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Abstract
Uncooled infrared thermal detectors are gaining increasing attention owing to their ability to operate at room-temperature and their low cost. This study proposes a plasmonic optomechanical resonator for ultrasensitive long-wave infrared wave sensing based on mode localization mechanism. The mode-localized effect confines the plasmonic energy in the resonators and induces a significant modal amplitude shift through infrared irradiation, thus achieving highly sensitive detection. The results show that the detection sensitivity can reach 1.304 /mW, which is three-order improvement compared to the frequency-shift sensing metrics. The research provides a new approach to further improve the detection sensitivity of uncooled infrared sensors.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Infrared detection technology has been widely used in various fields such as biomedicine [1], aerospace [2], and night vision imaging [3]. The uncooled infrared thermal detector, which can work at room temperature without additional large-volume refrigeration equipment, has attracted more attention in the field of infrared detector research. The development of thermal detectors has focused on low-cost, room-temperature, and high-photon-flux applications for long-wave infrared (LWIR) and very-long-wave infrared (VLWIR), where thermal detectors can outperform photoconductors (PCs) and photovoltaics (PVs) [4]. Currently, thermal detection methods primarily include thermoelectric [5], bolometric [6], and pyroelectric methods [7]. In recent years, novel optomechanical thermal sensing methods have been developed as a new technology for uncooled infrared thermal detectors [8–10]. Such optomechanical thermal detectors have gradually been developed into lab-on-chip microsystems with ultralow standby power by combining a micromechanical light switch [11] or a mechanical resonant sensing unit [12]. There are also a variety of other promising emerging optomechanical thermal detector technologies, including optomechanical detectors with dual-layer metasurface absorbers [13], optomechanical detectors with shape memory polymer materials [14], and optomechanical detectors with aluminum nitride cantilever covering fishnet-like metasurface absorbers [15].
However, recent nanophotonic developments and their impact on the sensitivity of infra-detectors are large challenges for thermal detectors, as they may be less sensitive than PCs or PVs even in the LWIR and VLWIR regimes, and the sensitivity performance of thermal detectors should be further improved. In this study, we propose a new type of optomechanical thermal detection method that combines mode localization and plasmonic resonance to further improve the sensitivity and performance of thermal detectors. The mode localization effect was proposed by Anderson in 1958 [16] and can be described as follows, in an ideal multi-degree-of-freedom weakly coupled mechanical resonant system, when the resonator is not disturbed, the amplitudes of each resonator are the same, whereas when one of the resonators is disturbed by external perturbations such as light-induced thermal stress, the mode amplitude of the resonator will change dramatically. It has been proven that the sensitivity of an acceleration sensor using mode localization is improved by a factor of over 1000 compared with the resonant frequency shift method [17–19]. Inspired by the outstanding performance of mode-localization sensors in the detection of extremely weak acceleration [20], magnetic field [21], electric charge [22], and mass [23], we combined mode localization and plasmonic resonance to detect LWIR with unprecedented optomechanical performance and thermal capabilities. It was designed using two weakly coupled mechanical resonators, forming a two-degree-of-freedom mode-localization system. The detector uses a metal-dielectric-metal plasmonic absorber covering the resonator to realize a high absorption rate of long-wave infrared radiation, which can be confined to the resonators by plasmonic resonance as an external perturbation for mode-localization excitation. Plasmonic resonance was induced using a nanotitanium cube array metasurface. Using finite element analysis (FEA), we systematically analyzed the optical near-field plasmonic modes, weakly coupled mechanical resonant modes, and their contributions to the formation of mode localization, and numerically studied the light absorptivity, modal amplitude, and detection sensitivity. The research results demonstrated that it is possible to achieve a high thermomechanical coupling between electromagnetic and mechanical resonances in weakly coupled resonators covering a metasurface. These attributes lead to the demonstration of an ultrasensitive uncooled infrared detector with over 82% absorption for an optimized spectral bandwidth (BW) of 8.99 µm ∼ 14.58 µm, with a sensitivity of more than 1.304 /mW, which is approximately three order improvement compared with frequency shift sensing metrics (0.00243 /mW). We believe that such a mode-localization-based plasmonic optomechanical infrared thermal detector can drive the development of ultrasensitive uncooled infrared detectors and can be applied in wearable devices and intelligent sensors.
2. Device design
A schematic diagram of the mode localization plasmonic resonator design is shown in Fig. 1. It consists of two double-end anchored resonators and a coupled beam, forming a two-degree-of-freedom weakly coupled resonant system. The resonators are designed with a silicon material, with a thickness of h = 25 µm, density of ρ = 2.33 × 10−15 kg/µm3, and Young's modulus of E = 169 GPa (other dimensions of the resonators are shown in Fig. 1(a)). An LWIR absorber was designed on the resonators for the effective absorption of electromagnetic waves. Figure 1(b) shows the smallest unit of the absorber structure; the length of the unit is p = 2000nm. From top to bottom, the absorber consists of a titanium cube array layer, germanium dielectric layer, titanium metal layer, and silicon substrate, corresponding to r = 800 nm, h1(Ti) = 22 nm, h2(Ge) = 500 nm, and h3(Ti) = 120 nm. When the LWIR is incident on the absorber, propagating surface plasmon resonance (PSPR) and local surface plasmon resonance (LSPR) can be excited in the absorber structure. These plasmonic resonances convert the energy from optical irradiation into a localized temperature increase owing to ohmic loss and the formation of a thermal stress perturbation in the resonator system. Therefore, the LWIR irradiation on the absorber can introduce a significant stiffness perturbation to excite the modal localization effect.
Fig. 1. Schematic of the structure of the LWIR detector. (a) Weakly coupled resonant structures, its geometric parameters are shown in the picture. (b) Ti-Ge-Ti plasmonic absorber.
3. Near-field optical research of LWIR absorber
An infrared absorber with wide absorption BWs and large absorption efficiency are essential for infrared sensor; however, the existing research on infrared absorbers do not have a satisfied BW of which less than 2 µm [24,25]. Therefore, the LWIR absorber was carefully designed and its optical and electric near-field interactions by strong LSPR and PSPR were deeply investigated. The electromagnetic properties of the LWIR absorber under normal incidence were numerically simulated using CST Microwave Studio computer software, and the model was built using the smallest unit of the absorber with periodic boundary conditions in x and y directions. A perfect matching layer was set to eliminate boundary scattering along the z direction. Because the Si substrate is extremely thick for light to pass through, the transmission rate (T) of the LWIR absorber can be approximately zero; thus, the absorptivity (A) and reflectivity (R) satisfy the relationship A + R = 1. The absorption result of the LWIR is shown in Fig. 2(a), which has two electromagnetic resonance absorption peaks in the wavelength range of 7 µm ∼ 17 µm, located at 9.61 µm and 13.44 µm, with absorptivity of 99.6% and 99.9%, respectively. The results show that the proposed LWIR had a continuous high absorptivity of over 82% in a wideband range of 8.99 µm ∼ 14.58 µm, that is, the absorber had a BW of 5.59 µm.
Fig. 2. (a) Absorption spectra of the LWIR absorber under normal incident TE polarized light, (b)-(c), Distribution of electric field intensity (|E|) and magnetic field intensity (|H|) at wavelength 9. 61 µm (b) and 13.44 µm (c).
The distribution of electric field intensity (|E|) in the x-y plane and magnetic field intensity (|H|) in the x-z plane was calculated to analyze the near-field optical effect of the LWIR absorber and the TE-polarized light at the direction of normal incidence at the resonance wavelengths of 9.61 µm and 13.44 µm were used as the light source. The distribution of the electric field intensity |E| and magnetic field intensity |H| are shown in Figs. 2(b) and 2(c), where it is shown that the electric field was confined in the Ti cube and the magnetic field was distributed on top of the Ti cube and above the continuous Ga/Ti film. This indicates that strong resonant modes existed and were guided by the periodic nanocube array and the metal-dielectric films. At a wavelength of 9.61 µm, as shown in Fig. 2(b), the electric field was mostly distributed at the edge of the Ti cube, which caused strong field distribution in the air slots of adjacent unit cells. This suggests that the PSPR generated by the resonant oscillation of conduction electrons at the interface between negative and positive permittivity materials and magnetic field was distributed at the top of the Ti cube layer which also verifies the excitations of PSPR at the Ti-Ga films. Further, the LSPR was generated by the confinement of optical energy in the nanostructure comparable to or smaller than the wavelength of the illumination light. The distribution pattern of a strong electric field appeared in the area of adjacent Ti cubes and the magnetic field was mainly concentrated in the top of Ti cubes conforming to the LSPR effect. At a wavelength of 13.44 µm as shown in Fig. 2(c), the electric field was mainly confined at the edge of the Ti cube and the magnetic field was mainly distributed in the Ga dielectric layer. Hence, a Fabry-Perot (FP) cavity was formed by the Ti cube and Ti metal layers separated by the Ga layer. The incident light conducted constructive interferences with the reflected light. Moreover, the PSPR and LSPR may also play a role in the interaction by considering the wave-vector matching condition and light confinement by the nanostructure.
The property of incident-angle insensitivity is crucial for an infrared detector. Figures 3(a) and (b) show the absorption spectra under TE and TM polarizations with varying incident angles from 0-60°. A high absorption was maintained at a BW range of 8.99 µm ∼ 14.58 µm for the TM electromagnetic wave, while for the TE electromagnetic wave, the absorption at a BW range was kept over 80%, and only occurred at angles from 0-40°. This may have been attributed to the confinement of the light in nanostructures growing weaker in large incident angles. However, the absorption performance was to satisfactory when the incident light could be easily controlled within 40°.
Fig. 3. Absorption of (a) TE polarized light and (b) TM polarized light at different incident light.
4. Mode localization research in resonators
The two-degree-of-freedom weakly coupled harmonic resonator system can be modeled as a mass-spring-damping resonator system, as shown in Fig. 4(a), where m1, k1, c1, m2, k2, and c2 are the mass, bending stiffness, and damping factor of Resonators 1 and 2, respectively. f1 and f2 are the driving forces applied to the two resonators, and x1 and x2 are the displacements. kc is the stiffness of the coupled beam. To simplify the calculation model, we designed resonators with identical parameters, that is, m1 = m2 = m, k1 = k2 = k, c1 = c2 = c, the same LWIR absorbers were fabricated on both resonators, but on opposite surfaces, to introduce external optical perturbations only to a single resonator each time. The dynamic equation of the model can be expressed as [26]:
Fig. 4. (a) Mechanical model of the two-degree-of-freedom weakly coupled harmonic resonator system, (b) Vibration mode of the first mode (in-phase mode) and the second mode (out-of-phase mode), (c) Amplitude-frequency curve of the first and second mode under different external perturbations.
In the case of no perturbation (δ = 0), the corresponding vibration modes are shown in Fig. 4(b). The first vibration mode is in-phase mode, in which the two resonators move in the same direction, and the second vibration mode is out-of-phase mode, in which the two resonators move in opposite direction. The amplitude ratio is defined as
where the subscript i represents the order of the vibration mode, and then the amplitude radios of the two modes with no perturbation are a1 = 1, a2 = −1. In the weakly coupled system, the resonant frequencies ω1, ω2 of the vibration Mode1 and 2 are [27]The resonant frequencies of the weakly coupled system were simulated by COMSOL Multiphysics software. In the case of no perturbation, the angular resonant frequency of the first and second modes are ω1 = 4.3483 × 105 rad/s and ω2 = 4.3626 × 105 rad/s, based on the geometric relationships and material properties introduced above; thus, the coupling coefficient κ = [(ω2/ω1)2−1]/2 = 0.0033. To further analyze the modal amplitude response of the optomechanical resonators, we modeled each resonator vibrating as a simple harmonic oscillation of f = Feiωt and its displacement is represented by x = Xeiωt, where F is the excitation force amplitude, X is the displacement amplitude, and ω is the frequency of the driving force. We then set the driving conditions to f1 = f and f2 = 0, and the displacements of the two resonators are represented by (4).
The calculated amplitude-frequency curve of Resonators 1 and 2 under different external perturbations δ are shown in Fig. 4(c). The negative value of δ implies that the stiffness of the resonator reduces when the external thermal stress perturbation increases. It can be observed that when the perturbation is zero, the amplitudes of Resonators 1 and 2 are the same in vibration Mode 1 or 2. When the perturbation increases, the modal amplitude begins to change and the amplitude of Mode 1 of Resonator 1 decreases while its amplitude of Mode 2 increases, indicating that the vibrational energy is gradually transferred from the first mode to the second mode, that is, the phenomenon of mode localization takes place. For Resonator 2, the modal amplitude is often identical between the two modes and tends to decrease with an increase in the external perturbation, which is a significantly special phenomenon in which the vibration is confined to a specific mode; such a vibration mode has been regarded as the essence of mode localization [28]. To further analyze the effect of the mode localization, the vibration energy Ev = kx2/2 of the two resonators at the two modes were calculated based on Eq. (4) and (5). The energy distribution of the Resonator 1 at the first and second modes are shown in Fig. 5(a). The vibrational energy was distributed evenly when δ = 0, then it began to be transferred from the first to second mode: the energy proportion was 8.7% and 91.3% for Resonators 1 and 2 when δ was −0.004, and it became 1.6% and 98.4% when δ increases to −0.008, respectively. The energy distribution of Resonator 2 remained the same for the two modes, which confirms the conclusion regarding vibration confinement in a specific mode. Notably, the energy transfer occurred between the vibration modes and the two resonators, implying that the energy in a single-resonator system (system of Resonators 1 or 2) is not conserved. From Figs. 5(c) and (d), with the increase in external perturbation, the energy is transferred from Resonator 1 to Resonator 2 for the first mode and from Resonator 2 to Resonator 1 for the second mode; the latter plays a major role, which can explain why the modal amplitude of Resonator 2 gradually decreases with larger perturbations.
Fig. 5. Vibrational energy distribution of Resonators 1 and 2 under the first and second modes, (a) Energy distribution of the two vibration modes in Resonator 1, (b) Energy distribution of the two vibration modes in Resonator 2, (c) Energy distribution of the first vibration mode in Resonators 1 and 2, (d) Energy distribution of the second vibration mode in Resonators 1 and 2.
Because the external perturbation is induced by temperature variation, the relationship between the perturbation and temperature difference in the resonator was studied, and the incident LWIR radiation from a target-induced temperature change in the resonator based on the light absorptance. This temperature change led to a change in Young’s modulus of the resonator material, a thermal coefficient that can be represented by
where E is the Young’s modulus, ΔT is the temperature difference, and ΔE is the Young’s modulus variation. For a resonator with a given material, the larger the temperature variation, the larger the change in Young’s modulus. The Young’s modulus can be expressed based on its definition: where σ is a tensile stress and σ = F/A. F is a tensile force acting normally to area A. ɛ is the strain which is defined as the target object of original length, L0 is extended by an amount e, that is ɛ = e/L0. Thus we have E = σ/ɛ = FL0/(Ae), meanwhile, F = ke is based on Hooke’s law. Finally, we obtain a relationship of E = kL0/A, because L0 and A are all constant for a resonator with certain geometrics and materials; Hence, the resonator stiffness is proportional to the Young’s modulus and has a relationship of Δk/k = ΔE/E. Thus, the stiffness perturbation in the resonator can be expressed using Eq. (8) based on its definition: When the resonator is heated by the infrared illumination, the thermal energy absorbed by the resonator QA against temperature rise ΔT can be expressed by ΔT = QA/(csm), where cs is the specific heat capacity of the resonator. The total energy absorbed by the resonator is provided by the LWIR absorber with an absorption of αA, that is, QA = αA*P0 t and P0 is the power of infrared illumination. Therefore, we obtained the relationship between the external perturbation and infrared illumination power per unit time, which can be expressed as follows: where constant Γ = TCE*αA/(csm). When the wavelength of the illumination light was 9.61 µm, for example, the absorption of the LWIR absorber was αA = 0.99, TCE of the silicon resonator was approximately −60 ppm/K based on the experimentally measured value in Ref. [29]. The mass and specific heat capacity of the resonator were 1.7475 × 10−8 kg and 700 J/(kg•K) [30], respectively; hence, Γ = −4.8559 was calculated. In summary, the external perturbation has a linear relationship with the IR illumination power; thus, the external perturbation can be detected using a modal amplitude shift based on the mode localization mechanism and then converted back to an IR power. In this study, the amplitude ratios defined in Eq. (2) were used for the modal amplitude shift readout scheme, that is, they can be expressed as in (10) based on Eq. (4).Figure 6(a) shows the result of the amplitude ratio variation with the detected IR power signal, which exhibited a linear shift with IR power. When the driving frequency ω equal to the resonance frequency ω1 and ω2, the modal amplitude reaches its maximum. Hence, the amplitude ratio of the mode localized photothermal disturbance system can be represented by:
Here, we assume that the system is ideal, damping factor is neglected to simplify the modeling, and quality factor Q is infinity. Figure 6(b) shows the relation curves of the amplitude ratio and IR power at the resonant Modes 1 and 2. It is shown that if the amplitude ratio at the resonant frequencies is taken as the output metrics, the variation is no longer strictly linear, and the detecting sensitivity (the curve slope) for the second resonant mode is much higher than the first resonant mode. This result is consistent with the amplitude variation in Fig. 4(c), in which the amplitude shift in Mode 2 is much larger than in Mode 1. Moreover, the stiffness of coupling between Resonators 1 and 2 has a significant impact on the detecting sensitivity. Figure 6(b) shows that the smaller the coupling coefficient κ, the better the detecting sensitivity. However, as the value of κ decreases, the frequency difference between the first and second resonant modes decreases, as shown in Fig. 6(c), The frequency difference decreased from 300 to 160 Hz when the coupling coefficient changed from 0.0043 to 0.0023. If the frequency difference between the two resonate modes is extremely small, the two modes will be merged together. Therefore, the in-phase and out-of-phase modes become indistinguishable from each other: the mode-aliasing occurs [31]. Hence, in applications, it is necessary to consider both sensing sensitivity and mode-aliasing issues to determine the optimal solution. In this study, by balancing the sensitivity and mode-aliasing, the optimal value of the coupling coefficient κ was approximately 0.0033 (red lines shown in Figs. 6(b) and (c)).
Fig. 6. (a) Variation of amplitude ratio with IR power at different vibration frequencies, (b) Variation of the amplitude ratio with IR power under vibration Modes 1 and 2, (c) Variation of the resonant frequencies with IR power at Modes 1 and 2.
The LWIR sensor uses the mode amplitude ratio between resonators to achieve the highest sensitivity for detection. Because the variation of the mode amplitude can reflect the weak drift of the photothermal disturbance, as shown in Figs. 4(c) and 6(b). The coupling stiffness mainly affects the amplitude ratio of resonance Mode 2, while the amplitude ratio of Mode 1 was slightly changed, which determines the detection sensitivity and range of the LWIR sensor. Figure 7 shows the evolution of the detection sensitivity and range of the sensor operated at resonance Modes 1 and 2, respectively, where the ideal detection should be in the linear region in the amplitude ratio and light power relation curve. For the sensor in the first resonance mode, the linear region is approximately located at 1 mW ∼ 2.5 mW and the detection sensitivity is approximately 0.168 /mW. When the sensor is operated in the second resonance mode, the detection sensitivity is significantly higher, approximately 1.304 /mW, and the linearity when the sensor was operated in Mode 2 was also better than that in Mode 1, with almost the same detection range. In applications, the LWIR sensor operated in Mode 2 will be the best. In comparison, the detection sensitivity based on the mechanical frequency shift was only 0.00243 /mW and the detection sensitivity of the LWIR sensor based on the mode-localization mechanism was improved by approximately three orders of magnitude compared with the frequency-shift sensing method. This novel LWIR detection method based on a modal-localization-sensitive mechanism provides an ultrasensitive method to further improve the detection sensitivity of infrared metamaterial resonant detectors and has important applications for realizing high sensitivity and fast response of uncooled infrared thermal detectors.
Fig. 7. Analyzation of detection sensitivity and range of the LWIR sensor under (a) First resonance mode and (b) Second resonance mode.
5. Conclusion
In this study, a plasmonic optomechanical resonator for ultrasensitive long-wave infrared wave sensing based on a modal localized mechanism was proposed. The detector uses a plasmonic absorber consisting of a titanium cube array, germanium dielectric, and titanium metal layers covering the resonator to realize a high absorption rate of long-wave infrared radiation. The mode-localized effect confines the mechanical energy of the resonators in the second resonator mode and induces a significant modal amplitude shift through the stiffness disturbance caused by the infrared irradiation, thus achieving highly sensitive long-wave infrared detection. The results show that the detection sensitivity in the second resonance mode was approximately 1.304 /mW, which is a three-order improvement compared with the frequency-shift sensing metrics (0.00243 /mW). The method of using a mode-localization mechanism to realize infrared wave sensing provides a new approach to further improve the detection sensitivity of uncooled infrared sensors. We believe that such a mode-localization-based plasmonic optomechanical infrared thermal detector will drive the development of ultrasensitive uncooled infrared detectors and can be applied in wearable devices and intelligent sensors.
Funding
National Natural Science Foundation of China (52105595), Natural Science Foundation of Zhejiang Province (LTGS24E050002).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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