In this paper we calculate

4

A

2

(

S

=-3/2)→

2

E(

S

=-1/2) photon echo decay induced by Al nuclear spin flip in ruby. Using simple random telegraph model

we investigate Δ

i

which is the variation of Cr resonant frequency caused by each Al nuclear spin(i) flip

and obtain the analytic expression of 〈

E

i

(

t

21

)〉 through calculating total flip rate W i of Al nuclear(the i th) and Δ

i

. Since the contribute to Cr optical dephasing from each Al nuclear spin flip is approximately independent

the total intensity is the product of 〈

E

i

(

t

21

)〉 caused by all Al nuclears. The obtained echo decay can be fitted by

I

=

I

0

exp〔-(4t/t

m

)

x

〕with

x

t

m

values of 2.56

and 50.6 μs which agree with experimental and computer simulated values.