164
10 Study of the Optical Characteristics of Thin Layer of the Biological Sample
= α
1
n
2
1
−
∂ E 1
∂z
| z=0 +
∂ E 1
∂ x
∂ H
∂ x
| z=0 +
∂ E 1
∂ y
∂ H
∂ y
| z=0
+
+α
1
n
2
1
−H
∂
2 E 1
∂z 2 | z=0 + H
∂
2 E 1
∂ x∂z
| z=0 ·
∂ H
∂ x
+
∂
2 E 1
∂ y∂z
| z=0 ·
∂ H
∂ y
−
−α
1
n
2
1
∂ E 1
∂z
| z=0
(∇ H )
2
2
+
H
2
2
∂
3 E 1
∂z 3 | z=0 + · · ·
.
∂ E 2
∂n
| z=H (x,y) =
= α
1
n 2
2
−
∂ E 2
∂z
| z=0 +
∂ E 2
∂ x
∂ H
∂ x
| z=0 +
∂ E 2
∂ y
∂ H
∂ y
| z=0 − H
∂ 2 E 2
∂z 2 | z=0 + H
∂ 2 E 2
∂ x∂z
| z=0 ·
∂ H
∂ x
+
+ α
1
n
2
2
∂
2 E 2
∂ y∂z
| z=0 ·
∂ H
∂ y
−
∂ E 2
∂z
| z=0
(∇ H )
2
2
+
H
2
2
∂
3 E 2
∂z 3 | z=0 + · · ·
. (10.7)
Then, a boundary condition of type (10.4) taking into account (10.6) and (10.7)
assumes the form
1
n 2
1
∂ E 1
∂z
| z=0 −
∂ E 1
∂ x
∂ H
∂ x
| z=0 −
∂ E 1
∂ y
∂ H
∂ y
| z=0 + H
∂ 2 E 1
∂z 2 | z=0 − H
∂ 2 E 1
∂ x∂z
| z=0 ·
∂ H
∂ x
−
−
1
n
2
1
∂
2 E 1
∂ y∂z
| z=0 ·
∂ H
∂ y
+
∂ E 1
∂z
| z=0
(∇ H )
2
2
+
H
2
2
∂
3 E 1
∂z 3 | z=0
=
(10.8)
=
1
n 2
2
∂ E 2
∂z
| z=0 −
∂ E 2
∂ x
∂ H
∂ x
| z=0 −
∂ E 2
∂ y
∂ H
∂ y
| z=0 + H
∂ 2 E 2
∂z 2 | z=0 − H
∂ 2 E 2
∂ x∂z
| z=0 ·
∂ H
∂ x
−
−
1
n
2
2
∂
2 E 2
∂ y∂z
| z=0 ·
∂ H
∂ y
+
∂ E 2
∂z
| z=0
(∇ H )
2
2
+
H
2
2
∂
3 E 2
∂z 3 | z=0
.
We will seek the reflected field in medium 1 and the field transmitted to medium 2
in the form
E 1 (x, y, z) = E inc (x, y, z) +
∞
n=0
E
n
01 (x, y, z),
(10.9)
E 2 (x, y, z) =
∞
n=0
E
n
02 (x, y, z),
(10.10)