Biophotonics_Concepts_to_Applications

rjj¼ry¼

E0r

E0i



y

¼

n 2 cosh 1 n 1 cosh 2

n 1 cosh 2 þn 2 cosh 1

ð 2 : 26 Þ

t?¼tx¼

E0t

E0i



x

¼

2n 1 cosh 1

n 1 cosh 1 þn 2 cosh 2

ð 2 : 27 Þ

tjj¼ty¼

E0t

E0i



y

¼

2n 1 cosh 1

n 1 cosh 2 þn 2 cosh 1

ð 2 : 28 Þ

If light is incident perpendicularly on the material interface, then the angles are
h 1 ¼h 2 ¼0. From Eqs. (2.25) and (2.26) it follows that the reflection coefficients
are

rxðh 1 ¼ 0 Þ¼ryðh 2 ¼ 0 Þ¼

n 1 n 2

n 1 þn 2

ð 2 : 29 Þ

Similarly, forθ 1 =θ 2 = 0, the transmission coefficients are

txðh 1 ¼ 0 Þ¼tyðh 2 ¼ 0 Þ¼

2n 1

n 1 þn 2

ð 2 : 30 Þ

Example 2.8Consider the case when light traveling in air (nair= 1.00) is

incident perpendicularly on a smooth tissue sample that has a refractive index

ntissue= 1.35. What are the reflection and transmission coefficients?

Solution: From Eq. (2.29) with n 1 =nairand n 2 =ntissueit follows that the

reflection coefficient is

ry¼rx¼ðÞ 1 : 35  1 : 00 =ðÞ¼ 1 : 35 þ 1 : 00 0 : 149

and from Eq. (2.30) the transmission coefficient is

tx¼ty¼ 21 ðÞ: 00 =ðÞ¼ 1 : 35 þ 1 : 00 0 : 851

The change in sign of the reflection coefficient rxmeans that thefield of the

perpendicular component shifts by 180° upon reflection.

Thefield amplitude ratios can be used to calculate thereflectanceR (the ratio of
the reflected to the incidentflux or power) and thetransmittanceT (the ratio of the
transmitted to the incidentflux or power). For linearly polarized light in which the
vibrational plane of the incident light is perpendicular to the interface plane, the
total reflectance and transmittance are

2.4 Reflection and Refraction 41