In this paper, we study the dynamics of a vertically emitting micro-cavity operated in the Gires–Tournois regime that contains a semiconductor quantum-well and that is subjected to strong time-delayed optical feedback and detuned optical injection. Using a first principle time-delay model for the optical response, we disclose sets of multistable dark and bright temporal localized states coexisting on their respective bistable homogeneous backgrounds. In the case of anti-resonant optical feedback, we identify square-waves with a period of twice the round-trip in the external cavity. Finally, we perform a multiple time scale analysis in the good cavity limit. The resulting normal form is in good agreement with the original time-delayed model.

1.
S. T.
Cundiff
and
J.
Ye
,
Rev. Mod. Phys.
75
,
325
(
2003
).
2.
T.
Udem
,
R.
Holzwarth
, and
T. W.
Hänsch
,
Nature
416
,
233
(
2002
).
3.
S. T.
Cundiff
and
A. M.
Weiner
,
Nat. Photonics
4
,
760
(
2010
).
4.
S. A.
Diddams
,
J. Opt. Soc. Am. B
27
,
B51
(
2010
).
5.
A.
Pasquazi
,
M.
Peccianti
,
L.
Razzari
,
D. J.
Moss
,
S.
Coen
,
M.
Erkintalo
,
Y. K.
Chembo
,
T.
Hansson
,
S.
Wabnitz
,
P.
Del’Haye
,
X.
Xue
,
A. M.
Weiner
, and
R.
Morandotti
,
Phys. Rep.
729
,
1
(
2018
).
6.
T.
Herr
,
V.
Brasch
,
J. D.
Jost
,
C. Y.
Wang
,
N. M.
Kondratiev
,
M. L.
Gorodetsky
, and
T. J.
Kippenberg
,
Nat. Photonics
8
,
145
(
2014
).
7.
F.
Leo
,
S.
Coen
,
P.
Kockaert
,
S.
Gorza
,
P.
Emplit
, and
M.
Haelterman
,
Nat. Photonics
4
,
471
(
2010
).
8.
A. C.
Tropper
,
H. D.
Foreman
,
A.
Garnache
,
K. G.
Wilcox
, and
S. H.
Hoogland
,
J. Phys. D: Appl. Phys.
37
,
R75
(
2004
).
9.
A.
Laurain
,
M.
Myara
,
G.
Beaudoin
,
I.
Sagnes
, and
A.
Garnache
,
Opt. Express
18
,
14627
(
2010
).
10.
Z.
Wang
,
K.
Van Gasse
,
V.
Moskalenko
,
S.
Latkowski
,
E.
Bente
,
B.
Kuyken
, and
G.
Roelkens
,
Light: Sci. Appl.
6
,
e16260
(
2017
).
11.
C.
Schelte
,
A.
Pimenov
,
A. G.
Vladimirov
,
J.
Javaloyes
, and
S. V.
Gurevich
,
Opt. Lett.
44
,
4925
(
2019
).
12.
T. G.
Seidel
,
J.
Javaloyes
, and
S. V.
Gurevich
,
Opt. Lett.
47
,
2979
(
2022
).
13.
E. R.
Koch
,
T. G.
Seidel
,
S. V.
Gurevich
, and
J.
Javaloyes
,
Opt. Lett.
47
,
4343
(
2022
).
14.
C.
Schelte
,
P.
Camelin
,
M.
Marconi
,
A.
Garnache
,
G.
Huyet
,
G.
Beaudoin
,
I.
Sagnes
,
M.
Giudici
,
J.
Javaloyes
, and
S. V.
Gurevich
,
Phys. Rev. Lett.
123
,
043902
(
2019
).
15.
J.
Mulet
and
S.
Balle
,
IEEE J. Quantum Electron.
41
,
1148
(
2005
).
16.
F.
Gires
and
P.
Tournois
,
C. R. Acad. Sci. Paris
258
,
6112
(
1964
).
17.
B.
Golubovic
,
R. R.
Austin
,
M. K.
Steiner-Shepard
,
M. K.
Reed
,
S. A.
Diddams
,
D. J.
Jones
, and
A. G. V.
Engen
,
Opt. Lett.
25
,
275
(
2000
).
19.
K.
Engelborghs
,
T.
Luzyanina
, and
D.
Roose
,
ACM Trans. Math. Softw.
28
,
1
(
2002
).
20.
D.
Hessel
,
S. V.
Gurevich
, and
J.
Javaloyes
,
Opt. Lett.
46
,
2557
(
2021
).
21.
T. G.
Seidel
,
S. V.
Gurevich
, and
J.
Javaloyes
,
Phys. Rev. Lett.
128
,
083901
(
2022
).
22.
D. A. W.
Barton
,
B.
Krauskopf
, and
R. E.
Wilson
,
J. Differ. Equations Appl.
12
,
1087
(
2006
).
23.
J.
Knobloch
and
T.
Wagenknecht
,
Phys. D
206
,
82
(
2005
).
24.
P.
Parra-Rivas
,
E.
Knobloch
,
D.
Gomila
, and
L.
Gelens
,
Phys. Rev. A
93
,
063839
(
2016
).
25.
C.
Schelte
,
D.
Hessel
,
J.
Javaloyes
, and
S. V.
Gurevich
,
Phys. Rev. Appl.
13
,
054050
(
2020
).
26.
L. A.
Lugiato
and
R.
Lefever
,
Phys. Rev. Lett.
58
,
2209
(
1987
).
27.
P.
Parra-Rivas
,
D.
Gomila
,
F.
Leo
,
S.
Coen
, and
L.
Gelens
,
Opt. Lett.
39
,
2971
(
2014
).
28.
P.
Parra-Rivas
,
D.
Gomila
, and
L.
Gelens
,
Phys. Rev. A
95
,
053863
(
2017
).
29.
S. V.
Gurevich
and
J.
Javaloyes
,
Phys. Rev. A
96
,
023821
(
2017
).
30.
J.
Hausen
,
K.
Lüdge
,
S. V.
Gurevich
, and
J.
Javaloyes
,
Opt. Lett.
45
,
6210
(
2020
).
31.
M.
Peil
,
M.
Jacquot
,
Y. K.
Chembo
,
L.
Larger
, and
T.
Erneux
,
Phys. Rev. E
79
,
026208
(
2009
).
32.
J.
Javaloyes
,
T.
Ackemann
, and
A.
Hurtado
,
Phys. Rev. Lett.
115
,
223901
(
2015
).
33.
J.
Mulet
,
M.
Giudici
,
J.
Javaloyes
, and
S.
Balle
,
Phys. Rev. A
76
,
043801
(
2007
).
34.
A.
Gavrielides
,
T.
Erneux
,
D. W.
Sukow
,
G.
Burner
,
T.
McLachlan
,
J.
Miller
, and
J.
Amonette
,
Opt. Lett.
31
,
2006
(
2006
).
35.
S.-S.
Li
,
X.-Z.
Li
,
J.-P.
Zhuang
,
G.
Mezosi
,
M.
Sorel
, and
S.-C.
Chan
,
Opt. Lett.
41
,
812
(
2016
).

Supplementary Material

You do not currently have access to this content.