Optical Sources, Detectors, and Systems

Appendix A: Answers to Problems

1.1 (a) 3.2x10-^^

(b) r = 7.9 xlO^ photons/sec

1.2 du =

2hvdv IkTdv

c(e^y/^T

^i)^ c

1.3 P = 128 W;r =

6.45xld^^

photons/sec

1.4 e = 0.49

1.5 dT = 7.5K

1.6 T(mercujy) = 483 K

T(Pluto) = 47.7K

1.7 Gfi = 6.13 W/m^K

1.8 T=820K

1.9 (l/P)(dP/dT) = 0.016 K-i

1.10 N = 2.1x10^^ photons

1.11 NEAT = 1.3 X10-^ K

1.12 N/A = 8.6 X

10^^

photons/cm2

1.13 Q.E.D.

1.14 Tungstm,2.9%

Halogen, 5 %

1.15 T = 904K

1.16 r = 1.1x10^^ photons/sec

2.1 Q.E.D.

2.2 (a) 2.3 A, 86 GHz

0>)rt=23.4cnr^

2.3 X^^ = 69fim

3.1 X=76A,a = 4.6A

3.2 r]ext = [Mfim)ll24]P/I

3.3 T = 18540 K

3.4 ia)D = 4.9km

Qj)D = 3fim

4.1 (a) i^ =3.9xlO-^^A^

0))is=^1.9xlO-^ATA

ic) NEAT = 3.3 X10-^ K

4.2 il=lxl(r^^A^

NEAT = 33xl(r^K

4.3 Q.E.D.

4.4 St^nMEIllA/W

1.24

4.5

(a)

Rjn = 231 a Ti^

=

22K

(\)){in)^f = 23pAl^z

(c) NEP = 2.85 X

10-^0

w

5.1 NEP = 3.3xl0-^W

5.2 t) = 0.0014

5.3 (a)r] =

a-e-«rf;

(\>)d = 0.693/a

5.4 (NEP)sL = 2rhvB/Ti

hv

(NEP)DI=

—J2qn^B

7]q

5.5 G = 1.14xl(P

5.6 T = 253K

5.7 (a) Rin =

231

a T^ = 84.8 K

(b) (f^)^ = 4.5 X 10-^2 ^/Hz3/2

(c)

(NEP)j^^

= 5.6 xlO-^o Y/

5.8 (a)

1^

= 6.7x10^ A

Qo)

(NEP)j^l = l.l xlO-^ W

ic)P^JNEP = 7500

191

192

Appendix A

5.9 (a)|2 =

2^FM2/soB

+ ^^

M + JM^ + =—

(b)/so

=

^FB+jr^™2+ig^

M Kir,

(c)NEP =

2.65x10-^^

{d)(NEP)^„=3.7xmsw

7.2 (a) Sensitivity = - 59.2 dBm

(b) R = 296 km

7.3 ia)Ps =

4.6xlO-^0\^

(b)NEP =

3.6xia-n

7.4

G^4Ailf^X^

'•'

'^'hiT-^'"'^

(c) (il)shot =2.6x10-^^ A^

6.2 Q.E.D.

6.3

(a=

Y^

2^VBJN+—^

7.1 (a) dW/(iT = 0.19 W/m^K

(b) iPs/tiT = 4.8 X

10-^0

w/K

(c)NEP = 3 xlO-^Oy^

(d) ^T =

2.1

K

7.5 pn,0] = 0.019

7.6 U =

7.5xia7j,P

= 60W

7.7 (a)Av = 76MHz

(b) A =

0.81

mm^

(c) Ps = 7.7 xl0-^^W,p = 0.01

(d)(S/N)p = 28 = 14.5dB

7.8 (a)Ps = 2.1xlO-^W

Q:>)(S/N)p

= 240

ic)Pio»2.9mW