modelling of spectral line shapes in electrodeless discharge lamps

IAPS,University of Latvia

COST 529, April 12-16, Madeira, Portugal

Modelling of spectral line shapes in electrodeless discharge lamps

G. Revalde1, N. Denisova2, A.Skudra1

1 High-resolution spectroscopy and light source technology laboratory, Institute of Atomic Physics and Spectroscopy, University of Latvia2 Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

E-mail: [email protected]: http://www.atomic-physics.lv



Electrodeless lamps:

Bright radiators in the broad spectral range (VUV - IR);

Filled with a gas or metal vapor+buffer gas;

No electrodes – long working life

Inductive coupled/ capacitatively coupled;

Hf, Rf Electromagnetic field excitation;

Different designs and types in dependence on application



Our experience and technology:

manufacturing of electrodeless lamps containing such elements as Sn, Cd, Hg, Zn, Pb, As, Sb, Bi, Fe, Tl, In, Se, Te, Rb, Cs, I2, H2, He, Ne, Ar, Kr, Xe as well as combined Hg-Cd, Hg-Zn, Hg-Cd-Zn, Se-Te etc (also isotope fillings, as example Hg202) etc.

for different applications



Examples

300 400 500 600 7000

1000

2000

3000

4000

Inte

nsity

, rel

. un.

Wavelength, nm

He

200 300 400 500 600 700 8000

1000

2000

3000

4000

Inte

nsity

, rel

. un.

Wavelength, nm

Hg



Spectral line profile is important

• to control self-absorption or radiation trapping for design consideration of low pressure lamps for lighting

application - resonance radiation of Hg at 185 nm and 254 nm

in all cases when narrow spectral line is necessary – for atomic absorption, optical pumping, quantum standards, for spectral reference

• to get important plasma parameters (such as gas temperature, lower state density, collisional broadening)



Example of atomic absorption spectrometry

• Narrow, not self-absorbed spectral line is neccessary -- >

to get high differential cross section of atomic absorption --> low limits of detection



• But with self-absorption dependent on– working regime– filling pressure,– filling content– lamp geometry– excitation geometry

Possibilty to avoid the self-absorption – optimisation of all parameters



Capillary

Lamp

Capillary

Monochromator

Power supply

Fabry – Perrot interferometerPhotomultiplierComputer

LensLens

Vacuum chamberAmplifier

Line profile measurements

High-resolution scanning Fabry-Perrot interferometer



High-resolution scanning Zeeman spectrometer for resonance lines

Hme

c

41



Hg 253,7 nm• Natural filling Hg 202 isotope

In dependence on the Tcold spot

On the working regime



Line shape modeling

Observed spectral line profile: f x f x y f y dy x( ) `̀ ( ) (̀ ) ( )

,

where f ’(x) - real profile, f’’(x) - instrumental function, (x) - function characterising random errors. Task –to get real spectral line profile and parameters characterising plasma by means of a quite universal program for spectral line shape fitting. Model include:

1)

G I

T

G

G

( ) exp ln

,

0 00

2

7

4 2

7 16 10 1

; Gaussian shape

2) L L

L

( )

0

02 24

,

where L =nat+coll+res. Lorentzian shape



3) Voigt profile

V a a y dya y

( , ) exp( )( )

2

2 2 , where yG

( ) ln 2 ,

aL

G

ln 2 ,

2 20( ) ln G

4) self-absorption drdxxnxvPsrvPrnIvIr

aaee

)(),(exp),()()( 0

, where ;)()(a

aa N

rnrn e

ee N

rnn )(

; N n r dra a

12

( ) ; N n r dre e

( ) , We can assume )(),(),( vPlvPlvP ae ,

drdxxnwPwP

srnwPIvIr

ae

)()()(

exp)()()(0

0

Excitation function E yn rn r

e

a

( )( )( )



;)()(2

)(

1

n

raae dxxnrnnrn E y

n y y

ny y

n

n( )

,

( ) ,

20 1

22 1 2

1

1 , y n x dxar

( ) - relative

number of atoms capable of absorbing the line present per unit cross-section between the point under consideration and the outside of the source

1) )0()(;

!2!)()( 0

0

2

0 PPlk

njnePII

j

j

(Cowan and Dieke)

n Z , P()V() by a=const, k0l - optical density

2) , if n=1 homogenous radiation source

II P

k lk l P

P( )

( )exp ( )

( )

0

002

10

3) if n completely inhomogeneous radiation source

I I P k l PP

( ) ( )exp ( )( )

0 0 0 ,



5) Manifold of HFS and isotope components having intensities I1, I2,,...,Ik

and respective shifts 1 2.. k 6) Convolution of the self-absorbed Voigt profile with an instrument function

a) for Fabry-Perrot I IRR

0

22

1

1 41 2( )

sin,

2

, - opt. diff. of

interfering rays, R- effective refraction coefficient b) absorption profile (Gaussian or Voigt) for Zeeman spectrometer c) numerical or other

7) Generation of random errors (x).

8) Fitting of the modelled function to the experimental using

2

1

2

N

ii criterion

by means of multi-parameter fitting procedure, where ii

i iyy f x

1

( ) are

deviations of the experimental data yi from the theoretical values f(xi) at the position of xi, weighted by the experimental errors yi . 9) Results G (gas temperature), L, (collisions), k0l (nlower), n, instrum, and intensities and shifts



Zeeman spectrometer Fabry-Perrot spectrometer

Necessity to take into account the instrument function, also by a small FWHM value of instrument profile due to the influence on the self-reversal

Examples of experimental and modeled profiles

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,0

0,2

0,4

0,6

0,8

1,0

Inte

nisi

ty, r

el. u

n.

Wavenumber, cm-1

Experimental Theoretical Real

Hg202+Ar

253.7 nm,i=160 mA,without cooling

0,0 0,2 0,4 0,6 0,8 1,00,0

0,2

0,4

0,6

0,8

1,0

Inte

nisi

ty, r

el. u

n.Wavenumber, cm-1

Experimental Calculated Real

Hg202+Ar, 10 Torr253.7 nm

i=160 mAt=45oC



0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

0,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity

, re.

un.

Wavenumber, cm-1

Experimental Theoretical Real

Hg202 - 90% +Ar (2 Torr)253.7 nm,i=140 mAwithout thermostabilisation

Optical density 6.8

dopl = 0,044 cm-1(T=488 K)Reff= 0,84%

Hg202/Ar(2 Torr) experimental and modeled profiles of 253.7 nm line, spherical discharge



160 mA, Tc.spot.=72oC

50 mA, Tc.spot.=72oC

Example, Hg 202 (99.8 %) 253,7 nm line

Distribution of the intensitites other isotopic components (0.2 %) also fitted

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

model experimental real

Inte

nsity

, arb

.un.

Wavenumber, cm-1

0,0 0,2 0,4 0,6 0,8 1,0-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

Inte

nsity

, rel

. un.

Wavenumber, cm-1

experimental model real

20 30 40 50 60 70 800

50

100

150

200

160 mA

50 mA

Opt

ical

den

sity

, k0l

Temperature, oC



Hg202/Ar capillary

0,0 0,2 0,4 0,6 0,8 1,0

0

5

10

15

20

25

25oC 45oC

Inte

nisi

ty, r

el.u

n.

Wavenumber, cm-1

253. 7 nm

Hg202+Ar, capillary, 10 Torri=160 mA

65oC

0,0 0,5 1,0 1,5 2,0

0,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity

, rel

. un.

Wavenumber, cm-1

experimental theoretical real

Hg 202 +Ar 10 Torr

20 25 30 35 40 45 50 55 60 65 70 75 80

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

160 mA 100 mA

Opt

ical

den

sity

Cold spot temperature, oC

Experiment

Reff = 0,8% (ninstr =0,071 cm-1).



Hg202/Ar (10 Torr) capillary, 253.7 nm line, Tcold spot= 25oC

80 90 100 110 120 130 140 150 160 170360

380

400

420

440

460

480

500

520

540

560

580

600

620

HF generator current, mA

Tem

pera

ture

, K

80 90 100 110 120 130 140 150 160 1700,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

Opt

ical

den

sity

80 90 100 110 120 130 140 150 160 1700,116

0,118

0,120

0,122

0,124

0,126

0,128

0,130

0,132

Tota

l FW

HM

, cm

-1

The estimated optical density in the line center

The total experimental spectral line FWHM as a function of the HF generator current

The estimated temperature of the emitting atoms



Hg202/Ar (2 Torr) capillary, 253.7 nm line, Tcold spot= 65oC

80 100 120 140 160 180 2003

4

5

6

7

8

9

10

11

12

13

14

Opt

ical

den

sity




Comparison- spherical and capillary

0,6 0,8 1,0 1,2 1,4

0,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity

, rel

.un.

Wavenumber, cm-1

spherical capillary

160 mA and T cold spot =25oC, pAr=10 Torr



Hg visible triplett

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,350,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity

, rel

.un.

Wavenumber, cm-1

40 mA 100 mA 140 mA

404.7 nm

Experimental 404.7 nm line shapes in dependence on the HF generator current for a HF isotope electrodeless lamp

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

0,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity

, rel

. un.

Wavenumber, cm-1


404.7 nm, Hg

Example of the line shape fitting of Hg 404.7 nm line, HF generator current i=100 mA. Fitted parameters wG=0,032 cm-1; wL=0,002 cm-1; R=0,72, kol=1,8, n=13, using the model of Cowan and Dieke

40 60 80 100 120 140

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

300

400

500

600

700

800

900

1000

Opt

ical

den

sity


Temperature, oC



Experimental radial distributions of Hg 404.7 nm line intensity, emitted from HF electrodeless lamp by two different discharge power values.

-1,0 -0,5 0,0 0,5 1,0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

220000

240000

260000

Inte

nsity

, rel

. un.

r/r0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

0,0

0,2

0,4

0,6

0,8

1,0

In

tens

ity, r

el.u

n.

Wavenumber, cm-1


546.1 nm, Hg

Example of the line shape fitting of 546.1 nm Hg line, i=140 mA. Fitted parameters wG=0,033 cm-1; wL=0,002 cm-1; R=0,8; kol=35; with taking into account the measured distributions.



Helium example

Optical density in the line center in dependence on the HF generator current estimated for 501,6 nm and 567,8 nm lines in the helium electrodeless discharge using the model of uniformly excited source.

80 100 120 140 160 180

0,5

0,6

0,7

0,8

0,9

Opt

ical

den

sity

Generator current, mA

501,6 nm 567,8 nm

0 1 2

1

2

3

4

5

6

Inte

nsity

, rel

.un.

Radiuss, cm

28,0 W58,3 W

587.6 nm He

Experimental radial distributions of He 587,6 nm line intensity, emitted from helium HF electrodeless lamp by two different discharge power values.



Thank you for your attention!



0 50 100 150 200 250

1E-3

0.01

0.1

1

10

100

pHg,

torr

Tcold spot, oC

p Hg vapor, Torr

modelling of spectral line shapes in electrodeless discharge lamps

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