Far Off-Resonance Laser Frequency Stabilization Technology

applied sciences

Review Far Oﬀ-Resonance Laser Frequency Stabilization Technology

Chang Liu 1 , Ziqian Yue 1, Zitong Xu 1,* , Ming Ding 2,3 and Yueyang Zhai 2,3,*

1 School of Instrumentation and Optoelectronics Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China; [email protected] (C.L.); [email protected] (Z.Y.) 2 Research Institute for Frontier Science, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100083, China; [email protected] 3 ZHEJIANG LAB, Building 10, China Artiﬁcial Intelligence Town, 1818 Wenyi West Road, Hangzhou 310000, China * Correspondence: [email protected] (Z.X.); [email protected] (Y.Z.)

Received: 15 April 2020; Accepted: 4 May 2020; Published: 7 May 2020

Abstract: In atomic physics experiments, a frequency-stabilized or ‘locked’ laser source is commonly required. Many established techniques are available for locking close to an atomic resonance. However, in many instances, such as atomic magnetometer and magic wavelength optical lattices in ultra-cold atoms, it is desirable to lock the frequency of the laser far away from the resonance. This review presents several far oﬀ-resonance laser frequency stabilization methods, by which the frequency of the probe beam can be locked on the detuning as far as several tens of gigahertz (GHz) away from atomic resonance line, and discusses existing challenges and possible future directions in this ﬁeld.

Keywords: laser; far oﬀ-resonance; frequency stabilization

1. Introduction In 1958, Townes and Schawlow took the first step on the road to the laser by establishing general physical conditions for light amplification by the stimulated emission of radiation (LASER) [1]. In the 1960s, Theodore H. Maiman ushered in a new age by crossing the threshold of laser oscillation and demonstrated the construction of the world’s first laser [2]. Since then, different types of lasers and laser control technologies have been developed rapidly. Frequency stabilization is an important indicator of lasers, as it is required for high precision. Frequency-stable laser sources are central to several applications, such as gravitational wave detection [3], low-phase-noise microwave generation [4], precision spectroscopy [5], and quantum computation [6]. The essence of frequency stabilization is to maintain the stability of the optical path length of the resonant cavity. Based on the dependence of frequency stabilization on an external reference frequency source, frequency stabilization is divided into passive frequency stabilization and active frequency stabilization. Passive frequency stabilization refers to the maintenance of the cavity length to stabilize the laser frequency by controlling temperature, using complementary cavity materials, and vibration isolation. With poor reproducibility, lasers operating in the passive frequency stabilization mode are generally used in situations where the frequency stabilization and accuracy are not too high. In contrast, active frequency stabilization refers to the selection of a stable frequency reference point. The frequency discriminator provides an error signal when the frequency of the laser deviates from the reference frequency. Then the error signal is fed back into the laser system using the servo system in order to achieve stability. Generally, there are two purposes for locking laser frequency to reference according to the applications. Improving the short-term stability of the laser suppressing the phase noise and

Appl. Sci. 2020, 10, 3255; doi:10.3390/app10093255 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 3255 2 of 15 reducing the linewidth is one of the two aims. The other is to obtain long-term stability calibrating the frequency of the laser. Notably, many established active frequency stabilization techniques are available for locking close to an atomic resonance, including frequency-modulation spectroscopy [7], saturated absorption spectroscopy [8], polarization spectroscopy [9], dichroic atomic vapor laser locking (DAVLL) [10], and Sagnac interferometry [11]. Light-atomic interactions offer grand promise for broad range of applications, such as atomic magnetometer [12], cold atoms [13], atomic gyroscopes [14], and other precision measurement and metrology; however, sometimes the frequency of the probe beam should be locked on the detuning as far as several tens of gigahertz away from atomic resonance line. Unfortunately, frequency stabilization at such a large detuning cannot be achieved via the above-mentioned methods. For several applications, highly stable Fabry–Pérot (F–P) cavity is selected as the reference. F–P cavities and similar resonant optical cavities exhibit excellent frequency discrimination performance, and thus are widely used for the frequency stabilization and tuning of lasers. Common resonant optical cavity-based frequency stabilization techniques include Pound–Drever–Hall (PDH) technique [15–17] and tilt-locking [18–20]. Moreover, a laser locking technique based on the transfer of the frequency stability from an F–P cavity is useful for applications that require stabilization of lasers at a large-detuned atomic-reference frequency [21]. Like a one-step reduction gear, the optical frequency combs can connect optically to different frequencies. Based on this, frequency transfer using optical frequency combs is also an excellent method for far off-resonance laser stabilization. Recently, the Faraday effect was used for the stabilization of a laser frequency at large detuning from the atomic reference line [22]. It seems feasible to monitor the wavelength in real time using a wavelength meter for far off-resonance laser frequency stabilization. However, the low frequency stability and the high cost of the wavelength meter seriously limit the practical application of this method. This review presents comprehensively the far off-resonance laser frequency stabilization technologies. The remaining part of the review is structured as follows: Section2 reveals principles and applications of PDH technique. Section3 discusses large detuning laser frequency stabilization by using the Faraday effect. In Section4, far o ff-resonance frequency locking systems based on transfer cavity are presented. Conclusions and outlook are presented in Section5.

2. Far Off-Resonance Laser Frequency Stabilization by Pound–Drever–Hall Technique In 1946, R. V. Pound first reported that microwave oscillators successfully derived stabilization of their frequency from a resonant cavity [23]. In 1983, after Pound’s studies on radio frequency microwave stabilizer, Drever et al. first locked a dye laser and gas laser onto a stable F–P reference interferometer, and jet stream dye lasers could achieve sub-100 Hz linewidth [24]. Subsequently this technique was called Pound–Drever–Hall (PDH) technique. The PDH technique is based on signals reflected from a stable F–P cavity. A schematic illustration of the PDH technique is presented in Figure1. A laser beam, the electric field of which is given iωt by E = E0e , is phase-modulated using an electro–optic modulator (EOM) with a phase modulation frequency of Ω at local oscillator (LO) range and a depth of β. After the beam passes through this EOM, its electric field is given by E = E ei[ωt+β sin (Ωt)]. When β < 1, the electric field can be simplified 0 0 i as E = E [J β)eiωt + J (β)ei(ω+Ω)t J (β)ei(ω Ω)t with Bessel functions [15,25]. This indicates the 0 0 0 1 − 1 − existence of actually three different beams being incident on the cavity: a carrier, with frequency ω; and two sidebands with frequencies ω Ω. Further, the modulated light is incident into an F–P cavity, ± and the reflected beam from the F–P cavity is sent into a photodetector using a polarizing beam splitter (PBS) and a quarter wave plate (λ/4). Output of photodetector is compared with the signal of LO via a mixer. The mixer’s output contains signals at both direct current (or very low frequency) and twice the modulation frequency. After passing through a low-pass filter, the frequency discrimination signal (the PDH signal) is obtained as ε = 2 √PcPsIm[F(ω)F (ω + Ω) F (ω)F(ω Ω)][15,25], which then passes ∗ − ∗ − through a servo and into the tuning port on the laser, thus locking the laser to the cavity. Appl.Appl. Sci. 2020,, 10,, 3255x 33 ofof 1514

PBS λ/4 FP Cavity

Laser EOM

Local Oscillator Servo Phase Photodetector Shifter

Low-pass filter Mixer

Figure 1. Schematic illustration of the PDH technique. PDH: Pound–Drever–Hall; EOM: electro–optic modulator;Figure 1. Schematic PBS: polarizing illustration beam of splitter;the PDHλ /technique.4: quarter PDH: wave Pound–Drever–Hall; plate; and F–P: Fabry–P EOM:érot. electro–optic modulator; PBS: polarizing beam splitter; /4: quarter wave plate; and F–P: Fabry–Pérot. In 1984, Hough et al. mounted the cavity in a cradle on a 5-wire pendulum suspension to minimize vibrationalIn 1984, disturbances Hough et andal. lockedmounted a ring the dye cavity laser in to thisa cradle independent on a 5-wire cavity pendulum [26]. By heterodyning suspension the to lightminimize from twovibrational such independent disturbances systems and locked and studying a ring thedye fluctuations laser to this in independent the resulting cavity beat frequency [26]. By spectrum,heterodyning single the laser light linewidths from two of thesuch order independen of 750 Hzt weresystems successfully and studying achieved the and fluctuations this corresponds in the to a standard Allan variance of about 2.2 10 13 with integration time of 1 s. Furthermore, they also resulting beat frequency spectrum, single× laser− linewidths of the order of 750 Hz were successfully investigatedachieved and a this number corresponds of other to sources a standard of noise Allan such variance as residual of about optical 2.2 feedback × 10 with from integration laser light scatteredtime of 1 ors. Furthermore, reflected back they into also the cavities investigated using a external number optical of other components. sources of noise such as residual opticalIn 1992,feedback Day etfrom al. lockedlaser light two-diode scattered laser-pumped or reflected Nd:YAG back into lasers the tocavities an F–P using interferometer external optical with a finessecomponents. of 27,500, yielding a robust and easily repeatable beat note linewidth of 700 mHz [27]. InIn 1999,1992, YoungDay et etal. al.locked at the two-di Nationalode Institutelaser-pumped of Standards Nd:YAG and lasers Technology to an F–P (NIST) interferometer narrowed with the linewidtha finesse of of 27,500, a 563 nm yielding laser beam a robust to 0.6 and Hz easily by the repeatable PDH technique. beat note The linewidth fractional of frequency 700 mHz instability[27]. for the light locked to the cavity was found to be 3 10 16 at 1 s [28]. The performance of the previous In 1999, Young et al. at the National Institute ×of Standards− and Technology (NIST) narrowed the studylinewidth on narrow-linewidth of a 563 nm laser beam lasers to was 0.6 limited Hz by th bye lengthPDH technique. instability The of optical fractional reference frequency cavities instability due to imperfect vibration isolation. Young et al. isolated the high-finesse ( > 150, 000) F–P cavity, where the for the light locked to the cavity was found to be 3×10 at F1 s [28]. The performance of the spacerprevious between study theon cavitynarrow-linewidth mirrors was composedlasers was of limited a low-thermal-expansion by length instability material. of optical The cavity reference was protectedcavities due from to vibrationalimperfect vibration noise by mountingisolation. Young it on an et aluminum al. isolated v-block the high-finesse inside an evacuated (ℱ > 150,000 chamber.) F–P Thecavity, vacuum where chamber the spacer was between mounted the on cavity a passively mirrors isolated was composed optical table of whicha low-thermal-expansion was suspended by verticalmaterial. strands The cavity of surgical was protected tubing stretched from vibrational to ~3 m. The noise method by mounting for vibration it on reduction an aluminum was complex v-block andinside thus an hardevacuated to realize. chamber. In 2004, The Webster vacuum et chamber al. at National was mounted Physical on Laboratory a passively (NPL) isolated placed optical an opticaltable which reference was cavitysuspended on an by active vertical vibration strands isolation of surgical platform tubing to reducestretched external to ~3 vibrationm. The method noise [ 29for]. Thevibration laser lockedreduction by thewas PDH complex technique and thus achieved hard to sub-hertz realize. In linewidth 2004, Webster and relative et al. at frequency National Physical stability 15 ofLaboratory10− level (NPL) at 5 s. placed Since then, an optical commercially reference passive cavity or on active an vibrationactive vibration isolation isolation platforms platform have been to adoptedreduce external for vibration vibration reduction noise [ 30[29].–32 ].The laser locked by the PDH technique achieved sub-hertz linewidthNotcutt and et relative al. introduced frequency the stability first vibration-insensitive of 10 level at 5 opticals. Since cavity then, commercially at the Joint Institute passive for or Laboratoryactive vibration Astrophysics isolation (JILA) platforms in 2005 have [33 ].been Figure adopted2 shows for that vibration it is a vertically-oriented reduction [30–32]. low-expansion glassNotcutt cavity, andet al. the introduced cavity support the first points vibration-insensitive are arranged to beoptical in the cavity symmetry at the plane Joint betweenInstitute thefor twoLaboratory mirrors Astrophysics on the cavity (JILA) ends. Noteworthy,in 2005 [33]. thisFigure design 2 shows takes thethat advantage it is a vertically-oriented of potential constant low- lengthexpansion distance glass betweencavity, and the the two cavity mirrors support by setting points the are optical arranged axis alongto be thein the direction symmetry of gravity. plane Thebetween acceleration the two alongmirrors the on direction the cavity of gravityends. Notewort causes thehy, compression this design takes of the the upper advantage part accompanied of potential byconstant stretch length of the lowerdistance part, between which resultsthe two in mirrors an unchanged by setting length the ofoptical the optical axis along cavity. the The direction associated of reductiongravity. The of theacceleration vibration along sensitivity the direction of the eff ectiveof gravity cavity causes length th resultede compression in a simple of the and upper compact part referenceaccompanied cavity by system stretch for of laserthe lower stabilization part, which at the results level of in 1 an Hz unchanged linewidth. Ludlowlength of et the al. atoptical JILA lockedcavity. aThe diode associated laser to reduction the thermal-noise-limited of the vibration passivesensitivity optical of the cavity effective in vertical cavity mountinglength resulted configuration in a simple by PDHand compact technique reference [31]. When cavity the system resolution for laser band stabiliz widthation (RBW) at was the reducedlevel of 1 to Hz 150 linewidth. mHz, linewidths Ludlow ofet 220al. at mHz JILA could locked be a observed diode laser with to non-negligiblethe thermal-noise-limited power in low-frequency passive optical noise cavity sidebands. in vertical Based mounting on the designconfiguration concept by of PDH the vibration-insensitive technique [31]. When optical the re cavity,solution horizontally-oriented band width (RBW) vibration-insensitive was reduced to 150 mHz, linewidths of 220 mHz could be observed with non-negligible power in low-frequency noise Appl. Sci. 2020,, 10,, x 3255 4 of 14 15 sidebands. Based on the design concept of the vibration-insensitive optical cavity, horizontally- orientedoptical cavities vibration-insensitive were also designed optical similarly cavities throughwere also numerically designed similarly simulations through by finite-element numerically simulationsanalysis [34 –by36 ].finite-element analysis [34–36].

FigureFigure 2. 2.SchematicSchematic of ofa vertical a vertical vibration-insensitive vibration-insensitive optical optical cavity. cavity. (Figure (Figure reproduced reproduced from [33].) from [33]).

High frequency-stabilized, narrow-linewidth lasers have been constructed by PDH technique to lock thethe laserlaser frequencies frequencies to to the the resonance resonance of referenceof reference cavities. cavities. The frequencyThe frequency stability stability of a laser of a which laser whichis locked is locked to a reference to a reference cavity iscavi dominatedty is dominated by the by eff ectivethe effective length length stability stability of the referenceof the reference cavity. Tocavity. maintain To maintain the stability the stability of the cavity of the length, cavity glasslength, or glass single or crystal single silicon crystal with silicon ultra-low with ultra-low thermal thermalexpansion expansion coefficient coefficient (ULE), vacuum (ULE), chambersvacuum chambe with highrs with temperature high temperature stability, specialstability, geometry, special geometry,and mounting and configurationsmounting con forfigurations reference for cavities reference were cavities developed were for developed less sensitivity for less to vibrationsensitivity and to vibrationtemperature and fluctuation temperature [32 fl,37uctuation–40]. [32,37–40]. Thermal noisenoise arisesarises from from the the Brownian Brownian motion, motion which, which can becan naturally be naturally reduced reduced by cooling by cooling optical opticalcavities cavities to cryogenic to cryogenic temperature. temp Anerature. optical An cavity optical supported cavity insupported a vibration-insensitive in a vibration-insensitive configuration wasconfi designedguration bywas Physikalisch-Technische designed by Physikalisch-Technisc Bundesanstalthe (PTB) Bundesanstalt and JILA. The(PTB) cavity and spacerJILA. The and mirrorcavity spacersubstrates and made mirror of single-crystalsubstrates made silicon of single-crystal were cooled to silicon 124 K [were41]. The cooled thermal-noise-limited to 124 K [41]. The frequency thermal- noise-limitedinstability was frequency estimated instability to be around was7 estimated10 17. With to be vibration-insensitive around 7×10. configuration With vibration-insensitive for the optical × − concavity,figuration a laser atfor1.5 theµ mopticalwas lockedcavity, toa laser the optical at 1.5 cavity, was resulting locked to in athe linewidth optical cavity, of less resulting than 40 mHz in a linewidthand a fractional of less frequencythan 40 mHz instability and a fractional of 1 10 frequency16 at short instability timescales of in 1×10 2012. In 2017, at short the individualtimescales × − inlaser 2012. linewidth In 2017, obtained the individual from the laser phase linewidth noise spectrum obtained or from the directthe phase beat noise note betweenspectrum the or twothe direct lasers wasbeat asnote small between as 5 mHz the two at 194 lasers THz was [42 ].as small as 5 mHz at 194 THz [42]. In PDH technology, a laser is usually locked to the the F–P F–P cavity. cavity. With With a a very very narrow narrow cavity cavity mode, mode, the high-finessehigh-finesse cavitycavity can can reduce reduce the the linewidth, linewidth, suppress suppress the the phase phase noise, noise, and and improve improve the short-termthe short- termstability stability of the of laser.the laser. Narrow-linewidth Narrow-linewidth lasers lasers achieved achieved by by the the PDH PDH locking locking technique technique areare central to precision spectroscopy, opticaloptical atomic clocks, gravitational wave detection, and tests involving fundamental physics. Longsheng Longsheng Ma’s Ma’s group group at at th thee East China Normal University is committed to the research on narrow-linewidth laserslasers and has made some progress [[43–45].43–45]. PDH technology is not only widely used in the field field of narrow-linewidth la lasers,sers, but also in various types of quantum optical experimental systems [[46,47].46,47]. The PDH technology offers offers the advantages such as flexibleflexible frequency stabilization range, high frequency stabilization accuracy, accuracy, narrow linewidth, and and high high stability. stability. However, However, vibration vibration isolation, isolation, special structural design, and mounting con configurationsfigurations of of reference cavities for less sensitivity to environmental vibration,vibration, the the increase increase in in the the length length of theof referencethe reference cavity, cavity, glass orglass single or single crystal crystal silicon withsilicon ULE, with cryogenic ULE, cryogenic cooling, coolin andg, vacuum and vacuum chambers chambers with with high high temperature temperature stability stability to reduce to reduce the thethermal thermal noise noise limit limit increase increase the costthe co andst and diffi difficultyculty of the of experiment.the experiment.

3. Far Off-Resonance Laser Frequency Stabilization by Using the Faraday Effect In 1845, Faraday added a piece of glass consisting of a pair of magnetic poles, and interestingly found that the polarization plane of the incident light in the direction of the applied magnetic field Appl. Sci. 2020, 10, 3255 5 of 15

3. Far Off-Resonance Laser Frequency Stabilization by Using the Faraday Effect In 1845, Faraday added a piece of glass consisting of a pair of magnetic poles, and interestingly Appl. Sci. 2020, 10, x 5 of 14 found that the polarization plane of the incident light in the direction of the applied magnetic field was transmitted through the glass. This phenomenon was later called the Faraday effect [48]. The Faraday was transmitted through the glass. This phenomenon was later called the Faraday effect [48]. The effect is a magneto-optical phenomenon, in which an electromagnetic wave propagates through a Faraday effect is a magneto-optical phenomenon, in which an electromagnetic wave propagates medium and gets affected by the presence of quasi-static magnetic field. This effect can be exploited through a medium and gets affected by the presence of quasi-static magnetic field. This effect can be in alkaliexploited metal in media.alkali metal As Figure media.3 shows, As Figure when 3 shows, a heated when alkali a heated metal vaporalkali metal cell is vapor placed cell in anis placed axial in magnetican axial field, magnetic the magnetic field, the field magnetic causes field the atoms causes to the undergo atoms Zeemanto undergo splitting. Zeeman The splitting. atomsrespond The atoms diffresponderently to differently left and right to left circularly and right polarized circularly components polarized of components the linearly polarized of the linearly light, whichpolarized results light, in awhich rotation results of linearly in a rotation polarized of linearly light entering polarized the light cell. entering The rotation the cell. angle The of rota thetion linear angle polarization of the linear planepolarization changes with plane the changes laser frequency. with the laser frequency. B

Linearly polarized light Rotation angle θ θ

A heated alkali metal vapor cell

Figure 3. Rotation of polarization plane of light, as it travels through a heated alkali metal vapor cell placedFigure in a 3. magnetic Rotation field. of polarization plane of light, as it travels through a heated alkali metal vapor cell placed in a magnetic field. We can use the phenomenon described above to stabilize the laser frequency on the large detuning away fromWe thecan resonance.use the phenomenon Here is a brief described description. above When to stabilize the Faraday the laser effect frequency occurs in on the the alkali large metaldetuning vapor cell.away There from is the rotation resonance. of linearly Here polarizedis a brief description. light in the central When frequencythe Faraday band effect of theoccurs atomic in the resonancealkali metal region, vapor but thecell incident. There lightis rotation cannot of finally linearly pass polarized through light the gas in cellthe duecentral to strong frequency resonance band of absorption.the atomic However, resonance in theregion, frequency but the band incident far away ligh fromt cannot resonance, finally therepass through is both light the rotationgas cell anddue to incompletestrong resonance absorption. absorption. We can obtain However, these in transmitted the frequency lights band with far di awayfferent from frequencies resonance, through there is the both designlight of rotation the optical and path. incomplete The peak absorption. points of these We can transmitted obtain these light signalstransmitted are always lights based with ondifferent the frequencyfrequencies of the through atomic the transition design line,of the which optical can path. be used The aspeak a stable points reference. of these transmitted We can lock light the laser signals frequencyare always to these based transmission on the frequency peak frequencies of the atomic away from transition the resonance line, which region. can Moreover, be used whenas a thestable strengthreference. of the We axial can magnetic lock the fieldlaser or frequency the temperature to these of transmission the gas chamber peak increase, frequencies the transmissionaway from the peakresonance will be fartherregion. awayMoreover, from when the atomic the strength transition of th line,e axial which magnetic means field the detuningor the temperature will increase. of the Basedgas onchamber the above increase, principles, the transmission far off-resonance peak laser will frequency be farther stabilization away from can the be atomic achieved transition by using line, thewhich Faraday means effect the in thedetuning alkali metal will vaporincrease. cell. Based on the above principles, far off-resonance laser frequencyIn 2009, stabilization Siddons et al. can studied be achieved and analyzed by using the Faraday off-resonance effect absorptionin the alkali and metal dispersion vapor cell. of Doppler-broadenedIn 2009, Siddons atomic et mediaal. studied and madeand analyzed approximate the off-resonance calculations toabsorption the electric and susceptibility dispersion of of atomicDoppler-broadened media [49]. Onatomic the media large detuningand made away approximate from the calculations resonance, to the the relative electric absorption susceptibility of of dispersionatomic media dominates [49]. theOn atom–lightthe large detuning interaction away [50]. fr Inom 2011, the Kempresonance, et al. the proposed relative an absorption analytical of modeldispersion of off-resonant dominates Faraday the atom–light rotation in interaction hot alkali metal[50]. In vapors 2011, [51Kemp]. The et faral. oproposedff-resonant an Faraday analytical rotationmodel angle of off-resonant can be determined Faraday rotati by usingon in the hot temperature alkali metal ofvapors the cell [51]. and The the far optical off-resonant path length. Faraday Androtation they proposed angle can a simplebe determined model to by predict using the the detuning temperature of the of locking the cell points. and the optical path length. AndFurthermore, they proposed in 2011, a simple Marchant model et to al. pred proposedict the detuning a simple of technique the locking for points. stabilization of a laser frequencyFurthermore, off resonance in 2011, by using Marchant the Faraday et al. proposed effect in aa heatedsimple rubidiumtechnique (Rb)for stabilization vapor cell with of a anlaser appliedfrequency magnetic off resonance field [52]. Theyby using used the the Faraday setup shown effect inin Figure a heated4 to rubidium produce the (Rb) Faraday vapor signal.cell with an applied magnetic field [52]. They used the setup shown in Figure 4 to produce the Faraday signal. Appl. Sci. 2020, 10, x 6 of 14 Appl. Sci. 2020, 10, x 6 of 14 Appl. Sci. 2020, 10, 3255 6 of 15

Wavemeter Wavemeter PD1 PD1

λ/2 B λ/2 B

Rb cell PBS1 PD2 PBS2 λ/2 Rb cell PBS1 PD2 PBS2 oven λ/2 oven

Locking 780nm servoLocking Laser780nm servo Laser FigureFigure 4. 4.ExperimentalExperimental setup. setup. PBS PBS:: polarizing polarizing beam beam splitter; splitter; /2λ/:2 half: half wave wave plate; plate; PD: PD: photo photo detector. detector. : (Figure(FigureFigure reproduced reproduced 4. Experimental from from [52].) setup. [52]). PBS polarizing beam splitter; /2: half wave plate; PD: photo detector. (Figure reproduced from [52].) InIn order order to to lock lock to to a azero zero crossing crossing in in the the Faraday Faraday signal, signal, they they used used a ahome-built home-built locking locking servo. servo. Finally,Finally,In they theyorder demonstrated demonstrated to lock to a zerostabilization stabilization crossing ofin of thea a780 780Faraday nm nm laser lasersignal, detuned detuned they usedup up to a to home-built14 14 GHz GHz from from locking the the 85 servo.85RbRb Finally, 2 they demonstrated2 stabilization of a 780 nm laser detuned up to 14 GHz from the 85Rb D 52 5/S1/=22F = 2toto 55P/3/2F0=3= 3 transition.transition. The The locking locking of of the the ~6–14 ~6–14 GHz GHz red red and and blue blue detuned detuned from from resonanceresonance 5 / can=2 can be beachieved to achieved 5 / by byadjusting=3 adjusting transition. the temperatur the The temperature lockinge of ofthe ofthe vapor the ~6–14 vapor cell GHz and cell red the and andmagnetic the blue magnetic detuned field. They field. from obtainedTheyresonance obtained a root can amean be root achieved meansquare square by (rms) adjusting (rms)fluctuation fluctuation the temperatur of 7 ofMHz 7 MHze ofover the over 1vapor h 1without h cell without and stabilization the stabilization magnetic of offield.the the cell They cell temperaturetemperatureobtained a or root or magnetic magnetic mean field.square field. (rms) fluctuation of 7 MHz over 1 h without stabilization of the cell temperatureInIn 2016, 2016, Quan Quan or magnetic et et al. al. proposed proposed field. a afar far off-resonance off-resonance laser laser frequency frequency stabilization stabilization method method by by using using multipassmultipassIn 2016,cells cells inQuan in Rb Rb Faradayet Faraday al. proposed rotation rotation a spectroscopyfar spectroscopy off-resonance [22]. [22 laser ].Figure Figure frequency 55 exhibits exhibits stabilization the the setup setup usedmethod used by by bythem, them, using demonstratingdemonstratingmultipass cells the the in far farRb off-resonance o Faradayff-resonance rotation frequency frequency spectroscopy stabiliz stabilizationation [22]. method. method.Figure 5A Aexhibits Rb Rb cell cell with the with setupa alength length used of of 50by 50 mm them, mm andanddemonstrating a adiameter diameter of of the25 25 mmfar mm off-resonance was was placed placed inside frequency inside a amagn magnet stabilizet with withation the the method. same same length. length.A Rb cell The The with plate plate a lengthbeam beam splitter of splitter 50 mm splitsplitand the thea lightdiameter light into into oftwo two 25 bunches. mm bunches. was The placed The optical optical inside path path a magnlength lengthet ofwith of the the thetransmitted transmitted same length. light light The was was plate L L == 50 beam50 mm mm splitterand and thatthatsplit of of thethe the reflectedlight reflected into light two light wasbunches. was about about The 2L 2L =optical= 100100 mm. mm.path Th Theylengthey used used of a the aservo servo transmitted controller controller light (model (model was of L of LB1005)= LB1005)50 mm to and to locklockthat to to ofthe the the zero zero reflected crossings crossings light in in wasthe the Faradayabout Faraday 2L signal. signal.= 100 mm. They used a servo controller (model of LB1005) to lock to the zero crossings in the Faraday signal.

B B Rb cell Rb cell

PBS1 PD1 BS λ/2 λ/2 PBS1 PD1 λ/2 Heater BS λ/2 Heater PD2 780nm PD2 Laser780nm PBS3 PD3 PBS3 Laser PD3

Servo PD4 controller Servo PD4 controller Figure 5. Experimental setup. PBS: polarizing beam splitter; λ/2: half wave plate; PD: photo detector; FigureBS: plate 5. Experimental beam splitter. setup. (Figure PBS: reproduced polarizing from beam [22 splitter;]). /2: half wave plate; PD: photo detector; BS:Figure plate beam 5. Experimental splitter. (Fig setup.ure reproduced PBS: polarizing from beam[22].) splitter; /2: half wave plate; PD: photo detector; ExperimentalBS: plate beam results splitter. demonstrate (Figure reproduced that the from number [22].) of lock points of the reflected light was two moreExperimental than that of results the transmitted demonstrate light. that The the red number detuning of lock of the points first-order of the zeroreflected crossing light point was oftwo the Experimental results demonstrate that the number of lock points of the reflected light was two morereflected than lightthat of is largerthe transmitted than that oflight. the The transmitted red detu light.ning of This the showsfirst-order that thezero detuning crossing ofpoint the lockingof the more than that of the transmitted light. The red detuning of the first-order zero crossing point of the reflectedpoint can light be extendedis larger than to a fartherthat of the area transmitte by increasingd light. the This optical shows path that length. the detuning of the locking pointreflected can be light extended is larger to a than farther that area of the by transmitte increasingd the light. optical This pathshows length. that the detuning of the locking point can be extended to a farther area by increasing the optical path length. Appl. Sci. 2020, 10, 3255 7 of 15 Appl. Sci. 2020, 10, x 7 of 14

InIn 2018,2018, FangFang etet al.al. presentedpresented aa farfar ooff-resonanceff-resonance laserlaser frequencyfrequency stabilizationstabilization methodmethod thatthat couldcould adjustadjust thethe frequencyfrequency locklock pointspoints inin thethe rangerange ofof tenstens toto hundredshundreds ofof megahertzmegahertz basedbased onon thethe FaradayFaraday rotationrotation spectroscopy spectroscopy [53 [53].]. They They used used the setupthe setu shownp shown in Figure in Figure6 to demonstrate 6 to demonstrate the far o ffthe-resonance far off- frequencyresonance stabilizationfrequency stabilization method. First, method. the transmitted First, the beamtransmitted is sent throughbeam is asent half-wave through plate a half-wave and PBS cube,plate leavingand PBS a smallcube, proportionleaving a small of the proportion total output of light the fortotal the output Faraday light beam. for Thenthe Faraday it is combined beam. Then with theit is acousto–optic combined with modulator the acousto–optic (AOM) to control modulator and move(AOM) the to laser control frequency. and move Furthermore, the laser infrequency. order to eFurthermore,ffectively compensate in order theto effectively deviation compensate from the propagation the deviation direction from ofthe the propagation first-order didirectionffracted of light, the afirst-order double-pass diffracted AOM system light, a is double-pass used. AOM system is used.

Double-pass AOM system

PBS1

PD1 B λ/2 Cs cell

ECDL PD2 PBS2 Heater

Servo controller

10 U

Figure 6. Experimental setup. PBS: polarizing beam splitter; λ/2: half wave plate; PD: photo detector;Figure 6. Double-pass Experimental AOM setup. system: PBS: polarizing a system consists beam splitter; of acousto–optic /2: half wave modulator, plate; quarterPD: photo wave detector; plate, plano-convexDouble-pass AOM mirror system: and reflector; a system ECDL: consists an external of acousto–optic cavity diode modulator, laser at 852 quarter nm. (Figure wave plate, reproduced plano- fromconvex [53 mirror]). and reflector; ECDL: an external cavity diode laser at 852 nm. (Figure reproduced from [53].) In the experiment, they got the Faraday rotation spectra under large detuning by using a cesium (Cs) cellIn the heated experiment, to 130 ◦C. they The got AOM-derived the Faraday radio rotation frequency spectra was under 65 MHz. large Notably,detuning the by Faraday using a opticalcesium rotation(Cs) cell spectrum heated to corresponding 130 °C. The AOM-derived to the first-order radio light frequency produced was a red65 MHz. shift relative Notably, to the originalFaraday spectrum.optical rotation Based spectrum on this method, corresponding the frequency to the lockfirst-order pointwith light detuning produced of a red6.2 GHzshift relative was precisely to the 1 − shiftedoriginal by spectrum. 130 MHz, Based and theyon this obtained method, a frequencythe frequency drift lock of 3.3 point MHz withh− detuningand an rms of fluctuation−6.2 GHz was of 1 · 0.6precisely MHz h −shifted. by 130 MHz, and they obtained a frequency drift of 3.3 MHz ∙ h and an rms · fluctuationAs a scheme of 0.6 of MHz using ∙ h the. atomic transition frequency as a reference, the main purpose of the Faraday schemeAs isa toscheme improve of using the long-term the atomic stability transition of the freq frequencyuency as far a awayreference, from the resonance.main purpose The of PDH the schemeFaraday discussed scheme is in to Section improve2 is the to find long-term an optical stabilit cavityy of as the a reference. frequency Normally, far away thefrom linewidth the resonance. of the referenceThe PDH cavity scheme is verydiscussed narrow, in butSection its center 2 is to frequency find an driftoptical is serious,cavity as which a reference. means theNormally, short-term the stabilitylinewidth of of the the PDH reference scheme cavity can beis very very narrow, high [15 bu]. Whilet its center the center frequency frequency drift is stability serious, ofwhich the atomic means transitionthe short-term line asstability a frequency of the PDH reference scheme is can very be high, very inhigh theory, [15]. While the Faraday the center scheme frequency will havestability an excellentof the atomic long-term transition stability line [as51 ].a frequency However, wereferenc comparede is very the high, experimental in theory, data the inFaraday the reference, scheme such will ashave frequency an excellent drift andlong-term fractional stability frequency [51]. instability,However, andwe foundcompared that the Faradayexperimental scheme data is worsein the thanreference, the PDH such scheme as frequency in terms drift of itsand short-term fractional stability frequency and instability, long-term and stability. found We that speculate the Faraday that thescheme main is reason worse for than this the phenomenon PDH scheme is in that terms the Faradayof its short-term scheme hasstability extremely and long-term high requirements stability. We on temperaturespeculate that and the magnetic main reason field stabilityfor this phenomenon [52], and its frequency is that the stabilization Faraday scheme effect ishas easily extremely affected high by temperaturerequirements and on magnetictemperature field. and magnetic field stability [52], and its frequency stabilization effect is easilyIn addition affected toby being temperature susceptible and magnetic to temperature field. and magnetic fields, it is found that the laser frequencyIn addition stabilization to being technique susceptible in Faradayto temperature effect also and hasmagnetic other shortcomings.fields, it is found This that frequency the laser stabilizationfrequency stabilization scheme requires technique complex in Faraday calculations effect to also obtain has the other temperature shortcomings. corresponding This frequency to the desiredstabilization frequency scheme stabilization requires complex point. It calculations takes tens of to minutes obtain forthe the temperature temperature corresponding to gradually reachto the desired frequency stabilization point. It takes tens of minutes for the temperature to gradually reach stability, and there are some problems of large hysteresis and poor repeatability. It is difficult to Appl. Sci. 2020, 10, 3255 8 of 15 stability, and there are some problems of large hysteresis and poor repeatability. It is difficult to achieve fast and accurate adjustment of the frequency stability. Deepening of the research on far off-resonance laser frequency stabilization by using the Faraday effect has resulted in its continuous improvement. Moreover, the off-resonance Faraday effect also finds applications in high-bandwidth slow-light atomic probes [54], optical isolators [55], and so on.

4. Far Off-Resonance Laser Frequency Stabilization Using Transfer Cavities The principle of far off-resonance frequency stabilization with a transfer cavity involves locking the length of the F–P cavity with a reference laser that has been stabilized. Then the F–P cavity transmission peak is used to perform laser detuning and frequency stabilization. Noteworthy, by selecting different transmission peaks, the laser can be locked at different detuned frequencies. This method mainly uses the transmissivity of the F–P cavity. Before the frequency stabilization with the transfer cavity, the method of frequency offset locking is reviewed [56,57]. Barger et al. used an F–P cavity and method of dither locking to stabilize the frequency of a dye 10 laser with a frequency instability at the order of 10− [58]. In the dither-lock method, the frequency at the F–P cavity transmission peak was selected as the reference frequency, the different slopes on both sides as the criterion, and the laser frequency was locked with the reference frequency. However, the shortcoming of this method is obvious, i.e., it cannot distinguish between the power jitter and the frequency jitter of the laser, and the former can result in the change of transmitted light intensity. At the same time, the feedback circuit considers it to be a frequency jitter and makes a wrong feedback regulation. In order to reduce the influence of the power jitter on the frequency stabilization, a frequency offset locking method was proposed. The maximum slope point should theoretically be the lock point; however, the frequency corresponding to half the maximum of the transmitted light intensity is usually selected as the frequency standard because of convenience and similarity [59]. The hypotenuse of the detected transmission curve of the laser passing through the F–P cavity can convert frequency to amplitude. Two photodetectors were used to prevent the laser power jitter from affecting the frequency stabilization. One was used to detect the transmitted light of the selected frequency behind the cavity and the other detected the partial beam of the laser. The input of the servo amplifier corresponded to differential signal between the outputs of two detectors. When the frequency was at the target frequency, the two photocurrents were close to each other. When the frequency was far from the target frequency, the detector outputs were not equal. Thereby, the laser frequency could be controlled to be constant. In 2009, Li et al. at the State Key Laboratory of Precision Spectroscopy proposed a peak-seeking servo-controlled technology which can be used in laser cavity-enhanced spectroscopy experiments. When the laser frequency is scanned, it can be uninterruptedly locked with resonant frequency of the cavity [60]. In 2012, Zhao et al. at Tsinghua University used a high-finesse F–P cavity to suppress laser phase noise, and its technical block diagram is illustrated in Figure7. In particular, at the Fourier frequency of 17 kHz (approximately the linewidth of the F–P reference cavity), the laser phase noise was significantly suppressed by more than 92 dB. The full width at half maximum linewidth of the laser was reduced from 7 MHz to 4.4 Hz. In Lorentz fitting, its instantaneous linewidth was 220 MHz [61]. Appl. Sci. 2020, 10, 3255 9 of 15 Appl. Sci. 2020, 10, x 9 of 14

Output1 Output2

Laser PZT

PZT

F-P

Laser

PBS PD Mixer EOM

Figure 7. SchemeScheme of of the the narrow narrow linewidth laser setup. EO EOM:M: electro–optic electro–optic modulator; PBS: polarizing beam splitter; PD: photo detector; PZT: piezoelectric transducer. (Figure (Figure reproduced reproduced from [61].) [61]). With the development of quantum sensing, stabilization of the laser frequency on the fixed With the development of quantum sensing, stabilization of the laser frequency on the fixed frequency point has been inadequate to meet the requirements. For example, in the spin-exchange frequency point has been inadequate to meet the requirements. For example, in the spin-exchange relaxation-free atomic magnetometer, the inert gas is filled in the atomic cell. Affected by this relaxation-free atomic magnetometer, the inert gas is filled in the atomic cell. Affected by this pressure, the frequency of pumping light should deviate from the resonance frequency by several pressure, the frequency of pumping light should deviate from the resonance frequency by several GHz. Besides, in order to prevent the ultra-high optical thickness from affecting the detection of the GHz. Besides, in order to prevent the ultra-high optical thickness from affecting the detection of the signal-to-noise ratio, far off-resonance of more than 100 GHz is often required [12,22]. Such a large signal-to-noise ratio, far off-resonance of more than 100 GHz is often required [12,22]. Such a large range of detuning cannot be achieved using an AOM or an EOM. Thus, the approach to stabilize far range of detuning cannot be achieved using an AOM or an EOM. Thus, the approach to stabilize far off-resonance frequency via a transfer cavity was explored. off-resonance frequency via a transfer cavity was explored. In 2006, Du et al. at the State Key Laboratory of Quantum Optics and Quantum Optics Devices In 2006, Du et al. at the State Key Laboratory of Quantum Optics and Quantum Optics Devices of Shanxi University locked the 852 nm laser to the Fg = 4-Fe = 4, 5 transition of Cs atom, and then of Shanxi University locked the 852 nm laser to the Fg = 4-Fe = 4, 5 transition of Cs atom, and then locked the reference cavity as a bridge to the stabilized frequency. Then the lasers at 830 and 908 nm locked the reference cavity as a bridge to the stabilized frequency. Then the lasers at 830 and 908 nm were locked to the other longitudinal modes of the reference cavity. The two lasers resonated with were locked to the other longitudinal modes of the reference cavity. The two lasers resonated with the reference cavity at the same time, which realized the stabilization of multiple lasers at different the reference cavity at the same time, which realized the stabilization of multiple lasers at different wavelengths through the optical cavity [62]. wavelengths through the optical cavity [62]. During the same year, Bohlouli-Zanjani et al. stabilized a transfer cavity using a Radio Frequency During the same year, Bohlouli-Zanjani et al. stabilized a transfer cavity using a Radio Frequency (RF) current-modulated diode laser which is injection locked to a 780 nm reference diode laser. (RF) current-modulated diode laser which is injection locked to a 780 nm reference diode laser. A A Ti:sapphire ring laser at 960 nm was locked on the optical transfer cavity. The RF modulation Ti:sapphire ring laser at 960 nm was locked on the optical transfer cavity. The RF modulation frequency could be changed for precise scanning, thereby changing the detuning frequency [63]. frequency could be changed for precise scanning, thereby changing the detuning frequency [63]. In 2011, Qu et al. at the Chinese Academy of Sciences used an ultra-stable laser at 729 nm locked In 2011, Qu et al. at the Chinese Academy of Sciences used an ultra-stable laser at 729 nm locked via PDH technology as a reference laser and a scanned F–P cavity as the transmission medium to via PDH technology as a reference laser and a scanned F–P cavity as the transmission medium to achieve long-term locking of a 397 nm semiconductor laser. After frequency stabilization, the drift achieve long-term locking of a 397 nm semiconductor laser. After frequency stabilization, the drift of of the 397 nm laser within 1 h was less than 1 MHz, and the Allan variance of 100 s was less than the 397 nm laser within 1 h was less than 1 MHz, and the Allan variance of 100 s was less than 1× 1 10 10 [64]. 10× −[64]. In 2014, G. Zheng at the State Key Laboratory of Precision Spectroscopy at East China Normal In 2014, G. Zheng at the State Key Laboratory of Precision Spectroscopy at East China Normal University realized laser frequency stabilization of an optical transfer cavity based on PDH technology. University realized laser frequency stabilization of an optical transfer cavity based on PDH Figure8 presents the block diagram of the experimental device. The part in the dotted frame is the F–P technology. Figure 8 presents the block diagram of the experimental device. The part in the dotted cavity locked on the laser at 780 nm. The main aim of the part outside the dotted frame is to achieve frame is the F–P cavity locked on the laser at 780 nm. The main aim of the part outside the dotted the frequency locking of the dye laser (718.6 nm) on the F–P cavity [65]. frame is to achieve the frequency locking of the dye laser (718.6 nm) on the F–P cavity [65]. Appl.Appl. Sci. 20202020,, 1010,, 3255x 1010 ofof 1514 Appl. Sci. 2020, 10, x 10 of 14

780nm 718.6nm laser780nm 718.6nmlaser laser laser Phase shifterPhase shifter Oscillograph Oscillograph 20MHz EOM PBS AOM Mixer 20MHz EOM PBS AOM Mixer Mixer Mixer PD PD PBS Phase EOM 10MHz PD PBS EOM shifterPhase PD 10MHz shifter

F-P F-P PZT Dichroic PBS PZT Dichroic PBS PD mirror PD mirror

Figure 8. Schematic illustration of the frequency stabilization system with a transfer cavity. EOM: FigureFigure 8. 8.Schematic Schematic illustration illustration of of the the frequency frequency stabilization stabilization system system with with a a transfer transfer cavity. cavity. EOM: EOM: electro–optic modulator; AOM: acousto–optic modulator; PBS: polarizing beam splitter; PD: photo electro–opticelectro–optic modulator; modulator; AOM: AOM: acousto–optic acousto–optic modulator; modulator; PBS: PBS: polarizing polarizing beam beam splitter; splitter; PD: PD: photo photo detector; PZT: piezoelectric transducer. (Figure reproduced from [65].) detector;detector; PZT: PZT: piezoelectric piezoelectric transducer. transducer. (Figure (Figure reproduced reproduced from from [65 [65].)]). InIn 2019,2019, SubhankarSubhankar etet al.al. at NIST stabilized lasers at 556 and 798 798 nm nm through through optical optical cavities [66]. [66]. In 2019, Subhankar et al. at NIST stabilized lasers at 556 and 798 nm through optical cavities [66]. ForFor a fixedfixed cavity length, the distance between the transmissiontransmission peaks corresponds toto the free spectral For a fixed cavity length, the distance between the transmission peaks corresponds to the free spectral rangerange (FSR).(FSR). TheThe opticaloptical cavitycavity isis scannedscanned inin thethe rangerange slightlyslightly largerlarger thanthan thethe FSRFSR toto obtainobtain threethree range (FSR). The optical cavity is scanned in the range slightly larger than the FSR to obtain three peaks,peaks, withwith thethe master–slave–mastermaster–slave–master (M-S-M(M-S-M′) sequence.sequence. The frequency of thethe laserlaser waswas correlatedcorrelated peaks, with the master–slave–master (M-S-M0 ′) sequence. The frequency of the laser was correlated withwith thethe arrivalarrival timetime ofof thethe peakpeak andand aa signalsignal capablecapable ofof stabilizingstabilizing thethe averageaverage cavitycavity length,length, andand thethe with the arrival time of the peak and a signal capable of stabilizing the average cavity length, and the slaveslave laserlaser frequencyfrequency waswas obtained.obtained. slave laser frequency was obtained. InIn thethe samesame year,year, LiLi etet al.al. atat thethe SchoolSchool ofof InstrumentationInstrumentation andand OptoelectronicOptoelectronic EngineeringEngineering In the same year, Li et al. at the School of Instrumentation and Optoelectronic Engineering proposedproposed aa transfertransfer cavitycavity method to transfer laserlaser frequency stability, realizing the far ooff-resonanceff-resonance proposed a transfer cavity method to transfer laser frequency stability, realizing the far off-resonance ofof 150 GHz, and the laser laser frequency frequency drift drift after after stabilization stabilization was was 1 1 MHz ∙h ℎ1 [67 [67].]. TheThe technicaltechnical blockblock of 150 GHz, and the laser frequency drift after stabilization was 1 · ∙ ℎ− [67]. The technical block diagramdiagram isis illustratedillustrated inin FigureFigure9 9.. TwoTwo lasers lasers were were used, used, one one of of which which was was locked locked on on the the saturation saturation diagram is illustrated in Figure 9. Two lasers were used, one of which was locked on the saturation absorptionabsorption peakpeak ofof thethe 8787Rb atom D2 line. The The magnitude magnitude and direction of the deviation was identifiedidentified absorption peak of the 87Rb atom D2 line. The magnitude and direction of the deviation was identified byby thethe control control system system with with the the modulation modulation and and demodulation demodulation algorithm algorithm and a and DC voltagea DC voltage was output. was by the control system with the modulation and demodulation algorithm and a DC voltage was Theoutput. PZT The was PZT adjusted was adjusted to control to the control cavity the length. cavity After length. the After stabilization the stabilization of the cavity of the length, cavity the length, target output. The PZT was adjusted to control the cavity length. After the stabilization of the cavity length, laserthe target was lockedlaser was by thelocked dither-lock by the dither-lock method. method. the target laser was locked by the dither-lock method.

PBS PBS Servo Rb Servo cellRb cell PD PD 780nm laser780nm laser PZT 767nm PZT 767nm F-P laser F-P laser

Servo Servo

FigureFigure 9. Block diagram of frequency stabilization experimental system. PBS: polarizing beam splitter; Figure 9. Block diagram of frequency stabilization experimental system. PBS: polarizing beam splitter; PD:PD: photophoto detector;detector; PZT:PZT: piezoelectricpiezoelectric transducer.transducer. (Figure(Figure reproducedreproduced fromfrom [ 67[67].)]). PD: photo detector; PZT: piezoelectric transducer. (Figure reproduced from [67].) BasedBased on this, this, during during the the same same year, year, Li Liet al. et al.stud studiedied the effect the e ﬀofect the of length the length of the of50 theand 5030 andmm Based on this, during the same year, Li et al. studied the effect of the length of the 50 and 30 mm 30F–P mm cavity F–P on cavity the frequency on the frequency stability. stability. When the When cavi thety length cavity was length shorter, was shorter, the cavity the and cavity theand control the F–P cavity on the frequency stability. When the cavity length was shorter, the cavity and the control controlsystem systemwere less were sensitive less sensitive to external to external vibration. vibration. Moreover, Moreover, when the when cavity the length cavity decreased length decreased by 40%, system were less sensitive to external vibration. Moreover, when the cavity length decreased by 40%, bythe40%, frequency the frequency stability stability of the of system the system increased increased by byapproximately approximately one one order order of of magnitude. the frequency stability of the system increased by approximately one order of magnitude. Furthermore, the cavity length and FSR were observed to be inversely and linearly proportional to Furthermore, the cavity length and FSR were observed to be inversely and linearly proportional to the range of laser frequency detuning [21]. the range of laser frequency detuning [21]. Appl. Sci. 2020, 10, 3255 11 of 15

Furthermore, the cavity length and FSR were observed to be inversely and linearly proportional to the range of laser frequency detuning [21]. With the development of optical processing technology, the finesse of the F–P cavity is significantly increasing, and it can meet the needs of special experiments. However, the transfer cavity frequency stabilization method needs two or more lasers, which increases the volume and the complexity of the optical path. Although the requirements of the F-P cavity are much simpler than those in the PDH, it still requires more design and calculation than some methods. Besides, a laser is stabilized as the reference in an additional approach which should be able to reach a high stability. Those factors limit the scope of the applications. Another method that uses frequency transmission to stabilize the frequency is an optical frequency comb. Femtosecond laser and optical comb technology have been used in absolute frequency measurement and research on optical clocks [68–73]. At present, laser frequency stabilization technology based on optical frequency combs has been able to achieve very good results. In 2001, Ye et al. locked the laser on the transition line of the iodine atom, and the stability was transferred to each comb component in the entire optical octave bandwidth with an accuracy of 3.5 10 15. Moreover, the stability of the × − optical clock was measured as 4.6 10 13 over a year [74]. In 2014, Fordell et al. at the Centre for × − Metrology and Accreditation used the saturation absorption spectrum of Rb atoms as the frequency standard to lock the laser on the optical comb, and finally, the laser linewidth was in the order of MHz [75]. Moreover, the optical frequency comb is also important for detuning and frequency stabilization. In 2017, C. Li used an optical comb to achieve 1.5 µm laser frequency stabilization with a 12 stability of the order of 10− and showed that the method can achieve detuning above 10 GHz [76].

5. Conclusions and Future Perspectives This review introduces several different techniques for far off-resonance frequency stabilization, each with different characteristics and applications. The PDH frequency stabilization has a flexible frequency stabilization range but strict requirements on optical reference cavities in special geometry shapes, including precise temperature control, vacuum condition, and vibration isolation. The Faraday optical rotation frequency stabilization can realize frequency stabilization far from the resonance line. However, it requires the long-period adjustment of the temperature and encounters the problems of large hysteresis and poor repeatability. The frequency stabilization with a transfer cavity requires at least two lasers, one of which is stabilized as the frequency standard. It could realize off-resonance frequency stabilization at any frequency, but the optical path is complicated. The method of optical frequency comb is insensitive towards external temperature or magnetic field changes because the comb is strictly locked to the frequency standard. Besides, it can achieve large frequency detuning above 10 GHz. However, the large volume and the high cost limit its miniaturization and portability. These techniques can be optimized from the optical and circuit aspects. In terms of the optical aspects, devices can be miniaturized and integrated. In terms of circuits, by introducing modern intelligent control systems, optimizing PID controllers, and employing digital signal processing technology and LabVIEW processing platforms to optimize the feedback system, a better long-term stability and accuracy can be successfully realized. Moreover, the frequency stabilization systems in this paper are placed in a laboratory environment. If the application is gradually expanded from the laboratory environment to outdoor, even underwater and outer space, environments, it is necessary to develop a portable frequency stabilization system. Through miniaturization, integration, and automation, far off-resonance frequency stabilization technology may have broader application prospects.

Author Contributions: C.L. initiated the manuscript. C.L., Z.Y., Z.X., M.D., and Y.Z. participated in the revision of the manuscript. Y.Z. provided overall supervision. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China under Grant 61703025 and Zhejiang Lab under Grant 2019MB0AE03. Conﬂicts of Interest: The authors declare no conﬂict of interest. Appl. Sci. 2020, 10, 3255 12 of 15

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