Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator

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Optimization of laser stabilization via

self-injection locking to a

whispering-gallery-mode microresonator:

experimental study

ARTEM E. SHITIKOV,1,* ILYA I. LYKOV,1OLEG V. BENDEROV,2

DMITRY A. CHERMOSHENTSEV,1,2,3 ILYA K. GORELOV,1,4 ANDREY N.

DANILIN,1,4 RAMZIL R. GALIEV,5NIKITA M. KONDRATIEV,5STEEVY

J. CORDETTE,5ALEXANDER V. RODIN,2ANATOLY V. MASALOV,1,6

VALERY E. LOBANOV,1IGOR A. BILENKO,1,4

1Russian Quantum Center, 143026 Skolkovo, Russia

2Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia

3Skolkovo Institute of Science and Technology, Moscow 143025, Russia

4Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

5Directed Energy Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates

6Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

*Shartev@gmail.com

Abstract:

Self-injection locking of a diode laser to a high-quality-factor microresonator

is widely used for frequency stabilization and linewidth narrowing. We constructed several

microresonator-based laser sources with measured instantaneous linewidths of 1 Hz and used them

for investigation and implementation of the self-injection locking eﬀect. We studied analytically

and experimentally the dependence of the stabilization coeﬃcient on tunable parameters such as

locking phase and coupling rate. It was shown that precise control of the locking phase allows

ﬁne tuning of the generated frequency from the stabilized laser diode. We also showed that it

is possible for such laser sources to realize fast continuous and linear frequency modulation by

injection current tuning inside the self-injection locking regime. We conceptually demonstrate

coherent frequency-modulated continuous wave LIDAR over a distance of 10 km using such a

microresonator-stabilized laser diode in the frequency-chirping regime and measure velocities as

low as sub-micrometer per second in the unmodulated case. These results could be of interest

for cutting-edge technology applications such as space debris monitoring and long-range object

classiﬁcation, high resolution spectroscopy and others.

1. Introduction

The development of narrow-linewidth and highly stable lasers is one of the key tasks of cutting-

edge technologies. Such lasers provide unique opportunities in variety of progressive areas as

coherent communication [1,2], ultrafast optical ranging [3

–

5], atomic clocks [6], astronomy [7],

and others. Narrow-linewidth lasers are used in coherent Doppler LIDARs for aircraft wake

vortex measurements [8], aerosol detection [9] and remote spectroscopic measurements [10].

Highly stable single frequency lasers are critically important in inverse synthetic aperture LADAR

systems (ISAL). ISAL is actively used for space debris monitoring and controlling [11], long

distance object classiﬁcation with spatial resolution far beyond diﬀraction limit of the receiving

aperture [12].

Self-injection locking (SIL) of a diode laser frequency to an eigenfrequency of a high-Q

whispering gallery mode (WGM) microresonator provides outstanding results in laser spectral

arXiv:2210.05309v2 [physics.optics] 24 Nov 2022

characteristics enhancement [13]. It proved to be a simple and robust way of laser stabilization.

Since it was demonstrated for the ﬁrst time [14] SIL still attracts increasing interest and still

evolving. The comprehensive theory of the SIL was developed in [15] and optimal regimes

of laser stabilization were discussed in [16]. Laser stabilization to sub-Hz linewidth was

demonstrated with crystalline microresonator in [17], and with on-chip microresonator in [18].

Recently, simultaneous stabilization of two diode lasers by one microresonator has been studied

theoretically and experimentally [19]. Furthermore, it was shown that SIL phenomena could be

eﬃciently used to demonstrate the formation of bright [18, 20

–

23] and dark [24, 25] microcomb

solitons, ultra-low-noise photonic microwave oscillators [26], frequency-modulated continuous

wave LIDARs [27]. The advantages of using SIL phenomena of semiconductor laser diodes

with integrated microresonators are the possibility of on-chip realization [28] of such system

that makes the technology compact and inexpensive. Lasers based on the self-injection locking

of laser diodes to integrated microresonators from silicon nitride demonstrate outstanding

performance [25, 29, 30]. Nevertheless, crystalline microresonator-based SIL lasers provides

better phase noise [26, 31] and greater opportunities for research and optimization of the key

parameters of the eﬀect due to the ﬂexibility unattainable for integrated systems.

In this work we demonstrate comprehensive study of self-injection locking phenomenon, with

accurate tunability of diﬀerent experimental parameters and controllable switching between

diﬀerent SIL regimes. We discuss the possibility of adaptation of the parameters of the self-

injection locking scheme for various applications. We studied the inﬂuence of the phase shift of

the backscattered wave (locking phase) and laser-to-microresonator coupling eﬃciency (loading)

on the performance of the self-injection locked laser (the spectral characteristics of the resulting

radiation, the stabilization coeﬃcient, the width of the locking range, and the resulting laser

frequency) and found out interesting opportunities for some up-to-date applications.

For detailed experimental SIL investigation we assembled several experimental setups with

precise translation stages to vary key parameters including two fully-packaged turn-key SIL

diode lasers. The beatnote signal of two laser diodes stabilized by high-Q MgF

crystalline

microresonators demonstrated an instantaneous 1 Hz linewidth. Special attention was paid to the

dependence of the SIL parameters on the locking phase deﬁned by the optical path between laser

and microresonator. Using spectrogams, we visualized experimental tuning curves for diﬀerent

locking phases. Varying the locking phase, we found out the possibility of the fast ﬁne-tuning of

laser diode generation frequency. Also, it was revealed that, at particular value of the locking

phase for high-Q WGMs, the tuning curve splitting can be achieved.

Another parameter, that can be precisely controlled by the adjustment of the gap between the

coupler and the microresonator, is the coupling rate. We analyzed experimental dependence of

the stabilization coeﬃcient and showed that its maximum does not coincide with critical coupling,

unlike locking width. The experimental results are in good agreement with ours theoretical

predictions [32].

Beside frequency modulated continuous wave (FMCW) LIDARs, continuous tunability of a

laser frequency is very attractive for tunable diode laser absorption spectroscopy (TDLAS) [33]

and laser cooling. Studying tuning curves in the self-injection locking regime, we revealed that

there is an area where the frequency changes linearly with driving current. We demonstrated that

the frequency tuning inside locking range can be realized up to dozens MHz without dramatic

linewidth degradation. We showed that this fact can be used to realize linear frequency modulation

up to 200 kHz and the amplitude of the frequency chirp can be controlled by the locking phase.

Tuning the frequency of a laser in the self-injection locking regime in a linear way without

using an additional acousto-optic modulator seems to be an extremely attractive opportunity

for the implementation of devices such as LIDARs, spectrographs, and optical sensors. We

experimentally demonstrated the possibility of coherent detection of a self-heterodyne signal

through a delay line of 10 km using such frequency modulation (laser chirping) in the self-injection

locking regime.

2. Stabilization coefﬁcient control via loading and locking phase: theory

The stabilization coeﬃcient

𝐾

is determined as the inverse derivative (slope) of the generation

frequency over the free laser frequency (laser cavity):

𝐾=𝛿𝜔gen

𝛿𝜔free −1

𝐾free

𝐾lock

,(1)

where

𝛿𝜔free

is the frequency variation in the free-running regime,

𝛿𝜔gen

is the generation

frequency variation, which is small in the locked regime providing high

𝐾

. In experiment it is

convenient to present the stabilization coeﬃcient as a ratio of the free-running laser frequency

change with the injection current

𝐾free

in unlocked regime to the locked laser frequency change

𝐾lock. The stabilization coeﬃcient 𝐾determines the linewidth of the locked laser [32,34]:

𝛿𝜈locked =

𝛿𝜈free

𝐾2,(2)

where 𝛿𝜈locked and 𝛿𝜈free are the linewidths of the locked and free-running laser, respectively.

We used the expression from [16] for the stabilization coeﬃcient as a function of ﬁve SIL

parameters. We suppose the detuning of the laser frequency

𝜁=

(𝜔−𝜔𝑚)/𝜅𝑚

from the WGM

eigenfrequency close to zero, since we consider the case of optimal stabilization [16]. Here

𝜅m=𝜅mc +𝜅mi

is the microresonator’s mode decay rate with

𝜅mi

determined by the intrinsic

losses and

𝜅mc

by the coupling;

𝜔

and

𝜔𝑚

are the pump output frequency and eigenfrequency of

the microresonator. In this case, one can obtain the following expression for the stabilization

coeﬃcient:

𝐾=1+4¯𝜅do

𝜅mi

𝜂(1−𝜂)𝛽(2+𝜅m𝜏𝑠

2(𝛽2+1))cos𝜓

(𝛽2+1)2,(3)

where

¯𝜅do

is the laser eﬀective output beam coupling rate. The corresponding values of the

loaded and intrinsic quality factors are deﬁned as

𝑄m=𝜔/𝜅m

𝑄int =𝜔/𝜅mi

and

𝜂=𝜅mc/𝜅m

is the coupling coeﬃcient characterising microresonator loading,

𝛽=

𝛾/𝜅m

is the normalized

mode-splitting coeﬃcient [35],

𝛾

is the forward-backward wave coupling rate,

𝜏𝑠

is the feedback

round-trip time.

Let us take the following equation from [36] for the critical coupling regime (𝜅mi =𝜅mc):

¯𝜅do =

3√3𝛿𝜔crit 𝜅mi

𝛾,(4)

where

𝛿𝜔crit

is the width of the locking range of the stabilized laser in the critical coupling regime.

This equation can be substituted in

(3)

. After that considering the limit of small

𝛽≤

1, that is

exact true for high-Q crystalline microresonators in the most cases, one can simplify (3):

𝐾=1+64

3√3𝛿𝜔crit 𝜅mc𝜅mi

(𝜅mi +𝜅mc)3cos𝜓. (5)

If critical coupling is assumed, then (5) will take the following form:

𝐾=1+8

3√3

𝛿𝜔crit

𝜅mi cos𝜓. (6)

That equation directly bounds stabilization coeﬃcient and locking phase, the parameters that

can be measured in experiment.

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Optimizationoflaserstabilizationviaself-injectionlockingtoawhispering-gallery-modemicroresonator:experimentalstudyARTEME.SHITIKOV,1,*ILYAI.LYKOV,1OLEGV.BENDEROV,2DMITRYA.CHERMOSHENTSEV,1,2,3ILYAK.GORELOV,1,4ANDREYN.DANILIN,1,4RAMZILR.GALIEV,5NIKITAM.KONDRATIEV,5STEEVYJ.CORDETTE,5ALEXANDERV.RODIN,2AN...

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Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator

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