ULTRA-SENSITIVE INTRACAVITY SPECTROSCOPY WITH MULTIMODE LASERS

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ULTRA-SENSITIVE INTRACAVITY

SPECTROSCOPY WITH MULTIMODE LASERS

V. Baev, A. Weiler, P. Toschek

To cite this version:

V. Baev, A. Weiler, P. Toschek. ULTRA-SENSITIVE INTRACAVITY SPECTROSCOPY WITH MULTIMODE LASERS. Journal de Physique Colloques, 1987, 48 (C7), pp.C7-701-C7-706.

�10.1051/jphyscol:19877173�. �jpa-00226997�

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ULTRA-SENSITIVE INTRACAVITY SPECTROSCOPY WITH MULTIMODE LASERS

V.M. BAEV('), A. WEILER and P.E. TOSCHEK

1. Institut fiir Experimentalphysik, Universitdt Hamburg, Jungiusstrasse 9, 0-2000 Hamburg 36, F.R.G.

Intracavity laser spectroscopy is characterized by extreme sensitivity of the emission spectrum to narrow spectral perturbations such as absorption, gain or light injection. Intracavity absorption spectra obey a modified Lambert-Beer law, where the length of the absorption cell is substituted by 1 = c.t, where c is the velocity of light, and t is the duration of the laser pulse.

The time resolution of intracavity measurements is limited only by the sensitivity required for the detection of the exti ction k, such t h a t c a l/kc. With

5

-f

the minimum detectable absorption being 10- cm

,

e.g., the resolvable time is on the order of a microsecond.

The ultimate sensitivity of intracavity spectroscopy with a cw laser is limited by one of two competing factors: spontaneous emission, and non-linear mode interaction, such as stimulated Brillouin ~cattering.~Depen$$ng on laser parameters,

-

¹

minimum detectable extinction is in the range 10- -10- cm

.

Non-linear mode interaction can also give rise to distortion of the line shapes observed with intracavity spectroscopy.

High sensitivity along with time resolution opens a wide field of practical application for intracavity spectroscopy such as pollution detection, detection of forbidden and non-linear transitions, combustion and plasma diagnostics, and the study of kinetics of molecules and radicals.

1. INTRODUCTION

One of the most im~ortanat techniaues of ~ollution detection is differential absorption spectroscopy. This technique is based on recording the spectrum of the light passing through a cell which contains a sample. The resulting spectrum J(d), is governed bv Lambert-Beer law:

where J, is the intensity of the incident light, k(d) is the absorption coefficient of the sample, and 1 is the optical length of the cell. Absor tion coefficient is equal to N;~(w), where N is the concentration of the sample and C(m) its absorption cross-section.

The seneitivity to the detection of the absorber increases as 1 increases.

However, practically this length is limited to a few meters. With the multipass cell, this length can reach the value f 190 meters. With such a cell, a sample with the absorption coefficient of 10-'cm- will produce an absorption dip J(Q) = Jb/e, which can be easily detected in the spectrum.

Another way to increase significantly the optical absorption length 1 and therefore the sensitivity of measurements is provided by the intracavity laser spectroscopy (ICLS) /1-7/.

2. INTRACAVITY LASER SPECTROSCOPY (ICLS)

Lasers, invented in 1960, have become now the most powerful tool of spectroscopy.

The whole field of laser spectroscopy can be roughly devided into 2 parts: Narrow- band and broad-band laser spectroscopy.

("on leave from Lebedev Physikal, Institute of the Academy of Sciences of the USSR, Leninskij pr.53, 117924 Moscow, USSR

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19877173

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C7-702 JOURNAL DE PHYSIQUE

Narrow-band laser spectroscopy is characterized by the use of a single-mode laser, or a multimode laser, but with the emission line width at least smaller than the absorption lenwidth of the sample. This technique provides a very high spectral resolution, but the sensitivity to absorption is basically the same as in conven

-

tional measurements, even if the absorber is inside the laser cavity.

Broad-band laser spectroscopy, or intracavity spectroscopy (ICS), is characterized by the use of a multimode laser, with the emmission spectrum larger than the absorption linewidth of the sample. The sample should be placed inside the laser cavity.

This technique provides an extremely high sensitivity of absorption measurements.

The enchancement of the sensitivity can be as high as lo6 times that obtained with conventional absorption spectroscopy. The spectral resolutionof ICS in principle, is limited only by the linewidth of single modes and can be as,high as narrow-band laser spectroscopy.

The basic properties of intracavity laser spectroscopy (ICLS) can be understood by analyzing the rate equations of a multimode laser with homogeneously broadened gain /3,8,9/

where M is the photon number of mode q, N is the density of the inversion,

Y =

^T-I

is the !roadband cavity loss rate, k c is the narrow-band absorption rate, P is Pke pump rate, andcis the decay time of the inversion. The mode number q extends up to q the total number of modes, n. The first term on the right-hand side of Eq.(2) desc- ribes the cavity loss, the second one the gain, and the third one the narrow-band loss by intra-cavity absorbers. In Eq.(3), the second and the third terms on the rhs describe spontaneous and stimulated decay of the inv:tsion, respectively.

So far, Eqs. (1) and (2) give the mean values of the parameters that characterize the laser dynamics. Fluctuations of the light field due to its quantum nature re- quire us to amend Eq. (1) by a Langevin term F_(t), normalized as

c

^~~(t),= ^0; (~~(t)~~(t*)> = r ~ ~ ~ > S l ~ ~ ~ ( t - t * )

Interaction of field modes can play a significant role at elevated power levels.

This interaction is taken into account by an additional term

Z ~ ( M

^M . ) on the rhs of Eq. (2), whereq(M M ) gives the transfer of light to'modeqqqf*om the i-th neighboring mode by nonli!e~$~mode coupling, e.g., by Brillouin scattering.

For some simple but important cases, Eqs. (2) and (3) are easily solved analytically:

(i) With lack of intra-cavity absorption (k = 0), negligible fluctuations due to time averaging /F (t) = 0/, same gain for pll $odes (B B), and with the inversion adiabatically f olPowing the field (gc 'C

-

)

,

the s t a t ~ o i a r ~ solution of Eqs. (2) and (3) is

NO =b/lB

,

( 4 )

MO = (4-1) P /fn ₍₅₎

where P = /Br istehe pump threshold, and n = P/Pth is the normalized pump rate.

th

(ii) If we add loss k in one particular mode q, i.e., k = k, threshold and inversion are determined by the remaining modes with small a8d nonspfcific loss.

After N and M have reached stationary values NO and MO for t

>)' ,

^{the light}

flux in mode

8-

decays according to q yo

The minimum detectable absorptivity is defined as k . = (ct )-I 5 1;'

mln 1

where tl is the laser pulse duration. Thus, an ICA line is equivalent to a line of conventional absorption with the optical path length in the absorber 1 = 1

with tl = lms

,

¹⁼^300km. ^P

The m~nimum

detectable

IC absorption k in is estimated to be equal to spontaneous emission kcMi = BN' = b//see ~~.(2)7; then

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With parameters of a typical laser,

Y =

³^r^{lo7 s-I}

,

^:^M = 3 x 10

,

we have k m i n = 3 x 1 0 - ~ ~ c m - ~

.

The laser pulse duration which is required if we want to efploit this sensitivity is tl = M /,f= 1 s with the equivalent pulse length 3 x 10 km.

(iii) With homogeneously broadened gain of bandwidth 9 f, the laser modes differ in their amplification. Close to its center, the gain profile may be approximated by a parabola 131:

B~ = B~ (1

-

/2(q-qo)

V I ~ I

2 , (9)

where

v

is the mode separation, and B is the gain of the central mode qo, which controls threshold and inversion ig the stationary state:

No = d//Bo

,

Pth,o = r/Boc

.

For high enough pump rate, maintained over the time

r-

1

^,

the laser starts oscilating all over the gain profile. Soon, the inversion stabilizes itself at N and the emission narrows 13,101 according to Eq.(l): ^0'

9 q (10)

The number of oscillating modes decreases in time as n = rll(,Yt) 112

(11) The dinamics of multimode lasers was proved to obey relations described above (eq.6,10,11) experimentally up to laser pulse duration of about 1 ms /3,4,10/. With l o n g e r laser p u l s e s t h e s e n s i t i v i t y d o e s n o t c h a n g e as p e r e q . ( 7 ) , b u t s t a y s o n t h e level of l0-~-10-~ cm-l /3,5,10/. The satisfactory explanation of this limitation has been achieved recently on the basis of mode coupling by stimulated Brillouin scattering (SBS)

181.

This mode coupling can be taken into account as an additional term

@(Mq~q+i) = D.M (Mq+i-Mq-i) in rate equations (2) with D being a coupling constant.

From a numericag integration of these rate equations it was found that the intensity of individual modes is fluctuating with an amplitude of about 100% and with the period inversly proportional to the average intensity of the mode:

tn = l/DWq> (12)

With & 7 - 106 this expression gives tn = 1 ms. It was found that this period determines ayso-the sensitivity of ICA measurements according to eq.(7) if tn< tl. These results are in a good agreement with a number of experiments 13-101.

Similar fluctuations of the intensity of laser modes originates from quantum nature of light 111-131, but their period is proportional to the intensity:

tq =<Mq>Tph (13)

The longest fluctuations and consequently the best sensitivity of ICA measurements are achieved when both periods are equal. Then for the limit of sensitivity we have:

Kmin =

. d x

Ic (14)

With Tph = 3:10-~ s and D = l ~ - ~ s - l , Kmin = 6.10-~ cm-l. This value represents the maximum sensltlvity reported so far in ICA measurements with CW dye lasers 13-5,8,10,14/.

Of course, this sensitivity can be accomplished only if fluctuations of technical origin are avoided such as gas bubbles in dye liquid, and, for a broader range of lasers, mechanical vibrations, dust in the optical path of the resonator, instability of the pump light level, and etalon effects due to reflection and/or scattering off resonator components.

Another question, which is important for ICA measurements is a true reproduction of the line shape. Weak absorption lines corresponding to molecular transitions with small cross-sections appeared in intracavity spectra as symmetric lines without distortions /1,3,4,14/ They can be satisfactory fitted by Voigt profiles with suitable contributions of Doppler and pressure broadening 1151.

Strong absorption lines were observed in some experiments to have diviations from true line shape. One of them is the red shift of laser spectrum due to SBS. As a result

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the absorption lines and the whole laser spectrum are asymmetric /8,9,16-18/. To rem- edy this line distortion the laser pump power must be reduced and the mode density increased by choosing a long laser cavity.

Another distortion of ICA lines is the enhancement of the light flux on those modes, which lie on one wing, or both wings of an ICA line /19-24/. This phenomenon seems to develop upon modulat$on of the (inverted) population in the gain medium. If the period of modulation slightly exceeds that of a round-trip of the light in the cavity, mode coup1ing.i~ maximum and loss is minimum in the wings of the absorption line, where the mode separation is smaller due to anomalous dispersion and matches the modulation. This phenomena has been demonstrated with external modulation of the laser gain /23,24/ but it can also show up upon (partial) mode locking of the laser due to its interaction with IC absorber. That usually occursat elevated IC laser power levels and with intracavity absorber having a transition of a large probability

Line asymmetry can also be a result of frequency-dependent mode stability near the absorption line, but they can be easily avoided by choosing the resonator configura- tion with minimum of diffraction loss /25/.

All the spectral distortions mentioned above depend upon the parameters of a multimode laser used for measurements. A proper choise of these parameters is suffi- cient to avoid distortions and to obtain the intracavity spectra with a true reproduction of absorption line.

3. APPLICATION OF INTRACAVITY LASER SPECTROSCOPY

From the very beginning, ILS has been considered a technique for the detection of very weak optical extinction. We have already shown that the spectral output, in mode q, of the multimode laser including loss obeys the modified Lambert-Beer law

J (c3,t) = Jq(t)-exfl-kq(w)ct), where the optical path ct corresponds to the length

02

the uninterrupted wave of a particular laser mode. From the temporal decay of the light flux, the absorption can be determined from at least two measurements of the instantaneous spectral flux at the absorption line, which are separated in time by the interval 0, and corresponding normalization measurements outside the line:

kq = (C 8 ) -1 1" ( Jq(t) Jq+ rq(t+8) Jq+ 8q(t) Jq(t+@> 1. (15) In this way, e.g., the absorption of rotational lines of the 000 - 043 transition of the C02 mole6ule was measured with a streak camera for time-resolved spectral recording /26/. With the laser light gated by an electro-optical switch for 10 ps, ro-vibrational overtone spectra of atmospheric.H20 /4/ and 02 /15/ were measured.

On the other hand, kq may be determined by a measurement of the time-integrated lightoflux, normalized to t@e flux outside the absorption line:

R = l~~(t)ex~(-k~ct)dt / Jq+ 8 q(t)dt

0 (16)

The relationship between k: and R is, in general, nonlinear. With constant flux during the pulse time tl, e.g., we have /26/:

As pointed out before, the light flux of homogeneously broadened laser is not constant in time, but rather varies as for modes in the central part of the emission profile. For these modes In R varies linearly with kq within 10% accuracy /27/. Although accuracy and sensitivity of this version of ILS measurements is slightly lower than that of time-resolved observation, it is much more convenient and has been used in most experiments so far.

The accuracy of ILS measurements depends also on the accuracy of a determination of the length of uninterrupted laser emission. This length can be fixed by a modulation of a multimode laser pumping with the pulses, which are shorter then the period of mode fluctuations / see Eq.(12), (13)/. The optimum duration of modulation tl can be found by observing the sensitivity saturation with growing modulation length. This way the sensitivity is slightly lower, but the accu;acy of absorption measurements can be within 10% /lo/.

As an example of extreme sensitivity, the spectrum of atmospheric absorption was measured with CW Rhodamine 6G dye laser /28/. With the sensitivitv of cm-l. 717 absorption lines were measured' in the range from 584 to 603 nm. ~imost half of these lines,were recorded for the first time due to high sensitivity and absence of solar absorption lines, masked the atmospheric absorption in previous measurements. Some of

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laboratory.

The sensitivity of the ICS technique is determined, as shown above, by the laser pulse duration tl, This duration determines the time resolution of measurements, which is limited only by the required sensitivity of the detection. Indeed, time resolution can be traded for sensitivity within wide limits, with 10 ns being the shortest practical resolution time. With the minimum detectable absorptivity 10-~cm-', e.g., the resolvable time is on the order of microsecond 127,291. Thus, ICS is applicable, if we want to track the variation of the macroscopic parameters of an absorber, as an afterglow, and/or the microscopic kinetics of its constituents. As an example, time resolved absorption spectra of He2 in the afterglow of a pulsed electric discharge were recorded with a multimode LiF:F + laser in the wavelength range between 900 and 930 nm and with the pulse duration o$ 200 ns. Each of the laser pulses was marked by spectral modulqtion,fryn the absorption by two ro-vibrational bands of the electronic transition c> - a

2

starting in the lowest metastable state. Hoenl-London plots derived from tEese meagurements enable one to determine the rotational temperature of the He2 molecules, its deviation from thermal equilibrium, and the variation of temperature and metastable population as functions of the time delay in the afterglow.

High sensitivity along with time resolution is a prerequisite for studies of the kinetics of radicals 130,311. Many kinetic constants of reactions involving radicals such as NH2, HCO, HNO, or pH2 were first measured only by using ICS technique.

The extention of ICS to studies of nonlinear absorption is straightforward. A two- photon absorption line, e.g., shows up in ICS, if the absorber is irradiated simulta- neously by additional strong narrow-band light. A photon from the broadband laser is chosen, which makes up for the energy defect between a photon of the narrow-band light and a two-photon resonance transition. This way the cross section of two-photon transitions in potassium was directly measured with narrow-band ruby laser and a broad band DOTS dye laser excited by the same ruby laser 1321.

Certain groups of modes of a multimode laser with a broad emission band may be en- hanced in amplitude rather than quenched if frequency-selective gain is made available inside its resonator. In an ICS experiments using a L ~ F : F ~ + color center laser, which was pumped by the green emission of a pulsed xenon laser, the strong gain was observed on numerous ro-vibrational lines, since left-over pump light inverted the corresponding transitions. In this way, pumping conditions and available inversible transitions can be studied systematically 1291.

Recently it was shown that ILS can be also used for the detection of spectrally narrow light emission 1331. It was shown that the light flux with the power of 3 . 1 0 - ~ ~ ~ can be detected with CW dye laser.

The examples mentioned above are not the only possible application of ILS. De- pending on practical requirements the scope of possible applications can be always extended further.

V.?4.B. wishes to acknowledge support from the Alexander von Humboldt Foundation.

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