COMMENTS ON PHOTOACOUSTIC AND PHOTOTHERMAL SPECTROSCOPY OF GASES COMPARED TO OPTICAL METHODS

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Submitted on 1 Jan 1983

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COMMENTS ON PHOTOACOUSTIC AND PHOTOTHERMAL SPECTROSCOPY OF GASES

COMPARED TO OPTICAL METHODS

Ch. Bordé

To cite this version:

Ch. Bordé. COMMENTS ON PHOTOACOUSTIC AND PHOTOTHERMAL SPECTROSCOPY

OF GASES COMPARED TO OPTICAL METHODS. Journal de Physique Colloques, 1983, 44 (C6),

pp.C6-593-C6-601. �10.1051/jphyscol:1983698�. �jpa-00223257�

COMMENTS ON PHOTOACOUSTIC AND PHOTOTHERMAL SPECTROSCOPY OF GASES COMPARED TO OPTICAL METHODS*

C h . J . Bordg

Laboratoire de Physique des Lasers-LA 282, Univevsite Paris-Nord, Avenue J. -B. Clement, 93430 Villetaneuse, France

Résumé - On analyse l'influence de quelques paramètres physiques (moment de transi- tion, temps de relaxation, pression ...) qui conditionnent la sensibilité ultime des détections photoacoustique et photothermique (PA/PT) que l'on compare aux méthodes de détection optique. On montre que c'est seulement à haute pression (faible résolu- tion) et/ou pour des transitions faiblement autorisées que les méthodes PA et PT sont avantageuses en spectroscopie. Dans le domaine sous-Doppler on aura intérêt à utiliser une détection optique pour les transitions fortes et une détection bolomé- trique pour les transitions faibles.

Abstract - We discuss the influence of some critical parameters, especially the pressure, on the sensitivity of photoacoustic and photothermal methods for high resolution spectroscopy. We show that these methods lose their sensitivity in the sub-Doppler regime where they are advantageously replaced by optical detection (for which the shot noise limit can be reached with high frequency modulation techniques) or by detection of the internal excitation energy carried by the molecules onto a bolometer.

When one wishes to detect a weak absorption of light by a molecular gas, one can either measure the change in light intensity (transmission spectroscopy) or the change induced in the gas itself by molecular excitation (e.g. the pressure in pho- toacoustic spectroscopy).

The sensitivity of the first technique may appear to be poor because it is difficult to detect a small change on top of a large signal.

On the contrary, photoacoustic (PA) or photothermal (PT) detection as "dark background methods" have been broadly used in gas spectroscopy because they seem to exhibit a tremendous sensitivity especially when coupled with powerful laser:sources.

One knows, for instance, that atmospheric pollutants have been detected by this, me- thod at concentrations as low as a fraction of PPB [ 1], Nevertheless one may wonder

Informal contribution to the Panel Discussion on Weakly Absorbing Systems.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983698

JOURNAL DE PHYSIQUE

a b o u t t h e l a c k o f s u c c e s s of t h e s e d e t e c t i o n schemes i n t h e f i e l d o f v e r y h i g h r e s o - l u t i o n s p e c t r o s c o p y and more g e n e r a l l y i n q u i r e a b o u t t h e p a r a m e t e r s which z i f f e c t t h e s e n s i t i v i t y o f PA/PT e x p e r i m e n t s when compared t o o p t i c a l d e t e c t i o n .

Interact ion Gas Cell Pressure

b

Volume V a

LW:

/ ^P

Laser - - _- '. , - _0.D

a p ! i b f

Beam -

*

2 2

P

,X ce, E, W ,

^b

4

0.D H ^Fluoresc-

v Mol. D

Fig. 1

I n Fig. 1 we have r e p r e s e n t e d t h e most s i m p l e s i t u a t i o n where a l a s e r beam o f 2 2

power P = ( n / 4 ) c % E o w o (Eo a m p l i t u d e o f t h e e l e c t r i c f i e l d , w beam w a i s t r a d i u s ) i s a b s o r b e d by t h e g a s of an e n c l o s e d c e l l ( l e n g t h L) and t h e v a r i o u s ways of d e t e c t i n g t h e g a s a b s o r p t i o n :

*By m e a s u r i n g t h e t r a n s m i t t e d i n t e n s i t y w i t h a s u i t a b l e o p t i c a l d e t e c t o r ( O D ) ,

*By m e a s u r i n g t h e c o n v e r s i o n of a b s o r b e d e n e r g y i n t o t r a n s l a t i o n a l d e g r e e s of freedom by p h o t o a c o u s t i c s i n t h e c o l l i s i o n regime ( h i g h p r e s s u r e ) o r by m o l e c u l a r e n e r g y d e t e c t i o n on t h e " w a l l s " i n t h e f r e e - f l i g h t r e g i o n (low p r e s s u r e ) ,

*By m e a s u r i n g t h e f l u o r e s c e n c e e m i s s i o n ( a t low p r e s s u r e ) .

The m o l e c u l a r s y s t e m is assumed t o e x h i b i t a n o p t i c a l t r a n s i t i o n a t t h e l a s e r f r e q u e n c y , between a lower s t a t e l a

>

and an u p p e r s t a t e i b

>

whose r e l a x a t i o n r a t e s a r e r e s p e c t i v e l y y and Y b . We i n t r o d u c e a n a v e r a g e t r a n s i t i o n moment U from

where g i s a l e v e l degeneracy which we assume h e r e t o be same f o r both l e v e l s . When s t u d y i n g t h i s system from t h e p o i n t of view of a s p e c t r o s c o p i s t i n t e r e s t e d i n t h e h i g h e s t p o s s i b l e s e n s i t i v i t y o n e i s l e d t o a s k t h e f o l l o w i n g key q u e s t i o n s :

1) What maximum l a s e r power P a r e we allowed t o i r r a d i a t e on t h e sample ? max

The absorbed power (maximum s i g n a l power a v a i l a b l e ) i n c r e a s e s with t h e i n c i d e n t power and t h e l i m i t a t i o n comes from t h e s a t u r a t i o n of t h e a b s o r p t i o n by t h e e l e c t r o - magnetic f i e l d . Indeed, t h e a b s o r p t i o n s t a r t s t o be s t r o n g l y reduced and t h e l i n e

2 2 2

s e r i o u s l y power-broadened when t h e s a t u r a t i o n parameter S = 11. E T T

/&

g e t s

0 1 2

l a r g e r t h a n 1 . I n t h i s e x p r e s s i o n T1 and T2 a r e r e s p e c t i v e l y t h e r e l a x a t i o n times of t h e energy and of t h e o p t i c a l coherence and a r e given by :

From t h e e x p r e s s i o n s of S and P we f i n d t h e following v a l u e f o r t h e power c o r r e s - ponding t o S = 1 :

where a i s t h e f i n e s t r u c t u r e c o n s t a n t , e t h e e l e c t r o n charge and

rR

t h e r a d i a - t i v e l i f e t i m e of t h e upper l e v e l ( h e r e

rR

i s t h e r e c i p r o c a l of t h e E i n s t e i n c o e f f i - c i e n t A , a f o r t h e t r a n s i t i o n b ^-t a o n l y and i s t y p i c a l l y of t h e o r d e r of 0.01 t o 0.1 second f o r s t r o n g v i b r a t i o n - r o t a t i o n t r a n s i t i o n s ) .

I n t h e c o l l i s i o n broadening regime t h e r e l a x a t i o n r a t e s a r e p r o p o r t i o n a l t o t h e p r e s s u r e p ( t y p i c a l l y ya/2n and yb/2n a r e of t h e o r d e r of 10 MHz/Torr) and P _max i s t h e n p r o p o r t i o n a l t o p 2

.

From (1) one can deduce t h a t , a t l e a s t f o r small v a l u e s of t h e t r a n s i t i o n moment and i n any c a s e f o r p r e s s u r e s above one T o r r , many w a t t s of i n c i d e n t power may be used(*)to e x c i t e t h e molecular system whereas u s u a l l y o p t i c a l d e t e c t o r s cannot s t a n d more t h a n a few mW.

( * ) ~ n t h i s regime w can be made a s l a r g e a s p o s s i b l e t o optimize t h e t o t a l f l u x .

JOURNAL DE PHYSIQUE

T h i s p o i n t i s o b v i o u s l y i n f a v o r of t h e PA/PT d e t e c t i o n .

2) How much power A P i s t r a n s f e r r e d from t h e l i g h t t o t h e molecules and where does t h i s power go ?

I n t h e s a t u r a t i o n l i m i t ( S % I ) , t h e amount o f power A P which i s m i s s i n g f r o m t h e i n c i d e n t power P i s of t h e o r d e r of :

v h e r e n i s t h e p o p u l a t i o n of a b s o r b i n g molecules p e r u n i t volume and where V i s t h e i n t e r a c t i o n volume (". L w 2 ) .

It i s of i n t e r e s t t o n o t e t h a t , because of t h e l i n e a r p r e s s u r e dependence of n and l / T 1

,

A P i s p r o p o r t i o n a l t o t h e s q u a r e of t h e p r e s s u r e . Also, i n an i d e a l experiment t h e p r o d u c t n.L s h o u l d b e i n c r e a s e d a s much a s p o s s i b l e t o r e a c h t h e l i m i t A P % Pmax.

A P i s now a v a i l a b l e f o r t h e v a r i o u s c h a n n e l s of d e t e c t i o n a s shown i n F i g . 1.

Which c h a n n e l i s i t b e t t e r t o use ? The answer h a s of c o u r s e t o do w i t h t h e e f f i - c i e n c y and t h e n o i s e p r o p e r t i e s of each of them.

For h i g h enough p r e s s u r e s c o l l i s i o n s t u r n A P i n t o l o c a l h e a t i n g of t h e gas and t h e PA/PT d e t e c t i o n channel i s widely open.

3) What a r e t h e n o i s e l e v e l s of t h e v a r i o u s d e t e c t i o n channels ?

Using an o p t i c a l d e t e c t i o n , one d e a l s w i t h many k i n d s of n o i s e s [ 2 ] : Johnson n o i s e , generation-recombination n o i s e , l / f n o i s e , b a c k g r o u n d - r a d i a t i o n n o i s e and s h o t n o i s e . To t h e s e we s h o u l d a l s o add t h e p r e a m p l i f i e p n o i s e and t h e l a s e r power i n s t a b i l i t i e s . When working p r o p e r l y ( i . e . w i t h s u i t a b l e quantum d e t e c t o r s and f i l - t e r s c o o l e d a t l i q u i d n i t r o g e n o r helium t e m p e r a t u r e , w i t h s u i t a b l e modulation o r w i t h h i g h frequency h e t e r o d y n e t e c h n i q u e s ) a n d above a g i v e n power l e v e l , t h e s h o t n o i s e happens t o b e t h e u l t i m a t e l i m i t i n g f a c t o r :

where B i s t h e bandwidth ( B = 1 / 4 r ,

r

i n t e g r a t i o n time) and Q t h e quantum e f f i - c i e n c y of t h e d e t e c t o r .

U n f o r t u n a t e l y i n most e x p e r i m e n t s h i g h frequency modulation of t h e a b s o r p t i o n

and extends over a few MHz f o r dye l a s e r s and a few t e n s of k i l o h e r t z f o r gas l a s e r s ) . I n c o n t r a s t t o t h i s c a s e where t h e n o i s e i s p r o p o r t i o n a l t o t h e l a s e r power and hence t o t h e a v a i l a b l e s i g n a l power, dark-background methods o f f e r a n o i s e power

("1

which i s , i n f i r s t approximation,independent of t h e l a s e r power

.

I n a high performance p h o t o a c o u s t i c c e l l (working a t atmospheric p r e s s u r e ) l i m i t e d by t h e Brownian motion of t h e gas molecules on t h e membrane of t h e micro- phone t h e n o i s e i s e q u i v a l e n t t o lo-'' watt/- [ 3 1 which i s comparable t o t h e photon s h o t n o i s e power f o r P i n t h e m i l l i w a t t range and, anyhow, much s m a l l e r t h a n t h e t e c h n i c a l n o i s e power on t h e l a s e r i n t e n s i t y .

Therefore,from t h e t h r e e p o i n t s of view of a v a i l a b l e s i g n a l power, n o i s e power and d e t e c t i o n channel e f f i c i e n c y and, a s f a r a s high p r e s s u r e experiments a r e concerned, PA/PT d e t e c t i o n i s more s e n s i t i v e t h a n c l a s s i c a l o p t i c a l d e t e c t i o n , b u t what i s going t o change a t lower p r e s s u r e when r e s o l u t i o n i s needed ?

4) What happens i f we want r e s o l u t i o n ?

Let us r e c a l l t h a t when reducing t h e pressure p i n t h e c e l l one goes c o n t i - nuously from a c o l l i s i o n regime ( i n which t h e l i n e s a r e f i r s t pressure-broadened and then Doppler-broadened) t o a f r e e - f l i g h t regime s u i t a b l e f o r u l t r a - h i g h r e s o l u t i o n sub-Doppler spectroscopy.

The main consequences of t h i s p r e s s u r e lowering a r e t h e f o l l o w i n g :

-

The maximum l a s e r power allowed by s a t u r a t i o n d e c r e a s e s a s p2 ( s e e

5

1) dropping q u i c k l y i n t h e m i l l i w a t t range i n which o p t i c a l d e t e c t o r s may be used. I n t h e f r e e - f l i g h t regime TI and T2 a r e r e p l a c e d by t h e average t r a n s i t time w / u where u i s t h e most probable v e l o c i t y

( d m )

and formula (1) i s r e p l a c e d by t h e formula g i v i n g t h e n p u l s e power [ 4 1 :

which can be as low a s a few microwatts (e.g. SF6 a t 10 pm).

( * ) u s u a l l y , however, p r a c t i c a l l i m i t a t i o n s such a s windows a b s o r p t i o n may reduce t h e u l t i m a t e s e n s i t i v i t y of a PA c e l l .

JOURNAL DE PHYSIQUE

-

Since t h e a b s o r p t i o n l i n e s g e t narrower and narrower, high frequency modulation o r o p t i c a l heterodyne techniques can b e used t o g e t r i d of t h e t e c h n i c a l n o i s e and t o reach t h e photon s h o t n o i s e l i m i t 1 4 1

.

Eventually t h i s s h o t n o i s e power w i l l g e t s m a l l e r t h a n t h e NEP of most PA/PT d e t e c t o r s . Combining formulas (1) o r ( 4 ) with

( 3 ) we o b t a i n i n t e r e s t i n g formulas f o r t h e signal-to-noise r a t i o : 112 B-1/2

112 Wo TR

1 / 2 f o r t h e c o l l i s i o n regime (T1 T2)

' I 2

B - ' / ~

f o r t h e f r e e - f l i g h t regime

where .C i s t h e s i g n a l c o n t r a s t A P / P .

-

The absorbed power d e c r e a s e s a s p 2 ( s e e § 2) a s long a s t h e homogeneous width

Yba i s l a r g e r than t h e Doppler width k u . Beyond t h i s l i m i t only a s m a l l f r a c t i o n 6v / U of t h e molecules a v a i l a b l e i n t h e v e l o c i t y space ( z i s along t h e o p t i c a l a x i s ) ii used f o r a b s o r p t i o n and s i n c e 6vZ Q, yba/k i n t h e c o l l i s i o n regime t h i s adds an e x t r a power of p t o t h e previous law. To compensate f o r t h i s l o s s t h e only c h o i c e i s t o i n c r e a s e t h e i n t e r a c t i o n l e n g t h I, through m u l t i p a s s c e l l s o r Fabry- Perot r e s o n a t o r s . But i n any c a s e t h e absorbed power cannot exceed

Pmax given by (1) o r (4) ( C

<

1 ) .

-

As t h e c o l l i s i o n r a t e i s reduced t h e amount of t h i s absorbed energy which i s converted i n t o t r a n s l a t i o n a l k i n e t i c energy g e t s lower and lower and o t h e r d e t e c t i o n channels t a k e p l a c e such a s f l u o r e s c e n c e (e.g. s a t u r a t e d f l u o r e s c e n c e of C02 has been widely used 1 5

1

)

.

As a consequence, when going t o high r e s o l u t i o n , a s we t u r n t h e p r e s s u r e down, t h e r e i s always a c r o s s o v e r p o i n t f o r which o p t i c a l d e t e c t i o n i s more s e n s i t i v e t h a n p h o t o a c o u s t i c d e t e c t i o n .

Moreover l e t us p o i n t o u t t h a t sub-Doppler spectroscopy b a s i c a l l y r e q u i r e s t h e s m a l l e s t p o s s i b l e p e r t u r b a t i o n s t o molecular v e l o c i t y ( s e n s i t i v e v a r i a b l e through t h e Doppler e f f e c t ) which i s completely a n t a g o n i s t i c t o t h e i d e a of t r a n s f e r r i n g a n o t i c e a b l e p a r t of t h e l i g h t energy i n t o t r a n s l a t i o n a l degrees of freedom. Thus PA d e t e c t i o n of sub-Doppler resonances seems t o be l i m i t e d t o p r e s s u r e s h i g h e r than

6

'

NH3 o r CH30H a t 10 W) f o r which t h e homogeneous w i d t h i s i n t h e MHz r a n g e , whereas o p t i c a l d e t e c t i o n h a s been proved t o be s u i t a b l e i n t h e f r e e - f l i g h t regime down t o T o r r ( w i t h a l i n e w i d t h i n t h e s u b - k i l o h e r t z r a n g e ) 1 4 1.

A t l a s t , f o r v e r y s m a l l d i p o l e moments and c o r r e s p o n d i n g l y v e r y l o n g l i f e t i m e s b o t h t h e u s u a l PA/PT d e t e c t i o n and o p t i c a l methods b r e a k down a t low p r e s s u r e s because o f t h e v e r y weak a b s o r p t i o n o v e r r e a l i s t i c o p t i c a l p a t h s and of t h e f a c t t h a t a l l t h e i n t e r n a l e n e r g y i s c a r r i e d t o t h e w a l l . One s h o u l d t h e n l o o k f o r t h e a b s o r b e d power where i t i s , t h a t i s on t h e w a l l !

.

So, i n o r d e r t o e x t e n d t h e f i e l d of PA/PT h i g h r e s o l u t i o n s p e c t r o s c o p y of m o l e c u l e s , I would l i k e t o p r e s e n t a n e x p e r i m e n t which compares o p t i c a l and t h e r m a l d e t e c t i o n s i n t h e f r e e - f l i g h t regime i n which t h e a b s o r b e d e n e r g y i s t r a n s f e r r e d away from where t h e m o l e c u l e s a r e e x c i t e d . A s u p e r s o n i c m o l e c u l a r beam of

F6 seeded i n He i n t e r a c t s w i t h a C02 l a s e r beam p e r p e n d i c u l a r t o i t s d i r e c t i o n of p r o p a g a t i o n ( F i g . 2 ) . The a b s o r b e d power can b e measured e i t h e r by m o d u l a t i o n of t h e m o l e c u l a r beam and d e t e c t i o n on t h e o p t i c a l . d e t e c t o r (HgCdTe a t 77K) o r modulation of t h e o p t i c a l beam and t h e r m a l d e t e c t i o n w i t h a b o l o m e t e r (helium- c o o l e d s i l i c o n c h i p ) [ 6 ] .

Thanks t o a t e c h n i q u e o f i n t e r a c t i o n w i t h f o u r s p a t i a l l y - s e p a r a t e d t r a v e l l i n g waves ( o p t i c a l Ramsey f r i n g e s [ 4 , 7 , 8 1 ) t h e l i n e w i d t h can be reduced t o 2 . 5 kHz (HWHM)

.

I n t h e c a s e of t h e SF6 l i n e s u s e d i n t h i s e x p e r i m e n t one s t i l l g e t s a h i g h e r s i g n a l - t o - n o i s e r a t i o w i t h t h e o p t i c a l d e t e c t o r ( s e n s i t i v i t y i n a b s o r p t i o n o f a b o u t

f o r

r =

l s ) b e c a u s e t h e s e l i n e s c o r r e s p o n d t o a r a t h e r l a r g e d i p o l e moment

(% 0.21 D) f o r which t h e n / 2 p u l s e power i s o n l y 32 WJ.

Thanks t o h i g h f r e q u e n c y m o d u l a t i o n of t h e m o l e c u l a r beam (1.5 kHz) one c a n r e a c h t h e c o r r e s p o n d i n g photon s h o t n o i s e l i m i t ( w i t h i n a f a c t o r 3) ^% 10 -12 W f o r one second a v e r a g i n g time. T h i s n o i s e power happens t o be s m a l l e r t h a n what c a n b e a c h i e v e d w i t h u s u a l b o l o m e t e r s used a s d e t e c t o r s o f e x c i t e d m o l e c u l e s . C l e a r l y t h i s s i t u a t i o n would b e r e v e r s e d w i t h s m a l l e r d i p o l e moments ( a n d much l a r g e r l a s e r

JOURNAL

DE

PHYSIQUE

powers) f o r which t h e bolometer (optothermal) technique i s p r e s e n t l y t h e only way t o achieve high r e s o l u t i o n of weak v i b r a t i o n - r o t a t i o n l i n e s .

C02 Laser

w

30 pW

Supersonic Optical

Molecular Detector ( ~ g Cd Te) Beam

(7%SF6

in He) [

Fig. 2

I n conclusion, t h e few c o n s i d e r a t i o n s r a i s e d about t h e c r u c i a l p r e s s u r e depen- dence of t h e PA/PT s i g n a l c l e a r l y i n d i c a t e t h a t t h e methods a r e h i g h l y c o m p e t i t i v e , when compared t o o p t i c a l d e t e c t i o n , a t high p r e s s u r e (low r e s o l u t i o n ) and f o r weak t r a n s i t i o n s whereas t h e y a r e not s u i t a b l e f o r low p r e s s u r e and high r e s o l u t i o n exp;- riments. The case of very weak t r a n s i t i o n s a t u l t r a - h i g h r e s o l u t i o n i s s t i l l an i n t e r e s t i n g c h a l l e n g e f o r experimental p h y s i c i s t s and an a c t i v e f i e l d of r e s e a r c h f o r which t h e combination Ramsey f r i n g e s / b o l o m e t e r appears a s a promising method.

-

d

REFERENCES

[ 1 1 PATEL C.K.N., Science 202,157 (1978).

[ 2 ] KINGSTON R.H., D e t e c t i o n of O p t i c a l and I n f r a r e d R a d i a t i o n , Springer-Verlag (1978).

KEYES R . J . , O p t i c a l and I n f r a r e d D e t e c t o r s , Springer-Verlag (1977).

NUDELMAN S., Applied Optics

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627 (1962).

I

l i 1 L

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CJ

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1

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/sec lo-'

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^BORDE Ch. J . , Ddveloppements r s c e n t s e n spectroscopic i n f r a r o u g e 2 u l t r a - h a u t e r d s o l u t i o n , Revue du CETHEDEC-ONDES e t SIGNAL NS 83-1, 1 (1983).

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ACKNOWLEDGMENT

The a u t h o r would l i k e t o acknowledge a s t i m u l a t i n g and most h e l p f u l exchange w i t h Drs C. BOCCARA and D. FOURNIER which gave b i r t h t o t h i s p r i n t e d form of h i s n a i v e i d e a s .