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Jia-Ming Liu
Photonic Devices
CHAPTER 11. LASER OSCILLATORS
11.1.4 We have a cavity in free space with l = 0.5 m, R1 = 100% = 1, and R2 = 90% = 0.9. Thus,
(a)
(b)
2l
2 0.5 1
s = 3.3 ns,
=
c
3 108
1
= 300 MHz.
L =
T
1/4 1/4
R1 R2
(1 0.9)1/4
F =
=
= 59

4
Jia-Ming Liu
Photonic Devices
CHAPTER 1. GENERAL BACKGROUND
1.1.1 Maxwells equations and the continuity equation are:
B
,
t
D
,
J+
t
0,
,
.
t
E
=
H
=
B
D
=
=
J
=
From Section 1.1, we know that E, D, and all change sign under spatial inversion but not

Jia-Ming Liu
552
Photonic Devices
CHAPTER 10. LASER AMPLIFIERS
10.2.1 We have Nt = 1.38 1026 m3 given. For Nd:YAG at 1.064 m, the lower laser level is 4 I11/2 ,
which is empty. Thus, N1 0 and g = N2 e N1 a = N2 e . We nd that e = 9 1023 m2
from Table 10.1

Jia-Ming Liu
Photonic Devices
31
1.7.2 With P = 1 W, = 532 nm, and w0 = 10 m, the peak intensity I0 at the beam waist and
the beam divergence can be found:
I0
=
=
2P
21
=
W m2 = 6.37 GW m2 ,
w2
(10 106 )2
0
2
2 532 109
=
rad = 34 mrad.
w0
10 106
At z =

Jia-Ming Liu
Photonic Devices
179
5.1.2 (a) For a perfectly phase-matched DBR, R = = tanh2 |l. For R = 99%, |l = 3. From
(5.84), | = 4n/ and = /2n for a step-index grating with q = 1 and . Therefore, the
length l and the number N of grating periods for th

Jia-Ming Liu
Photonic Devices
173
4.3.11 A symmetric two-waveguide codirectional coupler is always phase matched. Therefore, the
likely causes for it to have = 0 are (i) the coupling coecient has a zero value: ab = = 0,
ba
PM
PM
and (ii) the coupler lengt

Jia-Ming Liu
Photonic Devices
1.5.2 With the given parameters, = 15.48 and = 0.284. Thus,
characteristics for silicon at 532 nm wavelength:
n
9
. We nd the following
1 + = 1 + 15.48 = 4.06,
2 4.06 1
2n
=
m = 4.8 107 m1 ,
=
532 109
0.284 1
= 2 = 4.8 107

Jia-Ming Liu
Photonic Devices
549
10.1.6 From (10.36),
e =
c2
2
g() =
g (),
8n2 2 sp
8n2 sp
where is the peak emission wavelength. For a homogeneously broadened medium,
g () =
2
h
with a peak value of g(21 ) =
.
2[( 21 )2 + (h /2)2 ]
h
Therefore, as in (1

604
Jia-Ming Liu
Photonic Devices
CHAPTER 11. LASER OSCILLATORS
11.3.2 For the double-pass pumping scheme, the laser cavity is the same as that considered in Exsat
ample 11.4; only the pumping scheme is changed. Therefore, Pout = 1.18 mW, as found in
Exam