30
J. Eur. Opt. Society-Rapid Publ. 21, 32( 2025)
Figure A1. Geometrical relationship between incident beam and EOM crystal.
�n 3 3 c h ¼ atan 33 sin x m t n 13 c 13 � n 33 c 33 cos x m t: ðA9Þ
Applying |
the |
experimental |
condition |
of |
f m ¼ 5 |
kHz |
and |
L R � L T ¼ 350 mm, x m t 7:3 10 �5, |
and |
the |
modulation |
index m is rewritten as |
|
|
|
m ¼ pl kd qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðn 13 c 13 � n 33 c 33 Þ 2 þ ðn 33 c 33 x m tÞ 2 V EOM; ðA10Þ
The term ðn 3 1 c 13 � n 3 3 c 33 Þ 2 is stational. The term n 3 3 c 33 x m t must be considered to designe appropriate phase modulation. We rewrite the modulation index as equation( 3) using K EOM ðtÞ for simple representation. K EOM ðtÞ is written as
Figure A2. Relationship between L R � L T the modulation frequency f m is 5 kHz.
K EOM ðtÞ ¼ and K EOM ðtÞ if
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð
1 þ n 3 3 c 33 x m tÞ 2: A11 ðn 13 c 13 � n 33 c 33 Þ 2
The relationship between the optical path difference and K EOM ðtÞ at the modulation frequency f m ð ¼ x m = 2pÞof 5 kHz is shown in Figure A2. Thevalueoff1 � K EOM ðtÞg at 350 mm is less than 10 �4 order then the effect of delay time t is ignored.