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The Phonon-Limited-Linewidth of Brillouin Lasers at Cryogenic Temperatures -
Supplemental Material
Myoung-Gyun Suh, Qi-Fan Yang, and Kerry J. Vahala
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA.
BRILLOUIN LASER LINEWIDTH UNDER CASCADED OPERATION
The linewidth formula Eq. (1) in the main text has been observed to hold under cascaded operation [1]. Strong
coherent interaction of the Stokes waves that might impact the linewidth formula could be possible if cavity disper-
sion and Brillouin mode pulling [1] created Stokes waves having equal frequency spacing. This arrangement was not
observed here.
BRILLOUIN GAIN BANDWIDTH AND n
T
MEASUREMENT
The Brillouin gain bandwidth (∆
ν
B
) is also extracted from a quadratic fit of the curves in Fig. 2(b) [1]. We measure
20 MHz at 300 K, 25 MHz at 77 K, and 35 MHz at 8 K. These linewidths reflect the damping rate of the Brillouin
process and have been the focus of theory and experiment in silica optical fiber [2, 3]. The measured temperature
dependence is not consistent with theory and is believed to result from different optical and acoustical mode families
participating in the Brillouin process at different temperatures. To partially test this hypothesis, Brillouin linewidths
were measured at room temperature by inducing Brillouin laser action on a range of different cavity modes. Linewidths
in the range 15 MHz - 45 MHz were measured suggesting that damping of the Brillouin process is strongly affected
by the spatial structure of the mode. This could, for example, result from differences in the surface interactions of
the various spatial acoustical modes with the wedge resonator dielectric-air interface. It is important to note that this
behavior in no way affects the measurement of
n
T
since it is the measured value of
g
and not the theoretical value of
g
that matters.
vahala@caltech.edu
[1] J. Li, H. Lee, T. Chen, and K. J. Vahala, Optics express
20
, 20170 (2012).
[2] S. Le Floch and P. Cambon, Optics communications
219
, 395 (2003).
[3] R. O. Behunin, P. Kharel, W. H. Renninger, H. Shin, F. Carter, E. Kittlaus, and P. T. Rakich, ArXiv e-prints (2015),
arXiv:1501.04248 [quant-ph].