Analysis of the suppression of spurious frequencies by the blocking effect in an injection-locked optoelectronic oscillator

Weijie Xu; Chun Yang; Ziye Wang

doi:10.1364/AO.415600

Applied Optics
Vol. 60,
Issue 6,
pp. 1710-1718
(2021)
•https://doi.org/10.1364/AO.415600

Analysis of the suppression of spurious frequencies by the blocking effect in an injection-locked optoelectronic oscillator

Weijie Xu, Chun Yang, and Ziye Wang

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Weijie Xu, Chun Yang, and Ziye Wang, "Analysis of the suppression of spurious frequencies by the blocking effect in an injection-locked optoelectronic oscillator," Appl. Opt. 60, 1710-1718 (2021)

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- Optical Devices, Sensors, and Detectors
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About this Article
History
- Original Manuscript: November 20, 2020
- Revised Manuscript: January 18, 2021
- Manuscript Accepted: January 19, 2021
- Published: February 17, 2021

Abstract

The blocking effect causing the suppression of spurious frequencies in an injection-locked optoelectronic oscillator (IL-OEO) is studied in this paper. The blocking effect analysis in nonlinear systems is carried out using the Volterra series and is experimentally measured in a microwave amplifier. The blocking effect in the nonlinear system helps in analyzing the suppression of spurious frequencies in an IL-OEO. Under injection locking, the spurious frequencies in the IL-OEO are significantly suppressed, and the spurs are further suppressed when the power of the reference signal is increased.

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$F_{1}$	$\frac{1}{2^{5}} \frac{5!}{3! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$	$G_{1}$	$\frac{1}{2^{5}} \frac{5!}{3! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$
$F_{2}$	$\frac{1}{2^{5}} \frac{5!}{2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}, j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (j ω_{1}, - j ω_{1}, - j ω_{1}, j ω_{2}, - j ω_{2}) \end{array}]$	$G_{2}$	$\frac{1}{2^{5}} \frac{5!}{2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}, j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (j ω_{2}, - j ω_{2}, - j ω_{2}, j ω_{1}, - j ω_{1}) \end{array}]$
$F_{3}$	$\frac{1}{2^{5}} \frac{5!}{2! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (- j ω_{1}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$	$G_{3}$	$\frac{1}{2^{5}} \frac{5!}{2! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (- j ω_{2}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$
$F_{4}$	$\frac{1}{2^{3}} \frac{3!}{2!} [\begin{array}{l} H_{3, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}) + \\ H_{3, s y m} (j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$	$G_{4}$	$\frac{1}{2^{3}} \frac{3!}{2!} [\begin{array}{l} H_{3, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}) + \\ H_{3, s y m} (j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$
$F_{5}$	$\frac{1}{2^{3}} (3!) [\begin{array}{l} H_{3, s y m} (j ω_{1}, j ω_{2}, - j ω_{2}) + \\ H_{3, s y m} (- j ω_{1}, j ω_{2}, - j ω_{2}) \end{array}]$	$G_{5}$	$\frac{1}{2^{3}} (3!) [\begin{array}{l} H_{3, s y m} (j ω_{2}, j ω_{1}, - j ω_{1}) + \\ H_{3, s y m} (- j ω_{2}, j ω_{1}, - j ω_{1}) \end{array}]$
$F_{6}$	$\frac{1}{2} [H_{1} (j ω_{1}) + H_{1} (- j ω_{1})]$	$G_{6}$	$\frac{1}{2} [H_{1} (j ω_{2}) + H_{1} (- j ω_{2})]$

$A_{1}$	$V_{1}$	$B_{1}$	$V_{2}$
$A_{3}$	$\frac{3}{4} V_{1}^{3} + \frac{3}{2} V_{1} V_{2}^{2}$	$B_{3}$	$\frac{3}{4} V_{2}^{3} + \frac{3}{2} V_{1}^{2} V_{2}$
$A_{5}$	$\frac{5}{8} V_{1}^{5} + \frac{15}{4} V_{1}^{3} V_{2}^{2} + \frac{15}{8} V_{1} V_{2}^{4}$	$B_{5}$	$\frac{5}{8} V_{2}^{5} + \frac{15}{4} V_{1}^{2} V_{2}^{3} + \frac{15}{8} V_{1}^{4} V_{2}$

	Linear	−30 dBm	−20 dBm^a	−10 dBm
$P_{0, i n}$	Nonlinear	2.4 dBm	3.6 dBm^a	4.5 dBm
$P_{s, i n}$	Sweep in 0.5 dB step from −37 dBm to 8 dBm

Component	Model	Parameters
LD	EMCore 1782	Power: 100 mW
		RIN: −153 dB/Hz
MZM	LN81S	$V_{π}$ : 5.6 V
		Insertion Loss: 4 dB
PD	DSC40S	Responsivity: 0.85 A/W

$F_{1}$	$\frac{1}{2^{5}} \frac{5!}{3! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$	$G_{1}$	$\frac{1}{2^{5}} \frac{5!}{3! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$
$F_{2}$	$\frac{1}{2^{5}} \frac{5!}{2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}, j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (j ω_{1}, - j ω_{1}, - j ω_{1}, j ω_{2}, - j ω_{2}) \end{array}]$	$G_{2}$	$\frac{1}{2^{5}} \frac{5!}{2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}, j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (j ω_{2}, - j ω_{2}, - j ω_{2}, j ω_{1}, - j ω_{1}) \end{array}]$
$F_{3}$	$\frac{1}{2^{5}} \frac{5!}{2! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{1}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) + \\ H_{5, s y m} (- j ω_{1}, j ω_{2}, j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$	$G_{3}$	$\frac{1}{2^{5}} \frac{5!}{2! 2!} [\begin{array}{l} H_{5, s y m} (j ω_{2}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) + \\ H_{5, s y m} (- j ω_{2}, j ω_{1}, j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$
$F_{4}$	$\frac{1}{2^{3}} \frac{3!}{2!} [\begin{array}{l} H_{3, s y m} (j ω_{1}, j ω_{1}, - j ω_{1}) + \\ H_{3, s y m} (j ω_{1}, - j ω_{1}, - j ω_{1}) \end{array}]$	$G_{4}$	$\frac{1}{2^{3}} \frac{3!}{2!} [\begin{array}{l} H_{3, s y m} (j ω_{2}, j ω_{2}, - j ω_{2}) + \\ H_{3, s y m} (j ω_{2}, - j ω_{2}, - j ω_{2}) \end{array}]$
$F_{5}$	$\frac{1}{2^{3}} (3!) [\begin{array}{l} H_{3, s y m} (j ω_{1}, j ω_{2}, - j ω_{2}) + \\ H_{3, s y m} (- j ω_{1}, j ω_{2}, - j ω_{2}) \end{array}]$	$G_{5}$	$\frac{1}{2^{3}} (3!) [\begin{array}{l} H_{3, s y m} (j ω_{2}, j ω_{1}, - j ω_{1}) + \\ H_{3, s y m} (- j ω_{2}, j ω_{1}, - j ω_{1}) \end{array}]$
$F_{6}$	$\frac{1}{2} [H_{1} (j ω_{1}) + H_{1} (- j ω_{1})]$	$G_{6}$	$\frac{1}{2} [H_{1} (j ω_{2}) + H_{1} (- j ω_{2})]$

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Applied Optics