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Abstract
A magneto-optic spectrometer based upon dispersion associated with the 852 nm absorption line in atomic cesium vapor is demonstrated with high frequency resolution appropriate for measuring motion (Doppler shift). The spectrometer measures frequency without depletion of signal from atomic absorption, and has an 11% total signal extinction from the optic elements of which it is constructed. Also demonstrated is an optical filter with a high transmission region that coincides with the operating range of the spectrometer useful for blocking background light. Possible applications may include ground based LIDAR for long range targets such as space debris and free space optical communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Faraday polarization rotation spectroscopy with paramagnetic atoms and molecules subjected to a magnetic field has been utilized for a variety of applications. Among them is the detection of the presence and concentration NO, NO2, O2 [1–4], measurement of magnetic field strength [5], and used in LIDAR and free space optical communication for filtering of background light [6–10]. Faraday rotation spectrometers using dispersion from absorption lines [11] and two-photon absorption lines [12,13] have demonstrated resolution high enough to measure Doppler shift but with significant absorption.
The objective of this research is to build a Faraday polarization rotation spectrometer for use in LIDAR or free space optical communication, which has high frequency resolution while minimizing signal depletion. To put this spectrometer in context, first a review of other methods of measuring frequency (or velocity) used in LIDAR.
Other methods of measuring frequency at Doppler shift resolution useful for LIDAR include absorption line edge spectroscopy, interference techniques, and coherent detection. Absorption line edge methods rely upon relative absorption in vapors such as sodium and iodine [14,15]. Fabry-Perot interferometers [16,17] have the advantage that they can be constructed for any wavelength and desired frequency pass-band width. The more narrow the pass-band the lower the transmission. A theoretical comparison of Fabry-Perot interferometers and relative absorption techniques designed to measure Doppler shift assigns signal transmission of 40% for both methods [18]. Because of the large loss, direct detection Doppler LIDAR is generally only used for measuring wind.
Measurement of motion and range of hard targets with LIDAR can be accomplished with a pulsed transmitter or with a Frequency Modulated Continuous Wave (FMCW) transmitter. In pulsed systems, line of sight motion of a hard target can be derived from range calculations: Doppler shift may not be measured and a spectrometer is not a mandatory component of the receiver. However pulse duration introduces uncertainty in time of flight. For distant objects such as space assets or space debris monitored with LIDAR from the ground, high power transmitters are necessary. Accompanying a ramp up to higher energy pulses is longer pulse duration, decreasing range and velocity resolution [19].
With FMCW LIDAR, Doppler frequency shift and relative phase between incoming and outgoing signals is measured by the receiver to determine motion and range. Coherent detection FMCW LIDAR measures velocity and range without signal depletion, nor is it hampered by background light. It also can be made compact, down to chip scale LIDAR [20]. The disadvantage of coherence detection used in LIDAR is coherence distance limitations [21]. FMCW LIDAR also has superior range/velocity accuracy and resolution compared to pulsed LIDAR [22]. This provides incentive to measure light frequency for use in FMCW LIDAR by direct detection for long range applications, if it can be accomplished with minimal signal depletion.
Magnetic field induced birefringence in paramagnetic vapors provides opportunity to measure frequency with minimal loss because dispersion can be utilized that is adjacent to absorption. Atomic absorption line Faraday filters utilize dispersion in the frequency region between Zeeman split absorption lines, where dispersion from each line contributes to rotation. An instrument composed of dual atomic absorption line Faraday filters has been used as a spectrometer [23]. Other foreknown absorption line Faraday spectrometers [24] without absorption utilize dispersion varying with frequency from split absorption lines, but the frequency region where they are capable of measuring frequency without absorbing signal is outside the split lines instead of between them. In that frequency region outside the split lines, dispersion and rotation is manifested primarily from only the closest line. To create a higher resolution spectrometer, the variation of dispersion with frequency needs to be steeper. Just as absorption line Faraday filters benefit from dispersion from two split absorption lines, a spectrometer can benefit from dispersion from two lines as well [25]. A tandem vapor cell spectrometer is demonstrated below with high absolute transmission and adjustable frequency operating range/resolution. A matching optical filter for daylight background blocking is also presented.
2. Theory
Faraday rotation optical filters and spectrometers both implement birefringence but in a different manner to accomplish their respective functions. The optical filter consists of a birefringent medium in between crossed polarizers. A narrow frequency pass-band of light, that may be intentionally polarized to pass through the first polarizer, is rotated 90 degrees in a birefringent medium so that it will pass through the second polarizer. All other light outside the pass-band is blocked by the crossed polarizers. The optical spectrometer is comprised of a birefringent region that changes rapidly with frequency. Frequency is then determined from the amount light polarization is rotated.
Rather than use index of refraction which is typically associated with birefringence, the electric susceptibility is used to describe dispersion and absorption. The relationship between the complex index of refraction n, and the susceptibility is [26]:
To create a birefringent medium a magnetic field is applied to a paramagnetic vapor. By the Zeeman effect [27,28], a longitudinal magnetic field will split and frequency shift a single absorption line of alkali metal vapors into two lines, where each line allows absorption of circular polarized light, but of opposite polarization from the other. The frequency region between lines that absorb light of opposite polarization are utilized in optical filters. While the frequency region between lines that absorb light of the same polarization is utilized in the optical spectrometer. Hypothetical examples of susceptibility for the spectrometer are shown in Fig. 1, and filter in Fig. 2. Note that in Figs. 1 & 2 the susceptibility is dimensionless and that frequency is scale is arbitrary. Also note that alkali metal atomic vapors exhibit hyperfine splitting of absorption lines corresponding to ground states of different energy. The cesium D2 absorption lines are separated by 9.2 GHz [28], far enough away from each other that the instruments constructed here were manifested by manipulating just one of the lines without being influenced by the other line.
Fig. 1. Hypothetical susceptibility curves of light passing through two vapor cells sequentially with distinct applied magnetic fields pointing in the same direction acting upon a single absorption line. It shows a region of rapidly-changing difference in the real portion of susceptibility (χ’+)–(χ’-), leading to rapidly changing birefringence as used in optical spectrometer.
Fig. 2. Hypothetical susceptibility curves of light passing through two vapor cells sequentially with distinct applied magnetic fields pointing in opposite direction. The difference in the real portion of susceptibility, (χ’+) – (χ’-), induces polarization rotation for filtering in the frequency region that is coincident with the optical spectrometer.
To build a spectrometer where two lines work together, tandem cells are employed. Consider light passing through two cesium vapor cells sequentially, each having longitudinal magnetic fields applied but of different magnitudes. Two distinct split absorption lines will be manifested from the single absorption line. Magnetic fields pointing in the same direction will induce equivalent susceptibility similar to that shown in Fig. 1. In the region between the small and large line frequency shifts of Fig. 1, susceptibility and birefringence changes rapidly. After propagating through the rapidly-changing birefringent medium, the light is transmitted through a polarizer. The polarizer, oriented at 45 degrees relative to initial polarization, measures light polarization to infer frequency.
Because the frequency range of operation of the spectrometer is displaced away from the center of the absorption line, the transmission spectrum of a traditional atomic line Faraday optical filter may not align with the spectrometer spectrum. An optical filter with a transmission range that coincides with the spectrometer range can be constructed with tandem cells having opposing magnetic fields with equivalent susceptibility as shown in Fig. 2.
3. Experimental results
The experimental setup and resulting spectra of the tandem vapor cell spectrometer and filter is shown in Figs. 3 –5. The spectrometer spectrum of Fig. 4 shows polarization rotation that rapidly changes with frequency without absorption loss in bold. Frequency as measured by the polarizer is determined from the difference divided by the sum of the two outputs. Frequency resolution and operating range have an inverse relationship and are managed by choice of magnetic fields, cell length and temperature. The parameters were selected to produce spectra features that can be easily interpreted. Much higher spectral resolution is possible. The spectrum produced by the tandem cell filter with high transmission region shifted away from line center is shown in Fig. 5.
Fig. 3. Experimental setup. The filter polarizers are in crossed orientation. The spectrometer polarizer is oriented at 45 degrees relative to initial input light polarization.
Fig. 4. Tandem vapor cell optical spectrometer relative transmission spectrum: range of operation in bold. Frequency is determined from the difference divided by the sum of the two outputs. The dotted line is sum of transmission curves and shows atomic absorption. The range of operation is 0.88 GHz or 375 m/sec in terms of (LIDAR) velocity. Note that for LIDAR, light is Doppler shifted twice, on outbound and return. Multiplication of the spectra by a factor of 89.4% yields absolute transmission.
Fig. 5. Twin vapor cell optical filter relative transmission spectrum is shown in solid. Dotted line is sum of transmitted and rejected (2nd polarizer) light and shows atomic absorption. Multiplication of the spectra by a factor 86.7% yields absolute transmission.
There is another way to build an optical filter that has a transmission spectrum that coincides with the spectrometer. A traditional atomic line Faraday filter has a three lob transmission spectrum. Increasing the absorption and rotation of the light by increasing temperature can reduce the center lob transmission (by a combination of absorption and exceeding 90 degrees rotation) and increase the outer lob transmission. This was accomplished and shown in Fig. 6.
Fig. 6. Single vapor cell (conventional) optical filter relative transmission spectrum is shown in solid. Dotted line is the sum of transmitted and rejected light and shows atomic absorption. The absolute transmission factor is 93%.
It can be seen in the spectra shown in Fig. 4 and Fig. 5 that there is line broadening in the upshifted lines compared to the downshifted lines. Under influence of the longitudinal magnetic field, degeneracy of the magnetic field quantum numbers (MJ electronic and MI nucleus) is ceased and there are distinct energy levels for each quantum number. Some absorption lines are broadened while some lines are not, depending upon if the magnetic quantum number energy levels between allowed transitions shift in unison or shift opposed. For these instruments, the chosen line had minimal broadening. This effect is shown graphically with rubidium in Ref. [27]. The allowed transitions from the ground states of cesium are:
Below are some specifics on the components and experiment. The light source used to generate the experimental results is a linear polarized, free space DBR (Distributed Bragg Reflection) laser manufactured by Photodigm [29]. To avoid saturation, an ND2 filter was used to reduce the power down to ∼1 mW. Table 1 shows the specifications of each instrument. Each cesium cell is anti-reflection coated on both internal and external surfaces. The magnetic fields were generated with neodymium block magnets arranged cylindrically around the vapor cells. The strong magnetic field strength was beyond the measurement capability of the Hall Effect sensor used for measurement so the field strength was estimated from the spectra. Measured magnetic field strength varied about 10% over the length of the cells. The passive transmission through the optic elements shown in Table 1 was measured with polarizers oriented to transmit linear polarized light, and with frequency away from resonance. Vapor cell temperature was chosen so that polarization rotation from each cell was somewhat balanced.
Table 1. Instrument Parameters Magnetic Field B (Gauss) Temperature T (C) Cell Length L (mm)
The 25 mm cell length is reasonable for some applications, but it may be desirable to reduce cell length further. Note that rotation is linearly dependent upon both cell length and the difference in susceptibility. Cell length reduction can be achieved by increasing susceptibility. The susceptibility is proportional to the number density of atoms [26]. Steck [28] shows a chart of cesium vapor pressure (and number density by use of ideal gas law) versus temperature rising exponentially, a decade between 75C and 110C. The leeway between temperatures used here and maximum manufacturer recommended vapor cell temperature of 120C allows for reducing the cell length by several factors. Also, because of the exponential rise in number density with temperature and the steepness of the susceptibility curves, the instrument spectra are sensitive to temperature fluctuations.
4. Applications
Among possible applications of the spectrometer and filter combination is use in LIDAR for tracking space debris from the ground. Situational awareness in space was declared inadequate in Presidential Space Directive 3 of 2018 [30] due primarily to limitations of current observation technology. New instrumentation is needed to overcome gaps in space situational awareness. RADAR, LIDAR and passive telescopes are each ground deployed instruments that are important for space observation. RADAR is an instrument with broad transmitter beam and broad field of view. LIDAR has a narrow transmitter beam and narrow field of view with the potential to detect smaller objects at greater distance compared to RADAR [31]. Despite LIDAR potential, its utilization is largely neglected.
The spectrometer demonstrated here can measure Doppler shift from a stationary frequency transmitter. If the transmitter is operated FMCW (Frequency Modulated Continuous Wave) both range and velocity can be measured. When coupled to the optical filter, measurement can be made with daylight background present. A transmitter could be composed of an FM modulated seed laser coupled to an array of tapered diode amplifiers. A tapered diode amplifier producing nine Watts of continuous wave power at 852 nm has been reported with a ceiling reached with the power measuring apparatus, not laser power [32]. Five Watt continuous wave tapered diode amplifiers are available commercially. For comparison, EOS space systems short pulse duration (10-20 pico-sec) doubled Nd:YAG transmitter used in LIDAR for ranging of space objects has a maximum average power of 2 Watts [19].
Another opportunity may arise from a spectrometer/filter combination using rubidium vapor and the D2 line at 780 nm. Forty-three Watts of continuous wave light at 780 nm has been demonstrated [33]. Built from doubling two 1560 nm fiber lasers, it has the attributes of fast tuning and narrow line width appropriate for FMCW LIDAR. Those authors also propound that power could probably be ramped up to over 100 Watts with additional pumping.
Another application is free space optical communication. The optical spectrometer can be used as demodulator for direct detection FSK (Frequency Shift Keying) free space optical communication. A transmitter could be seeded and frequency modulated by an electro-optic tuned DBR laser [34], also called ECDL (External Cavity Diode) laser. Hypothetical FSK can be compared to coherent detection BPSK (Binary Phase Shift Keying) encoding. Both BPSK and direct detection (Binary) FSK have one degree of freedom per polarization [35]. Since both the BPSK system and a hypothetical direct detection FSK system as promoted here are modulated using the electro-optic (Pockels) effect, it could be expected that they could achieve close to the same data transmission rates. While not feasible for ranges sought for space debris LIDAR, coherence detection has been demonstrated for satellite to ground free space optical communication. A downlink from a low earth orbit satellite to ground demonstrated a data rate of 5.6 Gbt/s [36] using BPSK encoding.
Faster communication rates are anticipated from coherent detection. QPSK (Quadrature Phase Shift Keying) has two degrees of freedom per polarization [35]. QPSK modulation and Orbital Angular Momentum (AOM) multiplexing have been implemented together with a data capacity of 80 Gbt/s between the ground and a drone [37]. While probably not competitive with coherent detection for low earth orbit and inter-satellite communication, there may be other applications for direct detection FSK using the spectrometer introduced here.
Direct detection FSK can contend with turbulent atmospheric conditions better than coherent detection. Atmospheric turbulence causes phase distortion and the position of the incoming signal beam to wander. In coherent detection, electric field mixing requires the fields of the signal beam and local oscillator to be spatially coincident. Adaptive optics [38] has been employed to mitigate turbulence effects but it remains a problem diminishing data rates. Another complication for optical communication between ground and space is that the turbulent portion of the path occurs near the end of travel for downlink, but near the beginning of travel on uplink; consequently uplink beam deviation is larger than downlink deviation. Direct detection FSK is not as constrained by beam wander and not at all by coherence. Multiplexed into other optical channels, a direct detection FSK channel can serve as a pointing beacon and guide star for adaptive optics. Direct detection FSK may be a viable option for communication between satellites and remote/temporary low elevation locations where there is may be greater turbulent effects and also more aerosol particles. An example would be the marine layer where scintillation from fog can disrupt beam coherence. Direct detection FSK may also be considered for optical communication between earth and spacecraft beyond low earth orbit.
Depending upon the wavelength of transmitter light, Doppler shift between two satellites can be as high as + -7 GHz [39]. Doppler shift is doubled for LIDAR applications as the shift happens on outgoing and incoming legs of the journey. Despite huge Doppler shifts, it is expected that this spectrometer would be implemented in high resolution, narrow operating range configuration. This is because it is assumed that the velocity of space debris tracked with LIDAR is somewhat predictable. The frequency of the transmitter light is adjusted to compensate for predicted Doppler shift. In free space optical communication with relative motion, both FSK and QPSK require Doppler compensation. For QPSK the local oscillator of the homodyne detection laser is tuned to a predicted Doppler shift with optical Phase Locked Loop (PLL) circuitry to eliminate residual error [40].
To gauge the amount of residual velocity error that can be expected to be encountered, comparison can be made with satellite radio communication. Communication between satellites in low earth orbit and the ground using radio frequency at 2.4 GHz with Doppler compensation derived from predicted trajectory has a Doppler shift error of around 250 Hz [41]. Doppler shift is inversely proportional to wavelength and applying the same error in predicted relative velocity to 852 nm would yield a Doppler error of around + -20 MHz. With tuning of the transmitter to predicted Doppler shift, the spectrometer should be able to tolerate Doppler error without further compensation. Another possibility is shifting the transmission of the spectrometer/filter with electromagnets to correct error.
5. Conclusion
A simple, passive, minimal loss optical spectrometer for measuring frequency at Doppler shift resolution has been demonstrated. Also demonstrated is an optical filter with a pass-band that coincides with spectrometer to remove background light. With free parameters of paramagnetic vapor, temperature, cell length and magnetic field strength, these instruments have lot of versatility albeit with limited lines.
Disclosures
The author declares that there are 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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