Final Technical Progress Report Differential

0 downloads 0 Views 5MB Size Report
Nov 7, 1989 - 500 eV. Tile continuously variable altitude grid allows altitude steps of ..... by a plus while the excitation ...... T()RR FT ti ...... and P. A. Sachet,.
i 4

Differential

Final Technical Progress Report Collision Cross-Sections for Atomic

Contract

Oxygen

NAS8-36955

Delivery

Order

48

George C. Marshall Space Flight Center Space Sciences Laboratory National Aeronautics and Space Administration Marshall Space Flight Center, Alabama 35812

by

Dr. Douglas G. Torr Principal Investigator The University of Alabama in Huntsville Center for Space Plasma and Aeronomic Research and Physics Department Huntsville, Alabama 35899

February

1991

N91-24547

(NA_A-CR-/_'Z/_/// CROSS-$ECTIn.NS Technic,_I

Jut.

]990

OTFFE"ENTTAL CI3LLTSTON FjP _TqMiC OXYGEN final PFO_F,_.SS Report, II Jui. 19Q9 - IO (A1,_bdma Univ.) I_8 p CSCL 20H G3/7_

Unclas 0330320

.-Report _?3Ce

1. Report

Title

4.

Documentation

Page

AOm_:_Br,al

@ O _ f',l

TI-

•,-I _

2_ ,iO

.D

w IE2

_N

t_ •,-t 4J ,..-t m o'. I n" e* I

b.I

•,i't _-t

WO_dlSONV

_3d

SHOI3-1IVB

NI

IIISN31NI

,I_

llllllllIlllIIIIIIllIlllllIIIIIIlllllllIIlllIIIlllllllrTIllIIIIlililiillililil

14 0 -,-t

GO

i

ill

ii

L

@ J_ (D -_I

z

"o w

@

-_I _D CO 0_

i

0 rr k-u_ (__ Z

IL. I h iL. • 0

0 _J @ U]

I 'II'

0

(N Z

W J

w

"Ii

,.n

-

(D r_J Z r_ W _J w

Z

S

gg

_0 .,i t .1_ w _D p.. L_

Ii-

_-_

.T_.I-II

o" I

I

(_ rO ,:r

w 6-

lllIllllIllllllllllllillllllIlllllllllIllllllllllltiiilllillliiillllIllllllll

_0 _DPO

.0 _,i

I

WO_ISgNV

W3d

SHgI39kVW

NI

I

AIISN31NI

T

T

o

"_

0

i

IIIIIIIIIIIIIIIIIIIIIlllllltlllllllllllltlltllllll|]l|lillllllllltlllllllllll_

o_-_ 0

E_ E_ 00 E_

(11 •,-t .,-t @ @

O3 E_

0

_

E_ _O O3 O" U _ (.,'3 o rr or) E_ cN i tD co o,,I I

Z

e14 ° O_

z

@ @ m

-IE_ E_ Lo r,J z r_ i,i _J bJ

[, Z

_ -,.-t _

,D Xl

w _D r_ L_

_

_'"_

E_ o" L_

I

E_

!

_O

@

@_0 _0_

E_ II

IIIIIIJlllllllllilllllllll_l

III[lllllttlllllllll

illtllllltliiill

Q O0

H0_ISgN_

_3d

SHOI3"]IV_

N]

-,.-I Q).,-I

tlillflllll

qO E_OO CO f

L_

f

_I]SN31NI

I

I

123

i I I

I I I

I I I

I'1

t

I I I

I I I

i I I

I I I

I I

I I I

I I I 11

I

I I I I I

I I I

I I I1

I I|

I

I I

I I 1 I

I I I

I il

i

ii

i

i

i

1 i

i

I 1 I

I't

I

C 0 CO

C .,.4 C

-CO 0

C 0

:c"

r o

o M

Fto z

0

_r

z !

@ -r

!

_D o,J Z W

iic

_D

W I'N

W 0 0 @ _4 @ U_

,D ._ ,-t

..@ r--

m

I--

o-

m_

I

n,m I

fXl

6IIIIIIIIlllllllllllilllllllllllllllllllltlllllllllllLllllllllllllll!llllllllll


* lad

/ io o

I

I

'

"%'"J

io o

,

J : =.l.lJ

I01

10 2

ENERGY Fig. 1. Average electron energies The

average

energy (E,,.)

ionization

excitation

potential

JO 4

(ev)

losses per collision and average secondary as a fu.nction of primary electron energy. potential

ergy loss per ionization potentials are indicated tential is set equal to

10 3

is labelled

I and

the

total

en-

is labelled I+E,,,. The average excitation by an asterisk and the O; excitation pothat of N2. Note that below 6 eV, the N2

is set

at

1 eV.

The dependence of the average secondary energy on the primary energy is shown in Figure 1 along with the average total energy loss of the primary (I + E_). The average energy of the secondaries increases steadily from 0 near threshold to 52 eV for 10 keV primary electrons. The total energy loss per ionizing collision for 10 keV electrons is 72 eV, when the 20 eV ionization potential is included. The average energy of the secondaries is approximately equal to the ionization energy for 200 eV primary electrons. A quantity of interest, in relation to energy degradation of high energy electrons, is the average energy required to produce each electron-ion pair. The average energy required to produce e_ch electron-ion pair is a quantity that is independent of electron energy and is also remarkably independent of the species being ionized. The experimental value for the energy lost per electron-ion pair for high energy electron is 35 eV [V_lentine and Cgrran, 1958]. This energy loss per electron-ion pair was used in early auroral electron deposition codes [Rees, 1963: Rees et al. 1969; Rees and Jones, 1973]. An approximate value for the energy loss per electronion pair can be deduced by using the average energy losses depicted in Figure 1, assuming that for electron energies above approximately 100 eV the energy lost to excitation collisions is small and can be neglected. With this assumption, it requires about 160 ionizing collisions to thermalize a single 10 keV electron. Thus, on the average, 62 eV is lost in the creation of each of the 160 electron-ion pairs. Since the ionization energy is 20 eV for electron energies above 100 eV, the average energy of the secondaries is -_42 eV. This means that

I0.340

the

RICHARDS

160 secondary

create

one

daries

created

number per

electrons

more

of

an

reality

would

excitation the

does

ergy and produced 160.

would not

processes

ionization

320

begin

to

and

excitation

attd

only

a 42

half

sections

than

a half,

of

primaries

100

eV

10

the

[Richards

and

Tore,

electron

would

ion

pairs

electron-ion

pair

an

eV.

This

calculation

including

the

value.

actual

[1971]

that

to

system

the

act

auroral

ergy

loss

per

than

our

estimate

the

by

al.

loss

and

we

obtain

pair

but

Foz

and

average

electron

has

per

to do

likely

to

the of

[1988]

using

their

with

a 1 keV

the

loss

per

37 eV

tend

electron

will

average

of only

tllem

undergo

than

they sion

are

much

less

Richards

and

Tore

established

cross sections and are much

cross

sections

decay less im-

both

because

because the energy loss per total ionization cross sections

than there

the

are

total

some

Dunn, 1966]. We have ionization cross sections

excitation

cross

differences

adopted of Rapp

colliare sec-

[Kieffer

and

the N2 and O2 total and Englander-Golden

[1965] elers.

which have also been used by most other modThe total ionization cross section for O is from

Brook

et al.

[197'8].

The

important We have

because used tile

al. [1988] The total

and also their cross sections

shown

in Figure but

at high because

fluxes.

The

land ours

at higher

section. total

et

section

[1988] The

below

differences

little effect on the calculated fluxes cross section is smaller than the However,

30 eV produce

N.,

cross

et al.

energies.

very

coefficients. model are

excitation

Solomon

are

transport. Solomon

differences

comparable

excitation

cross

in cross

differences section

of

in

$teiek-

et al. [1983] is ahnost a factor of two larger than at all energies and their fluxes would be a facof

two

where of

of

sections

backscatter in our auroral

N2 total

that

is smaller

cross

cross

in inhibiting sections of

elastic used

2. Our to

below

elastic

of their role elastic cross

energies have the excitation

ionization

lower

below

Nx is the

Solomon

et

primary

tion.

Moreover,

30

eV,

donfinant

at

least

species.

al,

[1988]

by

sunmfing

and

the for

possibility example, Strickland

below

The

Strickland tile

cross

of double those that

km

sections

et al.

partial

et al.

200

cross

[1983] sections

counting some lead to dissocia-

[1983]

included

large

energies degrade are

10"14

.......

,

........

,

........

I

.......

ex-

ionizing

eV before have an

likely

excitation energy

ionization and The

although

there is sections;

22

to the

tile

are smaller is smaller.

better

by

energies.

portant

and cross

For

of 45 electrons

to higher

between

which

only

loss

published

the same cross sections have been used they have been reparameterized to ex-

100 eV, the with increasing

obtained

ionization.

energy secondary

been

Basically study but

were

as they

secondaries

25 eV compared

and

the

have

RATR

Above rapidly

tor was

discrete

initial

collision

secondary

an average Thus, the

and

higher

energy

collisions with it thermalizes.

the 10 keV electrons additional ions.

laboratory

relationship

energy with

higher generate

energy

with value

electron

energy

produce

en-

is smaller

The reason that the energy is not a strong function of

Electrons

a greater they

in our

average

which

higher

Victor

secondary

energy.

an

of 35 eV,

in agreement

rate

EMISSION

100 eV

[1988]. in this

25 eV

ef

A

is comparable

be lost

energy

production

A slightly

energy

ample,

will

ion

energy loss method. per electron-ion pair

more

of

to determine Banks

the

per

detailed

by

total

electron-ion

value.

obtained

but

loss

a more

out

240

estimate

electrons

to increase

calculation,

measured

suffer

all

is required

pointed

original

about

energy

and

de-

below

the

low

sections

SUlnmed

full

the

pair

by

pair.

We have

electron

Thus

is only

backscattered

and

electron-ion

local lost

was

to pro-

energies

3371

tions

equal

produce

transport It

en-

ionization

is created

average

electron-ion

escaping

total

be expected

1985b].

yield

per

with

approximately

ultimately

and

lost

eV,

electron

with

of 42

the energy

100

effectively

ionization

secondaries

electron

eV.

pair. This agrees with show that a third rather

and

keV

to 31

below

the

could

total

total

energy

electron-ion pairs would be less than

are

the secondaries

to

secon-

the

62

available

electron

duce all additional electron-ion our previous calculations that graded

from

additional electrons

eV

cross

pair,

compete the

all

average

because,

for

the number of by the secondary for

If

the

decrease

happen

processes

In fact,

and

AURORAL

energetic

each.

electron-ion

be

pair

this

pair

additional

pairs

TORR:

sufficiently

electron-ion

electron-ion

In

are

AND

42 eV for

I0"

IS

E

to produce

I 10-*°

2.4.

Cross

Sections

In a number photoelectron tation tween

cross theory

of previous flux we have

by

section

Pitchford with

where

atomic

sion duced

cross

Phelps PES

oxygen

sections

good

surements.

the

was

measurements.

total

by

between cross

found At

dominant

measured

mobility

theory

high

species,

Zipf and sections

to

and for

At to-

studies be

altitudes

PES energies

0 i0-17

iO-II I i0 0

,

L|*.J,i

: _0 !

.

|:.*.,I

I I0 z

I

Ill

*HI 10 3

I

I

I I''" 10 4

com-

the emis-

co-workers

0

bemea-

et al., 1980]. species, the

electron

[1982]

is the

agreement These

front

ionospheric total exci-

good agreement spectrometer

AE-E satellite [Lee N2 is the dominant

obtained and

patible

of the measured

sectious that produce and the photoelectron

surements front tile low altitudes where tal cross

studies chosen

promeabe-

£NER(;Y

(,V)

Fig. 2. Total elastic, excitation, and ionization cross sections employed in the model. The ionization cross sections arc indicated by a plus while the excitation cross sections are indicated by an asterisk.

RICtIARDS

AND

TORn:

3371

AURORAL

Rydberg cross sections from Green and S_olarski [1972] which have been revised sharply downward by Porter et al. [1976]. There is now good agreement between the total cross section of Pitchford and Phelps [1982] and the sum of the partial excitation cross sections of Cartwright et M. [1977a, b] as revised by Trajmar et aI. [1983], below 20 eV. Above 20 eV, the ionization cross section becomes an increasingly important component of the total inelastic cross section and it is not easy to compare the two cross sections. The total atomic oxygen excitation cross section employed by Solomon et al. [1988] is a factor of 2 larger than ours above 15 eV and will produce a siluilar difference in flux above 250 km where O is the dominant species but the atomic oxygen cross section has little effect on the integrated emission rates. Our atomic oxygen excitation cross section was obtained by summing the measured emission cross sections for 1304, 1356, and 1027 _. [Zipf and Erdman, 1985], the 989 cross section from Gulctcek and Doertng [1988], and the theoretical ID and 1S from Henry et al. [1969]. hnplicit in this procedure is the assumption that the higher lying triplet and quintet states are included in the 1304 and 1356 emission cross sections via cascade. We have left out some theoretical Rydberg cross sections proposed by Jaekman et al. [1977] and some minor states that radiate directly to the ground state but for which there is no experimental data. Thus, our cross section must be regarded as a lower limit. Figure 3 shows the excitation cross sections for the second positive (C3r.) and Lyman-Birge-Hopfield (air,l) systems of N._. Also shown is the cross section

A

EMISSION

10.341

RATE

by multiplying the 3371 ./_ cross section of Imami and Borst [1974] by 4 and the (air,l) cross section is front Ajello and Shemansky [1985]. We have examined the sensitivity of the emission rate ratios to cross sections and this will be discussed later. In all these calculations we have used the 1 erg cm-'_s -t Gaussian incident flux distribution, and the neutral atmosphere employed by StrickIand ef al. [1983]. 3. 3.1.

Comparison

RBSULTS

With

We have calculated

Previous

Work

the N._ 3371 ./_, N + 3914 A., N +

4278 _, , O 1356 _ , and several N2 LBH band emission rates as a fimction of energy and these are shown in Figure 4. This figure shows that both the 3371/_. and 3914 _. emission rates are independent of the characteristic energy of the precipitating flux for energies above 2 keV in agreement with the results of Stricktand et al. [1983] and Daniell and S_rickland [1986]. Not only is the shape in good agreement but, except for the 1356 _. emission rates, the magnitudes are also in good agreement. Although the shape of the 1356 }k curve is in good agreement with that of Strickland et al. [1983], the magnitude is a factor of 2.5 lower owing to the use of the revised cross section of gipf and Erdman [1985].

3914

used for calculation of the 0(5S) 1356 _ emission rate. We obtained this cross section by reducing the measured cross section of Stone and Zipf [1974] by the factor 3.1 which is the same factor that the 1304 _ emission cross section of Stone and gipf[1974] was reduced by Zipfand Erdman

[1985].

The

(C3r,,)

cross

section

was obtained

,- "i l

al

e IO-17

0 0

2

0 -

I*l,*lZ||l|llJ

6

ENERGY

(keV)

-_llmllll._,*..

4

O

I0

I0-11' 0

5

I0

18

20

25

30

35

40

48

50

Fig.

4. Calculated

tic energy ENERGY

(eV)

energy are

Fig. the

3.

Cross

emissions

sections studied

for in

the this

three p_per.

excited

states

giving

rise

to

flux of i

taken

culations Daniell

emission

for a G aussian

into in and

erg

cm

account,

Figure Strtckland

rates energy

-2

s -i . When

there

(1986).

with

in cross

agreement

et al. (1983)

characteris-

a total incident

differences

is excellent

8 of Strickland

of the

as a function distribution

and

sections

with

the

Figure

cal11 of

ORIGINAl. PAGE '" OF POOR QUALITY I0.342

R[CHARDS

We have included affects both the bands

when

electrons

02 Schuman-Runge 1356 ]k and the

the

characteristic

penetrate

1983].

The

of

LBH

for

3914

tile

._

[1979]

N__ emissions.

ratio

and

is 0.3

our

3371

to 0.8 from Solomon agreement between ratios

but

there

parameters

3.2.

have

acterize

cross

is 0.98

uncertainty the

parameter

sensitivity

of the

ratio

a similar flux

0.3

to

rate. of up

sections

0.25

and of

of

10%

in

species. but

the

finally

and

of the

is next

through

he escaping

flux

ch

smaller

and

heat

of the

energy small

ill molecular more higher

Downward

on

are

available

shown

with

(20%)

wifile

backscattered than

the

45%

for high oxygen

energy

the

(35%).

is lost

This

escape

by

but

incident

fluxes.

Ab-

opposite

deeper

,





6



,

7

II









11

I0

Spectra

moving

fluxes

in Figure

pronounced

and

i

!

........

120,

174,

223,

incident

and

326

Gau_ian

of 1 erg cm-2s -t. The incident at 5 keV in Figure 6. At the there is very the degradation at

|

at

6 for a 5 keV

'

120

kin.

' ' ..... ,

'

little is

degradation noticeable

Because

there

' '''"'!

.......

at

is so

,to

10"

io'r

io I X ,.J 14,

IOB

IO4

absorption

energy the



Banks

use of different Below 1 keV, energy,

with



5

flux

electron the



Exci-

15%

obtained

Fluz

174 km

capture

for the shows



4

+her-

escape

oxygen



3

altitudes, flux but

5 shows tile excitations,

flux.

of atomic sinks

important

a greater proportion the characteristic e,

for

only

|

an energy flux be seen centered

patti-

N_ ions

energy

,

two highest of this initial

ionization

backscattered energy.

excitation

e important

becoming

and

effect

and

et al. [ "4], possibly as a result of the cross sec:ions and backscatter coefficients.

sorption

Electron

flux with flux can

relative

a possible

into space. Figure amongst ionizations,

heating

share

become

3.4.

the

is initially

as

!

2

pro-

km

negligible

flux

emerges

of characteristic

of N_

they

_,

excitation

of excitation

.

I

N2 the

oxygen inelastic cross

estimate

has

energy

number it

iectron

"uization

3914

and

t

Fig. 5. The initial partitioning of the incident I erg em -3 s -1 energy flux between ionization, excitotion, thermRl electron heating, and backscatter as a function of characteristic energy. The largest proportion of the energy (_35%) goes in::mlly into the ioldzation potential of the N + wlfile (--.20%) goes into N2 excitation. Only (_16%) is backscattered out of the thermosphere. O is an important absorber of energy at the lowest energies while 02 becomes increasingly important as the characteristic energy ncrenses.

IOI

is radiated partition

a function greatest

low

of the

is not sensitive to most other param-

average

this

the

for most

increase in the 100 eV reduces

We

computed

electron

before

thermal

a 30% above



0

ENERGY(keY)

Budget

mosphere or gross energy

is

input

positive

decreasing

coefficients,

the

a large

processes

et

to char-

second

atomic and molecular the O, O.+, and Nz

our

incident into

by

increasing

backscatter

Energy

tation

of tile

is responsible

by

ionization potentials our computed ratios.

tile

studies

The integrated ratio to a factor of two in

concentrations

as

the

emission rates to possible Obviously, a reduction of rate cross section would

effect

which

including: the cross sections,

T!:_

in

calculated and measured values into excellent but a 30% increase in tile N_. total excitation

from

tioned

compared

.0!

ratio

3.3.

et al.

differences.

some

has

"_." .... 1

to

./k ratio

_ emission. Likewise, ionization cross section

error

X

Solomon obtained better ratios and tile measured

3371 total

eters elastic

3371 Sharp

....

7.. 2

emisval-

[1989]. his model for

RATE

_____

from

._, to 4278

is sufficient

electron

duct:-, chan_es

our

EMISSION

the

taken

negative measured

10 keV,

A

et al.,

of Ratios

section

energy

and

from

to first negative integrated errors m the model inputs. 20% in the 3371 ./t emission bring the agreement

are

to first of the

performed

the

high

3371

which LBH

]k

to 0.25

to account

Sensitivity

We

At

compared

AURORAL

[Strickland

bands

Ajello and Shemansky [1985]. Our calculated second positive sion rate ratios are within 20% ues

are

altitudes

the

ToRn:

absorption 1200-1600

energies

to lower

ratios

AND

I0 a iOo

Thermal

electrons

of the :gy.

available

energy,

io |

IO 4

ENERGY (ev)

penetration

fluxes.

ioz

ioI

trend, capture the

lower

Fig. 6. Downward moving tudes for a 5 keV Gaussian flux is 1 erg cm -2 s -l

electron incident

flux spectra at several altiflux. The incident energy

RICHARD$ AND TORn: AURORAL little interaction with tile thermosphere for high energy electrons at the high altitudes, there are few degraded primaries to fill ill the region between 300 eV and 5 keV. However, at the lowest altitudes this intermediate energy range is filled in. Comparison of the downward fluxes in Figure 6 with tile upward fluxes ill Figure 7 reveals that, below 225 km, where transport is inhibited, the electron flux is isotropic for energies less than 300 eV. At 326 kin, tile upward (escape) flux is a factor of 2 larger than the downward flux at low energies and orders of magnitude larger at intermediate energies. 4.

3371 A

EMISSION

I0.343

RATE

REFEP_ENCES Ajetlo, J. M., and D. E. Shemansky, A reexamination of important N,. cross sections by electron impact with application to the dayglow: Tile Lyman-BirgeHopfield band system and N I (119.99 nm), J. Geophys. Res., 90, (A10), 1985. Banks, P. M. and C. R. Chappell, and A. F. Nagy, A new model for the interaction of auroral electrons with the atmosphere:

spectral

degradation,

backscat-

ter, optical emission, and ionization, J. Geophys. Res., 79, 1459, 1974. Borst, W. L., and E. C. Zipf, Cross section for electron-

CONCLUSIONS

We have developed an efficient two-stream auroral electron model that incorporates the concept of average energy loss. This model produces integrated emission rates that are in excellent agreement with the more sophisticated multi-stream model of Strickland et al. [1983] but is in disagreement with tile model of Rees and Lummerzheim [1989] with regards to tile energy dependence of the N_. 3371 A second positive emission rate. Our calculations give a value of 35 eV for tile average energy lost per electron-ion pair produced independent of primary electron energy and we have explained this behavior in terms of tile variation ill the energy of the secondary electrons. We find that more than 30% of the initial energy flux is stored initially as ionization energy of N + while about 20% goes into excited states of N_. while only 15% is backscattered out of tile thermosphere. All other processes are minor except at low incident energies where 20% of the energy is stored in atomic oxygen ions.

impact excitation of the (0,0) first negative band of N + from threshold to 3 keV, Phys. Rev. A, 1, 834, 1970. Brook, E., M. F. A. Harrison, and A. C. H. Smith, Measurements of the electron impact ionisation cross sections of He, C, O and N atoms, J. Phys. B, II, 3115, 1978. Cartwright, D. C., W. R. Peadleton, and L. D. Weaver, Auroral emission of the N_+ Meinet bands, J. Geophys. Res., 80,651, 1975. Cartwright, D. C., A. Chutjian, S. Ttajmar, and W. Williams, Electron impact excitation of the electro,tic states of N.,, I, Differential cross sections at incident energies from 10 to 50 eV, Phys. Rev. A, I6, 1013, 1977a. Cartwright, D. C., S. Trajmar, A. Chutjian, and W. Williams, Electron impact excitation of the electronic states of N.,, II, Integral cross sections at incident

energies from 10 to 50 eV, Phys. Rev. A, 16, 1041, Acknou, ledgments. This work was supported by NSF grants 1977b. ATM-8713693, ATM-8716036, ATM-8907808. and ATM-8714461 ; Daniell, R. E., and D. J. Strickland, Dependence of the and NASA grants NAGW-922, and NAGW-996 at The University of Alabama in Huntsville. auroral middle UV emissions on the incident electron The Editor thanks R. E. Daniell and M. H. Rees for their spectrum and neutral atmosphere, J. Geophys. Res., assistance in evaluating this paper gI, 321, 1986. Erdman, P. W., and E. C. Zipf, Dissociative excitation I0 l of the NI(OS) state by electron impact on N,.: Excitation function and quenching, J. Geophys. Res., 91, 1986. I01

7

Fox, J. L., and G. A. Victor, Electron energy deposition in N2 gas, Planet. Space Sci., 36,326, 1988. Garstang, R. H., Multiplet intensities for lines 4S-'-D of SII, OII and NI, Astrophys. J., 115, 506, 1952. Green, A. E. S. and R. S. Stolarski, Analytic nmdels of

I0 7

% o

i0I

X J

loSi

I0 4

I0 s

&

I0 o

l

l

Illlll

l

I0 !

I

I

Iml,ll

,

l

lO 1

I

l

tlllJ

I

I0 $

I

I

l

ill

I0 4

ENERGY(iV) Fig. 7. Upward moving electron flux spectra for the 5 keV Gaussian incident flux shown in Figure 6.

electron impact excitation cross sections, J. Atmos. Terr. Phys., 3_, 1703, 1972. Gulcicek, E. E., and J. P. Doering, Absolute differential and integral electron excitation cross sections of the atomic oxygen 3p and oP states at 30 eV, J. Geophys. Res., g2(A4), 3445-3448, 1988. Henry, R. J. W., P. G. Burke and A. L. Sinfailam, Scattering of electrons by C, N, O, N +, O + and O ++, Phys. Rev., 178 218, 1969. Jackman, C. H., R. M. Garvey, and A. E. S. Green, Electron impact on atmospheric gases, I. Updated cross sections, J. Geophys. Res., 8_, 5081-5090, 1977.

I0.344

RICHARDS ANDTORR:AURORAL 3371A EMISSION RATE

Kieffer,L. J., andG. ization diatomic

cross

section

molecules:

H. Dunn, Electron impact iondata for atoms, atomic ions and I. experimental

data,

Rev.

Mod.

phy,., as, l, 1966.

ondary electrons in aurora, Planet. Space Sci., 17, 1997, 1969. Richards, P. G., and D. G. Tort, An investigation of the consistency of the ionospheric measurements of the

Lee, J. S., J. P. Doering, T. A. Potemra, and L. H. Brace, Measurements of the ambient photoelectron spectrum from Atmosphere Explorer, I, AE-E mea-

photoelectron flux and solar E2zV flux, d. Geophys. Res., 89, 5625, 1984. Richards, P. G., and D. G. Tort, The altitude variation

surements below 300 km during solar ufinimunl conditions, Planet. Space 5cz., _8, 947, 1980. Liliana, D, and J. A. D. Stockdah, Dissociative ioniza-

of the ionospheric photoelectron flux: a comparison of theory and measurement, J. Geophys. Res., 90, 2877, 1985a. Richards, P. G. and D. G. Tort, On the production of N + by energetic electrons, Y. Geophys. Res. 90, 9917, 1985b. Richards, P. G., and D. G. Tort, Ratio of photoelectron to EUV ionization rates for aeronomic studies

tion of molecules by electron impact, II, Kinetic energy and angular distributions of N + and N ++ ions from N_,, J. Chem. Phys., 63, 3898-3908, 1975. Lummerzheim, D., M. H. Rees, and H. R. Anderson, Angular dependent transport of auroral electrons in the upper atmosphere, Planet. Space Sci., 37, 109, 1989. Mahmood, I, and Walter L. Borst, Electron excitation of the (0,0) second positive band of nitrogen from threshold to 1000 eV', d. Chem. Phys., ai, 1115, 1974. Nagy, A. F., and P. M. Banks, the ionosphere, d. Geophys. Opal, C. B., W. K. Peterson, surements of secondary-electron

Photoelectron fluxes in Res., 75, 6260, 1970. and E. C. Beaty, Measpectra produced by

J. Geophys. J2es., 93, 4060, 1988. Sharp, W. E., M. H. Rees, and A. I. Stewart, Coordinated rocket and satellite measurements of an auroral event, 2, The rocket observations and analysis, d. Geophys. Res., 8_, 1977, 1979. Shepherd, G. G., J. D. Winningham, F. E. Bunn, and F. W. Thirkettle, An empirical determination of the production efficiency for auroral 6300- _ enfission by energetic electrons, J. Geophys. Res., 85,715, 1980. Solomon, S. C., Auroral excitation of the N,. 2P(0,0)

electron impact ionization of a number of simple gases, J. Chem. Phys., 55, 4100, 1971. Pitchford, L. C., and A. V. Phelps, Comparative calculations of electron swarm properties in N,. at moder-

and VK(0,9) bands, J. Geophys. Res., 95, 17215, 1989. Solomon, S. C., P. B. Hays, and V. J. Abreu, The auroral 6300 _, emission: Observations and modeUng,

ate E/N values, Phys. Rev. A _5, 540, 1982. Porter, H. S., C. H. Jackman, and A. E. S. Green, Efflciencies for production of atomic nitrogen and oxygen by relativisitic proton impact in air, Y. Chem. Phys.,

J. Geophys. Res., 93(A9), 9867, 1988. Stone, E.J., and E.C. Zipf, Electron-impact excitation of the 3S_ and 5S° states of atomic oxygen, J. Chem.

65, 154-167, 1976. Rapp, D., and P. Englander-Golden, tions for ionization and attachment tron impact I, Positive ionization..L

Total cross secin gases by elecChem. Phys.,

43, 1464, 1965. Rees, M. H., Auroral ionization and excitation dent energetic electrons, Planet. Space Sci., 1963. Rees, M. H. ,rod R. A. Jones, Time dependent of the aurora, II, Spectroscopic morphology,

by inci11, 1209, studies Planet.

Phys., 60, 4237, 1974. Stricktand, D. J., J. R. Jasperse,

and J. A. Whalen,

De-

pendence of auroral FUV emissions on the incident electron spectrum and neutral atmosphere, J. Geophys. Swartz,

Res., 88, 8051, 1983. W. E., Optimization

ergy degradation

calculations,

of energetic d. Geophys.

electron Res.,

en90,

6587, 1985. Trajmar, S., D. F. Register, and A. Chutjian, Electron scattering by molecules, II, ExperimentM methods and data, Phys. Rep., 97, 219, 1983. Vallance Jones, A., A model for the excitation of electron .arora and some applications, Can. J. Phys.,

Space Sci., 21, 1213, 1973. Rees, M. H., and D. Luckey, Auroral electron energy 53, 2276, 1975. derived from the ratio of spectroscopic emissions, 1, Zipf, E. C., and P. W. Erdman, Electron impact exciModel computations, J. C,eophys. Res., 79, 5181, tation of atonfic oxygen: Revised cross sections, J. 1974. Geopays. Res., 90, 11087, 1985. Rees, M. H., and D. Lunuuerzheim, Characteristics of auroral electron precipitation derived from optical spectroscopy, J. Geophys. Res., 95, 6799, 1989. Rees, M. H., D. Lummerzheim, R. G. Roble, J. D. WinP. G. Richards and D. G. Tort, University of Alabama, Research Institute C-10, Huntsville, AL 35899. ningham, J. D. Craven, and L. A. Frank, Auroral Energy deposition rate, characteristic electron energy and ionospheric parameters derived from Dynamics Explorer 1 images, J. Geophys. Rees, M. H., A. I. Stewart, and

Res., 93, 12841, 1988. J. C. G. Walker, See-

(Recieved October accepted November

18, 1989; 28, 1989.)

G_:,G,',_. ;,.. _,,.GE

JOURNAL

OF

GEOPHYS[CAL

The Dependence

RESEARCH.

of Modeled

VOL.

Auroral

Emissions G.

Space

0I

S_ iem'e

A.

Luboratorv,

95.

1356

GERMANY

PAGES

M.

Space

R.

7725-7733.

Lyman

N2

Neutral

aND

Mar,dufll

A6.

and

on the

NASA

NO.

JUNE

IS

I. 1990

Birge

Hopfield

Atmosphere TORR

Fl&,ht Center,

Huntsvdle.

Alabama

P. G. RICHARDSAND D. G. TORR of Alabama

University

m Huntsville,

Huntsvdle,

Alabama

Images of the enure auroral oval at carefully selected wavelengths contain information on the global energy influx due to energetic panicles and some information on the characteristic energy of the precipitating panicles In this paper we investigate the sensitivity of selected auroral emissions to changes in the neutral atmosphere. In parlicular, we examine the behavmr o( Ol 1356 A and two Lyman Birge Hopfield (LBH) bands and their ratios tt'_ each other with changing atmosphenc composmon. The two LBH bands are selected so that one lies in the region ol slrong O2 ab_,orptu)n it 46..1 A) and one lies at a wavelength where Oz absorption is effectively negligible ( 1838 A ). We find that for annc_pated average uncertainties in the neutral atmosphere (factor of 2 at auroral altitudes), the resultant change m the modeled intensities _s comparable to or less than the uncertainty in the neutral atmosphere. The smallest vanatmns, for example, are R)r 1 1838 (approximately 10 to 20%) while the largest varmtmn Is seen m the t)l 1356 A ,emission which is linear with IO] to within 20%. We have also investigated the dependence ol these intensities, and their ratios, to much larger changes in the composition tie.. [OI/IN:I) xuch as m_ght be encountered m large magneuc storms, or over seasonal or solar cycle extremes. We find that the variatmn in the I 1356d 1838 ratio over the equivalent of a solar cycle is less than 50%. The ',ummer-to-wmter changes are approximately a factor of 2, The I 1356/I 1838 ratio is a very. sensitive indicator of the characteristic energy, showing a change of 13 over the energy range 200 eV to l0 keV The corresponding change in the LBH long-to-short wavelength ratio is much less (about a factor of 3). However. the latter is insensitive to changes in the neutral atmosphere ! :i bt_er :llliludc;_ilh the renullin_ hi_zher emission

41 and beyond

r

.

°° _

qucnchin,.: t_iII__iII_ilh

14[¢.

l, li,

ti .I } I

I •



dominalcs

-t _ " °

{.1. •"" • "

• •

• :



iii

lhe _-

,mallcr ,talc hci,_'hc m

l

and

of alomic irl

Plalc

el bc.d time. This plalc

,how,, the exlcnl Io _liich ,,ea,,onaJhcmi,,pheric _l_,,mmelrles _rc rcduu'ed _hen

lhe dala arc pb[Icd

in lhi_ formal.

PI.=I¢ ] I-he7320-.-%.,. ,tmeem',,,i nrale ph_n..'`.:m_-'_:.i_p_ik_)_._h_averasa_un_`_n_ahi_ud_`i_ud_.a ndloculllilie _[,,il_lludcl or llft ('T Th,: upper pbl ,,h_w,, lh_ peak volume ¢111is_.iolIr;JlC only a', a luncllon ul l,,lliludc ,Ind local llme. l-he ,.ollJlll¢ _'mi,.,41m roll,..' i,, _u'i ;i b,-" ,_.,ik." The result,. ,ire onl,, _.,ilid V.ilhin lh¢ L _ 4 bound-',ri_.", ,h{_,._.n in Fi_zurc 5.

Pl,llC /UIlllh

2

Fhc ,InL'l'..'

7

___}-

FIle

_

_,t_lUnlC

"+_ilUIlIC

CI1)l_.xl()rl

rJIC (phc)ldrl_

¢rtl

_ _-' I ,11 the peJk

_)1 the [_t'_cr _

;1 IunctlOll

o| J]tilud¢.

[aliludc.

_ll_d ,_t}lJr

.+.'rlllx,,It)F] I',LIC Is ++T+l,I +t+_ xL'+IIC

600 +

550

.... ++"++':'+"FAG_

: :+ 7] _:;-,,,+-;,+'+_'+;'-

IS

C_ #+'c,C?P, QUALITY 500 I

450 I 400 _--

a 10 "_

10 0 Production

Fi-.6.

_.|idday.

,,1) _'._rthcrn

1 d-a

hcm_,,phcr,:

tudeproducti(m h+r 4() \.

12 [.T.

101 Rate

ndh_.,',raleslorO'l'P'_:l(ziJnd(l_)',t_uthernhcnli',ph \

(-,IF

10 2

O+ (2P) (cm ",1Im¢ "i )

CrCtt_r4F'_S.

[.T. ",,: 2H':( 30% FOR 130 < X < 200 nm

,,, 3 nm FWHM BLOCKING

< 10-3%

APPLICATIONS: SPECTRAL ISOLATION EMISSION FEATURES: HLy_

121.6

nm

OI

130.4

nm

OI

135.6

nm

AND OTHER FEATURES

OF THE TERRESTRIAL

FILTERS

FOR

CONCEPT

FOR THE DEVELOPMENT PERFORMANCE FILTERS

LACK OF LOW ABSORPTION

PROBLEMS:

VUV FOR ALL-DIELECTRIC

=_

ALTERNATIVES:

POOR TRANSMISSION,

REFLECTIVE AFFECTED

A MEASURE

TRANSMISSION

AND BLOCKING

COATINGS

HAVE A

PASSBAND

OF SUCCESS

PREVIOUSLY

FILTERS

EFFECTS

REFLECTIVE BROAD

IN THE

ARE NOT AS SEVERELY

BY ABSORPTION

RELATIVELY

FILM MATERIALS

BANDWIDTH

COATINGS

BUT TYPICAL

OF HIGH

HAS BEEN ACHIEVED

BY COMBINING

SEVERAL

REFLECTORS

IN TANDEM

£J&ELOJ£J

THE RATIO OF IN-BAND REFLECTIVITY

(RIN/RouT)N

=_

IMPROVED

TO OUT-OF-BAND

(R) INCREASES

AS

WHEREN = NUMBER OF REFLECTORS

BANDWIDTH

AND OUT-OF-BAND

BLOCKING

Our Objective Available VUV

and Commercially Narrowband Filters

T(X)

=@ ,J

T>35Z

4O 30

Bandwidth

20

i0

< 5 nm

T, (nm)

>

15

150

nm

160

I,,,,,4

CO 0"_

c5

¢',q

II

I!

Z

Z

r.O 0%

Z

\

\

0 ,

\ 0% •

0 ° e"'-I

c5

\ ,

\ O_ 0%

\ i

20 nm. t

Blocking

for terestrial

in the

FWHM

design

has relatively

useful

than

with

available

typical

centered

Lyman-a

= 9 nm.

filter

not very

the

hydrogen

- 135 nm; close filter

filters

and 25%

reported

centered

commercially

of transmittance

of the

20%

MalherbO

are

120 nm to 160 nm have

transmittance

10-s%.

that

much

of 25%, smaller

and experimentally

of a surface

plasma

wave

A variable from

7 nm

bandwidth

to 20 nm with

was centered windows

longer

Narrowband

some

nm

1° are

e-9.

smaller

available

band

and

Taking narrow

and

spectrum.

higher

waves

of the

metal

of vacuum

ultraviolet

high reflectivity

the

shape

reflection

can be achieved

The

filter

from

pass

that

for some

25%

the

by

developed centered

transmittance

at in

applications.

curve

a more

120 nm

reported

we have

greater

transmittance

applications

also

than

filters,

from

than

10 nm have

is similar

rectangular

shape

to that for the

is required.

as are

are

that

the

the VUV

available

certainly

and

in order

bandwidths

suffered

(VUV)

greater

all-dielectric

of the

For most

such

a measure

had

were

filters

transmittance were

it is clear

for this

in series

of some

with bandwidths

for metal-dielectric

2 achieved

reflectors

those

above

filters

and

filters,

peak

listed

broadband

transmittance

reasons

to those

blocking

filters

filters,

range

insumcient

broadband The

all-dielectric

provided

account,

for all-dielectric

more

Since

all this into

al

20% to 40%, respectively.

wavelength

bandwidths

with

filters t,4-s,l*.

VUV

Hunted

properties

5 nm

VUV

low transmittance

ultraviolet

FWHM

region

of Fabry-Perot-type pass

The than

wavelength

Currently relatively

optical

as low as 135 nm.

longer

from

by Elias _et

region.

for the vacuum

similar

authors

wavelengths the

reported

transmittance

wavelength

filters

with

other

recently

peak

filter

at 17fi rim, and as in the case of other

in the

to 230

transmission

in the

a lack

coupling

spectral visible

range

and infrared

of low absorbing

of the

incident

lacks

light

high parts

film materials into

plasma

quality of the in the surface

filters.

of success

in solving

to achieve

desired

polarizers

and

within

passband,

the

2

this

problem

spectral

analyzers. then

by combining

performance The

idea

the in-band

for the

is that

two or design

if sufficiently

exponential

loss of

reflectivity

with

out-of-band

additional

exponential

the

ratio

of in-band

eg.

90%

and

reflectivity

10%,

paper

reflection

into

desired ple,

The multilayer of several with

nm)

of 39.3%

next

centered

section

options

was

A multiple

of this

which

narrowband

A summary

In this

paper

called

including

is given

the

the

rl filters

filters thin

in Section

are

a throughput

is better

design

and

in Section and

in-band

so on.

and

broad-

combined and

the

For examcentral

wavelengths performance

of 11 nm and than

of 10,

at the

the

is of a

throughput

3x10-s%.

of quarterwave

film deposition,

the

then

of out-of-band

are presented

V.

reduce

applications.

a bandwidth

13. The

order

wavelengths

to illustrate

theory

be the

filters

net

to be viable,

of narrow

broadband and

to the

to 1%, and

for out-of-band

designed case

then

These

Blocking

blocking

reviews

broadband

techniques

was

should

fabrication

of 3.2 nm

Out-of-band

we have

and

and

approach

is reduced

and

blocking

achieved.

reflector

at 175 nm.

realized.

reflectivity

excellent

a bandwidth

54% was

experimental

preparation.

to provide

surface

90% reflectance.

with

10-4%. filter

desired

compared

for the

for example,

design

filtering

better

than

successful

narrowband

(135.6

greater

the

for both

wavelength

broadband

we report

shape

narrowband

than

out-of-band

the

at each

reflections,

the

reflector

spectral

Two

insignificant

However,

reflectivity

whereas

with

becomes

reduction.

respectively.

filters

a multiple

surfaces

reflectance

to out-of-band

to 81%,

In this band

reflective

(QW), spectral III.

substrate

and

other

performance

Section

IV deals

handling

and

II.

ABSORBING

A.

Reflectance

The

intensity

incident

MULTILAYERS

Transmittance

reflection

on a multilayer

and stack

and

Absorptance

transmission are given

coefficients

for a plane

electromagnetic

wave

by 14

(Mli + Ml:Ts)_o - (M_I + M227s) r = (MtI + M127s)7o + (M31 + M_27s)'

(1)

2_ t = (MH + M_27s)7o + (M2_ + M:27s)' where

,10 and

substrate,

7s, which

are

are the

defined

for s polarization,

effective

optical

functions

(2)

of the incident

medium

and

the

as

and

7o ----no ¢os8o,

(3)

7s = as ¢osOs

(4)

as cos_o

7o--

,

(5)

,

(0)

no

7s --

cos_s ns

for p and

polarization. the

substrate indices

that

the

therefore characteristic layers

e0 and

are measured

refractive both

Angles,

of the

substrate

relative

incident and

real optical

functions.

matrix

M which

e,, for light

to the normal

medium

incident The

propagation

and

medium terms

is defined

the have

through

the

to the film plane,

substrate, negligible

respectively. extinction

Mu, i, j = 1, 2 are the elements as the

product

of the

MI = (cos6, i7t sin 6z

_sin6,) cos 6t

"

matrices

incident

medium

n0 and

ns are the

It is assumed coefficients

and

of the

multilayer

of the

individual

Mr, where (7)

The

phase

thicknesses

of the

films

6 are

given

by

271"

6 = -_--Ntdl cos O.

(8)

,4O

where

_0 is the

referred

vacuum

to as "optical

wavelength constant")

of the incident of the

l-th

light.

layer

defined

Nt = nt(1 + iKt) = nz + inter

with the

,q = kdm. physical

The

where

and

thickness,

reflection

¢,

where

and

reflectance

et

and

are

nt is the

and

Oa is the

transmission

the

refractive

phase

R, transmittance

complex

Quarterwave

Multilayer stack

are

Tuned

stacks

usually

as

(9)

kz is the of the

r and

extinction

light

within

t are complex

coefficient, the

l-th

numbers

dt

is

film.

of the

form

t = Itl_'_',

(11)

on

reflection

absorptance

and

transmission.

A of a multilayer

are

The given

intensity

by

R = rr',

(12)

T = rl-s-tt', 7/0

(13)

1-(R+T).

(14)

Multilayers

formed

referred

(usually

(lO)

changes

T, and

function

, = I,.1_'_,

A=

B.

angle

optical

= nl + ikh

index,

coefficients

Nt is the

by high

to as tuned

and

low index

filters

or tuned

materials

alternating

multilayers.

The

throughout basic

design

a of

sucha multilayer stack is given in either symmetric [(HL),H] Symmetric of the

[(LH)pL]

basic

index

design,

medium

and

[(LH)p]

L designate

respectively,

of a stack

optical

and p

are determined

tuned

multilayers

thicknesses

is the number

by the refractive

represent of high

of (HI,) indices

form

of the

another

and

pairs.

[(HL)p]. form

low refractive

The

form

substrate

and

the

and incident

1'.

If the

optical

and

its refractive

film

is referred

on the fact interfaces

thickness index)

of a film (defined is equal

for an incident

will all be in phase,

with

shown

that

absorbing

following

to one

to as a quarterwave

that

We have stack

asymmetric

tt

film materials

symmetry

the

and

or asymmetric

quarter

(QW)

so the

at zero

of some

reference

beams

obtained

of incidence,

is achieved

,x, then

multilayers

reflected

of a film

from

this

are based the

various

is a maximum.

the

when

thickness

wavelength

of QW

A0 = A, the

reflectance

angle

of a physical

. Applications

wavelength

film materials

condition

as a product

the

maximum number

reflectance of (HL)

pairs

of a QW p

satisfies



( (

R

_H

-- t_L

))'

p = po = "_ tan-' i7 In"_L

'

(15)

where kH

_H= --,

(16)

nH

and kL

XL --



(17)

71L

nH and

nL are refractive

corresponding pairs

for which

extinction both

the

indices

of high

coefficients. absorptance

and Values

and

low index

film materials,

of v > p0 correspond

reflectance

of the

stack

and

ku and

to numbers are

constant

kL are of (HL)

and

sum

to unity

i.e. R+A---*

resulting

in a value

An

alternative

films

might

is the

ratio

theory wave

for the

stack

of the

in terms

of the maximum

it is the formed

ratio

QW

of the and

of the

by the

a symmetrical

transmittance

description

be given

standing

minimum

maximum

interference

the

R is the

maximum

reflectance

absorbing.

intensity

cannot

ultimate

stack

an exact

(20)

provides

able

with

an absorbing

the

stack.

However,

represent

reflectance,

stack

and

with

absorbing

18. The

SWR

in general

in a standing

electric

field

reflected

wave.

amplitude

In multilayer in the

electromagnetic

standing

waves.

For

QW

form

k_H_+ n_l.f

2_rn0

Eq.(20)

saturated

[(HL)pH]

stack

referred

is given

value

maximum

the

obtained

therefore

by ts

(20)

to as the

with

optical

for

the

7

the

Koppelmann

limit.

forming

the

Thus,

stack

maximum angle

Therefore,

approximations of a QW

maximum

properties

for zero

for 00 _ 0°.

some

reflectance

between

RK is derived

reflectance

and

are

R --, 1 as p--, oo.

relationship and

level

kL nL21

was derived

of the

simple

In addition, ultimate

1

SWR

R -, RK as p -_ oo, if film materials

calculation

the

--

(19) The

of the

is usually

that

an extremely

the

ratio

stack

1+v_ = -1-v_

film materials

be emphasized

as an estimate.

(SWR)

of the stack.

of a QW

For non-absorbing

replace

wave

of the incident

reflectance

of a QW

It should

of a QW

amplitudes

_

the

to zero.

stack lr

reflectance

RE, the

equal

properties

to minimum

RK

where

(18)

essentially

optical

SWR where

1,

of film

stack.

it

Equation

reflectance

obtain-

materials

forming

reflectance

must

of incidence

and

we shall

is and

reference

be treated it does the

not

exactly

calculated reflectance[Eq. (12)] as the

"Koppelmann

limit"

for a QW

stack

at any

angle

of incidence.

The

Koppelmann

limit

theoretical

and

of the

thicknesses

film

materials

BaF_

than

which

and

LaFs

are

They

both

below

200

techniques

for the

wavelength

range.

optical

thickness

film material VUV

all multilayer index H/L

< 1 have

with

have

values

< 1 instead

lower

and

Tuned

The

definition

of the

quarterwave

stacks.

thickness

is 100 times and

of above

QW

therefore

Since greater higher

index

thicknesses

of an

for which

order

than

low index

that

reflection

and

referenced to the

stacks H/L

VUV

with

the

= 1. MgFu entire

film

material

for

coefficient

of the

high

stacks

with

of MgF3, than

at

10 -2 for

of 10 -4 for almost

the extinction than

identified

applicable

multilayer

stacks

as the

materials greater

are not

of the

used

the

high

of the extinction

mentioned

is to utilize

coefficient

it is exclusively

film

coefficient

limit

of standard

in this paper.

index

extinction

problem

for

refinement

in the

values

of

reflectance.

high

most

of a number

numerical

amplitude

formulas

Koppelmann

extinction

LaFs)

absorption

assuming

that

to this

presented

(BaF_

means

of the

region 22, and

authors,

VUV

subject

involve

field

maximum

of the

the

electric

approximating the

been

approaches

the

available

This

it have

Some

Other

provide

only

of the

Thirdwave

optical

the

H/L

C.

of the

would

approach

values

designs

materials

derived

nm.

Our

wavelength

t°-2t.

to reduce

improvement

ratio

has

studies

10 -8,

pair

wavelengths

to extend

side of incidence.

(HL)

time 22.

how

in order

to the

lower

optimum

this

experimental

close

coefficient

and

stacks

the with

H/L

= 1.

Multilayers

thirdwave

equal

(TW)

It is defined to one

third

multilayers

here

as a tuned

of some

is not

standardized

multilayer

reference

which

wavelength,

as in the

case

has one material while

the

optical

thickness

of the

other

material

is equal

to one

nLdL

Since

kH/k

BaF:,

)___100 for presently

L

and

MgF2),

the

choice

available of which

sixth

=

high

of a reference

wavelength,

i.e.

--. 3

and

material

low index

should

materials

in the

have

the

optical

an

(HL)

pair

VUV

(LaF3,

thickness

of ;_r/6

is obvious.

The

two

H and

thickness

equal

Similarly,

an (HL)

which

again

principle

pair

D.

which

are discussed

at

has

phase

an overall

of the

next

optical

of the

TW

with

thickness

wavelength

concept

in the

phase

thickness

a reference

The

form

to a total

multilayer

to a total

stack.

multilayer

corresponds

of a TW

reflectance

of a QW

in a QW

which

corresponds

to that

multilayers

total

of the

thickness

pair

equal

of a TW multilayer

leads

pair

equal to r.

tuned

optical 6 = 7r. to At/2

Thus,

the

multilayer

to other

is

kinds

of

section.

II Multilayers

We define ,_,/2.

to ,L/2

of a high

similar

L films

a N multilayer

Optical

thicknesses

as one whose of individual

basic

H and

(HL)

L films

pair

has

a total

forming

a pair

optical satisfy

thickness the

of

following

condition

H + L = 5-' where pair

>,, is the is equal

special in phase,

cases

reference

to r,

i.e.

wavelength 6H + 6L = r.

of 17 multilayers.

while

of the

in a thirdwave

multilayer.

Thus,

other

The

quarterwave

In a quarterwave and

(2a)

stack

17 multilayers 9

total

and

light light

phase

thirdwave

thickness stacks

of the are

the is

reflected

from

all interfaces

reflected

from

each

(HL)

pair

is in phase.

Obviously,

in the

and

visible

than

other

do not lower

a 11 multilayer

of incidence.

It shows

stacks

plotted

(I-I/L).

The

against

filter

= 1/4.

This

The

55-layer

has

optical

ratio the

maximum

reflectance

zero

of incidence,

in the

maximum

VUV

smaller

the

where

of optical

as the

with The

reflectance

of H = ;_,/8 of 93.6% stacks

and

for the with

the

over what

35-layer

H/L

the

for zero

55-, and

LaF3

H/L

with

The

thicknesses

and

which

Fig.

< 1 provide

rl

as the low index

of optical

= 1/3

From

35-layer

is RK = 90.8%.

ratio

ratio

angle

film materials

of H = ),,/10

The

can be achieved

to L can provide

low index

high,

for H/L

II stack.

99-,

limit

thicknesses

L = 3,_,/8.

ratio

as the

when

of 95.3%

layers

film materials

extended

and

Koppelmann

to the optical

fewer

stack.

of high

of 96.5%

index

of H relative

for the

MgF2

(available

with

high

can be easily

thicknesses

reflectance

corresponds

of the

materials

reflectance

thickness

calculated

substrate.

maximum

higher

limit

is 145 nm,

film

low-absorbing

reflectance

reflectances

ratio

low-absorbing

provide

Koppelmann

maximum

reflectance

with

physical

higher

maximum

thicknesses

angle

with

how

silica

has the

H/L

in the

wavelength

fused

stacks

of spectrum)

therefore

the

reference and

99-layer

and

1 illustrates

materials,

parts

However,

absorptance

Figure

the

infrared

rl stacks.

exist,

quarterwave

L = 4a,/10.

corresponds

= 1/2

provides

1, it follows

a significant

to the

that

at

improvement

QW

stacks

for which

and

bandwidths

H/L

=

1.

Shown measured 55-,

in Figures

and

35-layer material

as the

for the

3 are

at half of reflectance

low index LaF3

2 and

QW

17 stacks, (H/L).

high index stack

maximum

nlaxinlum) plotted

The

material,

is R_- = 89.5%

respectively,

against

reference and

fused

reflectances

the

ratio

wavelength silica

0o = 450 at 10

calculated of optical is 135.6

as the

angle

nm,

(full

width

at 00 = 450 for the thicknesses with

substrate.

The

of incidence.

The

MgF2

of high

and

as the

low,

Koppelmann 99-and

99-,

limit

55-layer

17

multilayers the

(Fig.

ratio

high

and

2) have

a maximum

of optical

thicknesses

low index

film materials

reflectance

is H/L

= 1/3.

L

The

35-layer

optical

_ stack

thicknesses

(Fig.

1) has

for this

of 93.0% This

92.7%

corresponds

respectively,

to optical

when

thicknesses

of

3,_ 8

_

m

a maximum

H to L ratio

and

reflectance

of the

of 91.4%

17 multilayer

for H/L

are given

by

for the

QW

= 1/2.

The

3

The

lowest

number

of films

saturation the

decrease

is decreased

the

case)

within

the

level

for the

QW

From 135.6

nm,

stack

with

QW

Figs. the this

occurs

SWR

decreases

with

physical

thickness

of the

high

index

is largest

for the

QW

stack.

multilayer stacks the

stack

2 and 17 stack ratio

reflectance

99 to 35.

be expected

nm for the

maximum from

level of the

multilayers

should

of the

is achieved bandwidth

and

6.9 nm

3, it follows with has

H/L

optical

This

an increase

with

fewer

decreases for the

stack

for the

= 1/4

seems

thicknesses

design

of a narrowband

to be the

A nHdH

=m

10

4A L =

11

--.

10

(Fig.

by

most

feasible

since

the

Of all particular

SWR

saturation

to other

of of the

= 1/5

the

in this

the

compared

when

absorption.

(LaF8

Therefore,

H/L

expected

multilayer

material

a decrease

with

given

is certainly

of the

layers

with

that

nLd

result

stack

ratio

17 stacks. H/L.

As

It is 17

3).

reflector choice.

centered The

at

35-layer

Calculated values of the maximum reflectance

R_,_

= 7.2 nm.

Figure

4 shows

calculated

fused

as the

substrate

silica

135.6 nm is 88.3% bandwidth

while

of 7.2 nm

Figure

5 shows

a 29-layer

17 stack

The

H/L

ratio

the

material.

the

theory

agrees

the

measured

with

measured

with

BaF_

= 1/3,

and

and The

= 88.4%

measured

predicts

the

values

reflectance predictions.

and

calculated

reflectance

optical

index

material

thicknesses

are

silica

FWHM

stack

with

reflectance

of 88.4%.

fused

and

peak

The

at 45 ° angle

and

given

nm of this

of the

peak

theoretical

high

135.6

reflectance

the

as the

at

at

measured

of incidence as the

for

substrate.

by

nH d/_ = -8

rtLd L -

The

measured

nm.

The

E.

theory

Higher

The The

reflectance

first

width

predicts

Order

order of the

film inaterials

maximum 86.9%

at

)_, = 135.6

maximum

reflectance

II Multilayer

QW high

is given

stacks

8 nm

is 86.0%

and

with

6.8 nm

bandwidth

of 7.2

bandwidth.

Stacks

have

reflection

wider zone

high

reflectance

(A,_)H.R. of a QW

zone

than

multilayer

other

rl multilayers.

with

non-absorbing

by 2a

(A)_)H'R" = 2(m-- 1 1)+ 1 4,_,_ r sin_ 1 (n__H--nL) +nL

where

m is the

reflection gives indices

zone

a maximum nH and

order

of H multilayer.

is smaller width nL.

than

that

for a high Thus,

an

For absorbing calculated reflectance

alternative

film materials

using zone

Equation

obtainable

approach 12

(24)

for

(24).

the

width

Thus,

for materials the

design

of the

Equation with

of the

high (24)

refractive

narrowband

reflectors of the

is to utilize

order

of a II stack

from

,r -. ma'. The

order

of a II stack

low index of the the

fihn

stack.

second

used

as the

of the

the

total

QW

high

index

stack

in the theoretical

substrate

contaminations,

(Figs.

4 and

in the

QW

theoretical

stack

are

in increased

and

fused

experiment

while ,nay

calculation

the

film inhomogeneity. obtained

for the

second

more

affected

order

results QW

by the

of both

high

and

therefore

value

and

may

factors

reflectance

The

indicate neglected

Discrepancies

scattering,

for the

is

value

of physical

between

of

BaF3

calculated

is 69.9%.

volume

better

reflectance

of incidence.

presence

is much This

lower

obtained

agreement

physical

13

thickness

The

stack.

calculation.

the

by the

surface

pair

when

as the substrate.

as the

of an (HL) by A,/2

and

measured

an increase

is increased

at a 450 angle

be explained

such

However,

thickness

experimentally

nm

silica

m.

phase

physical

and

at 135.6

order

pair

absorptance

calculated

is 83.1%

experimentally

5) than

Increased

centered

and

a total

by unity.

material

and

higher

of an (HL)

the

reflectance

theory

with

thickness

results 6 shows

order

II stacks

1 to, say m, changes

is increased

Figure

and

or other

optical

neglected

prediction

QW from

materials

maximum

between

the

factors film and

the theoretical first

order

that

thicker

in the

filters films

multilayer

III.

MULTIPLE

A.

REFLECTION

Narrowband

Reflection

filters

shown

wavelength

of 86.0%

the

wavelength

shorter

wavelengths.

The

zone

can

upon

which

of four

and

light

in Figures

88.3%, region

outside

is incident

maximum

filters

of the

blocking

for wavelengths

can

be combined.

However,

the

combination.

The

thick

is 39.3%

than

10-_%

MgF2

of shorter

B.

The Ideally,

window wavelengths

for longer

wavelengths outside

adding

maximum

with

the

for longer is placed may

the

pass

filters

throughput

The

in

of 10% for the longer

or more

of the pass

reflection

transmissions

at the blocking

than

zone

filters

of combinations

is required,

and

than

the

6-filter The

0.07% of the

central

wavelength

for shorter

10-2%.

will reduce

of 3.2 nm.

be less than

two

overall

of the

entrance

high reflectance

7 and 8, respectively.

bandwidth

at the

at the central

and the bandwidth

from

is better

more

better

zone

combination

of 4.3 nm.

relatively

of the order

"pass"

in Figures

reflectances

have

reflections

4-filter

bandwidth

than

better

and

the

both

of 450 . The

are shown

of the

measured

reflectance

the filter's

at an angle

better

wavelength

0.7%

and

They

of multiple

throughput

nm is 53.7%

5 have

respectively.

by means

and six 29-layer

4 and

and an average

reflectance

be reduced

The 135.6

FILTERS

wavelengths

If further then overall

for shorter combination

6 or more

filters

transmittance at the

outside

the

pass

wavelengths. than

is

improvement

combination

blocking

,_ =

the

of

central zone

is

If a 4 mm transmittance

10-4%.

Broadband

pass

zone

the spectral

of a broadband components

filter of the

is bounded incident 14

light,

by a lower with

and

wavelengths

upper

wavelengths.

shorter

than

the

lower

and

of-band

longer

than

spectrum,

out-of-band

spectrum at shorter

material,

placed

and

CaF2

absorb

and

A1208

may

Because

better and

choice

design

for the

high

design

and

LaFa

strate.

The

measured

peak

at half

of the

reflectance

order

is RK = 94.4%

by the

value

, and

the

of the

QW

of these angle

The

average

Koppehnann

theoretically

and

bandwidth

reflectance

for the

for LaFs value

and

of the

=

1 are

the

measured

The

reference

silica

the

limit

predicted

fused

< 1 are not

H/L

9 shows

and

silica

145 nm 13,2_.

QW stack.

material,

The

of BaF_

fused

H/L

which

Figure

is 90.3%

made

above

with

for

for the 25-layer

reflectance

The

stacks

filters.

high index

is 19 nm.

H multilayers

stacks.

while

limit

of the

of the window

Windows

a lower pass

zone

QW

choice

with

as the

the

suitable

combination.

reflectors.

of 10%.

from

filters

fabrication

is used

reflections

to as the out-

wavelengths

125 nm respectively,

reflection

maximum

is of the

of multiple

follow,

and

at 45 o incident

is 175 nm,

that

referred

135 nm,

of broadband

wavelength

wavelength

below

together

examples

be improved

for broadband

reflectance

wavelengths

by means

filter,

of a multireflector

wavelengths

narrower

of the

design

might

entrance

be used

calculated

In the

are rejected

at the

the

wavelength

wavelengths

of the

for

upper

are rejected.

rejection

suitable

the

a

as the submeasured out-of-band

MgF2

peak

at this

reflectance

is 91.6%.

The second order

agreement order

QW

theoretical

Figure The

QW stack stack

are

the

(Fig.

more

theory

6).

and

Again

affected

the

this may

by

the

experiment indicate

physical

that

factors

is much

better

than

for the

thicker

films

in the

second

neglected

in the

multilayer

six of these

reflectors.

calculation.

10 shows

4-reflector

11.5 nm.

between

The

the

transmittance

combination rejection

of the

has

of combinations

a peak

out-of-band

of four

transmittance spectrum 15

and

of 66.3% up

and

to 300 nm

the

bandwidth

is better

than

of 0.1%.

If a 4 mm shorter

thick

wavelengths

combination bination of the fused

fused

has provides

combination silica

wavelengths

is used of the

silica

parallel

of the a peak much

out-of-band

better

out-of-band

of 54.04%

rejection

window

is used spectrum

transmittance

for out-of-band as the

plate

spectrum

the

with

16

than

than

then

the

3 x 10-8%.

of the 10-5%.

The

of 11 rim.

wavelengths. than

rejection

10-s%.

bandwidth

is less

transmittance

is less

window

is better

for out-of-band

wavelengths than

as the

The

6-reflector This

com-

transmittance

If a 4 mm

combination

of the

thick

for shorter

IV.

THE

EXPERIMENTAL

All depositions substrates

with

are

root

the supplier

(Acton

optical

soap

wash,

finally

a Freon

holders.

is kept

made

The free

for

the

for vacuum standard of 0.18

- 0.20

nm/sec

7.5x10

-_ while

the

materials.

The

to an aluminum center

is used with

temperature ring

an electron

fihn gun.

and

with

a typical The

pressure

diameter

thickness The

and gun

has

films

varies

between

with The

are deposited

1.7 and

thick

deposition

rate

voltage

and

stainless

the steel

monitoring. of 10 KV

substrate

of Alabama

giving

low

and

with

an

are

MgF3

for

prepared

(99.95%)

low deposition

pre-deposition 2.3x10

-s

holder

plate.

rates is

for all coating attached are

placed

A quartz

depositions

low power

is

pressure

thermocouple ring

oil-

probability

LaF3

while

are

Center.

pump

The and

the

Flight

a Chromel-Alumel substrate

17

The

in the

measurements

BaF2

of 99.9%

and

in Delrin

University

a very

materials

to 200°C.

by 6 mm

fixed

at the

providing

rinse,

in a laminar

chamber

a sorption

purity

heated

is monitored holder.

fihn

ethanol

is done

vacuum

by

procedure:

to mounting

holder

silica

are cleaned

environment

Space

and

therefore The

fresh

spectrophotometric

of a cryo-pump

fused

the following

prior

NASA/Marshall

and

substrates

room

are made and

of the

substrates

substrate

of a 40 mm

for the

Laboratory

material.

deposition

immediately

All depositions

by CERAC

on the

holders

to the

of the films.

coating

in a clean

bench

all depositions

deposition

packed

the

MgF2

bath,

from

consists

The

ultrasonic

substrate

Branch

contamination

BALZERS

are

then

in the

Aeronomy

for

soak

thick

using

Mounting

nitrogen.

Physics

1 nm.

Massachusetts)

Delrin

transport

system

environment

from

deposition.

Atomic

vacuum

ethanol

by 2 mm

less than

Acton,

substrates

removed

Optical

hydrocarbon

the

The

mm diameter

roughness

Corp.,

rinse,

in a flow of dry

at the

square

water

During

in Huntsville,

on 12.7

Research

are

holder

flow bench.

mean

rinse.

They

substrate

made

ARRANGEMENT

in

crystal are made

depositions

are

maintained is 500 mm

by supplying and

the source

low current to the

to the filament.

monitor

distance

18

The source is 350 mm.

to the substrate

distance

V.

SUMMARY

The the

idea

light

filters. the

of utilizing

is incident The

The

using

which

available

incidence

can

ratio

< 1 are

ments

of the

smallest

the

first

not

The

agreement

QW stacks QW

theoretical

with the

in the

filters

reflectance,

but

of the

high

for broadband zone

as wide

between

centered stack

with

the

4, and

at longer are

calculation

more such

the

lowest

value

reflectors

since

QW

theoretical

by

for the

as the surface

nm

stacks

and of

reflection for coating angle

rI stacks

with

further

the

by the

with

have

of

improve-

is limited

II multilayers do not

for

design

for zero

ratio

de-

reflectance

extended

when

generally

are

maximum

96%

H/L

filters

for the

can provide

experimental second

(Fig. the

than

Furthermore, they

for both

H/L

a width

of

stacks.

and

wavelengths

suitable

be easily

of the

broadband

QW

higher

QW stack

99 layers

films.

as the

affected

the

of more

than

index

5) than

more

as low as 135.6 more

classical

< 1 have

0o = 450 can

reflectance

for wavelengths

thickness

(Figs.

) and

A peak

Stacks

that

reflection

of the

are therefore

and

which

available.

narrowband

H/L

upon

performance

is currently

with

filters

narrowband spectral

< 1 instead

and

limit

of our

what

lI stacks

reflection

superior

It is demonstrated

VUV.

utilized.

basis

for the

I-I/L

QW stacks,

filters.

suitable

reflectance

order

the

maximum

high

in the

than

over

coatings

that

II multilayer

provide

filters

stacks

be achieved

feasible

< 1 are

the

00 = 0 ° (Koppehnann

materials

H/L

constitutes

multilayer

reflection

at both

from

broadband

reflective

bandwidth

reflections

combinations

= 1. It is shown

narrowband limit

the

1I multilayer

H/L

smaller

reflector

and

high

signed

at 450 angle

multiple

narrowband

multiple

9).

physical

and

film contamination. 19

volume

order This

may

factors scattering,

results QW

stack

indicate neglected

is much (Fig. that

better

for

6) and

for

thicker

in the

fihns

multilayer

film inhomogeneity,

and

REFERENCES

1. Acton Research Corporation, Optical

Filters, Catalog (1989).

2. A. Malherbe, "InterferenceFiltersfor the Far Ultraviolet",Appl. Opt. 13, 1275-1276 (1974).

3. A. Malherbe, 1276-1276

"Interference AppI.

5. L. R. Elias, the

Fairchild,

9. W.

for the

1209-1215

and

W.

Far

Ultraviolet",

and

the

AppI.

Opt.

13,

Ultraviolet

Surface

Plasmon

of Alu-

(1974).

M. Yen,

Lal_xCe_F3",

"Interference

"Special

92-97

8. B. K. Flint, 2,

for the

"Variable Appl.

Filters

for

the

Bandwidth

Opt.

12,

VUV

Transmission

138-139

Filter

for

(1973).

(1200-1900Zk)",

Appl.

Opt.

12,

(1973).

7. B. K. Flint, En 9. 18,

13,

Ultraviolet:

2240-2241

Res.

Opt.

Filters

R. Flach,

Vacuum

6. E. T.

Components

(1974).

4. E. Spiller, minum',

"Multidielectric

R. Hunter,

Coatings

for the

Vacuum

Ultraviolet

(VUV)",

Opt.

Adv.

Space

(1979).

"Recent

135-142

Application

Developments

in Ultraviolet

Filters

and

Coatings",

Proc.

SPIE,

(1983). "Review

of Vacuum

Ultraviolet

Optics",

140,

122-130

(1978). 10. M. Zukic,

D. G. Torr,

Ultraviolet Opt.

Optics,

All-dielectric

(Sept.

11. E. Spiller,

J. F. Spann,

and

Narrowband

M. B. Torr, Filters",

"VUV

paper

Thin

accepted

Fihns

Part

II: Vacuum

for publication

in Appl.

1, 1990).

"Multilayer B. J. Thompson

Interference and

R.R.

Coatings Shanon 2O

for the eds.

Vacuum

Proc.

Ultraviolet"

of the

Ninth

in Space International

Congress

of the

International

Sciences,

Washington,

12. W. R. Hunter,

Appl.

13. M. Zukic

and

ed.,

published

Opt.

17,

Chapter

by March

and

for Optics,

581-597

(National

Academy

of

1974).

Criteria

D. G. Torr,

H. Guenther

14. M. Born

D.C.,

"Design

Ultraviolet",

Commission

for Reflection 1259-1270

"VUV

Polarizers

and

Analyzers

in the

Vacuum

(1978).

Thin

Films",

VII,

Springer-Verlag

Principles

of Optics,

in Topics series

in

Applied

on Thin

Films,

Physics, in press

K. (to

be

1991).

E. Wolf,

Chapter

1 (Pergamon

Press,

Oxford

1983).

15. H. A. Macleod, York

Am.

"Prediction

of Absorption

52,

753-761

(1962).

and

J. H. Apfel,

17. C. K. Carniglia rors

18. G.

in the

Presence

Koppehnann,

Materials

and

German,

Leipzig

19. J. H. Apfel, Opt.

20.

16,

25,

of Slight

"On Their

1880-1885

291-298

the Use

Filters,

Chapters

2,5,

and

6 (Macmillan,

New

Loss in Multilayer

"Maxiinum

Absorption",

Theory

Reflectance J. Opt.

of Multilayers

as Interferometer

Interference

of Multilayer

Soc.

Am.

Consisting

Mirrors",

Filters",

Ann.

70,

Dielectric

523-534

of Weakly Phys.

J. Opt.

5,

Mir-

(1980).

Absorbing 388-396

(in

1960).

"Optical

P. H. Lissberger, Acta

Optical

1986).

16. L. Young, Soc.

Thin-Film

Coatings

Design

with

Reduced

Electric

Field

Intensity",

Appl.

(1977).

"The

Ultimate

Reflectance

(1978). 21

of Multilayer

Dielectric

Mirror",

Opt.

21.

M. Sparks tors",

22.

and

J. Opt.

M. Zukic,

M. Flannery, Soc.

Am.

D. G. Torr,

Constants

of BaF_,

accepted

for publication

23. P. Yeh,

Optical

"Simplified

69,

993-1006

J. F. Spann, CaF_,

Waves

and

LaF3,

in Appl.

in

Description

Layered

Dielectric

Reflec-

(1979). M. R. Torr,

MgF2, Opt.

of Multilayer

Al_O3,

(Sept.

Media,

"VUV HfO3,

Thin and

Films

Si_ Thin

Part

h Optical

Films"

paper

1, 1990).

Chapters

6 and

7, (Wiley,

New

York

1988).

24.

D. F. Heath on

the

and

Ultraviolet

P. A. Sachet,

"Effects

Transmittance

of a Simulated

of Optical

Appl. Opt. 5, 93 -943 (1006).

22

Materials

High-Energy Between

Space 1050

Environment 2_and

3000A",

FIGURE

Figure

1:

The maximum

at 145 am.

Diamonds

H = Lanthanum

Figure

2:

incidence

stacks.

limit

is 89.5%.

Figure

nm.

3:

The

the H/L

is shown

ratio

Diamonds

at half

4:

rI stack

for 45 degrees

in Fig.

The measured

with

H = Lanthanum

Figure

5:

The

measured

II stack

for 45 degrees

Figure layer

with

6:

The

second

order

= Barium

H = Barium

Fluoride,

measured

and

stack

1I stack

99-layer,

and

The

maximum

calculated

limit

55-layer, Fluoride.

maximum

of the of the

stacks.

is 90.8%.

for 45 degrees

triangles

reflectance

35-1ayer

Koppelmann

L = Magnesium

reflectance

squares

of incidence

angle

and squares The

35-

Koppelmann

II stacks

stacks

of

calculated

as a function

of

2.

and

calculated

and

of incidence Fluoride,

(squares)

and

and

at 135.6 nm.

calculated angle

reflectance The optical

thickness

ratio

of the 29-layer thickness

ratio

Fluoride.

(diamonds)

of incidence

of the 35-layer

Fluoride.

(diamonds)

L = Magnesium

Fluoride.

The optical

L = Magnesium

centered and

reflectance

at 135.6 nm.

calculated

for 45 degrees

L = Magnesium

(diamonds)

centered

Fluoride,

(squares)

angle

QW

The

of incidence

= 1/4

= 1/3

of the

(squares)

angle

and

for zero angle

55-layer,

Fluoride.

of the

Fluoride,

calculated

triangles

represent

of incidence.

Figure

H/L

99-layer,

reflectance

full width

angle

of the II stack

L = Magnesium

H = Lanthanum

for 45 degrees

H/L

and

maximum

135.6

layer

represent

Fluoride,

The at

reflectance

CAPTIONS

reflectance centered

of the

at 135.6

nm.

35H

FIGURE

CAPTIONS

(Continued)

Figure

7:

The

transmittance

5. The bandwidth

Figure

8:

The

is 4.3 nm,

QW

9:

is 3.2 nm,

The measured

combination

and a peak

transmittance

5. The bandwidth

Figure

of the

of four

transmittance

of the combination and

a peak

29-layer

at 135.6

filters

at 135.6

filters

shown

Figure

10:

The

25-layer

QW

stacks

in Figure

nm is 39.3%.

(squares) and calculated (diamonds) reflectanceof the 25-1ayer

stack for 45 degrees angle of incidence centered at 175 nm. H = Lanthanum

and L = Magnesium

in Figure

nm is 53.7%.

of six 29-layer

transmittance

shown

Fluoride,

Fluoride.

transmittance shown

in Fig.

of combinations 9.

of four

(solid

line)

and

six (dashed

line)

Zukic/Torr

I

I

I

I

I

I

I

I ,i,,,-4

I 0 0

CO Ob

I c.O C_

I _, _

I C_ _

v=d

ooue ooI. OEI

I 0 Ob

I O3 OD

I _ a3

I OD

C_ 00

Zukic/Torr

I

I

I

I

I

I

I

I

u_

qJ r_

cO 0

.=q

CL

t-0 cO C) u_ 0

_



0 L

Ca

_ 0

cO C) c_ 0

C) I 0 C)

a3 Ob

I c_ (y)

I _. Ob

I C_ (y]

oou looI O

I 0 Ob

I o3 03

H mnm .

I c_ cO

x FI

.-_

I 03

0 C_ o3

_-"_

C

-

Zukic/Torr

v==d

I

I

I

I

I

I

I

I

I

v--4

C3_

°ad 03

C) t"-

C) _

CO O

_

,I,,q

,J=l

°

,p,q

0

_

'-

0

x_ N

_

u_ C)

C) C_3

O c_ C)

C) I I,I,I

T

I,I,I Z

0 I,I= W a.

[

0

LL.

>. rr

O

0 I< n-

0 m ,< ..i >.

=S 0 ;[

0 rr UJ

,< ..I ,< 0 m II1.

0

-r"[3 rgm

Z

0

mm

0

m

< =S

(n I--




(/) ::)

nn

rr.

=S

0

m

m

o

uJ rr a.

IZ U.I

=S 0

=S m

u.

u..

0

0

!.1.

n-

n-

0

0

0

(n i2:

(.1 ,