High-precision digital optical phase locking for 10<sup>−12</sup> W order weak light for a spaceborne gravitational wave interferometer

Henglin Mu; Taoran Le; Xin Xu; Yidong Tan; Haoyun Wei; Yan Li

doi:10.1364/AO.490247

Applied Optics
Vol. 62,
Issue 20,
pp. 5494-5501
(2023)
•https://doi.org/10.1364/AO.490247

High-precision digital optical phase locking for 10⁻¹² W order weak light for a spaceborne gravitational wave interferometer

Henglin Mu, Taoran Le, Xin Xu, Yidong Tan, Haoyun Wei, and Yan Li

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Henglin Mu, Taoran Le, Xin Xu, Yidong Tan, Haoyun Wei, and Yan Li, "High-precision digital optical phase locking for 10⁻¹² W order weak light for a spaceborne gravitational wave interferometer," Appl. Opt. 62, 5494-5501 (2023)

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Abstract

We developed a digital optical phase-locking loop (DOPLL) for weak light phase locking in spaceborne gravitational wave interferometers (SGWIs). Using the system, we successfully locked the phase of the slave laser to the master laser with the power of only several picowatts, much smaller than the LISA requirement (100 pW). The system does not introduce steady-state errors, and the Bode diagram shows its stability. The out-loop phase noise floor (${2.3} \times {{10}^{- 4}}$ and ${5.2} \times {{10}^{- 4}}\;{\rm rad}/{{\rm Hz}^{1/2}}$) is very close to the shot noise limit. The Allan standard deviation of the heterodyne signal reaches ${3.1} \times {{10}^{- 17}}$ at 1000 s. With the previous automatic locking program designed by other researchers, the results demonstrate that DOPLLs have bright application prospects and can be applied in the transducer of the SGWI.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Part	Parameter Name	Value	unit
ADC	Number of sampling bits $N_{A D C}$	10	bit
	Sampling frequency $f_{A D C s a m p l i n g}$	1.25	GHz
	Range $U_{r a n g e}$	$\pm 0.2$	V
	Delay cycle $N_{c y c l e}$	4	1
PM	Bandwidth $B_{w - p h a s e m e t e r}$	1	MHz
	Number of PIR bits $N_{P I R}$	48	bit
	Number of PA bits $N_{P A}$	64	bit
	Phase-output ratio $k_{I}$	$125 / π$	mV/rad
LPF	Sampling frequency $f_{L P F s a m p l i n g}$	78.125	MHz
LPF	Cutoff frequency $f_{F c}$	50	kHz
	Number of bits $N_{P I}$	24	bit
Fast loop	Sampling frequency $f_{P I s a m p l i n g}$	78.125	MHz
	Proportional gain $k_{I I}$	$- 20$	dB
	Integrator crossover frequency $f_{P I - I}$	10	kHz
	Integrator crossover frequency $f_{P I - I I}$	10	Hz
Slow loop	Number of bits $N_{P I}$	24	bit
	Sampling frequency $f_{P I s a m p l i n g}$	78.125	MHz
	Proportional gain $k_{I I I}$	$- 30$	dB
	Integrator crossover frequency $f_{P I - I I I}$	0.4	Hz
DAC	Number of sampling bits $N_{D A C}$	16	bit
	Sampling frequency $f_{D A C s a m p l i n g}$	1.25	GHz
	Delay cycle $N_{c y c l e}$	306	1
	Proportional gain of fast loop $k_{I V}$	$+ 14$	dB
	Attenuation coefficient of slow loop $a_{T}$	$- 30$	dB

Name	Delay Time (ns)
PD	2.3
Analog bandpass filter	80
LNA (typical)	40
ADC	3.2
PM (the worst case)	50
Low-pass filter	51.2
PI controller (the worst case)	50
DAC	244.8
Cable	1
Total	522.5

Part	Parameter Name	Value	unit
ADC	Number of sampling bits $N_{A D C}$	10	bit
	Sampling frequency $f_{A D C s a m p l i n g}$	1.25	GHz
	Range $U_{r a n g e}$	$\pm 0.2$	V
	Delay cycle $N_{c y c l e}$	4	1
PM	Bandwidth $B_{w - p h a s e m e t e r}$	1	MHz
	Number of PIR bits $N_{P I R}$	48	bit
	Number of PA bits $N_{P A}$	64	bit
	Phase-output ratio $k_{I}$	$125 / π$	mV/rad
LPF	Sampling frequency $f_{L P F s a m p l i n g}$	78.125	MHz
LPF	Cutoff frequency $f_{F c}$	50	kHz
	Number of bits $N_{P I}$	24	bit
Fast loop	Sampling frequency $f_{P I s a m p l i n g}$	78.125	MHz
	Proportional gain $k_{I I}$	$- 20$	dB
	Integrator crossover frequency $f_{P I - I}$	10	kHz
	Integrator crossover frequency $f_{P I - I I}$	10	Hz
Slow loop	Number of bits $N_{P I}$	24	bit
	Sampling frequency $f_{P I s a m p l i n g}$	78.125	MHz
	Proportional gain $k_{I I I}$	$- 30$	dB
	Integrator crossover frequency $f_{P I - I I I}$	0.4	Hz
DAC	Number of sampling bits $N_{D A C}$	16	bit
	Sampling frequency $f_{D A C s a m p l i n g}$	1.25	GHz
	Delay cycle $N_{c y c l e}$	306	1
	Proportional gain of fast loop $k_{I V}$	$+ 14$	dB
	Attenuation coefficient of slow loop $a_{T}$	$- 30$	dB

Name	Delay Time (ns)
PD	2.3
Analog bandpass filter	80
LNA (typical)	40
ADC	3.2
PM (the worst case)	50
Low-pass filter	51.2
PI controller (the worst case)	50
DAC	244.8
Cable	1
Total	522.5

Abstract

Data availability

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Figures (6)

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Equations (22)

Applied Optics