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FADOF transmission and ENBW, depicted for the optimum points from a. A global optimum point can be associated to the maximum of the quotient of the FADOF transmission and the ENBW. (b) same for the D2-line.
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Narrow-band optical filtering is required in many spectroscopy applications to suppress unwanted background light. One example is quantum communication where the fidelity is often limited by the performance of the optical filters. This limitation can be circumvented by utilizing the GHz-wide features of a Doppler broadened atomic gas. The anomalous...
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... are marked by the green, dashed line in Fig. 3c and 3f. When the optimal points for each temperature and magnetic field combination are calculated, it is also possible to evaluate the resulting filter performance for each of the determined points. For all depicted optimal points for each temperature (orange, dashed line in Fig. 3b and 3e), Fig. 4 displays the total FADOF-transmission, the ENBW and their ratio, which was considered to give an indication of the optimal operating conditions as outlined above. By increasing the magnetic field and temperature it is possible to first increase the FADOF transmission, whereas the ENBW rises later, which is dis- advantageous. The ratio ...
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... Our research endeavors focus on devising and empirically analyzing a fresh strategy to counteract external noise in FMCW LiDAR. This novel approach uses the power of the Faraday anomalous dispersion filter (FADOF), known for its exceptional attributes of high transmittance, narrow bandwidth, and impressive noise rejection ratio [16], [17], Currently, FADOF has been developed and applied on alkali metal atoms such as Na (589 nm) [18], K (767 nm, 770 nm) [19], and its working range covers numerous frequency bands between 400 nm and 1600 nm [16], [20]. These qualities have already propelled FADOF to prominence within the optical domain, demonstrating exceptional performance. ...
This paper examines the potential of utilizing a Faraday anomalous dispersion optical filter (FADOF) to enhance noise reduction in a FMCW LiDAR (Frequency-Modulated Continuous-Wave Laser Detection And Ranging) system. While the FMCW LiDAR itself demonstrates a certain level of robustness, it may fail to operate effectively in the presence of significant background noise interference. To address this challenge, we have proposed a validation experiment utilizing FADOF technology. Specifically, we have introduced a FADOF component at the optical receiving end of the FMCW LiDAR, and we have implemented a dynamic frequency stabilization method that combines frequency stability with frequency modulation for the laser source in the transmitter. By integrating FADOF into the FMCW LiDAR system to mitigate external noise, we conduct indoor and outdoor validation experiments. In the outdoor experiment, we introduce real sunlight background noise into the system, allowing it to directly illuminate the receiver. We then filter the light using FADOF and a 10 nm filter, separately. The experimental results confirm that the FMCW LiDAR system, when equipped with FADOF, can operate normally in intense background light noise, with a noise resistance capability at least twice as effective as the 10 nm filter. Additionally, the system achieves a detection range of at least 17 meters under direct sunlight conditions. This study has the potential to extend the application of LiDAR systems to more extreme environments with strong background noise, enabling their functionality in a broader range of scenarios.
... In 1846, Faraday [1] discovered the rotation of the polarization plane of light as it propagated through glass placed in a longitudinal magnetic field, thereby discovering the prominent magneto-optical effect (also known as the Faraday effect). Studies of magneto-optical effects have achieved great success and a wide range of applications [2][3][4][5][6]. A significant driving force is the advent of highly reliable, inexpensive, and easily tunable diode lasers, which offer high-quality light sources for research in this field. ...
The measurement of optical rotation is fundamental to optical atomic magnetometry. Ultra-high sensitivity has been achieved by employing a quasi-Wollaston prism as the beam splitter within a quantum entanglement state, complemented by synchronous detection. Initially, we designed a quasi-Wollaston prism and intentionally rotated the crystal axis of the exit prism element by a specific bias angle. A linearly polarized light beam, incident upon this prism, is divided into three beams, with the intensity of each beam correlated through quantum entanglement. Subsequently, we formulated the equations for optical rotation angles by synchronously detecting the intensities of these beams, distinguishing between differential and reference signals. Theoretical analysis indicates that the measurement uncertainty for optical rotation angles, when using quantum entanglement, exceeds the conventional photon shot noise limit. Moreover, we have experimentally validated the effectiveness of our method. In DC mode, the experimental results reveal that the measurement uncertainty for optical rotation angles is 4.7 × 10−9 rad, implying a sensitivity of 4.7 × 10−10 rad/Hz1/2 for each 0.01 s measurement duration. In light intensity modulation mode, the uncertainty is 48.9 × 10−9 rad, indicating a sensitivity of 4.89 × 10−9 rad/Hz1/2 per 0.01 s measurement duration. This study presents a novel approach for measuring small optical rotation angles with unprecedentedly low uncertainty and high sensitivity, potentially playing a pivotal role in advancing all-optical atomic magnetometers and magneto-optical effect research.
... [16][17][18][19] The spectrum of the light transmitted through an atomic vapor cell subjected to an external magnetic field is dependent on the relative orientation of the magnetic field and the k-vector of the light. The most commonly used geometries are the Faraday configuration, [20][21][22] where the magnetic field is parallel to the k-vector of the interrogating light, and the Voigt configuration, 23 where the magnetic field is perpendicular to the k-vector. [24][25][26][27][28][29][30][31][32] The general case with an arbitrary angle between the magnetic field and the axis of propagation is more difficult to treat mathematically-and to optimize experimentally-as the working angular range of the magneto-optical filter is limited, and slight deviations from the optimum angle lead to reduced filter efficiency and spectral distortion. ...
... Indeed, solenoids have been used to generate fields exceeding 4 kG in magneto-optical filter experiments, although this requires water cooling. 22 It would, therefore, be possible to create a solenoidpermanent magnet setup capable of producing any chosen field orientation. It should be noted, however, that in the case of large magnetic field angles using this setup, the resultant field magnitude is highly dependent on the field angle. ...
Atomic bandpass filters are used in a variety of applications due to their narrow bandwidths and high transmission at specific frequencies. Predominantly, these filters are in the Faraday (Voigt) geometry, using an applied axial (transverse) magnetic field with respect to the laser propagation direction. Recently, there has been interest in filters realized with arbitrary-angle magnetic fields, which have been made by rotating permanent magnets with respect to the k-vector of the interrogating laser beam. However, the magnetic field angle achievable with this method is limited as field uniformity across the cell decreases as the rotation angle increases. In this work, we propose and demonstrate a new method of generating an arbitrary-angle magnetic field, using a solenoid to produce a small, and easily alterable, axial field, in conjunction with fixed permanent magnets to produce a large transverse field. We directly measure the fields produced by both methods, finding them to be very similar over the length of the vapor cell. We then compare the transmission profiles of filters produced using both methods, again finding excellent agreement. Finally, we demonstrate the sensitivity of the filter profile to changing magnetic field angle (solenoid current), which becomes easier to exploit with the much improved angle control and precision offered by our new design.
... The ENBW can be optimized, while the maximum transmission is on small and negligible values. For that, an additional optimization parameter has been established [58]. The so-called 'figure of merit' (FOM) maximizes the peak transmission while reducing the ENBW and can be calculated by taking the ratio of the peak transmission and ENBW. ...
The nature of atomic vapors, their natural alignment with interatomic transitions, and their ease of use make them highly suited for spectrally narrow-banded optical filters. Atomic filters come in two flavors: a filter based on the absorption of light by the Doppler broadened atomic vapor, i.e., a notch filter, and a bandpass filter based on the transmission of resonant light caused by the Faraday effect. The notch filter uses the absorption of resonant photons to filter out a small spectral band around the atomic transition. The off-resonant part of the spectrum is fully transmitted. Atomic vapors based on the Faraday effect allow for suppression of the detuned spectral fraction. Transmission of light originates from the magnetically induced rotation of linear polarized light close to an atomic resonance. This filter constellation allows selective acceptance of specific light frequencies. In this manuscript, we discuss these two types of filters and elucidate the specialties of atomic line filters. We also present a practical guide on building such filter setups from scratch and discuss an approach to achieve an almost perfect atomic spectrum backed by theoretical calculations.
... The spectrum of the light transmitted through an atomic vapor cell subject to an external magnetic field is dependent on the relative orientation of the magnetic field and the k-vector of the light. The most commonly used geometries are the Faraday configuration [20][21][22], where the magnetic field is parallel to the k-vector of the interrogating light, and Voigt configuration [23], where the magnetic field is perpendicular to the k-vector [24][25][26][27][28][29][30][31][32]. The general case with an arbitrary angle between the magnetic field and the axis of propagation is more difficult to treat mathematically -and to optimize experimentally -as the working angular range of the magneto-optical filter is limited and slight deviations from the optimum angle lead to reduced filter efficiency and spectral distortion. ...
... Larger B z , and correspondingly smaller θ B could easily be produced using a different solenoid/power supply combination. Indeed, solenoids have been used to generate fields exceeding 4 kG in magnetooptical filter experiments, though this requires water cooling [22]. It would therefore be possible to create a solenoidpermanent magnet set-up capable of producing any chosen field orientation. ...
Atomic bandpass filters are used in a variety of applications due to their narrow bandwidths and high transmission at specific frequencies. Predominantly these filters in the Faraday (Voigt) geometry, using an applied axial(transverse) magnetic field with respect to the laser propagation direction. Recently, there has been interest in filters realized with arbitrary-angle magnetic fields, which have been made by rotating permanent magnets with respect to the $k$-vector of the interrogating laser beam. However, the magnetic-field angle achievable with this method is limited as field uniformity across the cell decreases as the rotation angle increases. In this work, we propose and demonstrate a new method of generating an arbitrary-angle magnetic field, using a solenoid to produce a small, and easily alterable, axial field, in conjunction with fixed permanent magnets to produce a large transverse field. We directly measure the fields produced by both methods, finding them to be very similar over the length of the vapor cell. We then compare the transmission profiles of filters produced using both methods, again finding excellent agreement. Finally, we demonstrate the sensitivity of filter profile to changing magnetic-field angle (solenoid current), which becomes easier to exploit with the much improved angle control and precision offered by our new design.
... The ENBW can be optimized, while the maximum transmission is on small and negligible values. For that, an additional optimization parameter has been established [58]. The so-called "figure of merit" (FOM) maximizes the peak transmission while reducing the ENBW and can be calculated by taking the ratio of the peak transmission and ENBW. ...
The nature of atomic vapors, their natural alignment with interatomic transitions, and their ease of use make them highly suited for spectrally narrow-banded optical filters. Atomic filters come in two flavors: a filter based on the absorption of light by the Doppler broadened atomic vapor, i.e., a notch filter, and a bandpass filter based on the transmission of resonant light caused by the Faraday effect. The notch filter uses the absorption of resonant photons to filter out a small spectral band around the atomic transition. The off-resonant part of the spectrum is fully transmitted. Atomic vapors based on the Faraday effect allow for suppression of the detuned spectral fraction. Transmission of light originates from the magnetically induced rotation of linear polarized light close to an atomic resonance. This filter constellation allows selective acceptance of specific light frequencies. In this manuscript, we discuss these two types of filters and elucidate the specialties of atomic line filters. We also present a practical guide on building such filter setups from scratch and discuss an approach to achieve an almost perfect atomic spectrum backed by theoretical calculations.
... In solar physics studies, filters are realised by cascading light through multiple thermal vapour cells [42][43][44]. Recently, we have shown cascading can also be used to significantly improve the performance of atomic filters [45] that aim to maximise the figure of merit (FOM) [46] ...
... The simple two transition model is visible from the figure: an atomic contribution where two profiles cross, causing a minimum B which acts to shift the sigmoidal curves horizontally, and a second thermal contribution whose evolution depends on both atomic Doppler widths and transition line gradients. Similar sigmoidal behaviour was shown in [46]. At lower temperatures, we see the evolution is near Gaussian. ...
Cascading light through two thermal vapour cells has been shown to improve the performance of atomic filters that aim to maximise peak transmission over a minimised bandpass window. In this paper, we explore the atomic physics responsible for the operation of the second cell, which is situated in a transverse (Voigt) magnetic field and opens a narrow transmission window in an optically thick atomic vapour. By assuming transitions with Gaussian line shapes and magnetic fields sufficiently large to access the hyperfine Paschen-Back regime, the window is modelled by resolving the two transitions closest to line centre. We discuss the validity of this model and perform an experiment which demonstrates the evolution of a naturally abundant Rb transmission window as a function of magnetic field. The model results in a significant reduction in two-cell parameter space, which we use to find theoretical optimised cascaded line centre filters for Na, K, Rb and Cs across both D lines. With the exception of Cs, these all have a better figure of merit than comparable single cell filters in literature. Most noteworthy is a Rb-D2 filter which outputs 92% of light through a single peak at line centre, with maximum transmission 0.71 and a width of 330 MHz at half maximum.
... Most magnetooptical filters rely on thermal vapor cells due to their compact and resilient setups [50]. Thermal vapor filters can be tuned by varying the magnetic field, temperature and input polarization [51,52] and can switch between different D-line operation [53]. It has been shown that by cascading cells, line-center or wing features can be selected [54]. ...
... We find excellent agreement with data giving equivalent noise bandwidths and transmissions of 181 MHz, 42 % and 140 MHz, 17 % respectively. The first filter is the highest Figure of Merit (FOM) [52] passive filter to date. The second filter is the first sub-100 MHz FHWM passive design and is reconfigurable allowing the selection of line-center or wing features by solenoid current variation. ...
... Plotting Stokes parameters on a Poincaré sphere provides a useful way of visualizing polarization [52,[79][80][81]. In this paper, we explain filter performance by plotting the Stokes parameters as a function of the distance light has propagated through the vapor. ...
Non-Hermitian physics is responsible for many of the counter-intuitive effects observed in optics research opening up new possibilities in sensing, polarization control and measurement. A hallmark of non-Hermitian matrices is the possibility of non-orthogonal eigenvectors resulting in coupling between modes. The advantages of propagation mode coupling have been little explored in magneto-optical filters and other devices based on birefringence. Magneto-optical filters select for ultra-narrow transmission regions by passing light through an atomic medium in the presence of a magnetic field. Passive filter designs have traditionally been limited by Doppler broadening of thermal vapors. Even for filter designs incorporating a pump laser, transmissions are typically less than 15% for sub-Doppler features. Here we exploit our understanding of non-Hermitian physics to induce non-orthogonal propagation modes in a vapor and realize better magneto-optical filters. We construct two new filter designs with ENBWs and maximum transmissions of 181 MHz, 42 % and 140 MHz, 17% which are the highest figure of merit and first sub-100 MHz FWHM passive filters recorded respectively. This work opens up a range of new filter applications including metrological devices for use outside a lab setting and commends filtering as a new candidate for deeper exploration of non-Hermitian physics such as exceptional points of degeneracy.
... Most magnetooptical filters rely on thermal vapor cells due to their compact and resilient setups [50]. Thermal vapor filters can be tuned by varying the magnetic field, temperature and input polarization [51,52] and can switch between different D-line operation [53]. It has been shown that by cascading cells, line-center or wing features can be selected [54]. ...
... We find excellent agreement with data giving equivalent noise bandwidths and transmissions of 181 MHz, 42 % and 140 MHz, 17 % respectively. The first filter is the highest Figure of Merit (FOM) [52] passive filter to date. The second filter is the first sub-100 MHz FHWM passive design and is reconfigurable allowing the selection of line-center or wing features by solenoid current variation. ...
... Throughout when we write S 1 , S 2 and S 3 , we are using input normalized stokes vectors (N = I in ). When we write tildes,S 1 ,S 2 ,S 3 , we are denoting output normalized stokes vectors (N = I out ). Plotting Stokes parameters on a Poincaré sphere provides a useful way of visualizing polarization [52,[79][80][81]. In this paper, we explain filter performance by plotting the Stokes parameters as a function of the distance light has propagated through the vapor. ...
Non-Hermitian physics is responsible for many of the counter-intuitive effects observed in optics research opening up new possibilities in sensing, polarization control and measurement. A hallmark of non-Hermitian matrices is the possibility of non-orthogonal eigenvectors resulting in coupling between modes. The advantages of propagation mode coupling have been little explored in magneto-optical filters and other devices based on birefringence. Magneto-optical filters select for ultra-narrow transmission regions by passing light through an atomic medium in the presence of a magnetic field. Passive filter designs have traditionally been limited by Doppler broadening of thermal vapors. Even for filter designs incorporating a pump laser, transmissions are typically less than 15\% for sub-Doppler features. Here we exploit our understanding of non-Hermitian physics to induce non-orthogonal propagation modes in a vapor and realize better magneto-optical filters. We construct two new filter designs with ENBWs and maximum transmissions of 181~MHz, 42\% and 140~MHz, 17\% which are the highest figure of merit and first sub-100~MHz FWHM passive filters recorded respectively. This work opens up a range of new filter applications including metrological devices for use outside a lab setting and commends filtering as a new candidate for deeper exploration of non-Hermitian physics such as exceptional points of degeneracy.
... The detailed understanding of atom-light interactions in hot vapours has facilitated the development of exquisitely sensitive sensors with applications spanning a range of topics: detecting explosives [51]; medical imaging of soft tissues [52][53][54][55][56]; and microfluidics [57]. In addition, the ability to make quantitative predictions of the atom-light interaction for an atomic vapour in an external magnetic field has enabled the development of numerous magneto-optical devices [58][59][60][61][62][63][64][65]. ...
... [134]): (i) strong principal resonance lines in the visible or near infrared part of the electromagnetic spectrum [112,202,203], (ii) simple and well-understood atomic structure and interactions with fields [65,204], and (iii) the vapour pressure of these elements allow large resonant optical rotations at modest temperatures [205]. Atomic line filters have been demonstrated in different atomic species, including Cs [61,206], Rb [201,207,208], Na [60,209] and K [210]. Gerhardt [211] provides a comprehensive list of different Faraday filters realised with alkali metals, and discusses the role of anomalous dispersion in the generation of the transmission profile. ...
The spectroscopy of hot atomic vapours is a hot topic. Many of the work-horse techniques of contemporary atomic physics were first demonstrated in hot vapours. Alkali-metal atomic vapours are ideal media for quantum-optics experiments as they combine: a large resonant optical depth; long coherence times; and well-understood atom-atom interactions. These features aid with the simplicity of both the experimental set up and the theoretical framework. The topic attracts much attention as these systems are ideal for studying both fundamental physics and has numerous applications, especially in sensing electromagnetic fields and quantum technology. This tutorial reviews the necessary theory to understand the Doppler broadened absorption spectroscopy of alkali-metal atoms, and explains the data taking and processing necessary to compare theory and experiment. The aim is to provide a gentle introduction to novice scientists starting their studies of the spectroscopy of thermal vapours whilst also calling attention to the application of these ideas in the contemporary literature. In addition, the work of expert practitioners in the field is highlighted, explaining the relevance of three extensively-used software packages that complement the presentation herein.
