T
HE
I
NTERACTION OF
R
ADIATION AND
M
ATTER
: Q
UANTUM
T
HEORY
P
AGE
A 20
R. Victor Jones, April 27, 2000
H
IGHER
-O
RDER
C
ORRELATION
F
UNCTIONS
-- A
CLASSICAL EXPLICATION OF
THE FAMOUS
H
ANBURY
B
ROWN
-T
WISS EXPERIMENT
:
Generalizing Equation [ VIA-38a ],
the
degree of nth-order spatial-temporal
coherence
can be defined as
10
γ
n
( 29
(
r
r
1
,
t
1
;
KK
;
r
r
n
,
t
n
;
r
r
n
+
1
,
t
n
+
1
;
KK
;
r
r
2
n
,
t
2
n
)
≡
E
r
r
1
,
t
1
(
29
KK
E
r
r
n
,
t
n
(
29
E
r
r
n
+
1
,
t
n
+
1
(
29
KK
E
r
r
2
n
,
t
2
n
(
29
E
r
r
1
,
t
1
(
29
2
KK
E
r
r
n
,
t
n
(
29
2
E
r
r
n
+
1
,
t
n
+
1
(
29
2
KK
E
r
r
2
n
,
t
2
n
(
29
2
[ VIA-42 ]
In particular, the
degree of second-order temporal coherence
is defined as
γ
2
( 29
(
r
r
ref
,
τ
)
≡
E
r
r
ref
,
t
(
29
2
E
r
r
ref
,
t
+τ
(
29
2
E
r
r
ref
,
t
(
29
2
2
=
I
r
r
ref
,
t
(
29
I
r
r
ref
,
t
+τ
(
29
2
I
r
r
ref
,
t
(
29
2
[ VIA-43 ]
We shall see that this function is an important measure of the relative timing of of intensity
fluctuations.
11
As a first step, let first find an expression for the average intensity radiated
by a collection of independent oscillators --
viz.
10
R. J. Glauber, in
Quantum Optics and Electronics, Les Houches, 1964
(edited by C. DeWitt, A. Blandin, and
C. Cohen-Tannoudji), p63, Gordon and Breach (1965).
11
By the famous Schwartz inequality
a
*
b
2
≤
a
2
b
2
so that
I
r
r
ref
,
t
(
29
I
r
r
ref
,
t
+τ
(
29
2
≤
I
r
r
ref
,
t
(
29
2
I
r
r
ref
,
t
+τ
(
29
2
and quite generally
γ
2
( 29
(
r
r
ref
,
τ
)
≤
1