Xiaotian Zhang, Xiting Han, Tao Wang, Hui Zhong, Shuhao Liu, Yanqiu Li, Ke Liu
A new method, to the best of our knowledge, based on double-slit (DS) interference is proposed to accurately estimate the shear ratio of the system, with plane wave or spherical wave incidence. Existing shear ratio calibration methods, designed primarily for lateral shearing interferometry (LSI) with plane wave incidence, are not applicable to LSIs directly testing divergent or convergent spherical waves. Equations for calculating the shear ratio using the fringe spacing of the DS interferogram and the NA of the incident spherical wave are derived in this paper. The simulation result shows that the relative error of the shear ratio value is about 0.3%, when the shear ratio is 0.1. In the experiment, the quadriwave LSI is designed with a plug-in feature. The shear ratio at integer multiples of 1/6 Talbot distance from the modified Hartmann mask was calibrated using a DS, and the results were in good agreement with theoretical values, confirming the accuracy of the method. Subsequently, with the assistance of an inductance micrometer, the shear ratio was calibrated at intervals of 0.5 mm, and the results closely matched the theoretical variation of the shear ratio caused by displacement, confirming the high precision of the method.
{"title":"In situ calibration of shear ratio for quadriwave lateral shearing interferometry using double-slit interference.","authors":"Xiaotian Zhang, Xiting Han, Tao Wang, Hui Zhong, Shuhao Liu, Yanqiu Li, Ke Liu","doi":"10.1364/ao.519203","DOIUrl":"https://doi.org/10.1364/ao.519203","url":null,"abstract":"A new method, to the best of our knowledge, based on double-slit (DS) interference is proposed to accurately estimate the shear ratio of the system, with plane wave or spherical wave incidence. Existing shear ratio calibration methods, designed primarily for lateral shearing interferometry (LSI) with plane wave incidence, are not applicable to LSIs directly testing divergent or convergent spherical waves. Equations for calculating the shear ratio using the fringe spacing of the DS interferogram and the NA of the incident spherical wave are derived in this paper. The simulation result shows that the relative error of the shear ratio value is about 0.3%, when the shear ratio is 0.1. In the experiment, the quadriwave LSI is designed with a plug-in feature. The shear ratio at integer multiples of 1/6 Talbot distance from the modified Hartmann mask was calibrated using a DS, and the results were in good agreement with theoretical values, confirming the accuracy of the method. Subsequently, with the assistance of an inductance micrometer, the shear ratio was calibrated at intervals of 0.5 mm, and the results closely matched the theoretical variation of the shear ratio caused by displacement, confirming the high precision of the method.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"14 4","pages":"2331-2339"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140425254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to the fact that the existing generation of wireless communication cannot possibly keep up with the current traffic explosion and emerging applications, research and development on next-generation (i.e., sixth generation, 6G) wireless technologies is being carried out worldwide. In this regard, it is anticipated that the space-air-ground (SAG) network with free space optics (FSO) communication can provide the terabits per second throughput necessary to sustain various potential 6G applications. However, FSO communications are susceptible to atmospheric turbulence, pointing errors, and beam scintillation effects. To remedy the severe atmospheric effects, we propose a multiple high-altitude platform station (HAPS)-based SAG network with a HAPS selection scheme. For the proposed system, we have derived the closed-form expressions for outage probability, average symbol error rate (SER), ergodic capacity, and outage capacity over Málaga distribution with pointing errors. Further, the asymptotic expressions for outage probability, average SER, and outage capacity were derived to enhance the comprehension of the system from a practical standpoint. It is observed from the numerical results that the multiple HAPS-based FSO system performs better than the existing HAPS-based FSO systems.
{"title":"Multiple HAPS-based space-air-ground network with FSO communication: a performance analysis.","authors":"D. Singh, S. R., Anh Pham","doi":"10.1364/ao.515707","DOIUrl":"https://doi.org/10.1364/ao.515707","url":null,"abstract":"Due to the fact that the existing generation of wireless communication cannot possibly keep up with the current traffic explosion and emerging applications, research and development on next-generation (i.e., sixth generation, 6G) wireless technologies is being carried out worldwide. In this regard, it is anticipated that the space-air-ground (SAG) network with free space optics (FSO) communication can provide the terabits per second throughput necessary to sustain various potential 6G applications. However, FSO communications are susceptible to atmospheric turbulence, pointing errors, and beam scintillation effects. To remedy the severe atmospheric effects, we propose a multiple high-altitude platform station (HAPS)-based SAG network with a HAPS selection scheme. For the proposed system, we have derived the closed-form expressions for outage probability, average symbol error rate (SER), ergodic capacity, and outage capacity over Málaga distribution with pointing errors. Further, the asymptotic expressions for outage probability, average SER, and outage capacity were derived to enhance the comprehension of the system from a practical standpoint. It is observed from the numerical results that the multiple HAPS-based FSO system performs better than the existing HAPS-based FSO systems.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"90 1","pages":"2362-2375"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140426568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new, to the best of our knowledge, scheme for a wavelength division multiplexing passive optical network (WDM-PON) based on a flat optical frequency comb (OFC) is proposed. Using an OFC as the optical source of the system can realize the colorlessness of optical network units (ONUs), and the direct detection of the downlink data further simplifies the ONU structure. The coherent demodulation of the uplink data improves the system performance due to the coherence of the comb lines. In this research, the proposed system is studied for its performance and power budgeting. The results show the flexibility, effectiveness, and practicability of the proposed scheme, which can be applied to future high-capacity optical access networks.
据我们所知，本文提出了一种基于平面光频率梳（OFC）的波分复用无源光网络（WDM-PON）新方案。使用 OFC 作为系统的光源可以实现光网络单元（ONU）的无色化，下行数据的直接检测进一步简化了 ONU 结构。由于梳状线的相干性，上行数据的相干解调提高了系统性能。本研究对拟议系统的性能和功率预算进行了研究。研究结果表明了所提方案的灵活性、有效性和实用性，可应用于未来的大容量光接入网络。
{"title":"Scheme for a WDM-PON with colorless optical network units based on a flat optical frequency comb.","authors":"Yian Cao, Shibao Wu","doi":"10.1364/ao.516098","DOIUrl":"https://doi.org/10.1364/ao.516098","url":null,"abstract":"A new, to the best of our knowledge, scheme for a wavelength division multiplexing passive optical network (WDM-PON) based on a flat optical frequency comb (OFC) is proposed. Using an OFC as the optical source of the system can realize the colorlessness of optical network units (ONUs), and the direct detection of the downlink data further simplifies the ONU structure. The coherent demodulation of the uplink data improves the system performance due to the coherence of the comb lines. In this research, the proposed system is studied for its performance and power budgeting. The results show the flexibility, effectiveness, and practicability of the proposed scheme, which can be applied to future high-capacity optical access networks.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"5 1","pages":"2594-2600"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140426833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Three-dimensional (3D) optical authentication is important for modern information security. Existing 3D optical authentication methods rely on integral imaging devices, necessitating meticulous calibration and incurring high transmission overhead. To streamline the acquisition of 3D information, this paper introduces a novel 3D optical authentication approach, to the best of our knowledge, based on the construction of 3D data from multi-view images. The proposed method simplifies 3D projection by generating fixed-viewpoint elemental images, eliminating the need for additional viewpoint information during transmission and authentication. Compressed sensing is used for compression during transmission, and a deep learning network is designed for 3D reconstruction, enhancing the recovery. Experimental outcomes confirm the efficiency of our proposed approach for 3D authentication across diverse datasets.
{"title":"Three-dimensional image authentication from multi-view images.","authors":"Zhen Leng, Jing Chen, Bo-Lan Liu","doi":"10.1364/ao.514144","DOIUrl":"https://doi.org/10.1364/ao.514144","url":null,"abstract":"Three-dimensional (3D) optical authentication is important for modern information security. Existing 3D optical authentication methods rely on integral imaging devices, necessitating meticulous calibration and incurring high transmission overhead. To streamline the acquisition of 3D information, this paper introduces a novel 3D optical authentication approach, to the best of our knowledge, based on the construction of 3D data from multi-view images. The proposed method simplifies 3D projection by generating fixed-viewpoint elemental images, eliminating the need for additional viewpoint information during transmission and authentication. Compressed sensing is used for compression during transmission, and a deep learning network is designed for 3D reconstruction, enhancing the recovery. Experimental outcomes confirm the efficiency of our proposed approach for 3D authentication across diverse datasets.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"30 3","pages":"2248-2255"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140427302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a pixelwise calibration method designed for a structured light system utilizing a camera attached with a telecentric lens. In the calibration process, a white flat surface and a flat surface with circle dots serve as the calibration targets. After deriving the properties of the pinhole projector through a conventional camera calibration method using circle dots and determining the camera's attributes via 3D feature points estimation through iterative optimizations, the white surface calibration target was positioned at various poses and reconstructed with initial camera and projector calibration data. Each 3D reconstruction was fitted with a virtual ideal plane that was further used to create the pixelwise phase-to-coordinate mapping. To optimize the calibration accuracy, various angled poses of the calibration target are employed to refine the initial results. Experimental findings show that the proposed approach offers high calibration accuracy for a structured light system using a telecentric lens.
{"title":"Pixelwise calibration method for a telecentric structured light system.","authors":"Yuchen Yang, Song Zhang","doi":"10.1364/ao.509535","DOIUrl":"https://doi.org/10.1364/ao.509535","url":null,"abstract":"This paper introduces a pixelwise calibration method designed for a structured light system utilizing a camera attached with a telecentric lens. In the calibration process, a white flat surface and a flat surface with circle dots serve as the calibration targets. After deriving the properties of the pinhole projector through a conventional camera calibration method using circle dots and determining the camera's attributes via 3D feature points estimation through iterative optimizations, the white surface calibration target was positioned at various poses and reconstructed with initial camera and projector calibration data. Each 3D reconstruction was fitted with a virtual ideal plane that was further used to create the pixelwise phase-to-coordinate mapping. To optimize the calibration accuracy, various angled poses of the calibration target are employed to refine the initial results. Experimental findings show that the proposed approach offers high calibration accuracy for a structured light system using a telecentric lens.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"41 8","pages":"2562-2569"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140425558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Mourikis, Alexander Sahm, P. Hildenstein, K. Paschke, Guenther Traenkle
We present a laser module with dimensions of 76×43×15m m 3 that for the first time to our knowledge realizes a coherent beam combination in such a compact device, using two tapered amplifiers seeded by a distributed Bragg reflector ridge waveguide laser diode operating at 761 nm in a single longitudinal mode. The generated combined optical power is up to 5 W continuous wave with a combing efficiency of 85%. The phase of the system is controlled by the current in the ridge waveguide section of one of the tapered amplifiers. The phase-stabilization process is automated using a reverse hill-climbing algorithm and an ATmega328P microcontroller.
我们展示了一个尺寸为 76×43×15m m 3 的激光模块，据我们所知，该模块首次在如此紧凑的设备中实现了相干光束组合，它使用了两个锥形放大器，由分布式布拉格反射脊波导激光二极管播种，工作波长为 761 nm，采用单一纵向模式。产生的组合光功率可达 5 W 连续波，梳理效率高达 85%。系统的相位由其中一个锥形放大器的脊波导部分的电流控制。相位稳定过程采用反向爬坡算法和 ATmega328P 微控制器自动完成。
{"title":"Miniaturizing a coherent beam combining system into a compact laser diode module.","authors":"C. Mourikis, Alexander Sahm, P. Hildenstein, K. Paschke, Guenther Traenkle","doi":"10.1364/ao.516029","DOIUrl":"https://doi.org/10.1364/ao.516029","url":null,"abstract":"We present a laser module with dimensions of 76×43×15m m 3 that for the first time to our knowledge realizes a coherent beam combination in such a compact device, using two tapered amplifiers seeded by a distributed Bragg reflector ridge waveguide laser diode operating at 761 nm in a single longitudinal mode. The generated combined optical power is up to 5 W continuous wave with a combing efficiency of 85%. The phase of the system is controlled by the current in the ridge waveguide section of one of the tapered amplifiers. The phase-stabilization process is automated using a reverse hill-climbing algorithm and an ATmega328P microcontroller.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"21 3","pages":"2212-2217"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140425988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jikai Wang, A. Ghazagh, Sonam Ravi, Stefan Baumbach, Benjamin Dannecker, Michael Scharun, Dominik Bauer, Stefan Nolte, Daniel Flamm
A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to characterize particularly strong light sources from intensity measurements only. With complete information about the optical field of the unknown light source at hand, virtual back propagation can reveal weak points in the light path such as apertures or damaged components.
{"title":"Phase retrieval algorithm applied to high-energy ultrafast lasers.","authors":"Jikai Wang, A. Ghazagh, Sonam Ravi, Stefan Baumbach, Benjamin Dannecker, Michael Scharun, Dominik Bauer, Stefan Nolte, Daniel Flamm","doi":"10.1364/AO.516820","DOIUrl":"https://doi.org/10.1364/AO.516820","url":null,"abstract":"A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to characterize particularly strong light sources from intensity measurements only. With complete information about the optical field of the unknown light source at hand, virtual back propagation can reveal weak points in the light path such as apertures or damaged components.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"20 5","pages":"2518-2527"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140427226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The attenuated phase-shift mask (Att. PSM) is proven to be a promising resolution enhancement technology (RET) to improve the imaging performance in extreme ultraviolet (EUV) lithography. However, due to the reflective nature of the mask structure, the serious shadowing effect can affect the diffraction near field of the mask intensely and further impact the lithography imaging. With the purpose of improving the contrast of lithography imaging, a novel structure of the Att. PSM, to the best of our knowledge, is proposed in this paper. By introducing an absorbent sidewall along the edge of the mask absorber, the diffraction and shadowing effects can be mitigated. By applying the Kirchhoff approximation of mask diffraction, the ability of the novel structure to improve imaging performance is theoretically analyzed. Additionally, these analyses are confirmed by rigorous lithography simulations. The simulation results demonstrate that the proposed mask structure can improve the imaging contrast of EUV lithography, which has potential usage in advanced integrated circuit (IC) manufacturing.
{"title":"SCAPSM: attenuated phase-shift mask structure for EUV lithography.","authors":"Chen Li, Lisong Dong, Yayi Wei","doi":"10.1364/ao.517264","DOIUrl":"https://doi.org/10.1364/ao.517264","url":null,"abstract":"The attenuated phase-shift mask (Att. PSM) is proven to be a promising resolution enhancement technology (RET) to improve the imaging performance in extreme ultraviolet (EUV) lithography. However, due to the reflective nature of the mask structure, the serious shadowing effect can affect the diffraction near field of the mask intensely and further impact the lithography imaging. With the purpose of improving the contrast of lithography imaging, a novel structure of the Att. PSM, to the best of our knowledge, is proposed in this paper. By introducing an absorbent sidewall along the edge of the mask absorber, the diffraction and shadowing effects can be mitigated. By applying the Kirchhoff approximation of mask diffraction, the ability of the novel structure to improve imaging performance is theoretically analyzed. Additionally, these analyses are confirmed by rigorous lithography simulations. The simulation results demonstrate that the proposed mask structure can improve the imaging contrast of EUV lithography, which has potential usage in advanced integrated circuit (IC) manufacturing.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"37 1","pages":"2263-2270"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140424580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The temperature dependence of optical window materials remains an important issue for a variety of applications from spacecraft, laser components, to high-speed aircraft. Concerning the refractive index in regions of transparency, current models are empirically based polynomial fits for the Sellmeier model strength and mode location parameters. These polynomial fit functions limit the ability to accurately extrapolate beyond the experimental range used to develop the fit functions. Thus, the development of a physics-based model as a function of temperature is an important goal for these critical materials. Such a model will allow extrapolation to higher and lower temperatures as long as the physical mechanisms do not change. For vibrational modes, a thermal average of the anharmonically shifted energy levels is investigated and compared to experimental data. The first anharmonic term can be estimated using the Morse potential based on a multiphonon absorption model. Experimentally, these modes redshift, and this is consistent with the developed temperature-dependent index of refraction Sellmeier model. This redshifting phenomena can also be applied to electronic transition shifts. In addition, the temperature-dependent oscillator number density can be obtained from known expansion coefficient models and experimental data. Other model parameters, in particular the electronic and vibrational mode polarizability, still need experimental grounding for a given material. The method is incorporated into a modified Sellmeier model format.
{"title":"Temperature-dependent index of refraction Sellmeier model for crystalline and polycrystalline materials.","authors":"Michael Thomas","doi":"10.1364/ao.511188","DOIUrl":"https://doi.org/10.1364/ao.511188","url":null,"abstract":"The temperature dependence of optical window materials remains an important issue for a variety of applications from spacecraft, laser components, to high-speed aircraft. Concerning the refractive index in regions of transparency, current models are empirically based polynomial fits for the Sellmeier model strength and mode location parameters. These polynomial fit functions limit the ability to accurately extrapolate beyond the experimental range used to develop the fit functions. Thus, the development of a physics-based model as a function of temperature is an important goal for these critical materials. Such a model will allow extrapolation to higher and lower temperatures as long as the physical mechanisms do not change. For vibrational modes, a thermal average of the anharmonically shifted energy levels is investigated and compared to experimental data. The first anharmonic term can be estimated using the Morse potential based on a multiphonon absorption model. Experimentally, these modes redshift, and this is consistent with the developed temperature-dependent index of refraction Sellmeier model. This redshifting phenomena can also be applied to electronic transition shifts. In addition, the temperature-dependent oscillator number density can be obtained from known expansion coefficient models and experimental data. Other model parameters, in particular the electronic and vibrational mode polarizability, still need experimental grounding for a given material. The method is incorporated into a modified Sellmeier model format.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"8 3","pages":"2477-2486"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140426517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marianne Beaumont, I. Ventrillard, Daniele Romanini
We demonstrate an accurate high sensitivity method for cavity spectroscopy. We measure the frequency intervals of transverse electromagnetic modes relative to a fundamental mode in a high finesse optical resonator, and attribute their mode numbers unambiguously. A laser is frequency locked to a fundamental T E M 00 cavity mode by optical feedback, and phase modulation is used to obtain frequency side bands, which may come to resonance with other transverse cavity modes as the radio-frequency of the modulation is tuned. At these resonances, transmission of the side bands is sensitively detected by heterodyning with the carrier. We also analyze the transverse spatial profile of the heterodyne signal for identification of mode numbers. The adjustment of the Gaussian cavity model to the measured frequency intervals yields values of cavity length, mirror radius of curvature, and mirror ellipticity, with high precision to the ppm level.
我们展示了一种精确的高灵敏度空腔光谱分析方法。我们测量了高精细度光学谐振器中横向电磁模式相对于基频模式的频率间隔，并明确地确定了它们的模式编号。通过光反馈将激光频率锁定在基本 T E M 00 腔模式上，然后使用相位调制来获得频率边带，随着调制射频的调整，这些边带可能会与其他横向腔模式产生共振。在这些共振处，侧带的传输可通过与载流子的异频共振被灵敏地检测到。我们还分析了外差信号的横向空间剖面，以确定模式数。根据测量到的频率间隔调整高斯腔模型，可以得到腔长、镜面曲率半径和镜面椭圆度的数值，精度高达 ppm 级。
{"title":"Optical cavity spectroscopy using heterodyne detection with optical feedback laser frequency locking.","authors":"Marianne Beaumont, I. Ventrillard, Daniele Romanini","doi":"10.1364/ao.518338","DOIUrl":"https://doi.org/10.1364/ao.518338","url":null,"abstract":"We demonstrate an accurate high sensitivity method for cavity spectroscopy. We measure the frequency intervals of transverse electromagnetic modes relative to a fundamental mode in a high finesse optical resonator, and attribute their mode numbers unambiguously. A laser is frequency locked to a fundamental T E M 00 cavity mode by optical feedback, and phase modulation is used to obtain frequency side bands, which may come to resonance with other transverse cavity modes as the radio-frequency of the modulation is tuned. At these resonances, transmission of the side bands is sensitively detected by heterodyning with the carrier. We also analyze the transverse spatial profile of the heterodyne signal for identification of mode numbers. The adjustment of the Gaussian cavity model to the measured frequency intervals yields values of cavity length, mirror radius of curvature, and mirror ellipticity, with high precision to the ppm level.","PeriodicalId":503884,"journal":{"name":"Applied Optics","volume":"102 4‐5","pages":"2227-2233"},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140429105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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