A flat spectral Faraday filter for sodium lidarYang Yong,1,3 Cheng Xuewu,1,* Li Faquan,1 Hu Xiong,2 Lin Xin,1,3 and Gong Shunsheng1

1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physicsand Mathematics, Chinese Academy of Sciences—Wuhan National Laboratory

for Optoelectronics Wuhan 430071, China2Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, China

3Graduate School of Chinese Academy of Sciences, Beijing 100080, China*Corresponding author: lidar@wipm.ac.cn

Received January 31, 2011; revised March 9, 2011; accepted March 10, 2011;posted March 10, 2011 (Doc. ID 141890); published April 1, 2011

We report a flat spectral Faraday anomalous dispersion optical filter (FS-FADOF) for sodium lidar. The physical andtechnical considerations for obtaining a FS-FADOF with a 3:5GHz flat spectral transmission function are presented.It was found that the effective transmission of this filter was much higher (>94%) and more uniform than that of theultranarrowband FADOF, and therefore were less sensitive to laser-frequency drift. Thus, the FS-FADOF canimprove lidar efficiency and precision. © 2011 Optical Society of AmericaOCIS codes: 280.3640, 010.3640, 290.1310, 020.2930.

Resonance fluorescence lidar is one of the most powerfultools available to study the mesosphere and lowerthermosphere (MLT). Sodium number density was firstdetected by broadband sodium lidar. Three-frequency so-dium lidar extends temperature and wind measurementsin the MLT by means of the ratio technique [1–6].It has been demonstrated that daytime operation of li-

dar is important for investigating long-period changes inatmospheric parameters and dynamic processes in theMLT [2–4]. Faraday anomalous dispersion optical filter(FADOF) is required in daytime operation of resonancefluorescence lidar because of its narrow passband, hightransmission, and stability [1,4]. The lidar group at Color-ado State University introduced an ultranarrowbandFADOF (UN-FADOF) into a sodium lidar receiver to im-plement daytime measurements of sodium number den-sity, temperature, and wind in the mesopause region [2].The center-pass bandwidth of the UN-FADOF is only

about 2GHz, and the transmission function of thisFADOF changes sharply with frequency in the neighbor-hood of several gigahertz [7]. Thus, the expected lidarphoton count, which is proportional to the effectiveFADOF transmission (EFT) and the lidar efficiency, issensitive to the lidar echo spectrum and therefore tothe laser-frequency drift [8]. The uncertainty introducedby the laser-frequency drift cannot be eliminated by theratio technique or by normalizing the resonance fluores-cence signals with Rayleigh signals from a referencealtitude [3]. Moreover, the EFT and, therefore, the lidarefficiency is rather low (EFT <40%, with laser frequencytuned to νþ). Thus, the UN-FADOF significantly influ-ences the expected photon count because of its ultra-narrowband and strongly varying spectral profile.In this Letter, a flat spectral sodium FADOF

(FS-FADOF) was proposed for sodium lidar. The filterwas designed, built, and tested. In addition, the sodiumlidar echo spectrum was analyzed. It was found thatEFTs for three-frequency lidar fluorescence echoeswere much higher and more uniform than those of theUN-FADOF, and therefore were less sensitive to thelaser-frequency drift. Thus the proposed FS-FADOF im-proves the lidar efficiency and precision compared withthe UN-FADOF.

To produce the FS-FADOF, the absorption coefficientof the atomic vapor in a FADOF must be kept low, andthe circular dichroism should be kept high and nearlyuniform for all photons in the lidar echo spectrum. A neo-dymium magnet with a 3000G axial magnetic field wasdesigned and employed in the FS-FADOF. Because ofthe strong magnetic field, the overlap between theanomalous dispersion range of atomic vapor and the li-dar echo spectrum is very small, which makes theabsorption rather weak and the circular dichroismnearly unchanged.

However, the circular dichroism is not high enough toproduce the necessary Faraday rotation in a FADOF. Tocompensate, the temperature and length of the sodiumcell must be increased. Software was developed to opti-mize FADOF parameters. In addition, we set up an accu-rate temperature field for the sodium vapor cell toachieve the optimum temperature (182 °C).

The transmission function of the FS-FADOF was testedby scanning the frequency of a ring-dye laser (MatisseDS). In addition, a conventional UN-FADOF [9] with a1750G magnetic field and low temperature of 171 °C wasdesigned and tested. The experimental results showed anexcellent agreement with theoretical predictions, asshown in Fig. 1(d). The center-pass bandwidth is ∼2GHzfor the UN-FADOF and ∼4GHz for the FS-FADOF, whichis much narrower than that of a commercial interferencefilter. The range of the nearly uniform transmission func-tion attains 3:5GHz. The transmission function of theFS-FADOF is somewhat similar to that of the potassiumFADOF, which is efficient in daytime operation ofpotassium lidar [4]. The equivalent noise bandwidth(∼9GHz) of the FS-FADOF is larger than that of theUN-FADOF (∼5:3GHz); nevertheless, a ∼9GHz equiva-lent noise bandwidth is tolerable in daytime operationof the sodium lidar.

The EFT is defined as

TSνiðT; υÞ ¼

RISνiðνe; T; υÞFðνeÞdνeR

ISνiðνe; T; υÞdνe; ð1Þ

1302 OPTICS LETTERS / Vol. 36, No. 7 / April 1, 2011

0146-9592/11/071302-03$15.00/0 © 2011 Optical Society of America

where νe is the frequency of the echo photon, FðνeÞ is theFADOF transmission function, and ISνiðνe; T; υÞ is thelidar echo spectrum, which is sensitive to atmospherictemperature T , line-of-sight wind velocity υ, and laser fre-quency νi. The superscript S in Eq. (1) may take on twovalues: Na, which denotes sodium echo, and Ray, whichdenotes Rayleigh echo.Usually, TNa

νi ðT; υÞ ≠ TRayνi ðT; υÞ, thus the sodium num-

ber density nNaðzÞ would need to be corrected by thefactor rνi ¼ TNa

νi ðT; υÞ=TRayνi ðT; υÞ:

nNaðzÞ ¼ NnðzÞnRayðzRÞσRayνi ðT; υÞσNaνi ðT; υÞ

1rνi

: ð2Þ

Here NnðzÞ is the photon count normalized by theRayleigh signal from the reference altitude zR, nRayðzRÞis the air-molecular number density at zR, andσRayνi ðT; υÞ and σNa

νi ðT; υÞ are the Rayleigh and fluores-cence scattering effective cross sections, respectively.A three-frequency laser (i.e., νi ¼ νþ; ν−; νa) enables a

sodium lidar to measure temperature and wind velocity.The temperature-measurement ratio RT is the ratio of thenormalized signal at νa to the sum of the normalized sig-nal at νþ and ν

−[3]:

RT ¼ σNaνþ ðT; υÞrνþ þ σNa

ν−

ðT; υÞrν−

σNaνa ðT; υÞrνa

: ð3Þ

The wind-measurement ratio RW is the ratio of thenormalized sodium signal at νþ and ν

−[3]:

RW ¼ σNaνþ ðT; υÞ

σNaν−

ðT; υÞrνþrν

−

: ð4Þ

Temperature and wind velocity are derived from RTand RW through calibration curves, so it is necessaryto know the EFT and rνi with precision to derive sodiumnumber density, temperature, wind velocity, andrelated parameters in the MLT. Note that Eqs. (2)–(4)

are somewhat different from [3], where TNaνi ðT; υÞ ¼

TRayνi ðT; υÞ (i.e., rνi ¼ 1).A simple model for the sodium lidar echo spectrum is

presented herein, which may be extended to other reso-nance fluorescence lidar. A sodium atom in the groundstate jαii absorbs a photon ν and is promoted into theexcited state jβji. The atom then returns to ground statejγki by emitting a photon νe. Only backscattered photonsare detected by lidar. If the saturation effect of the so-dium layer is ignored, the fluorescence echo spectrum is

INaνi ðνe; T; υÞ ¼

X8i¼1

X16j¼1

X8k¼1

ZZ Sβjγk f ðυsÞ−υsc þ νβjγk − νe − i

4πτ

×Sαiβj PνiðνÞ

υsc þ ναiβj − ν − i

4πτdνdυs; ð5Þ

where τ is the lifetime of the sodium excited states 32P3=2,

f ðυsÞ ¼ N0ð m2πkBTÞ1=2 expð−

Mðυ−υsÞ22kBT

Þ is the Maxwellian velo-city distribution of atoms, m is the mass of the sodium

atom, PνiðνÞ ¼ P0 expð− ðν−νiÞ2σ2 Þ is the laser spectrum, σ

is ð2 ffiffiffiffiffiffiffiffiln 2

p Þ−1 of the emitted laser full width at halfmaximum (FWHM), P0 is ðσ ffiffiffiπp Þ−1 of the laser power, cis the speed of light in vacuum, and kB is the Boltzmannconstant. The quantities Sαiβj and ναiβj represent the ab-sorption probability and frequency, respectively, of thetransition jαii → jβji. Sβjγk and νβjγi represent the emis-sion probability and frequency, respectively, of the tran-sition jβji → jγki.

A simulation of the sodium fluorescence echo spec-trum is shown in Fig. 1. The simulation assumes νa isat the sodium D2a peak, ν� ¼ νa � 630MHz, T ¼ 200K,υ ¼ 0ms−1, and the laser line width FWHM ¼ 120MHz.The Rayleigh echo spectrum obtained by Heinrich et al.[5] is also shown in Fig. 1 for υ ¼ 0, T ¼ 250K. It isclear that these two spectra are quite different fromeach other.

The sodium echo spectra have two or more separatedpeaks in the vicinity of several gigahertz. The initialground state jαii and final ground state jγki are not al-ways the same atomic state. The difference betweenthe absorption and emission channels (i.e., νβjγi ≠ ναiβj )leads to a multipeak spectrum. Peak locations aresensitive to laser-frequency drift. Also, peak locationsshift from the centroid frequency of laser due to twiceDoppler shift. The peak widths are rather narrow; onlyabout 200MHz.

The sodium lidar at Wuhan Institute of Physics andMathematics (N30:5°, E114:3°) is a broadband lidarwhose laser bandwidth is 1:2GHz. It exploits a night-time channel without FADOF and a daytime channelwith a FADOF in the receiver [9]. Figure 2(a) showsthe normalized signal from two channels acquired atthe same time during the night. As expected, they are dif-ferent from each other because rνi ≠ 1. After correctionby the factor rνi ≃ 1:15, the sodium number density de-rived from the daytime channel is almost the same as thatfrom the nighttime channel, which indicates that the lidarecho spectrum model is reasonable.

Fig. 1. (Color online) Longitudinal coordinates are in arbitraryunits. (a)–(c) Solid curves represent the sodium fluorescenceecho spectrum with νi ¼ νþ; ν−; νa. (d) Theoretical and experi-mental results of the FS-FADOF and the UN-FADOF.

April 1, 2011 / Vol. 36, No. 7 / OPTICS LETTERS 1303

The EFTs of the FS-FADOF and the UN-FADOF for thethree-frequency lidar echoes are shown in Table 1. TheEFTs of the FS-FADOF attain 94% and are almost thesame for the three-frequency lidar echoes. But, whenνi ¼ νþ, the EFT of the UN-FADOF attains only 39.9%,because some peaks of sodium echo spectrum do notmatch the center peak of the UN-FADOF, as shown inFigs. 1(a) and 1(d). Consequently the lidar efficiencycan be raised by the FS-FADOF.According to Eqs. (3) and (4), the calibration curves of

temperature and wind velocity were obtained and shownin Fig. 3. Owing to the very different EFTs, the calibrationcurves for the UN-FADOF differ from those for the inter-ference filter (IF), whose effective transmissions forthree-frequency lidar echoes are identical [3]. However,the calibration curves for FS-FADOF are similar to thosefor the IF [1,3]; a result that we ascribe to the high anduniform EFT.Some peaks of the three-frequency lidar echo spec-

trum overlap with the sharp edge of the center peakof the UN-FADOF, which makes the EFT and rνi sensitiveto the laser-frequency drift in the emitting laser. A 1MHzlaser chirp [8] would lead to a deviation of 0.202% for rνiand exert significant influences on measurements of so-dium number density, temperature and wind. While theFS-FADOF is employed, the deviation for rνi is only0.038%, as the transmission function of the FS-FADOF isnearly uniform over the range of the echo spectrum. Interms of the broadband lidar [9], with respect to the laser-frequency drift, the quantity rνi for the FS-FADOF and,therefore, the measurements of sodium number density

are more stable, compared with those for the UN-FADOF, as shown in Fig. 2(b). Thus the precision of lidarmeasurements would be improved by the FS-FADOF.

In conclusion, a FS-FADOF was proposed for the so-dium lidar. A 3000G axial magnetic field and optimizedtemperature of 182 °C were employed to obtain the FS-FADOF with a 3:5GHz range of nearly uniform transmis-sion function. The sodium lidar echo spectrum wasanalyzed. With the FS-FADOF, the EFTs for three-frequency lidar fluorescence echoes are almost the sameand attain 94%, and the measurements of sodium numberdensity and temperature are insensitive to laser chirp.Consequently, the efficiency and precision in daytimeoperation of sodium lidar can be improved by theFS-FADOF.

This research was supported by the National NaturalScience Foundation of China (NSFC) (grants 10978003and 40905012) and the Chinese Meridian Project. Wethank Yang G. T., Yuan T., Song S. L., and Liu Y. J. fortheir constructive comments.

References

1. H. Chen, M. A. White, D. A. Krueger, and C. Y. She, Opt. Lett.21, 1093 (1996).

2. C. Y. She, J. Sherman, T. Yuan, B. P. Williams, K. Arnold,T. D. Kawahara, T. Li, L. F. Xu, J. D. Vance, P. Acott,and D. A. Krueger, Geophys. Res. Lett. 30, 1319 (2003).

3. X. Chu and G. C. Papen, Laser Remote Sensing, T. Fujii andT. Fukuchi, eds. (CRC Press, 2005), pp. 179–432.

4. J. Hoffner and C. Fricke-Begemann, Opt. Lett. 30,890 (2005).

5. D. Heinrich, H. Nesse, U. Blum, P. Acott, B. Williams, andU. P. Hoppe, Ann. Geophys. 26, 1057 (2008).

6. G. T. Yang, B. Clemesha, P. Batista, and D. Simonich,J. Geophys. Res. 115, D18104 (2010).

7. H. Chen, C. Y. She, P. Searcy, and E. Korevaar, Opt. Lett. 18,1019 (1993).

8. T. Yuan, J. Yue, C. Y. She, J. P. Sherman, M. A. White,S. D. Harrell, P. E. Acott, and D. A. Krueger, Appl. Opt.48, 3988 (2009).

9. X. W. Cheng, S. S. Gong, F. Q. Li, Y. Dai, J. Song, J. M. Wang,and F. Y. Li, Sci. China Ser. G 50, 287 (2007).

Fig. 3. (Color online) Calibration curves for (a) line-of-sightwind velocity and (b) temperature.

Table 1. Effective FADOF Transmission, Whereυ � 0, T � 250K for TRay

νi �T;υ� and T � 200Kfor TNa

νi�T;υ�

UN-FADOF FS-FADOF

νi TRayνi ðT; υÞ TNa

νi ðT; υÞ TRayνi ðT; υÞ TNa

νi ðT; υÞνþ 63.2% 39.9% 95.0% 94.7%νa 56.6% 62.3% 92.2% 96.5%ν−

43.7% 76.5% 83.1% 95.1%

Fig. 2. (Color online) (a) Sodium number density. (b) rνivaries with laser frequency νi.

1304 OPTICS LETTERS / Vol. 36, No. 7 / April 1, 2011