2024年5月7日发(作者：)

Optical properties

of the metals

Al, Co, Cu,

Au, Fe, Pb, Ni,

Pd,

Pt, Ag,

Ti, and W

in the

infrared and

far infrared

M. A. Ordal,

L. L. Long,

R. J. Bell, S.

E. Bell, R. R.

Bell, R. W. Alexander,

Jr., and C. A.

Ward

Infrared optical

constants collected

from the literature

are tabulated.

The data for the

noble metals and

Al, Pb, and W can

be reasonably fit using

the Drude model.

It is shown that

-El(W)

=

E2(W)

2/(2w')

at

the damping frequency

c

=

c,.

Also

-El(w

T)

_

-

(1/2)

el(0), where the

plasma frequency

is op.

1. Introduction

adjustable parameter;

i.e., the Drude model

parameters

Many measurements

were obtained from

the dc resistivity and

fitted with one

primarily at near IR,

of the optical constants

visible,

of

metals have been made,

free electron per atom for

gold and silver and 2.6

free

and UV wavelengths.

Brandli and Sievers'

have

electrons per atom for aluminum.

Brandli and Sievers

measured Au and

Pb in the far IR.

For the near and

far

have shown that the

Drude model is an excellent

fit to

IR we have compiled

these data and have

tabulated the

their far IR measurements

real and imaginary

parts of the dielectric

fit for gold with no adjustable

on lead and provides

parameters.

a good

function,

n and the

El

and

e

extinction

2

,

respectively, the

index of refraction

index k for each

metal.

Drude model

2

pa-

rameters giving a

reasonable fit to the

data are given for

11.

Definitions

and Equations

Au, Ag, Cu, Al, Pb,

is not expected to be

and W. In general,

appropriate for transition

the Drude model

metals

frequencies will be

In keeping

with IR spectroscopic

expressed in cm-

1

.

notation, all

in the near and middle

IR, but a good fit

can be obtained

for W with a

index of refrac-

The complex

dielectric function

es

and the complex

Weaver

et

Drude model dielectric

3

have compiled

extensive tables

function.

al.

or

tion

n, are defined as

optical properties of

metals which have

EC -el + ie2

n (n +

ik)

2

.

(1)

not extend beyond

been recently

published.

Most of their tables do

12-yum wavelength, while

our compilation extends to the

The Drude model dielectric

function is

2

longest wavelength for

which data are available.

An-

C = E-

-

other standard compilation

2

.

I

(2)

(1

+ I co w T

HANDBOOK.

AMERICAN

4

However, this includes

INSTITUTE

is that of Haas and Hadley

in the

OF PHYSICS

data only up

where

real and imaginary

c, cop,

and '-v, have units

parts yields

of cm-'.

Separating the

to 1967. Except for a few

cases, the data presented here

W2

are more recent.

Bennett and Bennett

5

el =

E-co

2

(3)

have shown that the Drude

model fits the measured

reflectance of gold, silver,

and

aluminum in

the 3-30-/Im wavelength

range with one

2=

+

U2

+

(4)

In

these equations, the plasma

frequency

6

is

1

47rNe

2

1/2

,(cm-l) =

_2rc me

(5)

When this work was done all authors

were with University of Mis-

where N is the free electron

density, e is the electron

souri-Rolla,

Physics Department,

Rolla, Missouri 65401; C. A.

W.

charge, m * is the effective

mass of the electrons,

and

e-

Krebs

is now with McDonnell

Douglas Astronautics

Company,

is the high frequency dielectric

Electrooptic Technology,

P.O. Box 516, St. Louis Missouri

w

expressed in cm-, is

constant.

The damping

63166; S.

frequency

E. Bell and R. R. Bell are now at

Route 4, Box 124, Rolla, Missouri

65401.

W (Cm-l) =

Received 12 October 1982.

27rc

1

(6)

T

0003-6935/83/071099-21$01.00/0.

where r is the electron lifetime

in seconds and c is the

© 1983 Optical Society

of America.

velocity of light. Note

that for low frequencies

1 April 1983 / Vol. 22, No.

7 / APPLIED OPTICS

1099

105

14)

N

In

Z

102

101

100

102

103

105

FREQUENC.W

(CM'1)

Fig. 1.

Aluminum:

-el(w) and

2(M)

vs frequency.

The solid line

is the Drude

model.

The data from

Ref. 7 are:

Shiles

et al.,

o

for

both -el and

2;

Bennett and

Bennett * for

-El

and

2;

Schulz, 0 for

-el

and

2-

106

105

14)

C3

Z

a:

10

3

W(

I

101

ino

10100

l2

103

104

105

FREQUENCY,

W

(CM')

Fig. 2.

Copper:

-el(W) and

2(O)

vs frequency.

The solid line

is

the Drude

model.

The data from

Ref. 8 are:

Schulz, 0 for

both -el

and

2;

Lenham and

Treherne,

Braunstein,

o3

* for

-el

for both;

and

2;

Hageman

Robusto

et

al., X for both;

and

and Dold

and

Mecke, A for

both.

1100

APPLIED OPTICS

/ Vol. 22,

No. 7 / 1 April

1983

106

105

14)

In

kV

Z

102

101

100

00

102

103

FREQUENCY,

W

(CM'l

Fig. 3.

Gold:

-e,(w)

and

e2(W)

vs frequency.

Drude model.

The solid line

The data

is the

from Ref. 9 are:

Bennett and

Bennett, *

for both -el

and

e2;

Schulz, 0

for both; Motulevich

and Shubin,

for

both; Padalka

and Shklyarevskii,

0 for both; Bolotin

et al.,

x

for both;

Brandli and Sievers,

+ for both;

Weaver

et al.,

A

for both.

104

nLI

Z

3

a:

10

tv

10'

10a

102

103

105

FREQUENCY,

W (CM

1

)

Fig. 4.

Lead:

-e

l

(w)

and

e2(u)

vs frequency.

resents the

Drude model.

The solid

line rep-

The data from

Ref. 10 are:

Brandli and

Sievers, x for

-el and +

for

2;

and Golovashkin

and Motulevich,

A

for

-el

and

oI

for

2-