In order to achieve high frequency stability in ultra-stable lasers, the Fabry-Pérot reference cavities shall be put inside vacuum chambers with large thermal time constants to reduce the sensitivity to external temperature fluctuations. Currently, the determination of thermal time constants of vacuum chambers is based either on theoretical calculation or time-consuming experiments. The first method can only apply to simple system, while the second method will take a lot of time to try out different designs. To overcome these limitations, we present thermal time constant simulation using finite element analysis (FEA) based on complete vacuum chamber models and verify the results with measured time constants. We measure the thermal time constants using ultrastable laser systems and a frequency comb. The thermal expansion coefficients of optical reference cavities are precisely measured to reduce the measurement error of time constants. The simulation results and the experimental results agree very well. With this knowledge, we simulate several simplified design models using FEA to obtain larger vacuum thermal time constants at room temperature, taking into account vacuum pressure, shielding layers, and support structure. We adopt the Taguchi method for shielding layer optimization and demonstrate that layer material and layer number dominate the contributions to the thermal time constant, compared with layer thickness and layer spacing.

1.
A. D.
Ludlow
,
M. M.
Boyd
,
J.
Ye
,
E.
Peik
, and
P. O.
Schmidt
,
Rev. Mod. Phys.
87
,
637
(
2015
).
2.
R. W. P.
Drever
,
J. L.
Hall
,
F. V.
Kowalski
,
J.
Hough
,
G. M.
Ford
,
A. J.
Munley
, and
H.
Ward
,
Appl. Phys. B
31
,
97
(
1983
).
3.
B. C.
Young
,
F. C.
Cruz
,
W. M.
Itano
, and
J. C.
Bergquist
,
Phys. Rev. Lett.
82
,
3799
(
1999
).
4.
S. A.
Webster
,
M.
Oxborrow
, and
P.
Gill
,
Phys. Rev. A
75
,
011801(R)
(
2007
).
5.
J.
Alnis
,
A.
Matveev
,
N.
Kolachevsky
,
Th.
Udem
, and
T. W.
Hänsch
,
Phys. Rev. A
77
,
053809
(
2008
).
6.
J.
Millo
,
D. V.
Magalhães
,
C.
Mandache
,
Y.
Le Coq
,
E. M. L.
English
,
P. G.
Westergaard
,
J.
Lodewyck
,
S.
Bize
,
P.
Lemonde
, and
G.
Santarelli
,
Phys. Rev. A
79
,
053829
(
2009
).
7.
Y. N.
Zhao
,
J.
Zhang
,
A.
Stejskal
,
T.
Liu
,
V.
Elman
,
Z. H.
Lu
, and
L. J.
Wang
,
Opt. Express
17
,
8970
(
2009
).
8.
H. Q.
Chen
,
Y. Y.
Jiang
,
S.
Fang
,
Z. Y.
Bi
, and
L. S.
Ma
,
J. Opt. Soc. Am. B
30
,
1546
(
2013
).
9.
Y. Y.
Jiang
,
A. D.
Ludlow
,
N. D.
Lemke
,
R. W.
Fox
,
J. A.
Sherman
,
L.-S.
Ma
, and
C. W.
Oates
,
Nat. Photonics
5
,
158
(
2011
).
10.
T.
Kessler
,
C.
Hagemann
,
C.
Grebing
,
T.
Legero
,
U.
Sterr
,
F.
Riehle
,
M. J.
Martin
,
L.
Chen
, and
J.
Ye
,
Nat. Photonics
6
,
687
(
2012
).
11.
C.
Hagemann
,
C.
Grebing
,
C.
Lisdat
,
S.
Falke
,
T.
Legero
,
U.
Sterr
,
F.
Riehle
,
M. J.
Martin
, and
J.
Ye
,
Opt. Lett.
39
,
5102
(
2014
).
12.
S.
Häfner
,
S.
Falke
,
C.
Grebing
,
S.
Vogt
,
T.
Legero
,
M.
Merimaa
,
C.
Lisdat
, and
U.
Sterr
,
Opt. Lett.
40
,
2112
(
2015
).
13.
S. L.
Rickman
and
E. K.
Ungar
, in
25th Aerospace Testing Conference
,
October 2009
.
14.
C.
Hagemann
, Ph.D. thesis,
University of Hannover
,
2013
.
15.
S.
Amairi
, Ph.D. thesis,
University of Hannover
,
2014
.
16.
X. J.
Dai
,
Y. Y.
Jiang
,
C.
Hang
,
Z. Y.
Bi
, and
L.-S.
Ma
,
Opt. Express
23
,
5134
5146
(
2015
).
17.
J.
Sanjuan
,
N.
Gürlebeck
, and
C.
Braxmaier
,
Opt. Express
23
,
17892
17908
(
2015
).
18.
J.
Zhang
,
Z. H.
Lu
,
B.
Menegozzi
, and
L. J.
Wang
,
Rev. Sci. Instrum.
77
,
083104
(
2006
).
19.
P.
Dubé
,
A. A.
Madej
,
J. E.
Bernard
,
L.
Marmet
, and
A. D.
Shiner
,
Appl. Phys. B
95
,
43
54
(
2009
).
20.
S. T.
Dawkins
,
R.
Chicireanu
,
M.
Petersen
,
J.
Millo
,
D. V.
Magalhães
,
C.
Mandache
,
Y.
Le Coq
, and
S.
Bize
,
Appl. Phys. B
99
,
41
46
(
2010
).
21.
J.
Burkart
,
D.
Romanini
, and
S.
Kassi
,
Opt. Lett.
38
,
2062
(
2013
).
22.
J.
Keller
,
S.
Ignatovich
,
S. A.
Webster
, and
T. E.
Mehlstäubler
,
Appl. Phys. B
116
,
203
210
(
2014
).
23.
G.
Taguchi
,
Introduction to Quality Engineering
(
Asian Productivity Organization
,
Tokyo
,
1990
).
24.
R.
Unal
and
E. B.
Dean
, in 13th Annual Conference of the International Society of Parametric Analysts, 1991.
25.
W. H.
Yang
and
Y. S.
Tarng
,
J. Mater. Process. Technol.
84
,
122
129
(
1998
).
You do not currently have access to this content.