of 4
Supplemental Document
Photonic millimeter-wave generation beyond the
cavity thermal limit: supplement
W
ILLIAM
G
ROMAN
,
1,2,3,
I
GOR
K
UDELIN
,
1,2,3
A
LEXANDER
L
IND
,
1,3
D
AHYEON
L
EE
,
2,3
T
AKUMA
N
AKAMURA
,
3
Y
IFAN
L
IU
,
2,3
M
EGAN
L. K
ELLEHER
,
2,3
C
HARLES
A. M
C
L
EMORE
,
2,3
J
OEL
G
UO
,
4
L
UE
W
U
,
5
W
ARREN
J
IN
,
4
K
ERRY
J. V
AHALA
,
5
J
OHN
E. B
OWERS
,
4
F
RANKLYN
Q
UINLAN
,
1,3
AND
S
COTT
A.
D
IDDAMS
1,2,3
1
Electrical Computer & Energy Engineering, University of Colorado, Boulder, Boulder, Colorado 80309,
USA
2
Department of Physics, University of Colorado, Boulder, 440 UCB, Boulder, Colorado 80309, USA
3
National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
4
Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa
Barbara, California 93106, USA
5
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California
91125, USA
william.groman@colorado.edu
This supplement published with Optica Publishing Group on 14 November 2024 by The Authors
under the terms of the Creative Commons Attribution 4.0 License in the format provided by the
authors and unedited. Further distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
Supplement DOI: https://doi.org/10.6084/m9.figshare.27233274
Parent Article DOI: https://doi.org/10.1364/OPTICA.536549
1.
ALLAN
DEVIATION
The
following
figure
shows
the
Allan
deviation
of
the
118.1
GHz
heterodyned
beat
and
the
Allan
deviation
of
the
self-injection-locked
laser
PDH-locked
to
the
vacuum
Fabry-Perot
cavity.
The
Allan
deviation
of
the
118.1
GHz
signal
is
not
200
THz/
120
GHz
1600
times
higher
than
the
Allan
deviation
of
the
out-of-loop
PDH-locked
laser
because
the
noise
limitations
of
the
two
are
different.
The
PDH-locked
laser
is
limited
by
the
cavity
thermal
limit,
while
the
118.1
GHz
signal
is
limited
by
the
PDH
locking
servos.
Fig. S1.
Allan deviation of the 118.1 GHz millimeter-wave beat resulting from the heterodyn-
ing of the two PDH-locked SIL lasers (red), and Allan deviation of one of the out-of-loop PDH-
locked SIL lasers (yellow).
2. CROSS-CORRELATION MEASUREMENT
The following figure shows a diagram of how the cross-correlation measurement was done to
measure the 94.5 GHz and 118.1 GHz phase noise. Two reference synthesizers are harmoni-
cally mixed (i.e. harmonically multiplied up in frequency, then mixed with RF signal) with
the millimeter-wave, which is split after photodetection. The signals are mixed such that the
intermediate frequency is 5 MHz, and those two 5 MHz signals are cross-correlated by a phase
noise analyzer. In our measurement of the
118.1
GHz millimeter-wave signal, we averaged for
12 minutes resulting in
70
correlations in the
1 Hz to
5 Hz bandwidth,
140
correlations in
the
5 Hz to
20
Hz bandwidth,
570
correlations in the
20
Hz to
75
Hz bandwidth,
1, 700
correlations in the
75
Hz to
265
kHz bandwidth,
6, 850
correlations in the
265
Hz to
890
Hz
bandwidth,
27, 400
correlations in the
890
Hz to
4 kHz bandwidth,
54, 800
correlations in the
4 kHz to
13
kHz bandwidth,
109, 600
correlations in the
13
kHz to
120
kHz bandwidth, and
198, 300
correlations in the
120
kHz to
1 MHz bandwidth. In the
10
kHz to
100
kHz range, this
corresponds to a noise floor of about
120 dBc/Hz.
Fig. S2.
a.) Cross-correlation measurement setup using two harmonic mixers (HP 11970W,
Harmonic Number N = 18 and Virginia Diodes VDI WR8.0-SHX, Harmonic Number N = 12)
and two reference synthesizers (Agilent E8257N and Holzworth HSX9002a). The intermediate
frequency (IF) from both arms of the harmonic mixers was
5 MHz, and is cross-correlated
against an external
5 MHz quartz crystal oscillator. The phase noise of the cross-correlated
signal is measured via the Timelab Microchip 53100A phase noise analyzer. b.) Phase noise
PSD of the two reference synthesizers scaled to 118.1 GHz in blue and green.
2
3. NOISE CONTRIBUTIONS CONSTITUENT PARTS
The following figure shows a the constituent parts of the noise contributions featured in the main
text. Included are the individual lasers’ in-loop phase noise titled
ν
1
and
ν
2
In-loop Phase Noise.
These are measured by taking the electronic PSD of the error signal from each laser while they are
PDH-locked and scaling them according to error loop unlocked slope (measured by taking the
V
pp
of the error signal while ramping the AOM current versus the Fabry-Perot cavity linewidth)
as per [
1
]. Additionally the servo loop signal-to-noise ratio is inferred by measuring the PSD of
the error signal noise when each laser is not PDH-locked and is slightly detuned off resonance.
These electronic PSD are converted to PSD phase noise by the same normalization method as the
in-loop phase noise.
Fig. S3.
a.) Plot showing the noise contributions (green) which is the quadrature sum of the
servo in-loop SNR phase noise for each laser (gray and red), and the individual lasers’ in-
loop phase noise (yellow and blue). b.) Since each laser experiences the same in-loop SNR
and phase noise, it may be more illustrative to look at one laser’s noise contributions to the cu-
mulative total. Here it is obvious that the servo in-loop contributes the most to the cumulative
phase noise limit at higher offset frequencies, while at lower offset frequencies, both the servo
SNR and in-loop feedback are the main limitations.
REFERENCES
1.
F. Bondu and O. Debieu, “Accurate measurement method of fabry-perot cavity parameters
via optical transfer function,” Appl. Opt.
46
, 2611 (2007).
3