Study on the sensitivity of optical cavity length
to light power fluctuation
Wen Qi (祁 文), Yanyi Jiang (蒋燕义)*, Xueyan Li (李雪艳), Li Jin (金 丽),
Zhiyi Bi (毕志毅), and Longsheng Ma (马龙生)
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
*Corresponding author: yyjiang@phy.ecnu.edu.cn
Received May 9, 2016; accepted August 5, 2016; posted online August 30, 2016
The length stability of optical cavities is vital in ultra-stable, cavity-stabilized laser systems. Using finite element
analysis, we study the length deviation of optical cavities due to thermal expansion and thermo-refractive effects
when the incident light power is changed. The simulated fractional length sensitivity of a 7.75-cm-long football
cavity to the power fluctuation of incident light is 5 × 10
−14
∕μW, which is in agreement with the experimental
results found by measuring the frequency change of a cavity-stabilized laser when the incident light power is
changed. Based on the simulation, the cavity sensitivity to light power fluctuation is found to depend on the
cavity size and material.
OCIS codes: 140.3425, 140.4780, 120.2230.
doi: 10.3788/COL201614.101401.
Ultra-stable narrow-linewidth lasers are essential in
many applications, such as the optical atomic clock,
high-resolution laser spectroscopy, tests of fundamental
physics, and gravitational wave detection
[1–3]
. Most of
those lasers are achieved by actively stabilizing the laser
frequency to the resonance of a Fabry–Perot (F-P) cavity
using the Pound-Drever-Hall (PDH) technique
[4]
. State-of-
the-art laser systems have been developed with a linewidth
below 1 Hz and fractional frequency instabilities at the
10
−16
level or better at a 1 s averaging time
[5–8]
.
In those cavity-stabilized laser systems, the laser fre-
quency stability is mostly limited by the length stability
of the reference cavities. A special design of optical cavities
as well as their supporting configurations has been per-
formed to achieve a low sensitivity to thermal fluctuation
and vibration
[8–10]
, approaching a thermal-noise-limited
performance
[11]
.
In a cavity-stabilized laser system, the power of light in-
cident onto a cavity is stabilized since the power fluctuation
of cavity resonant light induces temperature fluctuation
and thus the cavity length fluctuation is due to thermal ex-
pansion (TE) and the thermo-refractive (TR) effect. Frac-
tional power instability of 1 × 10
−4
can be achieved after
stabilization
[12]
. Usually, the power-dependent frequency
shift of a cavity-stabilized laser is measur ed to be a few
tens of hertz/microwatt (Hz/μW)
[12]
, corresponding to a
cavity length sensitivity at the 10
−14
m∕μW level. For a
10-cm-long cavity made of ultra-low expansion (ULE)
glass, the light power fluctuation-induced fractional
length instability is nearly 10
−16
, while the thermal-noise-
limited length instability of the cavity at room temperature
is approximately 8 × 10
−16
. In the pursuit of a laser fre-
quency instability of 10
−17
level or better, it is critical
to reduce the cavity length instabilit y resulting from light
power fluctuation. In this Letter, we study the sensitivity of
the cavity length to light power fluctuation (S), providing a
method to evaluate the sensitivity S for cavity-stabilized
laser systems, as well as providing a way to reduce S by
designing an optical cavity with a particular size and
material.
We use finite element analysis (FEA) to analyze the
length deviation of an F-P cavity when the power of inci-
dent light vari es. A portion of incident light is absorbed by
mirror coatings, resulting in a temperature change. By
performing a thermal-mechanical analysis, the displace-
ment between the cavity mirrors due to TE (ΔL
TE
) is ob-
tained. Meanwhile, the effective optical length change due
to the TR effect (ΔL
TR
) is considered into the total cavity
length change by evaluating the temperature variation
based on thermal analysis. The length sensitivity of a
7.75-cm-long football cavity to the power fluctuation of
incident light is simulated to be S ¼ 5×10
−14
∕μW. It
is in agreement with the experimental results, which are
obtained by measuring the frequency change of a cav-
ity-stabilized laser when the cavity incident light power
is changed. Based on the FEA, we find that a long cavity
made of materials with high thermal conductivity and a
small coefficient of TE (CTE) has a low sensitivity S.
Consider an F-P cavity with two highly reflective mir-
rors optically contacted to a spacer. To achieve a reflec-
tivity of 99.99%, the mirror substrates are usually
covered by dielectric coatings, such as multiple layers of
SiO
2
and Ta
2
O
5
. Usually the coatings have a CTE of
at the 10
−5
∕K level. Compared with mirror s ubstrates
and a cavity spacer that made of fused silica (FS) or
ULE glass whose CTE is on the order of 1 × 10
−7
∕Kor
less, the deformation of the coatings is unneglectable.
Therefore, mirror coatings must be taken into account
in the simulation. However, we simplify the N alternating
sequences of quarter-wavelength layers into one layer with
thickness (d), an averaging density (ρ), Young’s modulus
(E), and Poisson’s ratio (σ), which are listed in Table
1.
COL 14(10), 101401(2016) CHINESE OPTICS LETTERS October 10, 2016
1671-7694/2016/101401(5) 101401-1 © 2016 Chinese Optics Letters
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