JEOS RP ISSN03 | Page 71

64
J. Eur. Opt. Society-Rapid Publ. 22, 7( 2026)
Table 2. Beam radius at four cavity points for 5 cavities with different lengths.
Setup Beam radius( lm) at concave mirror( w t ¼ w s)
Beam radius( lm) at input of Nd: YAG crystal( w t ¼ w s)
Beam radius( lm) at output of Nd: YAG crystal( w t ¼ w s)
Beam radius( lm) at plane mirror( w t ¼ w s)
1
425.718
345.902
315.805
290.647
1
312
2
434.386
348.858
317.752
290.133
1
322
3
443.31
351.807
319.644
289.38
1
332
4
452.529
254.77
321.493
288.382
1
342
5
462.089
357.767
323.316
287.132
1
352
w t w s
L total
( mm)
Fig 4. Schematic of a concave – flat Q-switched Nd: YAG laser cavity incorporating a Cr 4 +: YAG crystal.
Table
3. Distances of four cavity arrangements of passive
Q-switched
Nd: YAG
laser
with
saturated
Cr: YAG
absorber.
Setup
L 1( mm)
L 1( mm)
L 3( mm)
L total( mm)
A
50
60
60
275
B
70
80
90
345
C
90
90
120
405
D
115
100
145
465
B) Cavity analysis in Q-switched operation
Figure 4 presents the schematic configuration of the passively Q-switched Nd: YAG laser, incorporating a Cr: YAG saturable absorber. The absorber crystal used in this study is 5 mm in thickness and 8 mm in diameter, with an initial transmission of 40 %. In the schematic, L1, L2, and L3 denote the optical path lengths between intracavity components, while d 1 and d 2 represent the physical lengths of the Cr: YAG and Nd: YAG crystals( 5 mm and 100 mm, respectively). The total cavity length( L total) encompasses all these segments and defines the longitudinal geometry of the Q-switched resonator.
According to Table 3, to study the behavior of the system, four different configurations with total cavity lengths of 275, 345, 405, and 465 mm were designed and investigated.
The round-trip transfer matrix for the beam, taking into account all optical elements inside the cavity shown in Figure 4, is written as follows:
Fig. 5. Resonator stability parameter as a function of cavity length.
M ¼ 1 0
1 L1 1 d1
n
1 L2 0 1 0 1 0 1 0 1
1
d2 n 1 L3
1 0
0 1 0 1 � 2 1 L3
1
R
0 1
1
d2 n 1 L2
1
d1 n 1 L1
: ð15Þ
0 1 0 1 0 1 0 1