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Keywords = F–P etalon

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13 pages, 3398 KiB  
Article
Orthogonally Polarized Dual-Wavelength Pr:LLF Green Laser at 546 nm and 550 nm with the Balanced Output Powers at All Pump Power Level
by Haotian Huang, Jing Xia, Nguyentuan Anh, Yuzhao Li, Yuanxian Zhang, Qian Zhang, Zhexian Zhao and Yanfei Lü
Photonics 2025, 12(4), 393; https://doi.org/10.3390/photonics12040393 - 18 Apr 2025
Cited by 4 | Viewed by 500
Abstract
A continuous-wave (CW) orthogonally polarized dual-wavelength (OPDW) Pr3+:LiLuF4 (Pr:LLF) green laser with a balanced output power on the 3P03H5 transition was demonstrated for the first time. We theoretically analyzed the conditions for achieving equal [...] Read more.
A continuous-wave (CW) orthogonally polarized dual-wavelength (OPDW) Pr3+:LiLuF4 (Pr:LLF) green laser with a balanced output power on the 3P03H5 transition was demonstrated for the first time. We theoretically analyzed the conditions for achieving equal output power in the OPDW laser operation using two intracavity etalons and experimentally realized the OPDW green laser in a Pr:LLF crystal. Under pumping with a frequency-doubled optically pumped semiconductor laser (2ω-OPSL) generating 10 W at 479 nm, an OPDW green laser at 546 nm in π-polarization and 550 nm in σ-polarization was obtained with a total output power of 1.68 W. The output powers of the two wavelengths were equal for all the pump power levels. Further, a CW ultraviolet (UV) laser at 274 nm by intracavity sum-frequency mixing was also achieved with a maximum output power of 386 mW. The OPDW Pr:LLF green lasers with the balanced output power were desirable for medical detection and the generation of UV lasers. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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11 pages, 6537 KiB  
Article
Cavity Wavelength on Erbium-Doped Fiber Ring Laser Depending on Fabry–Pérot Etalon Steering Angle
by Cheng-Kai Yao, Ting-Po Fan, Ming-Che Chan and Peng-Chun Peng
Appl. Sci. 2025, 15(2), 822; https://doi.org/10.3390/app15020822 - 15 Jan 2025
Viewed by 1007
Abstract
This study presents the liquid crystal Fabry–Pérot etalon (LC-FP) as the preferred laser wavelength tuning solution within a erbium-doped fiber ring laser architecture. The laser cavity wavelength can be adjusted by applying varying voltages to the LC-FP. Furthermore, tuning the laser wavelength can [...] Read more.
This study presents the liquid crystal Fabry–Pérot etalon (LC-FP) as the preferred laser wavelength tuning solution within a erbium-doped fiber ring laser architecture. The laser cavity wavelength can be adjusted by applying varying voltages to the LC-FP. Furthermore, tuning the laser wavelength can be facilitated by modifying the incident light through changes in the steering angle of the LC-FP, which is attributed to the angular dispersion characteristics of the device. The operational range for the steering angle of the LC-FP is ± 4 to 18 degrees. This architectural framework is adept at facilitating the generation of single-wavelength and dual-wavelength lasers within the C band. The tunable range for a single wavelength is approximately 13 nm, while the tunable range for dual wavelengths is around 14 nm, with a wavelength spacing of approximately 17.5 nm. These capabilities are primarily influenced by the operational wavelength of the erbium-doped fiber amplifier (EDFA), the operating wavelength of the collimator that directs the fiber optic beam into the LC-FP, and the fixed thickness of the LC-FP. Full article
(This article belongs to the Section Optics and Lasers)
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11 pages, 5675 KiB  
Communication
780 nm Narrow Linewidth External Cavity Diode Laser for Quantum Sensing
by Junzhu Ye, Chenggang Guan, Puchu Lv, Weiqi Wang, Xuan Chen, Ziyi Wang, Yifan Xiao, Linfeng Zhan, Jiaoli Gong and Yucheng Yao
Sensors 2024, 24(22), 7237; https://doi.org/10.3390/s24227237 - 13 Nov 2024
Cited by 1 | Viewed by 2157
Abstract
To meet the demands of laser communication, quantum precision measurement, cold atom technology, and other fields for narrow linewidth and low-noise light sources, an external cavity diode laser (ECDL) operating in the wavelength range around 780 nm was set up with a Fabry–Pérot [...] Read more.
To meet the demands of laser communication, quantum precision measurement, cold atom technology, and other fields for narrow linewidth and low-noise light sources, an external cavity diode laser (ECDL) operating in the wavelength range around 780 nm was set up with a Fabry–Pérot etalon (F–P) and an interference filter (IF) in the experiment. The interference filter type ECDL (IF–ECDL) with butterfly-style packaging configuration has continuous wavelength tuning within a specified range through precise temperature and current control and has excellent single-mode characteristics. Experimental results indicate that the output power of the IF–ECDL is 14 mW, with a side-mode suppression ratio (SMSR) of 54 dB, a temperature-controlled mode-hop-free tuning range of 527 GHz (1.068 nm), and an output linewidth of 570 Hz. Compared to traditional lasers operating at 780 nm, the IF–ECDL exhibits narrower linewidth, lower noise, and higher spectral purity, and its dimensions are merely 25 × 15 × 8.5 mm3 weighing only 19.8 g, showcasing remarkable miniaturization and lightweight advantages over similar products in current research fields. Full article
(This article belongs to the Section Optical Sensors)
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17 pages, 10572 KiB  
Article
Study on Linewidth and Phase Noise Characteristics of a Narrow Linewidth External Cavity Diode Laser
by Sheng Hu, Puchu Lv, Chenggang Guan, Shasha Li, Haixin Qin, Xiaoqiang Li, Xuan Chen, Linfeng Zhan, Weiqi Wang, Yifan Xiao and Minghu Wu
Sensors 2024, 24(4), 1103; https://doi.org/10.3390/s24041103 - 8 Feb 2024
Cited by 4 | Viewed by 2823
Abstract
In the field of inter-satellite laser communication, achieving high-quality communication and compensating for the Doppler frequency shift caused by relative motion necessitate lasers with narrow linewidths, low phase noise, and the ability to achieve mode-hop-free tuning within a specific range. To this end, [...] Read more.
In the field of inter-satellite laser communication, achieving high-quality communication and compensating for the Doppler frequency shift caused by relative motion necessitate lasers with narrow linewidths, low phase noise, and the ability to achieve mode-hop-free tuning within a specific range. To this end, this paper investigates a novel external cavity diode laser (ECDL) with a frequency-selective F-P etalon structure, leveraging the external cavity F-P etalon structure in conjunction with an auxiliary filter to achieve single longitudinal mode selection. The laser undergoes linewidth testing using a delayed self-heterodyne beating method, followed by the testing of its phase noise and frequency noise characteristics using a noise analyzer, yielding beat spectra and noise power spectral density profiles. Furthermore, the paper introduces an innovative bidirectional temperature-scanning laser method to achieve optimal laser-operating point selection and mode-hop-free tuning. The experimental results showcase that the single longitudinal mode spectral side-mode suppression ratio (SMSR) is around 70 dB, and the output power exceeds 10 mW. Enhancing the precision of the F-P etalon leads to a more pronounced suppression of low-frequency phase noise, reducing the Lorentzian linewidth from the initial 10 kHz level to a remarkable 5 kHz level. The bidirectional temperature-scanning laser method not only allows for the selection of the optimal operating point but also enables mode-hop-free tuning within 160 pm. Full article
(This article belongs to the Section Optical Sensors)
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20 pages, 4578 KiB  
Article
Novel Compact Polarized Martian Wind Imaging Interferometer
by Chunmin Zhang, Yanqiang Wang, Biyun Zhang, Tingyu Yan, Zeyu Chen and Zhengyi Chen
Remote Sens. 2023, 15(19), 4881; https://doi.org/10.3390/rs15194881 - 9 Oct 2023
Cited by 2 | Viewed by 1780
Abstract
The Mars Atmospheric Wind Imaging Interferometer offers several advantages, notably its high throughput, enabling the acquisition of precise and high vertical resolution data on the temperature and wind fields in the Martian atmosphere. Considering the current absence of such an Interferometer, this paper [...] Read more.
The Mars Atmospheric Wind Imaging Interferometer offers several advantages, notably its high throughput, enabling the acquisition of precise and high vertical resolution data on the temperature and wind fields in the Martian atmosphere. Considering the current absence of such an Interferometer, this paper introduces a novel Mars wind field imaging interferometer. In analyzing the photochemical model of O2 (a1Δg) 1.27 μm molecular airglow radiation in the Martian atmosphere and considering the impact of instrument signal-to-noise ratio (SNR), we have chosen an optical path difference (OPD) of 8.6 cm for the interferometer. The all-solid-state polarized wind imaging interferometer is miniaturized by incorporating two arm glasses as the compensation medium in its construction, achieving the effects of field-widening and temperature compensation. Additionally, an F-P Etalon is designed to selectively filter the desired three spectral lines of O2 dayglow, and its effect is evaluated through simulations. The accuracy of the proposed compact Mars polarized wind imaging interferometer for detecting Mars’ wind field and temperature field has been validated through rigorous theoretical derivation and comprehensive computer simulations. The interferometer boasts several advantages, including its compact and small size, static stability, minimal stray light, and absence of moving parts. It establishes the theoretical, technological, and instrumental engineering foundations for future simultaneous static measurement of Martian global atmospheric wind fields, temperature fields, and ozone concentrations from spacecraft, thereby significantly contributing to the dataset for investigating Martian atmospheric dynamics. Full article
(This article belongs to the Section Atmospheric Remote Sensing)
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9 pages, 9058 KiB  
Communication
Diode-Pumped Single-Longitudinal-Mode Pr3+:YLF Laser Based on Combined Fabry–Perot Etalons at 522.67 nm
by Weicheng Dai, Haozhu Wang, Long Jin, Chang Liu, Yuan Dong and Guangyong Jin
Photonics 2023, 10(9), 971; https://doi.org/10.3390/photonics10090971 - 24 Aug 2023
Cited by 4 | Viewed by 1657
Abstract
We create a rate equation theoretical model of a continuous-wave end-pumped Pr3+:YLF SLM laser that characterizes the output properties of a single-longitudinal-mode (SLM) green laser. After inserting two Fabry–Perot (F–P) etalons with thicknesses of 0.3 mm and 0.5 mm and angles [...] Read more.
We create a rate equation theoretical model of a continuous-wave end-pumped Pr3+:YLF SLM laser that characterizes the output properties of a single-longitudinal-mode (SLM) green laser. After inserting two Fabry–Perot (F–P) etalons with thicknesses of 0.3 mm and 0.5 mm and angles of 1.42° and 0.69° into the cavity, a single-longitudinal-mode green laser was generated. The maximum output power in single-longitudinal mode was 183 mW. The maximum absorbed pump power was 6.2 W. The corresponding linewidth is about 18 MHz. This work presents a simple method for generating a single-longitudinal-mode laser in the green spectral region, providing a practical approach for various green-laser-related applications. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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10 pages, 3389 KiB  
Communication
Self−Mode−Locked 2−μm GaSb−Based Optically Pumped Semiconductor Disk Laser
by Jian Feng, Bo Meng, Jinming Shang, Xin Zhang, Cunzhu Tong, Yu Zhang, Zhichuan Niu and Lijun Wang
Appl. Sci. 2023, 13(12), 6873; https://doi.org/10.3390/app13126873 - 6 Jun 2023
Cited by 3 | Viewed by 1751
Abstract
We present a mode−locked GaSb−based optically pumped semiconductor disk laser operating at 2 µm based on the self−mode−locked mechanism. Using the delay differential equation model, we discuss the influence of cavity length on the stability of self−mode−locking and design a Z−shaped long cavity [...] Read more.
We present a mode−locked GaSb−based optically pumped semiconductor disk laser operating at 2 µm based on the self−mode−locked mechanism. Using the delay differential equation model, we discuss the influence of cavity length on the stability of self−mode−locking and design a Z−shaped long cavity for self−mode−locking. Employing an aperture and an F−P etalon in the cavity length of ~365 mm, we obtain stable self−mode−locking at a center wavelength of 2034.5 nm, with a pulse duration of 255.48 ps and average output power of 173 mW at a repetition rate of 404 MHz. Full article
(This article belongs to the Section Optics and Lasers)
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14 pages, 6449 KiB  
Communication
A Model of Dual Fabry–Perot Etalon-Based External-Cavity Tunable Laser Using Finite-Difference Traveling-Wave Method
by Xinhao Du, Changda Xu, Ya Jin, Kunpeng Zhai, Wenting Wang, Wei Chen and Ninghua Zhu
Photonics 2023, 10(5), 579; https://doi.org/10.3390/photonics10050579 - 16 May 2023
Viewed by 2820
Abstract
A physical model of an external-cavity tunable laser (ECTL) utilizing the vernier effect of a dual Fabry–Perot (FP) etalon is presented and simulated using the finite-difference traveling wave (FDTW) method. In this paper, we provide a detailed explanation of the physical principle and [...] Read more.
A physical model of an external-cavity tunable laser (ECTL) utilizing the vernier effect of a dual Fabry–Perot (FP) etalon is presented and simulated using the finite-difference traveling wave (FDTW) method. In this paper, we provide a detailed explanation of the physical principle and construction process of the model, as well as the simulation results for the laser. The model is precisely established by studying the time-dependent changes in the carrier concentration and optical field of different wavelengths inside the laser before reaching a steady state. By determining multiple parameters in the tuning region and gain region, the proposed model can calculate and predict various laser parameters, such as output power and side-mode suppression ratio (SMSR). Moreover, the FDTW method displays the change process of various parameters, such as carrier concentration and spectrum, in the convergence of various positions in the laser with femtosecond time resolution. This capability is promising for in-depth research on the inner mechanism of lasers. Full article
(This article belongs to the Special Issue Integrated Microwave Photonics)
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7 pages, 1587 KiB  
Communication
1.55 μm Narrow-Linewidth Pulsed Laser Based on MgO:PPLN
by Yaling Yang, Guorui Lv, Lei Guo, Haiping Xu, Hui Kong, Jiaqi Wen, Jintian Bian, Qing Ye, Kejian Yang and Jingliang He
Photonics 2023, 10(1), 77; https://doi.org/10.3390/photonics10010077 - 9 Jan 2023
Cited by 1 | Viewed by 2612
Abstract
A high-power narrow-linewidth 1.55 μm pulsed laser, based on MgO:PPLN OPO, has been achieved using a F–P etalon. The pump source is a 1064 nm acousto-optical (AO) Q-switched Nd:YAG laser with a repetition rate of 10 kHz. Under the maximum pump power of [...] Read more.
A high-power narrow-linewidth 1.55 μm pulsed laser, based on MgO:PPLN OPO, has been achieved using a F–P etalon. The pump source is a 1064 nm acousto-optical (AO) Q-switched Nd:YAG laser with a repetition rate of 10 kHz. Under the maximum pump power of 18 W, the signal output power of 2.57 W is demonstrated at 1551.1 nm with a linewidth of 0.07 nm, corresponding to a slope efficiency of 16.1%. Different from traditional inversion lasers, the narrow-linewidth wavelength tunability of approximately 1.55 μm can be realized by changing the temperature. Full article
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8 pages, 3069 KiB  
Communication
Convolution Error Reduction for a Fabry–Pérot-Based Linewidth Measurement: A Theoretical and Experimental Study
by Xuanning Hun, Zhenxu Bai, Jianping Wang, Bin Chen, Can Cui, Yulei Wang and Zhiwei Lu
Photonics 2022, 9(12), 1004; https://doi.org/10.3390/photonics9121004 - 19 Dec 2022
Cited by 6 | Viewed by 2015
Abstract
Linewidth measurement of a short pulse single-longitudinal mode laser with a low repetition rate has been a big challenge. Although the Fabry–Pérot (FP) etalon in combination with a beam profiler is an effective approach to measure the linewidth, the convolution error introduced by [...] Read more.
Linewidth measurement of a short pulse single-longitudinal mode laser with a low repetition rate has been a big challenge. Although the Fabry–Pérot (FP) etalon in combination with a beam profiler is an effective approach to measure the linewidth, the convolution error introduced by the inherent transmission spectrum width of an FP restricts the measurement accuracy. Here, the source of convolutional errors of the FP etalon-based linewidth measurement is analyzed, and the convolutional fitting method is proposed to reduce the errors. The results show that the linewidth measurement using the FP cavity with low reflectance (95%) can achieve the same resolution as that with high reflectance (99.5%) based on this convolution error reduction method. The study provides a simple approach to accurately measuring the linewidth of pulsed lasers, even with low energy. Full article
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7 pages, 2471 KiB  
Communication
An Orbital-Angular-Momentum- and Wavelength-Tunable 2 μm Vortex Laser
by Xinmiao Zhao, Jingliang Liu, Mingming Liu, Ruobing Li, Luan Zhang and Xinyu Chen
Photonics 2022, 9(12), 926; https://doi.org/10.3390/photonics9120926 - 1 Dec 2022
Cited by 3 | Viewed by 1649
Abstract
In this paper, dual tuning of orbital angular momentum (OAM) and the wavelength of a Tm:YLF vortex laser was realized by off-axis pumping and F-P etalon. The tuning of Hermite–Gaussian (HG) modes by off-axis pumping was theoretically analyzed. In the experiment, the highest [...] Read more.
In this paper, dual tuning of orbital angular momentum (OAM) and the wavelength of a Tm:YLF vortex laser was realized by off-axis pumping and F-P etalon. The tuning of Hermite–Gaussian (HG) modes by off-axis pumping was theoretically analyzed. In the experiment, the highest 17th order HG17,0 mode was realized by off-axis pumping. The threshold power increased from 2 to 17.51 W with the increase in off-axis distance, and the curve of threshold power vs. off-axis distance was partially consistent with the theoretical simulation analysis. The Laguerre–Gaussian (LG) modes carrying OAM were produced by mode converter, and the beam quality of LG modes was good. The phase distribution of the LG modes was verified by interference. Subsequently, an F-P etalon was inserted into the resonant cavity to tune the wavelength. Finally, the OAM tuning of the vortex beam from LG1,0(OAM = 1) to LG16,0(OAM = 16) was realized, and the corresponding wavelength tuning range was from 1898–1943 nm to 1898–1937 nm. Full article
(This article belongs to the Special Issue Vortex Beams: Fundamentals and Applications)
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9 pages, 2999 KiB  
Article
An Accelerometer Based on All Silica In-Line Fiber Fabry-Perot Etalon for High Temperature up to 800 °C
by Jiang Qian, Pinggang Jia, Qianyu Ren, Hua Liu, Li Qin and Jijun Xiong
Micromachines 2022, 13(4), 548; https://doi.org/10.3390/mi13040548 - 30 Mar 2022
Cited by 3 | Viewed by 2208
Abstract
High-temperature accelerometers have been widely used in aerospace, nuclear reactors, automobile technologies, etc. In this paper, a fiber-optic Fabry–Perot accelerometer (FOFPA) with a cantilever beam for high temperature is designed and experimentally demonstrated. The FOFPA is formed by bonding an all-silica in-line fiber [...] Read more.
High-temperature accelerometers have been widely used in aerospace, nuclear reactors, automobile technologies, etc. In this paper, a fiber-optic Fabry–Perot accelerometer (FOFPA) with a cantilever beam for high temperature is designed and experimentally demonstrated. The FOFPA is formed by bonding an all-silica in-line fiber Fabry–Perot etalon (ILFFPE) to one surface of the uniform cantilever beam with the lumped mass at the free end for acceleration measurement. The all silica in-line fiber FP etalon is made by welding two gold-coat single-mode fiber (GSMF) and a hollow silica glass tube (HST). The research results indicate that the sensitivity of the FOFPA is 0.02328rad/g, and the resonance frequency is 1146.6 Hz in the range of 1 g ~ 10 g. The high-temperature performance of the FOFPA was also evaluated. From 20 °C to 800 °C, the temperature drift is about 0.3178 nm/°C. The FOFPA has the potential of being applicable in higher temperatures compared to conventional accelerometers. Full article
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8 pages, 1951 KiB  
Communication
A Narrow-Linewidth Optical Parametric Oscillator Inserted with Fabry–Perot Etalon
by Xuefang Hu, Changgui Lu, Niuniu Wang, Zhengqing Qi and Yiping Cui
Photonics 2021, 8(12), 528; https://doi.org/10.3390/photonics8120528 - 24 Nov 2021
Viewed by 2443
Abstract
Nowadays, the Fabry–Perot etalon (F–P) has been widely utilized in the optical parametric oscillator (OPO) to improve the filtering performance. In this paper, we reported an F–P etalon composed of two ultra-thin silicon wafers spaced with the air. The linewidth of the signal [...] Read more.
Nowadays, the Fabry–Perot etalon (F–P) has been widely utilized in the optical parametric oscillator (OPO) to improve the filtering performance. In this paper, we reported an F–P etalon composed of two ultra-thin silicon wafers spaced with the air. The linewidth of the signal laser and the threshold are 0.03 nm and 0.6 W, respectively when the proposed etalon is employed to a OPO system based on the MgO-doped LiNbO3 (MgO: PPLN). A stabilized output at 1492.4 nm is obtained, and a tunable, high-precision filtering performance can be achieved by varying the gap distance of the F–P etalon arbitrarily due to its ultra-thin thickness. In addition, the F–P etalon can work on a very wide bandwidth due to its weak absorption during the infrared and terahertz waveband. The high-precision tuning capability and wide-band function of proposed etalon may benefit many applications, including spectroscopy, filtering, and optical communication. Full article
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15 pages, 3659 KiB  
Article
Microdisplacement Measurement Based on F-P Etalon: Processing Method and Experiments
by Xiaoyan Shen, Shinan Zhou and Dongsheng Li
Sensors 2021, 21(11), 3749; https://doi.org/10.3390/s21113749 - 28 May 2021
Cited by 1 | Viewed by 2471
Abstract
Herein, a processing method is proposed for accurate microdisplacement measurements from a 2D Fabry–Perot (F-P) fringe pattern. The core of the processing algorithm uses the F-P interference imaging concentric ring pattern to accurately calculate the centre coordinates of the concentric ring. The influencing [...] Read more.
Herein, a processing method is proposed for accurate microdisplacement measurements from a 2D Fabry–Perot (F-P) fringe pattern. The core of the processing algorithm uses the F-P interference imaging concentric ring pattern to accurately calculate the centre coordinates of the concentric ring. The influencing factors of measurement were analysed, and the basic idea of data processing was provided. In particular, the coordinate rotation by the 45-degree method (CR) was improved; consequently, the virtual pixel interval was reduced by half, and the calculation accuracy of the circle centre coordinate was improved. Experiments were conducted to analyse the influence of the subdivision and circle fitting methods. The results show that the proposed secondary coordinate rotation (SCR) by 45 degrees method can obtain higher accuracy of the centre coordinate than the CR method, and that the multichord averaging method (MCAM) is more suitable for calculation of the centre coordinate than the circular regression method (CRM). Displacement measurement experiments were performed. The results show that the standard experimental deviation of the centre of the circle is approximately 0.009 µm, and the extended uncertainty of the displacement measurement in the range of 5 mm is approximately 0.03 μm. The data processing method studied in this study can be widely used in the field of F-P interferometry. Full article
(This article belongs to the Section Physical Sensors)
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7 pages, 1554 KiB  
Article
Minimally Intrusive Optical Micro-Strain Sensing in Bulk Elastomer Using Embedded Fabry-Pérot Etalon
by Jungwook Paek, Qiang Li, In Ho Cho and Jaeyoun Kim
Micromachines 2016, 7(4), 61; https://doi.org/10.3390/mi7040061 - 6 Apr 2016
Cited by 2 | Viewed by 6533
Abstract
A variety of strain sensors have been developed to measure internal deformations of elastomeric structures. Strain sensors measuring extremely small mechanical strain, however, have not yet been reported due mainly to the inherently intrusive integration of the sensor with the test structure. In [...] Read more.
A variety of strain sensors have been developed to measure internal deformations of elastomeric structures. Strain sensors measuring extremely small mechanical strain, however, have not yet been reported due mainly to the inherently intrusive integration of the sensor with the test structure. In this work, we report the development of a minimally intrusive, highly sensitive mechanical strain transducer realized by monolithically embedding a Fabry-Pérot (FP) etalon into a poly(dimethylsiloxane) (PDMS) block test structure. Due to the extreme sensitivity of the FP resonance condition to the thickness of the spacer layer between the two reflectors, the limit of detection in the mechanical deformation can be as low as ~110 nm with a 632.8 nm laser used as the probing light. The compatibility of PDMS with additive fabrication turned out to be the most crucial enabling factor in the realization of the FP etalon-based strain transducer. Full article
(This article belongs to the Special Issue Micro/Nano Photonic Devices and Systems)
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