Iue and alication in ultra-enitive molecular ectrocoy Chikako Ihibahi * a, Jun Ye b, and John L. Hall b JILA, a Univerity of Colorado and b National Intitute of Standard and Technology Boulder, Colorado 80309-0440 ABSTRACT We reent a ytematic analyi of ultra-enitive molecular detection method baed on an otical cavity and frequency modulation ectrocoy. Our goal i toward the imrovement of the limiting attainable erformance by the choice of otical configuration, amle ga reure, laer mode ize, laer intenity, and detection method wa dicued. The alication of enitive detection technique emhaized here i for laer frequency tabilization, leading to better otical frequency tandard and clock. Keyword: cavity-enhanced ectrocoy, frequency tandard. Introduction Cavity enhanced ectrocoy i one of the mot owerful tool for enitive molecular detection. The long abortion length in an otical cavity hel to realize highly enitive detection of weak molecular abortion. Another benefit of an otical cavity i enhancement of the otical ower, which i imortant for aturation ectrocoy of weak tranition. In 994 de Labachelerie et.al. oberved the aturation ectrum C 2 H 2 combination band in the.5 µm region. Ye et.al. oberved aturation abortion ectra of C 2 HD and CO 2 high overtone tranition at 064 nm, 2-5 and of C 2 H 2 in the 030 nm region. 6 The enitivity of the cavity-enhanced ectrometer i alo dramatically imroved by combination with a frequency modulation technique for ureion of amlitude noie in the tranmitted light. 4, 7 Thee technique were alo alied by Ihibahi et.al. to high reolution ectrocoy of CH 4 and CH 3 I in the.65-.66 µm region 8-0 Recently, Ye et.al. develoed a novel cheme of cavity ring-down ectrocoy uing frequency witching to achieve hot-noie limited enitivity with microwatt otical ower level. Uing thee reult a a guide, the uroe of thi aer i to conider the choice of otical toology and of exerimental arameter uch a laer intenity, laer beam mode ize, amle ga reure, and detection method, all of which influence/control the attainable enitivity. Ideally, we can identify an otimum cheme for a articular alication. The high enitivity of cavity-enhanced ectrocoy i imortant not only for the detection of weak molecular abortion but alo for attaining highly recie laer frequency tabilization, e.g. for metrological alication uch a frequency tandard and otically baed clock. The frequency intability of a laer locked to atomic or molecular abortion line i etimated by ν δν = =, () ν ( S / N ) Q ( S / N ) where ν i width of the abortion line, ν i the laer frequency, S/N i the ignal to noie ratio of the recovered reonance information, and Q i the reonance line quality factor. Hence, both narrower abortion line and better ignal to noie ratio are helful to imrove frequency tability. It i known that linewidth of atomic or molecular abortion are deendent on ontaneou decay rate, amle ga reure, tranit time, otical ower, and frequency ectrum of the interrogating radiation. Decribing the reonance linewidth over the full range of arameter would be a daunting tak: jut one examle i the evolution of a logarithmic ingularity at line center for a free-flying quantum aborber the o-called tranit-broadened linehae at low ower. However, to imrove the S/N with only modet additional broadening, one may chooe to ue a ignificant reure, for examle allowing colliion to increae, erha double, the aborber natural linewidth due to the ontaneou fluorecence, or the dimenionally defined tranit linewidth of u/(2πw 0 ), where u i the mean velocity of molecule and w 0 i the otical beam wait radiu. Under thee condition one find a linehae, which i rather accurately Lorentzian,
with an eentially linear reure broadening rate. A till richer ituation i obtained when the erective are broadened to include choice of another ize for the laer beam. Baically, the minimum reure-broadening roce include quenching of the otical diole moment which i the dominant roce when conidering a near-atmoheric reure range. However, in our high reolution domain at much lower reure (0-4 to 0-8 atm), the dominant reure effect are often due to velocity-changing colliion. The aturated-abortion roce rovide reolution below the Doler limit becaue the nonlinear aturation i concentrated in a narrow ectral/velocity window of width fixed by the relaxation rocee. Even for molecular iodine, with it ~ µ fluorecence decay time, we can achieve a linewidth 000-fold maller than the Doler cae. Thi correond to a velocity width for the aturated molecule in the range of 0.3 m/, arallel with the otical beam. Deending on reolution emloyed, thi velocity width will be caled accordingly. The intermolecular force between colliding molecule, even without reonant couling, will have at leat Van-der Waal otential ~ R -6, leading to an intermolecular force R -7. During the colliion, ome momentum will be tranferred, leading to a new axial velocity afterward. Some geometrical iue were worked out by Hall. 4 Additionally, in the cae where our tranition involve an electronically excited tate, we can exect ome imortant difference in the colliion otential between ground and excited tate. In thi cae, during the colliion, the ground and excited tate of the coherent wavefunction will have hae evolution at different rate, leading to a hae hift of the otical diole by the colliion. Thi i jut one of the rocee that would aear a a dehaing or T 2 roce in our reonance decrition. Thu the aarent reure-broadening rate i exected to be reolution-deendent ince even a tiny velocity hift will remove a article from the velocity-reonant acket if the ectral/velocity reolution i high. Studie at varying ub-doler reolution on the P(7) line in the CH 4 rotation-vibration ν 3 -fundamental band at 3392 nm howed an increaed broadening rate with reolution, relative to the low-reolution (Doler-broadened) limit. 5 For a homogeneouly broadened line, one exect a ower-broadening linear in the alied radiation intenity. Of coure, in the ga hae where all velocitie are reent, one will have the inhomogeneou broadening cae where the broadening of a ingle velocity acket i artially maked by the fact that the higher intenity can at leat artially talk to the omewhat non-reonant velocity neighbor. Thi inhomogeneou broadening limit ν i decribed by the comounding of natural linewidth Γ n, tranit time broadening Γ t, reure broadening Γ, and laer linewidth Γ l a ν = Γ + Γ + Γ + Γ S, (2) ( ) n t l + where S i the ratio (I/I ) of laer ower I, to the aborber aturation ower I, and i called the aturation arameter. Therefore to obtain a narrow ectrum, a low reure and a low aturation arameter are required. However, becaue the ignal ize of the aturation abortion ignal i roortional to amle ga reure, obtaining a high S/N i difficult with low amle reure and o highly enitive detection i neceary. From the oint of view of metrological alication, the ue of a low reure amle i additionally imortant for minimizing the colliion-induced reure hift and reducing the influence on the baeline by the linear Doler background. Additionally the comactne of a ectrometer i imortant in the alication of frequency tandard to achieve high temerature tability and convenience. In thi cae, a cavity enhanced ectrometer deign i again ueful to obtain high S/N with a hort cell while avoiding degradation of accuracy and/or reroducibility due to the wave front ditortion of laer beam, ince an otical cavity alo function a a good atial mode elector. We next conider otimizing the ectrometer deign for a highly table and reroducible frequency tandard uing a cavity enhanced ectrometer for tabilization of a.064 µm olid tate Nd:YAG laer to an I 2 abortion line. 2. Deign of ectrometer 2. Laer ource and aborber ga for otical frequency tandard To deign a enitive ectrometer for recie laer frequency control, we have firt to chooe the amle ga, ectral region, and laer ource. One can exect a much higher Q value, i.e. higher frequency tability, for frequency tandard in the otical region than for frequency tandard or clock etablihed in radio frequency or microwave region. Thi iue ha been tudied actively and widely uing laer with high frequency tability. In the infrared region, there are many trong molecular ro-vibrational tranition which are good frequency reference. For examle, frequency coincidence of the He-Ne laer with CH 4 abortion at a wavelength of 3.39 µm or the CO 2 laer with OO 4 at a wavelength of 0 µm abortion give frequency tability of a few 00 Hz and better.
Recently, diode umed olid tate laer were develoed which can rovide high frequency tability, even under free running condition. Our work i baed on a diode umed Nd-doed YAG (Nd:YAG) laer which oerate a a non-lanar ring ocillator (NPRO) at a wavelength of 064 nm. Thi commercial ytem ha a frequency tability of about 5 khz at m, which correond to ~.6 0 - at m. Thi FM noie would eriouly degrade the high S/N reonance we are execting, if a m ignal amling time were ued. Clearly, to achieve, let ay 0-4 at, a 50-fold better erformance of the utilized ource laer i neceary. Thi can be accomlihed in two te. Firt we could modulate much more quickly, ~ 00 khz, and o many ignal amle can be acquired within the ~00 µ half-eriod of the diturbance that lead to the NPRO linewidth. If the molecular frequency dicriminator ha ufficient S/N, we can guide the laer ource uch that it frequency excurion i trongly reduced. Conequently the otical hae doe not deart by radian from our ideal ine wave, o the Beel hae modulation index i very mall and we have little carrier ower cattered into thee high frequency ideband. A little ideband ower may remain at high Fourier offet frequencie, but erha 99 % of the ower will remain in the bright line we identify a the (nearly) ine-wave carrier. The good tability of the Nd:YAG laer a a laer ource, it high ower, and the trong iodine abortion matching frequency-doubled outut of the laer near 532 nm are attractive and in thi aer we conider the attainable frequency tability uing uch molecular abortion line a frequency reference. The econd quetion i whether the reonance S/N erformance will be ufficient: will we need to ue a cavity reonator to obtain the high tability at hort time, then ue the molecular reonance to ure drift and vibration noie from the cavity? To be ecific, after frequency doubling the 064 nm Nd:YAG laer, a frequency reference we ue I 2 electronic tranition near 532 nm. The a 0 hyerfine comonent of the R(56) 32-0 band i a tyical examle. The tranition diole moment are in a nice range, o that a line width of < MHz can reult, including natural, reure and intenity broadening. A meaured S/N of 20 in a 0 khz bandwidth ha been achieved. Exreing the frequency intability with Eq (), ν/(s/n), we exect aroximately 8 khz FM noie. The majority of the bandwidth which contribute to the noie i the lat octave, o we may take the frequency rate of the noie roce to be alo ~ 8 khz. Thi lead to a hae modulation index of ~ >, and conequently coniderable ower i lot into noie ideband near thi frequency. If we exre the meaurement bandwidth intead a 0.6 Hz, correonding to an averaging time of, the S/N i imroved by a factor of 60, 000 ~ 250. Now the FM deviation are held to 8 khz/250 ~ 30 Hz. The Allan deviation of the beat note between two I 2 -tabilized laer wa obtained a 5 0-4 / τ, with the integration time τ exreed in. Thi i a very trong indication that we need another factor of 25 in S/N to reach the ub-0-4 tability domain. Alternatively, a cavity may be ued to narrow the line by re-tabilization. However, it cannot be ued to attain better long-term erformance than the molecular reference ignal can rovide. If a S/N increae by a factor of 3 i oible, the hae modulation index would be reduced accordingly and our tabilized ource would change it linewidth from ~ 8 khz down to jut a few hundred Hz! Another candidate for frequency reference in the 064 nm region i a rotation-vibration combination band of C 2 HD (ν + 3ν 3 ). Although thi tranition i extremely weak, reviou work uing a high finee cavity and the frequency modulation technique called NICE-OHMS (noie immune cavity enhanced otical heterodyne molecular ectrocoy) realized the obervation of molecular ectra with S/N of 7670 at a time contant of and linewidth of 500 khz (HWHM) with a 0.20 Pa amle ga reure. 3 The laer frequency wa tabilized to the P(5) tranition, and the beat note frequency between I 2 tabilized Nd:YAG laer howed Allan deviation of 2.0 0-3 / τ. Uon, comaring the I 2 and C 2 HD tranition, it i incredible that erformance earated by only a factor of 4 can be obtained from aborber with an abortion coefficient ratio of 500,000! For imlicity at leat, we therefore conclude that the I 2 -tabilized Nd:YAG laer i the better candidate for an otical frequency tandard. However, it doe make u think that ome work on S/N for the I 2 ytem could buy u a big return in frequency tability. In the following ection, we will dicu the otimum condition for obtaining the larget (S/N)/ ν with thi ytem. 2.2 Detection method of molecular abortion To oberve atomic or molecular aturated abortion ectra with high enitivity, a long abortion length and adequate laer ower are required. In the reviou work of I 2 tabilized Nd:YAG laer, a.2-m long amle cell and.0 mwum and 0.26 mw-robe laer ower were ued. Although thi ytem ulie a near-adequate S/N, the length of the cell degrade it temerature tabilization, which may caue ignal ize, line center frequency, and linewidth variation. With a well-tabilized idearm temerature to fix the vaor reure, in rincile change would occur only via the econd-order Doler effect. However, one find a trong two-time-contant behavior after a te change of idearm
temerature, due to a torage effect by reidual binding of the I 2 molecule to the gla wall of the cell. Thu room temerature change can temorarily change the iodine reure. A comact geometry with good thermal control oibilitie could be rovided by a multi-a cell to uly a long abortion length that hel to maintain/increae the S/N. Diadvantage of the multi-a cell are that otical alignment can be difficult. Additionally one hould be careful to avoid interference effect which caue undeirable interference fringe in the ignal. An otical cavity i ueful to make the ectrometer comact but yet with enhanced abortion length, i.e. high S/N. A cavity alo work a a atial mode elector of the inut laer beam, which reult in a better defined Gauian mode inide the cavity and contribute to reliable reroducibility a mentioned in the ection 2.4. In thi aer, we conider the otimum deign of a cavity-enhanced ectrometer. Another imortant iue for deign the ectrometer i the detection cheme. The frequency modulation (FM) technique i one of the bet way to avoid low frequency noie and to achieve hot-noie limited enitivity. For laer frequency tabilization, the dierion linehae ignal obtained with FM ectrocoy i ued a the frequency dicrimination ignal for frequency locking. However when one ue a cavity a an abortion cell, there are ome difficultie uing the FM technique becaue a cavity alo work a a frequency dicriminator, which may add noie. Additionally, the modulation frequency i limited by the cavity reone time. Cavity dithering i often ued to avoid thi difficulty and to aly hae modulation to the otical field inide the cavity. Uually the modulation frequency of cavity dither i relatively low, ay u to a few hundred khz, becaue it i limited by the cavity mirror mechanical reone time. And the tranmitted radiation oibly contain amlitude modulation due to the imerfection of frequency tabilization to the cavity. Another cheme i to chooe the modulation frequency f m to match the cavity free ectral range ( f m = FSR = c/2l, c; eed of light, L; length of Fabry-Perot cavity). Thi method i called NICE-OHMS and i a owerful tool to utilize high frequency modulation to avoid low frequency noie. One feature of NICE-OHMS i that two ideband-generated molecular reonance ignal reult at frequencie f m /2 aart from the molecular center frequency. Thu one hould carefully chooe the modulation frequency, i.e. cavity length, to avoid being diturbed by thee extra reonance when the method i alied to molecule uch a I 2 that have dene ectra. See the dicuion in the following ection. If it i oible to ue a ring cavity, e.g. a bow-tie tye cavity, the modulation tranfer technique i available 2. In modulation tranfer, only the um beam i frequency modulated and a relatively weak robe beam i detected and demodulated. Becaue of the four wave mixing effect, modulation in the um beam i tranferred to the robe beam. Thi technique ha only a multilicative enitivity to a mall reidual amlitude modulation, comared with the uual additive enitivity. Conequently it i ueful in determining the center frequency of a molecular abortion line. 3 Long cell Laer Samle ga Multi-a cell Cavity cell Fig. : Abortion cell deign to enhance ignal to noie ratio.
Tranmiion ectrum (a) Laer Cavity (b) FM Frequency limitation Dither (c) FSR (d) fm = FSR Fig. 2 Frequency modulation cheme for cavity-enhanced ectrometer. (a) Cavity tranmiion ectrum, (b) Low frequency FM, (c) Cavity dither modulation, (d) NICE-OHMS 2.3 Etimation of attainable linewidth and ignal to noie ratio In thi ection, we dicu otimization of everal oerating arameter and the erformance of an iodine ectrometer. Here we aume the um/robe configuration deicted in Fig. 3. (We have omitted ome otical element in the ectrometer uch a olarizer, the AOM frequency hifter and other beam iolation element.) Saturation arameter are defined a S and S for aturation and robe beam, reectively. Laer ource EOM Iodine cell Saturation Probe Fig. 3 Baic configuration for aturation ectrocoy.
Conider firt the aturation arameter needed to obtain the maximum S/N loe. The aturation ignal contrat i decribed a: α = α 0 + S, (3) where α 0 i the linear abortion coefficient. In the tanding-wave cae where S = S = S, Eq (3) become α = α 0. (4) + 2S The ignal ize i roortional to the robe beam ower, and can be determined by Signal S + S. (5) For the two-beam-configuration aturation ectrocoy, the ower broadening decribed in Eq (2) i rewritten a + ν = ( Γn + Γt + Γ + Γl ), (6) 2 If the detection enitivity i limited by hot noie, it i rereented a Shot noie S + N am, (7) where N am i the equivalent amlifier noie of the detector. Therefore we obtain the aturation arameter-deendence of S/N loe a S / N S ν + S 2 + S + N am. (8) Figure 4 how the calculated S/N loe for S /S = 0.25, 0.5,.0. Each curve how the maximum S/N loe value, which mean the aturation arameter can be otimized to obtain maximum S/N loe value. For S /S = 0.25, 0.5, and, the S/N-loe curve ha a maximum value at S = 6.2 (S =.6), S = 4.0 (S = 2.0), and S = 2.5 (S = 2.5). In the ret of thi aer, we will etimate the exected frequency tability for auming S /S = 0.5 and S ~2.30 (S =.5), where we are acrificing about 6 % in enitivity to avoid unrewarded aturation broadening. (S /N )/ ν [Shot noie limited] 0.2 0.5 0. 0.05 0 0 2 4 6 8 0 S /S 0.25 0.5 S Fig. 4 Saturation-arameter deendence of S/N loe. N am wa taken to 0..
If the abortion i large, i.e. αl >, hot noie i rewritten by α L Shot noie S e + N am, (9) where α i the robe-aturated abortion coefficient decribed by α0 α =, (0) Next we conider the choice of a amle ga reure, laer beam ize, otical ower, and etimate the linewidth obtained with thi deign according to Eq (6) with exerimentally obtained arameter. Although a higher reure reult in a larger ignal ize, the temerature deendence i alo larger. A a reult the I 2 reervoir require better temerature tability to avoid frequency variation caued by the reure hift. For examle, the temerature-deendent reure loe at C i 0.45 Pa/ C. 6 Conidering thi with the reure hift of 3.2 khz/pa, 7 a temerature deendence of abortion frequency hift i obtained a.44 khz/ C. To obtain -Hz frequency tability, the ytem need < m C temerature tability, which begin to be difficult to achieve for long term. Therefore, a lower reure region may be more uitable for the frequency tandard. For examle, at 0.5 Pa ( 8 C), the temerature deendent frequency hift i etimated a 220 Hz/ C. The low reure amle ga i alo ueful to reduce reure broadening. Of coure, there i a trade-off between long-term frequency hift at elevated reure and reduced ignal abortion at low reure. To etimate the exected frequency tability of the laer, firt, we will etimate the oerating linewidth ν. Baed on meaurement at JILA, the natural broadening for iodine 532 nm tranition may be taken a 220 khz, while the reure broadening (alo HWHM bai) i aroximately Γ = 20 khz /Pa P. () At a reure of 0.5 Pa, thi contribution i 60 khz. Tranit time broadening for I 2 molecule i etimated uing a robable thermal velocity of 40 m/ at a room temerature a Γ t = 22 khz mm / w 0, (2) where w 0 i the laer beam radiu. The laer beam diameter 2w 0 i ~ mm, which give the tranit time broadening of Γ t ~ 44 khz. The tyical Nd:YAG laer ha linewidth of Γ l = 5 khz. From Eq (6), the total linewidth ν of the aturated abortion reonance at aturation arameter S = 2.30 and S =.5 i etimated to be 540 khz. Now we move to the etimation of S/N. The meaured unaturated abortion for iodine i ~ 0.003 cm - /Pa for an individual hyerfine comonent near Doler line center of the R(56) 32-0 band. With our adoted aturation arameter of S = 2.30 and S =.5, from Eq (3) we can exect a reonant aturated-abortion eak contrat of 2 % of the ingle line abortion, i.e. 2.7 0-4 cm - /Pa. Additional hyerfine comonent contribute aturable oacity, combining to ~ 0.006 cm - /Pa when their Doler frequency offet are conidered. Of coure thi i non-reonant oacity, but it i ureed by (2.5) ½ according to the aturation effect written by Eq (0). Thu the ingle beam aturation reduce the Doler ummed oacity to 0.007 cm - /Pa. A a concrete cae, conider the ue of Brewter-window iodine cell with a 0-cm active length and a 2-cm ti-ti length. At 0.5 Pa, the ignal oacity i.35 0-3 and the background ingle-a abortion i 3.6 %. Let tart without a cavity. The aturation ower for a 2w 0 = mm beam would be ~ 0.45 mw at the aumed 0.5 Pa. The adoted 2.30 and.5 aturation factor lead to inut ower of.0 and 0.52 mw for aturation and robe. The exected ignal i 0.7 µw in the tranmitted background otical ower of 0.50 mw, leading to a hot-noie limited S/N etimated a 8 0 4 at uing the equation of η Pig S / N =, (3) 2 eb P background where η i the reonivity of the detector, e i the electron charge, B i the detection bandwidth, and P ig and P background are otical ower of ignal and background, reectively. Here we ued the value of B = /2π Hz (for averaging time), η = 0.33 A/W. If P ig = P αl and P background = P ex( α L) ~ P, then Eq (3) i rewritten by S /. (4) η N = αl 2 eb P Uing FM ectrocoy to minimize technical noie, the ignal ize i determined by the beat note ower, o the frequency intability i rewritten a
ν δν =, (5) ν ( S N ) J ( β ) J ( ) / 0 β where J n (β) i n-th order Beel function. J 0 (β)j (β) ha the maximum value of 0.339 at β =.08. The rojected frequency intability would then be 3.4 0-4. (Roughly eaking, thi jut about matche our exerience, BUT we ued a cell about 2-fold longer. So it i quite likely another imortant noie ource i reent - which i mot likely the fat frequency noie of the NPRO ource). Next we conider the deirable cell length and cavity deign to enhance S/N. We uoe a bow-tie cavity configuration of about 50 cm length a hown in Fig. 5. The cavity finee i given by F = π T + l + α, (6) L cell where T i the tranmittance of the couling mirror, l i the total lo of the cavity mirror and cell window, and αl cell i the one a abortion by iodine molecule. A mentioned above, we uoe αl cell i 3.6 % (I 2 reure.0 Pa, L cell = 0 cm). If l i %, the total lo of light with one a of the cavity i about 4.6 %. We conider the cae that the mirror tranmittance T i almot the ame a the one-a lo, then F ~ 35. The effective otical a length i enhanced in the cavity by a factor of 2F/π, which i etimated a 22 for F = 35 cavity. Otical ower i alo enhanced in the cavity, which F T i exreed by. A mentioned above, if we uoe T = αl cell + l, the factor i F/2π. The inut π T + l + α L cell laer ower hould be reduced to kee the referable aturation inide the cavity, o a not to decreae the ignal ize. For the hot-noie limited detection, the S/N decreae due to the ower reduction by a factor of (2π/F) /2, which i calculated a 0.42 for F = 35. Hence the total S/N increae by a factor of 2 F S N 2 F π / = (7) and i etimated a 9.4 for F = 35 cavity. The frequency tability exected for the cell ectrometer i then re-etimated a 3.6 0-5 / τ, which i one order better than the reviou exeriment. A cavity arameter, we can exect, for examle, L cav = 50 cm, FSR = 600 MHz, and cavity fringe width of 7 MHz (FWHM). Saturation I2 cell Probe Lcell = 0 cm Fig. 5 Bow-tie cavity ectrometer for aturation ectrocoy of iodine. Thi moderate finee bow-tie cavity cell deign ha everal advantage. Firt the ectrometer ize i comact, and high temerature tabilization can be exected. Second, aturation and robe beam can be earated, becaue of the running-wave configuration of the cavity, which reult in better ignal contrat than in the equal ower configuration. Third, FM ectrocoy i available with thi ectrometer becaue of the broad cavity tranmittance ectra. Finally, the cavity work a a atial mode elector of the laer beam, hence we can exect good alignment reroducibility even with a comact ytem. The mode wait ize 2w 0 = mm i feaibly attained uing an R = 0 m mirror. Imortantly, the NICE-OHMS method i alo available for thi cavity ectrometer if the FSR i et near 540 MHz. The 540-MHz ideband in thi cae fall nicely into oen lace in the I 2 ectrum o there will be no undeired unbalance of the
NICE-OHMS FM ectrum, a would be caued by main line or cro-over reonance. Alo the FM ectrocoy aroach i enitive to ectral comonent offet by ½ the modulation frequency, due to Doler-generating croover reonance, o we alo have to avoid thee ide-band generated ectra. Amazingly for uch a comlex ectrum 8, it aear that a cavity length of 55.5 cm (c/l = 540 MHz) hould rovide an interference-free oeration. 2.4 Accuracy and reroducibility of ectra Although reviou otical frequency tandard have high tability in hort term (< 00 ), the long term tability and reroducibility are till roblematic. Temerature variation in the amle ga reervoir caue frequency intability eecially in cae of iodine becaue it change the iodine reure, leading to frequency hift. At the iodine oerating temerature about 8 C (vaor reure of 0.5 Pa), the temerature deendence of iodine reure i ~ 0.07 Pa/ C. For examle idearm (reervoir) the temerature variation eaily can be ureed le than 5 m C, and o the reure hift caued by temerature fluctuation i le than ~. Hz. However, a noted above, temerature change of the cell wall give rie to rather large if temorary reure change. Reidual amlitude modulation (RAM) in a frequency modulation ytem i an imortant iue for the dicuion of the accuracy and reroducibility of otical frequency tandard. RAM level can eaily aroach the ercent domain and eriouly degrade the enitivity and ditort the ectral hae in the FM ectrocoy. In thi new eoch when otical frequencie can be eaily and accurately meaured, RAM alo give undeirable offet and noie in error ignal for laer frequency tabilization, cauing frequency offet from the center of the frequency reference and aggravating the intability roblem, articularly at long time ince RAM amlitude i enitive to crytal temerature change or electric field inhomogeneity. Exerimental meaurement howed that, with ome care, a table RAM level of 2.3 m can be obtained directly uing an ADP crytal at a modulation frequency of 220 khz. Even thi RAM level till give noticeable frequency offet from the center frequency of frequency reference (molecular abortion line). For examle, in an I 2 ectrum with a linewidth of 540 khz, thi RAM caue about Hz frequency offet with modulation tranfer, and 0-00-fold more with imle FM detection. Though thi offet frequency doe not degrade the reroducibility a long a it i table, it i better to ure/tabilize RAM with an active feedback ytem. Alignment tability and reroducibility i alo imortant for the reroducibility of the otical clock becaue wave front ditortion of a laer beam will alo caue a frequency offet. Eecially a comact ectrometer ytem tend to have a low reroducibility of running-wave alignment becaue of the hort otical ath length. Again a cavity, which work a a mode elector for the laer beam, i ueful to increae reliability of alignment reroducibility. We believe the cavity ectrometer ytem hould have the ame - or uerior - reroducibility a the reviou ytem uing a long I 2 cell. 9 Therefore, the irreroducibility of thi cavity ectrometer hould be < 5 Hz. Thi rojected cavity-baed ytem i under contruction at JILA. 2.5 Other examle deign Here we conider ome other candidate for otical frequency tandard and the ectrometer deign. The examle calculation reult are ummarized in Table. The Yb:YAG laer (which ulie 030 nm radiation) alo ha table and narrow frequency erformance, and hence can be a candidate for frequency tandard. There i an acetylene vibrational overtone band at the laer wavelength and iodine band in the econd harmonic region. Though the acetylene overtone tranition i very weak, it ha been hown that a high finee cavity ectrometer and NICE-OHMS technique can attain high enitivity. In the reviou exeriment with a 75,000 finee Fabry-Perot cavity cell, the enitivity of 7 0 - wa obtained with acetylene (C 2 H 2 ). 6 The abortion coefficient ha been exerimentally obtained a 3.2 0-8 cm - /Pa. For the R(29) tranition, the aturation ower denity i I = 20 W/mm 2 with about.3-pa reure. According to Eq (8), the S/N loe ha maximum value at S = 2.5 for the Fabry-Perot cavity configuration (S = S = S). If we uoe the Fabry-Perot cavity ha a beam wait of 40 µm, to obtain S = 2.5 the otical ower needed i etimated a 3 W. Here we uoe the S =, i.e. -an otical ower of 5.2 W inide the cavity though the exected S/N loe i factor of 0.84 maller than the maximum value. In the cae of molecular overtone, the minimum abortion linewidth i rimarily determined by the tranit time broadening: Γ t = 35 khz for 40 µm beam ize. Preure broadening i etimated a 0 khz at Pa. Then the total
linewidth including the aturation effect i etimated a 30 khz. Suoe the cavity finee and tranmiion efficiency are 75,000 and 20 %, inut and outut otical ower hould be 0.90 mw and 0.8 mw to obtain 5.2 W inide the cavity. Uing thee arameter, hot-noie limited S/N i etimated a 5.0 0 5 at, which give the exected frequency tability of 6.5 0-5 / τ. Previou tudy of the I 2 ectral width around the 55 nm region howed narrower natural broadening than in the 532 nm region, 20, 2 and recently recie tudy of the natural broadening of I 2 ectra at 489-532 nm revealed Γ n ~ 50 khz at 56 nm, 22 which i 4.4 time narrower than that at the wavelength region of 532 nm. Therefore if the ame ectrometer deigned for 532 nm iodine ectrometer i alied to 56 nm ytem, we can exect 4.4 time better frequency tability. Table. Sectrometer deign and exected frequency tability. Molecule Wavelength (Laer) Tranition α 0 L cav & F Intability I 2 532 nm (SHG of Nd:YAG) X-B, R(56) 32-0.3 0-3 cm - /Pa 50 cm, 35 3.6 0-5 / τ C 2 H 2 03 nm (Yb:YAG) 3ν 3, R(29) 3.2 0-8 cm - /Pa 50 cm, 75000 6.5 0-5 / τ I 2 55 nm (SHG of Yb:YAG) X-B, P(6) 43-0 6 0-4 cm - /Pa 50 cm, 70 8.2 0-6 / τ 3. Concluion We dicued detailed ectrometer deign iue relative to increaing the erformance of a laer frequency tabilization ytem. The otimum condition of aturation arameter to obtain the bet (S/N)/ ν wa dicued. A cavity-baed aroach eem deirable for the bet erformance and, with a cavity finee of 35, the exected frequency tability of Nd:YAG laer tabilized to 532 nm iodine tranition wa etimated a 3.6 0-5 / τ. Reroducibility of thi ectrometer i exected to be le than 5 Hz. To realize thi erformance, the robe laer frequency tability will be required to be imroved. Acknowledgement We are grateful to W.-Y. Cheng and L.-S. Chen for fruitful dicuion about their exerimental reult of iodine ectra at 56 nm. Profeor L.-S. Ma i thanked for hi many contribution to thi work in it earlier tage. Thi reearch i uorted in art by NASA and by NSF, while NIST rovide continuing uort for reearch in the oible new realization of the fundamental tandard. Reference. M. de Labachelerie, K. Nakagawa, and M. Ohtu, Ultranarrow 3 C 2 H 2 aturated-abortion line at.5 µm, Ot. Lett. 9,. 840-842, 994. 2. L.-S. Ma, J. Ye, P. Dubé, and J. L. Hall, Laer Sectrocoy XII, World Scientific, Singaore, 996. 3. J. Ye, L.-S. Ma, and J. L. Hall, Sub-Doler otical frequency reference at.064 µm by mean of ultraenitive cavity-enhanced frequency modulation ectrocoy of a C 2 HD overtone tranition, Ot. Lett. 2,. 000-002, 996. 4. J. Ye, L.-S. Ma, and J. L. Hall, Ultraenitive detection in atomic and molecular hyic demontration in molecular overtone ectrocoy, J. Ot. Soc. Am. B 5,. 6-5, 998. 5. J. Ye, L.-S. Ma, and J. L. Hall, Ultratable otical frequency reference at.064 µm uing a C 2 HD molecular overtone tranition, IEEE Tran. Intrum. Mea. 46,. 78-83, 997.
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