Recent advances in laser self-injection locking to high-<i>Q</i> microresonators

doi:10.1007/s11467-022-1245-3

Front. Phys.

2023, Vol. 18

Issue (2) : 21305 https://doi.org/10.1007/s11467-022-1245-3

TOPICAL REVIEW

Recent advances in laser self-injection locking to high-Q microresonators

Nikita M. Kondratiev¹(

), Valery E. Lobanov², Artem E. Shitikov², Ramzil R. Galiev¹, Dmitry A. Chermoshentsev^2,^3,⁴, Nikita Yu. Dmitriev², Andrey N. Danilin^2,⁵, Evgeny A. Lonshakov¹, Kirill N. Min’kov², Daria M. Sokol^2,⁴, Steevy J. Cordette¹, Yi-Han Luo^6,⁷, Wei Liang⁸, Junqiu Liu^6,^7,⁹(

), Igor A. Bilenko^2,⁵

¹. Directed Energy Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
². Russian Quantum Center, Moscow, Russia
³. Skolkovo Institute of Science and Technology, Skolkovo, Russia
⁴. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia
⁵. Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
⁶. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁷. International Quantum Academy, Shenzhen 518048, China
⁸. Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
⁹. Hefei National Laboratory, University of Science and Technology of China, Hefei 230026, China

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Abstract

The stabilization and manipulation of laser frequency by means of an external cavity are nearly ubiquitously used in fundamental research and laser applications. While most of the laser light transmits through the cavity, in the presence of some back-scattered light from the cavity to the laser, the self-injection locking effect can take place, which locks the laser emission frequency to the cavity mode of similar frequency. The self-injection locking leads to dramatic reduction of laser linewidth and noise. Using this approach, a common semiconductor laser locked to an ultrahigh-Q microresonator can obtain sub-Hertz linewidth, on par with state-of-the-art fiber lasers. Therefore it paves the way to manufacture high-performance semiconductor lasers with reduced footprint and cost. Moreover, with high laser power, the optical nonlinearity of the microresonator drastically changes the laser dynamics, offering routes for simultaneous pulse and frequency comb generation in the same microresonator. Particularly, integrated photonics technology, enabling components fabricated via semiconductor CMOS process, has brought increasing and extending interest to laser manufacturing using this method. In this article, we present a comprehensive tutorial on analytical and numerical methods of laser self-injection locking, as well a review of most recent theoretical and experimental achievements.

Keywords self-injection locking laser stabilization microresonator nonlinearity single-frequency lasing multi-frequency lasing

Corresponding Author(s): Nikita M. Kondratiev,Junqiu Liu

Just Accepted Date: 16 January 2023 Issue Date: 20 February 2023

Cite this article:

Nikita M. Kondratiev,Valery E. Lobanov,Artem E. Shitikov, et al. Recent advances in laser self-injection locking to high-Q microresonators[J]. Front. Phys. , 2023, 18(2): 21305.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1245-3
https://academic.hep.com.cn/fop/EN/Y2023/V18/I2/21305

Fig.1 Artistic vision of self-injection locking of a diode laser to a microring resonator, which enables frequency comb generation seeded by its narrowed linewidth emission.

Fig.2 Schematics of laser self-injection locking. (a) Top panel: Schematics of laser self-injection locking to a WGM mode using a prism coupler. Bottom panel: Resonance profiles of the laser cavity (left) and the WGM reflected wave with normal mode splitting (right).

A

: the laser generation field amplitude.

ω L C

and

κ L C

: the laser cavity mode frequency and linewidth.

κ d o

: laser output mirror coupling rate.

B

: back-reflected wave amplitude.

S L C

and

S

: laser beam cross-section area at the laser aperture and on the prism surface.

τ s

: round-trip time of feedback

ψ

: locking phase.

A +

and

A ?

: Amplitudes of the forward and backward waves inside microresonator.

η

: microresonator coupling coefficient.

ω m

and

κ m

: The microresonator mode frequency and linewidth.

ω

: laser generation frequency. (b) An optimal self-injection locking curve with

ψ = 0

κ m τ s ? 1

, and

K 0 = 35

. The unstable branches are shown with dashed lines. The locking range is marked with a thick red line. The bi-stable transitions are marked with blue arrows. Panel (a) is reproduced from Ref. [105], and panel (b) from Ref. [106].

Fig.3 Illustration of tuning curve dependence on the locking phase and delay. (a) Tuning curves Eq. (6) for different initial phases

ψ

. Points I?IV correspond to phases

ψ = [0, π / 3, 2 π / 3, π]

with

κ τ s ? 1

. The envelope for the family of curves with different

ψ

is shown with the black dash-dotted line. In comparison, the solid green line shows a tuning curve for a free-running laser. (b) Tuning curves I?IV corresponding

ψ = 0

and long delay, so that

κ m τ s / 2 = [0, 1, 2, 3]

. This figure is reproduced from Ref. [106].

Fig.4 Analytical study of tuning curves with self-injection locking. (a) and (b) show the tuning curves for

β = 0.1

and

β = 10

respectively, with

K 0 / β = 400

and

κ m τ s = 0.011

. The red dashed lines show the slope of locking bands, and the red crosses mark the optimal points

ζ = ζ 0

[see Eq. (18)]. (c) shows the tuning curves for different

K 0

values. Curves I?III correspond to

ψ = π

and

K 0 = [5, 3, 1]

, respectively. Curves IV-VII correspond to

ψ = 0

and

K 0 = [0, 2, 4, 6]

, respectively. All quantities are plotted in dimensionless units. Panels (a, b) are reproduced from Ref. [105], and panel (c) from Ref. [106].

Fig.5 Calculated normalized transmitted power dependence on the detuning of the laser frequency from the WGM frequency for the different locking phases. The sum of the forward and backward locking ranges (FLR and BLR) can be measured experimentally. It is a good approximation of the total locking range

δ ω l o c k

in the case of a high

Q

factor when the inner overlap band

δ ω i n

is negligible. This figure is reproduced from Ref. [112].

Fig.6 Experimental and numerical study of optical spectra of a multi-frequency laser with and without self-injection locking. (a) Experimental (blue line) and numerically calculated (red line) emission spectrum of the free-running multi-frequency diode laser [Eq. (9), Eq. (10)]. (b) Experimental (blue line) and numerically calculated (red line) emission spectrum of the self-injection-locked multi-frequency diode laser. (c) Experimentally obtained spectra of the self-injection locked laser at different feedback levels (coloured solid lines) with numerically calculated envelopes (black lines) for

Γ 1 = 1 × 10 ? 2

Γ 2 = 1.2 × 10 ? 2

Γ 3 = 1.5 × 10 ? 2

, respectively. The green spectrum is not approximated well. (d) Numerically calculated dependence of the single-mode energy concentration

η

on the feedback level (blue line), and the experimentally obtained energy concentration points (squares). The circle corresponds to the green spectrum in panel (c), and the triangle corresponds to the free-running laser. This figure is reproduced from Ref. [70].

Fig.7 Optical spectra of the multi-frequency emission of the self-injection-locked laser. (a) Two-frequency regime; (b) four-frequency regime; (c) six-frequency regime. Additional feedback is added to corresponding modes. Blue data is the experimental data, orange curve is from the analytic model. (d) Upper panel: Scheme of the laser (red) and WGM (blue) mode frequencies in model.

d ξ

– difference between laser and microresonator intermode distances,

c κ

– first to second microresonator mode width ratio. Lower panel: Theoretical (red and blue-dashed) and modelled (blue, green, yellow) tuning curves for the same WGM mode widths (left) and different mode widths (right). Panels (a–c) are reproduced from Ref. [70], and panel (d) from Ref. [118].

Fig.8 Numerical study of parameters for optimal self-injection locking. The stabilization coefficient

K

[panel (a)] and the optimal detuning

ζ

[panel (b)] for

ψ = 0

κ 0 τ s = 0

κ d o / κ 0 = 1000

. Panel (c) shows the stabilization coefficient for

κ 0 τ s = 0.4

and the same other parameters. The solid line is the numerical maximum of

K

with respect to

η

. The dashed line is the second optimum branch for the zero-phase case. The dotted line corresponds to

β = 1

. All quantities are plotted in dimensionless units. This figure is reproduced from Ref. [105].

Fig.9 Numerical study of parameters for optimal self-injection locking. The stabilization coefficient

K

[panel (a)], the optimal detuning

ζ o p t

[panel (b)] and optimal

ψ o p t

[panel (c)] for

κ 0 τ s = 0

κ d o / κ 0 = 1000

. The solid line is the numerical maximum with respect to

η

. The dashed line is the second optimum branch for the zero-phase case. The dotted line corresponds to

β = β c r ≈ 0.68

. All quantities are plotted in dimensionless units. This figure is reproduced from Ref. [105].

Fig.10 Numerically obtained the transmission resonance curves Eq. (8) for the parameters taken from Ref. [21]. The parameter

ζ (ξ)

was evaluated using Eq. (6) (the dashed lines), and the corresponding LI curves were evaluated for the increasing frequency (the solid lines). The points on the transmission curves mark the optimal detuning values. All quantities are plotted in dimensionless units. This figure is reproduced from Ref. [105].

Fig.11 Schematic of laser self-injection locking with variable optical feedback. (a) The self-injection locking scheme with additional mirror and coupling prism. The amplitudes at the input port coupling point:

B i n

is the pump amplitude;

B t

and

B r

are amplitudes transmitted through and reflected from the prism coupler.

A +

and

A ?

are the amplitudes of counter-circulating modes of the microresonator. (b) Solid lines – left y-axis: Comparison of the stabilization coefficient for the case of absent Rayleigh scattering (red line) and the case of absent mirror coupling (blue line). Dashed lines – right y-axis: Comparison of the

| Γ |

for the case of absent Rayleigh scattering (red dashed line) and for the case of absent mirror coupling (the blue dashed line). This figure is reproduced from Ref. [123].

Fig.12 Experiments on laser self-injection locking to Fabry?Pérot cavities. (a) Ring-down measurement of the

Q

factor of a miniature FP cavity. (b) Schematic diagram of the narrow-linewidth laser employing the miniature FP cavity. This figure is reproduced from Ref. [42].

Fig.13 Typical theoretical solutions for tuning (left) and resonance (right) curves are shown for different pump values

f

(see right panel legend). In the left panel, dashed horizontal lines show the bi-stability start detuning, dotted lines shows the bi-stability end detuning, and dash-dotted lines shows the soliton existence border. This figure is reproduced from Ref. [184].

Fig.14 Tuning curve (left) and resonance curve (right) for different

r θ

. The cross-modulation coefficient is

α x = 1

. Green dashed, dotted and dash-dotted lines in the left panel define the bi-stability begin, end and soliton region end, respectively, over

ζ

for

r θ = 4

. This figure is reproduced from Ref. [185].

Fig.15 The diagram of the regimes arising upon pump frequency sweep with anomalous GVD for different combinations of the pump amplitude

f

and normalized back-scattering coefficient

β

. The dots show the calculated parameters. The shaded regions mark the extrapolation of the regime type. The white areas are either transient regions, or too far from the plotted points, to be certain. The legend is shown on the right and consists of panels with examples of characteristic regimes. This figure is reproduced from Ref. [110].

Fig.16 The diagram of the regimes arising upon pump frequency sweep with normal GVD for different combinations of the pump amplitude

f

and normalized back-scattering coefficient

β

. The dots show the calculated parameters. The shaded regions mark the extrapolation of the regime type. The white areas are either transient regions, or too far from the calculated points to be certain. The legend is shown on the right and consists of panels with examples of characteristic regimes. This figure is reproduced from Ref. [110].

Fig.17 Dual-self-injection-locking concept. Two laser diodes are coupled to an integrated high-

Q

microresonator. Both lasers are simultaneously self-injection-locked to different frequency modes of the microresonator, resulting in a stable and narrow-linewidth bichromatic output. This figure is reproduced from Ref. [189].

Fig.18 Tuning surface of the dual-laser self-injection locking in different views and a locking region diagram. The surface is calculated for normalized pump amplitudes

f + = f ? = 0.5

, where moderate nonlinear effects are present. Color in panels (a–c) represents the “?” laser intracavity detuning

ξ ?

. The black curve in panel (b) and black square in panel (d) correspond

f ± = 0.05

, where nonlinear effects are insignificant. The aqua and light-green curves correspond to the “+” and “?” laser individual locking regions. Dashed green line corresponds to

ξ + = ζ +

. This figure is taken from Ref. [189].

Fig.19 Dynamics of laser self-injection locking to two modes from different mode families. The transmission traces (a, d) and heterodyne spectrograms correspond to the frequency sweep of one laser (the blue laser in the left column and the red laser in the right column). In (b, f) the heterodyne measurement is performed on the same laser as the one being modulated; while in (c,e), on the other laser. This figure is reproduced from Ref. [189].

Fig.20 Frequency comb generation in the self-injection locking regime with a gain-switched laser. Spectra were obtained by means of the heterodyne method. Comb teeth are marked with red circles and red arrows, and green arrows correspond to the interference lines. (a) The 40-kHz-spaced comb. The spacing between adjacent lines is presented on the inset. (b) The 10-MHz-spaced comb with bandwidth wider than 1 GHz. (c) The 0.3-GHz-spaced comb. (d) The 0.5-GHz-spaced comb. (e) The 1-GHz-spaced comb. (f) The 10-GHz-spaced comb. This figure is reproduced from Ref. [203].

Fig.21 Low-noise lasers and turnkey soliton microcombs using laser self-injection locking to chip-based Si

3

4

microresonator. (a) Schematic of a tunable, self-injection-locked laser [94]. A DFB laser chip is butt-coupled to a chip-based Si

3

4

microresonator. When the laser emission is coupled into the microresonator, backreflected light from the microresonator into the DFB laser can trigger laser self-injection locking that change the laser dynamics. As a result, the DFB laser frequency is locked to a resonance mode of the microresonator, and its linewidth is significantly reduced. Piezoelectric actuators can be integrated directly on the Si

3

4

microresonator, offering fast frequency tuning. (b) Close-range photo of self-injection-locked laser consisting a laser diode chip edge-coupled to a Si

3

4

chip [85]. (c) Experimental results of laser frequency locked to different microresonator resonances [85]. Top panel shows the transmission spectrum of a Si

3

4

microresonator of 1.02 THz FSR, where the fundamental TE mode family is marked with red circles. Bottom panel shows the laser emission spectrum, as well as a typical split resonance that triggers laser self-injection locking. (d) Increasing backreflection, thus to enhance laser self-injection locking, can be realized using a loop mirror in the microresonator drop-port [95]. (e) Images of a self-injection-locked soliton microcomb module in a compact butterfly package [89]. (f) Demonstration of turnkey operation in the soliton module [89]. Top panel shows measured comb power versus time upon power on and off. Bottom panel shows the spectrogram of the measured soliton repetition rate during power switching. Images are reproduced from Ref. [94] [Panel (a)], Ref. [88] [Panels (b, c)], Ref. [95] [Panel (d)], and Ref. [89] [Panels (e, f)].

Fig.22 Theoretical model of the nonlinear self-injection locking. Model parameters for (a?f): the normalized pump amplitude

f = 1.6

, the normalized mode-coupling parameter

Γ = 0.11

, the self-injection locking coefficient

K 0 = 44

, the locking phase

ψ = 0.1 π

. (a, b) Model for the conventional case where the microresonator is pumped by the laser with an optical isolator, and

ζ = ξ

(dark green line). (c–f) Model for the self-injection locked regime. The solution of Eqs. (6)?(26) from Ref. [169] [thin red curves in (c, e)] is compared with the linear tuning curve

ζ = ξ

[thin black lines in (c, e)]. While tuning the laser, the actual effective detuning

ζ

and the intracavity power

| a (ξ) | 2

will follow red or blue lines with jumps due to the multistability of the tuning curve. The triangular nonlinear resonance curve [thick black in (b)] is deformed when translated from

ζ

frame to the detuning

ξ

frame (d, f) with corresponding tuning curve

ζ (ξ)

(c, e). The width of the locked state is larger for forward scan, but the backward scan can provide larger detuning

ζ

, which is crucial for the soliton generation. The figure is taken from Ref. [169].

Fig.23 Heterogeneous integration of lasers and modulators on Si

3

4

photonic chips. (a) Photographs showing a completed 100-mm-diameter wafer and its zoom-in view of chips and elements [188]. A Si

3

4

microring resonator and its interface with silicon is shown. (b) Schematic of laser soliton microcomb devices consisting of DFB lasers, phase tuners, and high-

Q

microresonators on a monolithic substrate. Bottom panel shows the simplified device cross-section. The laser is based on InP/Si, and the microresonator is based on Si

3

4

. The intermediate silicon layer with two etch steps is used to deliver light from the InP/Si layer to the Si

3

4

layer. (c) False-coloured scanning electron microscope (SEM) image of the Si

3

4

/AlN device cross-section, showing Al (yellow), AlN (green), Mo (red), Si

3

4

(blue) and the optical mode (rainbow) [229]. (d) Left panel shows a false-coloured SEM image of the sample cross-section with a PZT actuator integrated on the Si

3

4

photonic circuit. The piezoelectric actuator is composed of Pt (yellow), PZT (green) layers on top of Si

3

4

(blue) buried in SiO

2

cladding [94]. Right panel shows the optical micrograph of disk-shaped PZT actuator on top of Si

3

4

microring with 100 GHz FSR [94]. Images are reproduced from Ref. [188] [Panels (a, b)], Ref. [229] [Panel (c)], and Ref. [94] [Panel (d)].

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