Simulation of a microstructure fiber pressure sensor based on lossy mode resonance

Pressure sensors based on an optical fiber have been the subject of extensive research in recent years because optical fiber has a great many advantages over conventional electrical pressure sensors, such as a light weight and anti-electromagnetic interference.^1,2 Recently, a series of surface plasmon resonance (SPR) pressure fiber sensors have been proposed in the literature.^3–6 The light interaction between a metal and a dielectric interface generates a plasmon oscillation.⁷ The optical fiber SPR sensor has been utilized in detecting pressure, where maximum sensitivity reaches 1.75 × 10³ nm/MPa.⁸ Compared with sensors based on a Sagnac Interferometer and fiber Brag grating,^9,10 it is clear that the SPR pressure sensor has dramatically improved the sensor sensitivity. However, a recent study concluded that an lossy mode resonance (LMR) sensor has numerous advantages over an SPR sensor. There are many types of metal oxides and polymers that can be used to create an LMR effect on an optical fiber, such as SnO₂,^11–13 InO₂,¹⁴ ZnO,¹⁵ ZrO₂,¹⁶ and PAH.¹⁷ In addition, LMR fiber optic sensors can be manufactured in a variety of ways. Layer self-assembly and chemical vapor deposition are common coating methods.¹⁸ However, most of the proposed pressure sensors based on LMR utilize a plastic-clad silica fiber, which has a large core diameter and large numerical aperture. Therefore, the resonant peak has a wide full width at half maximum, which reduces the accuracy of the sensor.

Compared with traditional fiber structures, microstructure fibers based on photonic crystal fiber (PCF) have many design and manufacturing advantages.^19–23 To satisfy the phase matching condition, it is possible to change the geometric structure and adjust the effective refractive index (n_eff) of the fiber of the core guided mode.²⁴ There are various SPR sensors based on microstructure PCF. However, as yet, no one has proposed a PCF-based LMR pressure sensor.

In this work, we design and simulate an LMR pressure sensor based on exposed-core grapefruit PCF. The TiO₂/HfO₂ is coated on the exposed-core region to excite LMR. A bimetallic-oxide bilayer can dramatically increase the sensor sensitivity because of the high refractive index of HfO₂. In addition, the performance of the sensor is optimized by adjusting the type and thickness of the film.

A schematic diagram of the proposed exposed-core microstructure fiber sensor is shown in Fig. 1. The thickness of the quartz between two adjacent air holes and of the fiber core radius is 7μm and 1μm, respectively. The TiO₂/HfO₂ bilayer film thickness is 50/30 nm. It is possible to manufacture the fiber using micromachining techniques to make the exposed fiber core. A wet chemistry deposition or chemical vapor deposition technique can be utilized to coat the TiO₂/HfO₂ film on the exposed-core portion to excite the LMR effect.²⁴ It is clear that coating the film on the exposed-core area is far easier than coating the inner wall of the air hole. Also, the metallic oxide bilayer can dramatically increase the sensitivity of the microstructure fiber pressure sensor. This is because the overlay of HfO₂ film has a high dielectric, which can improve the sensor’s sensitivity.

We used COMSOL Multiphysics with the finite element method (FEM) to simulate the sensor performance. The entire proposed sensor was divided into numerous triangular regions and a scattering boundary condition was set as perfectly matched layers. The modal simulation was conducted in cartesian coordinates, with light propagating along the Z direction. Figure 2 shows electric field distribution and dispersion relations of the core modes with the sample refractive index (RI) = 1.33. Gaussian-like modes were used as the core modes because these are suitable for describing the excitation by standard Gaussian laser.²⁵ It is clear that the asymmetric LMR region results in strong birefringence and almost all light is coupled in a certain direction. The x-polarized and y-polarized resonance peaks can be utilized to detect RI. However, the y-polarized peak shifting is more rapid than the x-polarized peak when the sample RI is varied the same way. That is to say, y-polarization has a higher coupling efficiency and the sensitivity of the x-polarized peak is higher. Therefore, the shift of y-polarization is used to analyze the sensor’s performance in detecting analytes.

The microstructure optical fiber is made of fused silica. The dispersion characteristic of the fiber is described by the Sellmeier equation²⁶ 

where a₁ = 0.696166300, a₂ = 0.407942600, a₃ = 0.897479400, b₁ = 4.67914826 × 10⁻³μm², b₂ = 1.35120631 × 10⁻²μm⁻², and b₃ = 97.9340025μm². The Lorentz model can describe the dispersion characteristic of the permittivity of TiO₂, which can be written as²⁷ 

where ε_∞ is the high frequency dielectric constant, A_k is the amplitude, B_k is the center energy, and E is the photon energy. For simplicity in the simulation, the parameters were given values of ε_∞ = 1, A_k = 101 eV², and E_k =6.2 eV.

The dispersion characteristic of the HfO₂ dielectric constant can be expressed by the Lorentz oscillator model²⁸ 

Here, for simplicity, j = 1, A = 1.956, B = 6.73 × 10⁻¹⁰cm², v_p1 = 247cm⁻¹, v₁ = 187cm⁻¹, and $γ1=216cm−1=1λ$⁠. It has been shown in the literature that it is possible for the sensitivity of an LMR sensor to be affected by the permittivity of the material. The permittivity of HfO₂ has a real part that is higher, which enhances the proposed sensor’s performance. The confinement loss of the spectra is expressed as

where k = 2π/λ is the wavenumber and Im(n_eff) is the imaginary part of the effective mode of the microstructure fiber sensor.

The wavelength sensitivity is defined as

where λ_peak is the peak wavelength and Δn_a is the variation of the analyte RI.

For rubber polymer material, the relationship between pressure and refractive index can be written as²⁸ 

For the polymer, $(Dp∂np∂Dp)T≈0.5$ and V_p ≅ 1.0.

Sensor wavelength sensitivity is defined as the shift of resonance peak with applied pressure, which is written as

where K = 0.5 is constant and Yp = 1.0 MPa for rubber polymer.

To study the performance of the proposed microstructured fiber optic sensor, we simulate various sample RI ranges, from 1.33 to 1.39. These sample RI values represent polymer density variations because the RI of the polymer is a function of polymer density, which is demonstrated in Eq. (6). As shown in Fig. 3, there are a total four LMR peaks in the spectra. The asymmetric LMR region generates strong birefringence, the x-polarized and y-polarized resonance peaks. When the SPI changes because of the variation of the polymer’s pressure, the resonance wavelength has a considerable shift. In previous studies, it was determined that the thickness of the film has a great influence on the sensitivity of the LMR sensor. Thus, the influence of the thickness of the TiO₂ film on the sensor’s performance is not studied in this section. We utilized a TiO₂/HfO₂ bilayer in order to further enhance the sensor’s sensitivity. As shown in Fig. 4, the combination of TiO₂ and HfO₂ film can affect the LMR reflection spectra. Since the permittivity of HfO₂ is higher than that of TiO₂, the metallic oxide bilayer can excite stronger LMR. Therefore, if the HfO₂ layer is coated on the TiO₂ film, the resonant wavelength shift will be large. The simulation result shows that an extremely high RI sensitivity of 67,000 nm/RIU is obtained in the sensing range of 1.33–1.39. Also, we compare the RI sensitivity with the previous LMR sensors reported in Table I. The sensitivity of the LMR is affected by the type and thickness of the film, thus the sensitivity of the D-shaped LMR sensor can reach over 1 000 000 nm/RIU in the high RI range (1.448–1.449) in Ref. 12. It is clear that the proposed sensor has competitive performance in the RI range of 1.33–1.39, in terms of the sensitivity.

We explored the influence of the ratio of the thickness of TiO₂ to the thickness of HfO₂ film on the pressure sensitivity of the sensor. We simulated three different sensor probes based on the different proportion of TiO₂/HfO₂ film thickness, with the same total thickness d = 80 nm. Simulation results demonstrate that when the proportion of HfO₂ increases gradually from zero, the sensitivity of the sensor gradually increases. When the ratio of HfO₂ to TiO₂ reaches 30/50, the sensitivity of the sensor reaches a maximum. However, as the ratio of HfO₂ to TiO₂ continues to increase, the sensitivity of the sensor decreases. This phenomenon can be explained by the fact that although HfO₂ has a higher real part of the dielectric constant, the imaginary part of the dielectric constant is zero. Thus, when only HfO₂ is coated on the surface of the fiber, the LMR effect cannot be excited. As the proportion of HfO₂ increases, the proportion of TiO₂ decreases, leading to a gradual decrease in the sensitivity of the sensor.

Since the first LMR peak in the spectra is considered to be the most sensitive, we only select the first LMR peak to study the sensitivity of the sensor. We compare the sensitivity of the sensor coated with TiO₂/HfO₂ film with that coated with only TiO₂ film in Table II. Four sensors, with a TiO₂/HfO₂ bilayer of 60/20, 50/30, 40/40 nm, and with a single TiO₂ layer of 80 nm, were investigated. All the sensors were described with the various SRI due to the pressure change. The optimal sensor is coated with TiO₂/HfO₂ of 50/30 nm, and a pressure sensitivity of 5μm/MPa is reached. In contrast, the sensitivity of the sensor coated with a single TiO₂ film of 80 nm only achieves 3.8μm/MPa. It is clear that the proposed pressure sensor has a competitive sensitivity.

In addition, to evaluate the performance of the proposed sensor in this paper, we compared this with the previously reported optical fiber pressure sensors in Table III. The results show that the proposed sensor has an advantage in sensor sensitivity for detecting pressure.

In this paper, we theoretically analyzed and optimized a microstructure optical fiber sensor based on lossy mode resonance. The fiber structure of an exposed-core PCF has been successfully fabricated in SPR sensors.²⁹ Therefore, we believe that this structure can also be used in LMR sensors in an experiment. In terms of the sensitivity of the sensor, the LMR-based sensor has better performance than an SPR-based sensor. Future research will focus on the transition of LMR-based sensors from the laboratory to actual production applications, in the same way that SPR-based sensors have been widely applied.

We described a highly sensitive pressure sensor based on lossy mode resonance with an exposed-core microstructure fiber. The microstructure fiber sensor is manufactured with an exposed-core photonics crystal fiber, on which TiO₂/HfO₂ film is coated. Strong birefringence, with x-polarized and y-polarized peaks, is generated because of the asymmetric sensing region. We also investigated the influence of the ratio of the thickness of TiO₂ to the thickness of HfO₂ on the sensitivity of the pressure sensor. From the simulation results, we conclude that the proposed sensor has excellent pressure sensitivity.

This work was supported by the Fundamental Research Funds for the Central Universities under Grant N180402023, N182410001, N172002001, and National College Students Innovation and Entrepreneurship Training Program under grant 201810145075, and National Natural Science Foundation of China under grant 51607028. The author thanks Dr. Wan-Ming Zhao and M.Eng. Bo-Tao Wang for valuable comments on this paper.