Surface Plasmon Resonance Sensor Research Articles

Cross-sensitivity immune SPR sensor based on fan-shaped microstructured optical fiber for temperature and refractive index sensing.

To avoid coating and filling into the fiber holes, facilitate the phase-matching and eliminate cross-sensitivity problems, we propose a surface plasmon resonance sensor based on a fan-shaped microstructured optical fiber (MOF) for the simultaneous sensing of temperature and refractive index (RI). The fan-shaped structure is fabricated by polishing two sides of MOF with an angle of 120°. One side is coated with the gold film and polydimethylsiloxane layer for temperature sensing, and the other side is only coated with the gold film for RI sensing. The two sensing sides can support resonance peaks with two polarized directions at the angle of 120°, which are independent without cross-sensitivity. By monitoring the shifts of the two polarized peaks, our numerical results show that the temperature sensitivity is 2.932 nm/°C in the range of 30 °C to 40 °C, and RI sensitivity is 4235 nm/RIU in the range of 1.38 to 1.39, respectively.

Optimizing Stability and Performance of Silver-Based Grating Structures for Surface Plasmon Resonance Sensors.

The use of surface plasmon resonance sensors allows for the fabrication of highly sensitive, label-free analytical devices. This contribution reports on a grating coupler to enable surface plasmon resonance studies using silver on silicon oxide technology to build long-term stable plasmonic structures for biological molecule sensing. The structural parameters were simulated and the corresponding simulation model was optimized based on the experimental results to improve its reliability. Based on the model, optimized grating nanostructures were fabricated on an oxidized silicon wafer with different structural parameters and characterized using a dedicated optical setup and scanning electron microscopy. The combined theoretical and experimental results show that the most relevant refractive index range for biological samples from 1.32-1.46 may conveniently be covered with a highest sensitivity of 128.85°/RIU.

Highly sensitive fiber SPR sensor based on InSe nanosheets

Surface plasmon resonance (SPR) optical fiber sensors exhibit advantages such as small size, immunity to electromagnetic interference, and corrosion resistance, and are currently widely applied in the field of biodetection. However, their sensitivity and reusability are still limited in detecting biomolecules, trace concentrations, and weak signals. This paper proposes an approach by utilizing indium selenide (InSe) nanoflakes to enhance the surface electric field strength of the metal layer. InSe is a two-dimensional material that exhibits higher charge carrier mobility and refractive index compared to traditional two-dimensional materials, thereby promoting electron transfer and inducing a larger SPR effect. By testing the sensors composed of InSe nanosheets with different thicknesses, it is found that the sensitivity of InSe nanosheets with a thickness of 40 nm is up to 4655.76 nm/RIU, which is much higher than the sensitivity of traditional Au film sensors and 52 % higher than that of MoS2-Au film SPR sensors with the same structure. Moreover, the sensor has a higher FOM value of 33.25 RIU−1 and shows excellent characteristics in repeatability and stability experiments. In this paper, a new method is proposed to enhance the sensitivity of SPR sensors and realize the monitoring of lower biomolecule concentration and weak signal. In addition, the great potential of indium selenide nanosheets in optical applications is emphasized.

A zearalenone detection based on molecularly imprinted surface plasmon resonance sensor including sulfur-doped g-C3N4/Bi2S3 nanocomposite

In present work, a zearalenone detection based on molecularly imprinted surface plasmon resonance (SPR) sensor including sulfur-doped g-C3N4/Bi2S3 (S-g-C3N4/Bi2S3) nanocomposite was presented for selective determination of zearalenone (ZEA) in rice grain samples. After S-g-C3N4/Bi2S3 nanocomposite was synthesized by calcination method with high purity and in accordance with green chemistry, ZEA imprinted SPR chip based on S-g-C3N4/Bi2S3 was prepared in presence of methacryloylamidoglutamicacid (MAGA) as monomer, ethylene glycol dimethacrylate (EGDMA) as cross linker, N,N′-azobisisobutyronitrile (AIBN) as initiator and ZEA as target molecule by using UV polymerization. Then, the spectroscopic, microscopic and electrochemical methods were used for the characterizations of the nanocomposite and the proposed ZEA imprinted SPR chip based on S-g-C3N4/Bi2S3. The SPR sensor showed a linearity towards ZEA in range of 1.0 – 10.0 ng/L with a detection limit (LOD) of 0.33 ng/L. Thus, the developed sensor's high repeatability, stability, reproducibility and selectivity provided reliable ZEA determination in rice grain samples, ensuring safe food consumption.

High Sensitivity and Wide Range Refractive Index Sensor Based on Surface Plasmon Resonance Photonic Crystal Fiber.

In order to detect the refractive index (RI) of high refractive index materials such as trichlorobenzene and aniline in the near-infrared and mid-infrared spectra and expand the detection range of the refractive index, a surface plasmon resonance (SPR) photonic crystal fiber (PCF) sensor based on an elliptical sensing channel is proposed for high refractive index detection. The fiber core and the analyte channel are surrounded by two types of air holes with different sizes. When the surface plasmon resonance effect appears at the interface between the fiber core and the elliptical sensing layer, obvious resonance peaks appear in the near-infrared and mid-infrared bands. The full vector finite element method (FEM) is used to study the sensing characteristics of the sensor and the influence of structural parameters on the resonance peak. The results demonstrate that the sensor achieves detection in the refractive index range of 1.41-1.58, in the wavelength range of 1600-3200 nm. The average wavelength sensitivity is 9217.22 nm/RIU, and the refractive index resolution is 10.85 × 10-6 RIU. The proposed sensor realizes high refractive index detection in the near-infrared and mid-infrared bands, and obtains an ultra-wide detection range and higher sensitivity. The sensor has broad application prospects in chemical detection, biomedical sensing and other fields, and provides a theoretical reference for the design of a photonic crystal fiber surface plasmon resonance sensor.

Rapid and label-free screening of SARS-CoV-2 virus in the infected human nasopharyngeal swab samples using UiO-66-modified SPR chip

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) virus has become a dangerous human pathogen and caused severe illness that can lead to death. Yet, the standard practical diagnostic tools for detecting the SARS-CoV-2 virus require multi-step assay, including extraction and labeling steps. Thus, a simple and accurate detection tool is incredibly desirable to support on-site screening, preventing its spread. In this work, we developed a portable surface plasmon resonance (SPR) sensor chip modified with metal–organic frameworks (MOF) UiO-66 that serves as an immobilization matrix of single-chain variable fragment (scFv) receptors. Large surface area and good adsorption of UiO-66/scFv-modified surface lead to an improvement of binding capacity towards the protein target of the SARS-CoV-2 receptor binding domain (RBD). We further successfully demonstrated the use of this portable SPR to detect the SARS-CoV-2 virus from patients' nasopharyngeal swab samples. Interestingly, the SPR sensors can directly distinguish the positive and negative patients within 15 minutes on 23 samples, simultaneously, without the need for labeling, and the results are in line with the gold standard PCR tests. In addition, the detection limit of the sensors is 10.085 × 105 virus/mL, which follows the standard of practical screening tools. Therefore, these UiO-66 modified SPR chip sensors offer a rapid, label-free, and low-cost detection of the SARS-CoV-2 virus that can be potentially developed for other infectious diseases.

A L-glutamine binding protein modified MNM structured optical fiber biosensor based on surface plasmon resonance sensing for detection of L-glutamine metabolism in vitro embryo culture

A surface plasmon resonance (SPR) optical fiber sensor with multimode-coreless-multimode (MNM) structure was developed, which modified by L-glutamine-binding protein (QBP) for detection of L-glutamine (Gln). The QBP was immobilized on the surface of gold films by chemical cross-linking and exhibited a binding affinity for L-glutamine. The conformation of QBP can be changed from the “open” to the “closed”, which led to a red-shift of the SPR peak when QBP bounded to L-glutamine. There was a good linear correlation between is a dependence of the SPR peak on and the concentration of L-glutamine concentration in the range 10–100 μM, with a sensitivity of 10.797nm/log10[Gln] for L-glutamine in the in vitro embryo culture (IVC) medium environment, and the limit of detection (LOD) is 1.187 μM. This QBP-modified MNM structure optical fiber SPR sensor provides a new idea for the developmental potential assessment of embryos in the process of in vitro embryo culture.

Symmetrical dual D-shape fiber for waveguide coupled surface plasmon resonance sensing

A waveguide-coupled surface plasmon resonance (WCSPR) sensor consisting of two D-shape single-mode fibers is designed and analyzed by the finite element method (FEM). The optical field of the surface plasmon polaritons (SPPs) mode is confined in the dielectric cavity between the dual metallic thin films. Therefore, the effective refractive index of the SPP mode depends largely on the refractive index of the analyte and an anomalous dispersion relationship is observed between the SPP mode and x-polarized core-guide mode of the dual D-shape fiber. The excitation mechanism of surface plasmon resonance (SPR) in the coupling region is attributed to phase matching of the two modes. Further analysis shows that the narrow bandwidth peak in the loss spectrum of the core mode is determined by the sensor dimensions contributed jointly by the thicknesses of the silver film, dielectric layer, and titanium dioxide film. Compared to the single-fiber structure, the optimized dual D-shape WCSPR sensor achieves a maximum wavelength sensitivity of 52,200 nm/RIU with a full-width at half-minimum (FWHM) of 9.47 nm and a figure of merit (FOM) of 346.6 RIU−1 in the analyte refractive index range of 1.32–1.42.

Computational Modeling for Intelligent Surface Plasmon Resonance Sensor Design and Experimental Schemes for Real‐Time Plasmonic Biosensing: A Review

AbstractThe spectacular physical phenomenon of surface plasmon resonance (SPR) is the essence of present‐day plasmonic sensors. Meanwhile, the unique properties of the interaction between light and matter have been carved out into the development of modern‐day diagnostic biosensors. Plasmons, in simple terms, are oscillating free electrons in metallic nano‐structures triggered by an incoming electromagnetic (EM) wave. With the advantages of real‐time and label‐free bio‐sensing, plasmonic sensors are being utilized in multiple diverse areas of food technology, the bio‐medical diagnostic sector, and even the chemical industry. Although this review will be brief, readers can gain a comprehensive picture of the essential elements by taking a broader look into the exploration of SPR sensor design via simulated studies and representative experimental plasmonic schemes developed for bio‐sensing. In short, the various SPR sensing schemes that researchers have explored to realize enhanced SPR sensitivity are reviewed and summarized. Different experimental plasmonic sensors are also examined in which new SPR excitation schemes have been adopted. These "unconventional" designs, specifically those involving hybrid localized surface plasmon resonance (LSPR)‐SPR excitation, may inspire those in the plasmonic field.

Common-mode plasmon sensing scheme as a high-sensitivity compact SPR sensor.

A deep metal grating enables quasi-phase-matched simultaneous excitation of two counterpropagating surface plasmon modes by means of its +1st and -2nd diffraction orders. The resulting angular reflection spectra of the scattered -1st and zeroth orders exhibit three interleaved zeros and maxima in a range centered around the Littrow angle. The spectra differ thoroughly from the usual reflection dip resulting from single-order plasmon coupling that produces strong absorption. The zeroth and -1st orders exhibit two crossing angles enabling high-sensitivity common-mode detection schemes designed to reject variations in source power and environmental noise. The proof of concept and experimental assessment of this new surface plasmon resonance (SPR) sensing scheme are demonstrated by monitoring gases in a pressure-controlled chamber. A limit of detection (LOD) of 2 × 10-7 refractive index unit (RIU) was achieved.

Analysis of Plasmonic Sensors Performance Realized by Exploiting Different UV-Cured Optical Adhesives Combined with Plastic Optical Fibers.

Polymer-based surface plasmon resonance (SPR) sensors can be used to realize simple, small-size, disposable, and low-cost biosensors for application in several fields, e.g., healthcare. The performance of SPR sensors based on optical waveguides can be changed by tuning several parameters, such as the dimensions and the shape of the waveguides, the refractive index of the core, and the metal nanofilms used to excite the SPR phenomenon. In this work, in order to develop, experimentally test, and compare several polymer-based plasmonic sensors, realized by using waveguides with different core refractive indices, optical adhesives and 3D printed blocks with a trench inside have been used. In particular, the sensors are realized by filling the blocks' trenches (with two plastic optical fibers located at the end of these) with different UV-cured optical adhesives and then covering them with the same bilayer to excite the SPR phenomenon. The developed SPR sensors have been characterized by numerical and experimental results. Finally, in order to propose photonic solutions for healthcare, a comparative analysis has been reported to choose the best sensor configuration useful for developing low-cost biosensors.

Ring-Core Photonic Crystal Fiber Sensor Based on SPR for Extra-Wide Refractive Index Detection

Spurred by the rapid development of fiber optic sensing technology, photonic crystal fiber (PCF) sensors based on surface plasmon resonance (SPR) have received widespread attention. However, they can only detect a narrow range, and the coating process is complex. Herein, a wide-range SPR sensor is designed. It consists of a ring-core PCF filled with plasmonic materials. Compared to the process of depositing a coating inside the air hole, the analyte and gold nanowires fill our PCF, thus simplifying the manufacturing complexity. The ring-core structure enhances the directional power transmission between the guided mode and the surface plasmon polariton (SPP) mode. The sensor is numerically analyzed using the finite element method (FEM). The results show that the PCF-SPR sensor has a wavelength sensitivity and amplitude sensitivity of 40,000 nm/RIU and 2141 RIU−1, and the resolution is 2.5 × 10−6 RIU−1 for the detection range of 1.13–1.45. The high-sensitivity sensor boasting a wide refractive index detection range performs better than conventional solid-core PCF-SPR sensors, boding well for biochemical sensing.

In situ growth of AuNPs with a nanocavity on the surface of optical fibre for development of SPR sensor

Gold nanoparticles (AuNPs) integrated within optical fibres show great potential as sensor materials in the field of sensing, utilizing the Surface Plasmon Resonance (SPR) principle. This study presents a straightforward, cost-effective, and replicable approach for producing permanent in-situ embedding of AuNPs with nanocavities on the surface of optical fibres. The process involves chemical vapour etching (CVE), followed by gold sputtering and isothermal heat treatment. The analysis conducted using High-Resolution Transmission Electron Microscopy (HRTEM) and Energy-Dispersive X-ray Spectroscopy (EDX), confirmed the presence of nearly spherical AuNPs embedded on the surface of the optical fibre, with an average diameter of 60 ± 5 nm. Additionally, the detection of two distinct plasmon absorption peaks at 567 ± 5 nm and 620 ± 5 nm using a Fibre Optic Spectrometer further validated the presence of AuNPs. To verify the existence of nanocavities surrounding the AuNPs, Field Emission Transmission Microscopy (FESEM) was employed, along with subjecting the AuNPs embedded fibre to three different NaCl solutions of varying concentrations. The results supported the presence of a nanocavity encapsulating the AuNPs. A proposed mechanism was put forth to explain the spectral behaviour resulting from the creation of the nanocavity. This specialty optical fibre is expected to have broad applications in the development of SPR-based chemicals and biosensors, as it facilitates close interaction between the AuNPs and analytes through the nanocavity surrounding the AuNPs on the fibre surface. The fabrication process demonstrated excellent repeatability, with strong adhesion of AuNPs to the optical fibre surface, and no leaching even after repeated use. Thus, we believe that this fabrication method is an exceptional technique for permanently incorporating AuNPs into various glass-based optical waveguide materials for SPR-based sensing applications.

Ultrasensitive Fiber SPR Magnetic Field Sensor Using Au/TiO₂ Schottky Junction

This paper presents an ultrasensitive fiber surface plasmon resonance (SPR) magnetic field sensor using an Au/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Schottky junction coated on a plastic-clad multimode fiber (PMF) and immersed in the magnetic fluid (MF). The MF acts as the magnetic-sensitive material, and the Au/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film with a high dielectric constant excites SPR with high sensitivity. When the magnetic field strength applied to the MF changes, the MF’s refractive index alters accordingly, which changes the phase-matching condition of the surface plasmon polaritons, shifting the resonance dip in the fiber transmission spectrum. Therefore, the magnetic field strength can be measured by monitoring the resonance dip shift. The proposed sensor achieved a maximum magnetic sensitivity of -2.791 nm/Oe in the 5 to 35 Oe range, higher than most MF-based fiber magnetic field sensors. Additionally, the temperature response of the sensor was measured to be -0.4861 nm/°C, which has little effect on the magnetic sensing performance. The experimental results indicate that the proposed fiber SPR sensor can measure magnetic field strength variations with high sensitivity and accuracy, making it suitable for practical applications in various scenarios.

Au-strip structure dependent performance investigation of D-shaped SPR sensors for biosensing applications

Surface Plasmon Resonance (SPR)-based sensing technologies show great promise in diverse applications (e.g. biosensing) as one of the most innovative and exciting label-free sensing techniques in the last few years. In general, SPR-based sensors combine metal and dielectric interfaces, where the oscillation of metal’s free electrons occurs by the incident incoming photons. Thus, the SPR signal strength depends on the metal’s optical properties as well as the surrounding dielectric medium. This work thoroughly investigates the performance of a single mode D-shape SPR-based refractive index (RI) sensor with its gold (Au) strip topology to improve the detection sensitivity. Seven distinct Au strip designs: single-arc, inverted single-arc, multi-arc, inverted multi-arc, half-circle, coil, and sinusoidal wave are introduced to explore sensor performances, which are investigated numerically using Comsol Multiphysics. Systematic investigations are carried out for all seven proposed designs and relative comparisons are made in terms of sensitivity (wavelength and amplitude), resolution, and figure of merit (FoM). Coil and sinusoidal wave-shaped designs show excellent performance among all seven designs with a wide range of analytes’ RI (i.e. 1.31 to 1.39). The maximum wavelength and amplitude sensitivities are found to be 48000 nm/RIU and 18.55 RIU−1 respectively, with a wavelength resolution of 2.08 × 10-6 RIU and a consequent FoM of 141.18 RIU−1 for the sinusoidal wave-shaped Au-strip design. Alternatively, the coil-shaped design shows the maximum wavelength and amplitude sensitivities of 45000 nm/RIU and 32.17 RIU−1 respectively, with a wavelength resolution of 2.22 × 10-6 RIU and a FoM of 85.71 RIU−1. As a wide range of analyte’s RI can be detected by the proposed sinusoidal wave and coil Au-strip-based D-shaped sensors with improved sensitivity, these designs could be effectively used for the detection of different bio-analytes.

Detection of blood cancer using highly sensitive surface plasmon resonance sensor based on MXene 2D nanomaterial

The most common disease on the earth, cancer, has raised concerns about the health of humans. Early discovery is a crucial argument to increase treatment success. A surface plasmon resonance (SPR) biosensor having prism, silver, MXene and analyte is theoretically proposed and numerically simulated in this work for rapid and accurate detection of blood cancer cells. Many different prisms are examined. The structure with the lowest refractive index prism has shown the highest sensitivity, hence it is taken into consideration for additional studies. Since an MXene layer has a larger surface area, it enhances surface-biomolecule adsorption. The number of MXene sheets and silver layer thickness are optimized to improve the sensor sensitivity. The SPR sensor can attain a sensitivity of 232.25 deg/RIU for 50 nm silver with a bi-layer of MXene. We believe that the proposed sensor has a very simple structure to facilitate the fabrication and it will be encouraging to be used in biosensing.

Enhancement of transverse magneto-optical Kerr effect based on surface plasmon and its application in sensing

In recent years, the combination of magnetic and plasma properties of nanostructures has become a hot research topic. However, most such studies focuse on prism-based sandwich structures, which not only hinders device miniaturization but also has weak transverse magneto-optical Kerr (TMOKE) in amplitude. In this paper, a sub-wavelength periodic nanoporous Au/Co bilayer magneto-optical surface plasmon resonance (MOSPR) sensor is investigated, where the sensing principle is based on the measurement of TMOKE. By optimizing the geometric parameters of the nanostructure, a nearly perfect TMOKE spectrum with a FWHM of only 0.175 nm is obtained, which has a Fano-like pattern and an amplitude close to the theoretical maximum. It is proved that the excitation of high quality SPR enhances the magneto-optical effect. We then analyze the resonant angular shift associated with the TMOKE signal to monitor the change in the analyte refractive index, demonstrating the sensing sensitivity up to 220°RIU−1 and figure of merits (FOM) in excess of 103 in gas. The MOSPR system achieves higher resolution compared to the gold-based SPR system, yielding an order of magnitude higher FOM than the SPR system.

Development and Analysis of Multifeature Approaches in SPR Sensor Development

This paper presents the development and signal analysis of surface plasmon resonance (SPR)-based sensors in D-shaped polymer optical fibers (POFs). A gold-palladium (Au-Pd) coating was applied to the D-shaped region to obtain the SPR signal in the transmitted spectrum of the POFs, where different samples were fabricated using the same methods and parameters. In this case, the transmitted spectra of three sets of samples were compared, which indicated variations in the SPR signature that can influence the sensors’ application and reproducibility. Then, the intensity of and wavelength shift in the SPR signals were analyzed as a function of the refractive index variation, where it was possible to observe differences in the sensors’ sensitivities and the linearity of the different samples. In this regard, additional features, namely the area below the curve and the peak amplitude of the fast Fourier transform (FFT) applied to the transmitted spectra, were used to enhance the sensors’ accuracy and precision. To verify the use of such additional features in the sensor analysis, an unsupervised approach based on k-means clustering was used considering a single dataset with the results of all the sensors. The results showed clustering with the number of different refractive indices tested, which motivated the use of these features (intensity, wavelength, area and FFT amplitude) in the refractive index assessment. In this context, random forest was the supervised algorithm with the smallest root mean squared error (RMSE) among the algorithms tested, where an RMSE of 0.0057 was obtained considering all the datasets. For the analysis of each sensor (considering the three sets of sensor samples), the mean RMSE using random forest applied to the multifeature approach returned relative errors below 9%, considering the entire tested range of refractive index variation.

Tunable Au@SiO2/Au Film Metasurface as Surface Plasmon Resonance Enhancer for Direct and Ultrasensitive Detection of Exosomes.

Surface plasmon resonance (SPR) spectroscopy with non-labelling, sensitive, and real-time properties is critical for clinical diagnosis applications. However, conventional SPR sensors face the challenge of lower sensitivity and selectivity for trace exosomes assay in complex serum. We proposed a core-shell Au@SiO2-Au film (Au@SiO2-Au film) metasurface to enhance SPR signal based on systematic study on the relationship between gap modes and SPR enhancement. The self-assembled multifunctional peptide was designed as recognition layer with antifouling properties for ultrasensitive and selective detection of PD-L1+ exosomes in serum. The tuning electromagnetic (EM) field model by manipulating the gap was established to guide the preparation of Au@SiO2-Au film metasurface. The in-plane and out-of-plane coupling of Au@SiO2 nanoparticles (NPs) could greatly enlarge and enhance three-dimensional EM field to meet the size of exosomes located in the evanescent field. At the structural level, we achieved high sensitivity (0.16 particles/mL) and a broad response range (10-5 × 103 particles/mL) through optimizing the thickness of SiO2 and surface coverage of Au@SiO2. Furthermore, clinical sample assay achieved the optimal diagnostic accuracy (AUC = 0.97) for differentiating cancer patients from healthy controls. This work provides an opportunity for the construction of a tunable gap mode as SPR enhancer in a total internal reflection architecture. The systematic study on the relationship between gap modes and SPR sensitivity provides a broad scope for promoting direct, efficient, highly selective, and sensitive detection of SPR sensors for clinical application.

Polarization-independent tilted fiber Bragg grating surface plasmon resonance sensor based on spectrum optimization.

We experimentally demonstrated polarization multiplexing schemes in a tilted fiber grating (TFBG) to achieve polarization-independent fiber-optic surface plasmon resonance (SPR) sensors. The first used two orthogonal polarized lights separated by a polarization beam splitter (PBS) that are p-polarized in polarization-maintaining fiber (PMF) and precisely aligned with the tilted grating plane, so as to achieve the transmission of p-polarized light in two opposite directions of the Au-coated TFBG to excite SPR. Alternatively, polarization multiplexing was also achieved by exploring two polarization components to achieve the SPR effect through a Faraday rotator mirror (FRM). The SPR reflection spectra are polarization-independent of the light source and any perturbations to fibers, which are explained by the superposition of p- and s-polarized transmission spectra in equal proportions. The spectrum optimization is presented to reduce the proportion of the s-polarization component. A polarization-independent TFBG-based SPR refractive index (RI) sensor with a wavelength sensitivity of 555.14 nm/RIU and an amplitude sensitivity of 1724.92 dB/RIU for small changes is obtained, exhibiting unique advantages of minimizing the polarization alterations by mechanical perturbations.