarized waves undergo on reflection from the thin-film structure is retrieved. The new method is used in determining the thin-film thickness from ellipsometric phase measured for SiO(2) thin film on a Si substrate in a range from 550 to 900 nm. The thicknesses of three different samples obtained are compared with those resulting from polarimetric measurements, and good agreement is confirmed.

Spectral interferometry and reflectometry used for characterization of a multilayer mirror

A white-light spectral interferometric technique is used to retrieve a relative spectral phase and group delay of a multilayer mirror from the spectral interferograms recorded in a dispersive Michelson interferometer. The phase retrieval is based on the use of a windowed Fourier transform in the wavelength domain, and characterization of the multilayer mirror is completed by a three-step measurement of the reflectance spectrum of the mirror in the same interferometer.

Spectral-domain measurement of phase modal birefringence in polarization-maintaining fiber

We report on a new and simple method for measuring the wavelength dependence of phase modal birefringence in a polarizationmaintaining fiber. The method is based on application of a lateral pointlike force on the fiber that causes strong coupling between polarization modes and utilizes their interference resolved as the channeled spectrum. The change of the phase retrieved from two recorded channeled spectra that are associated with the known displacement of coupling point is used to determine the phase modal birefringence as a function of wavelength. A windowed Fourier transform is applied to reconstruct precisely the phase change and the phase ambiguity is removed provided that we know the phase change of the spectral fringes at one specific wavelength. The measured wavelength dependence of phase modal birefringence is compared with that resulting from the group modal birefringence measurement.

Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry

We present a new method for measuring the group dispersion of the fundamental mode of a holey fiber over a wide wavelength range by white-light interferometry employing a low-resolution spectrometer. The method utilizes an unbalanced Mach-Zehnder interferometer with a fiber under test placed in one arm and the other arm with adjustable path length. A series of spectral signals are recorded to measure the equalization wavelength as a function of the path length, or equivalently the group dispersion. We reveal that some of the spectral signals are due to the fundamental mode supported by the fiber and some are due to light guided by the outer cladding of the fiber. Knowing the group dispersion of the cladding made of pure silica, we measure the wavelength dependence of the group effective index of the fundamental mode of the holey fiber. Furthermore, using a full-vector finite element method, we model the group dispersion and demonstrate good agreement between experiment and theory.

Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film

We present a white-light spectral interferometric technique for measuring the absolute spectral optical path difference (OPD) between the beams in a slightly dispersive Michelson interferometer with a thin-film structure as a mirror. We record two spectral interferograms to obtain the spectral interference signal and retrieve from it the spectral phase, which includes the effect of a cube beam splitter and the phase change on reflection from the thin-film structure. Knowing the effective thickness and dispersion of the beam splitter made of BK7 optical glass, we use a simple procedure to determine both the absolute spectral phase difference and OPD. The spectral OPD is measured for a uniform SiO(2) thin film on a silicon wafer and is fitted to the theoretical spectral OPD to obtain the thin-film thickness. The theoretical spectral OPD is determined provided that the optical constants of the thin-film structure are known. We measure also the nonlinear-like spectral phase and fit it to the theoretical values in order to obtain the thin-film thickness.

Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization

Anisotropic lamellar sub-wavelength gratings (nanogratings) are described by Effective Medium Approximation (EMA). Analytical formulas for effective medium optical parameters of nanogratings from arbitrary anisotropic materials are derived using approximation of zero-order diffraction mode. The method is based on Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement between EMA and the rigorous model is observed, where slight differences are explained by the influence of evanescent higher Fourier harmonics in the nanograting.