Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field

0.77 MB·English

by  Jae K. Jang

Writing and erasing of temporal cavity solitons
by direct phase modulation of the cavity driving field
∗
Jae K. Jang, Miro Erkintalo, Stuart G. Murdoch, and St´ephane Coen
Dodd-Walls Centre for Photonic and Quantum Technologies,
and Physics Department, The University of Auckland,
Private Bag 92019, Auckland 1142, New Zealand
∗Corresponding author: [email protected]
Temporalcavitysolitons(CSs)arepersistingpulsesoflightthatcanmanifest themselvesincontin-
uously driven passive resonators, such as macroscopic fiber ring cavities and monolithic microres-
5
onators. Experimentssofarhavedemonstratedtwotechniquesfortheirexcitation,yetbothpossess
1
drawbacks in the form of system complexity or lack of control over soliton positioning. Here we
0
experimentallydemonstrateanewCSwritingschemethatalleviatesthesedeficiencies. Specifically,
2
we show that temporal CSs can be excited at arbitrary positions through direct phase modulation

n of thecavity driving field,and that thistechniquealso allows existing CSs to beselectively erased.
a Our results constitute the first experimental demonstration of temporal cavity soliton excitation
J
via direct phase modulation, as well as their selective erasure (by any means). These advances

1 reducethe complexity of CS excitation and could lead to controlled pulse generation in monolithic
2 microresonators.

]
s
Cavity solitons (CSs) are solitary waves that can persist ble soliton states have been reached by carefully tuning
c
i indrivennonlinearpassiveresonators[1]. Theirtendency the frequency of the cavity driving field [12, 13]. Both
t
p to broaden is balanced by nonlinear self-focusing, and methods yield CSs, but also possess drawbacks: optical
o all energy they lose is replenished by the coherent field addressingincreasesthesystemcomplexity[8],whilstad-
.
s driving the cavity. Several of them can simultaneously justing the driving laser frequency provides limited con-
c
co-exist, and they can be independently excited, erased troloverhowmanyCSsareexcitedandatwhattemporal
i
s andmanipulated[2–5]. ThesepropertieshaveledtoCSs positions [15]. Moreover,neither of these techniques can
y
being identified as promising candidates for bits in all- easily be adapted to achieve controlled erasure of exist-
h
p optical buffers and processing units [6–8]. ing CSs. XPM has been numerically proposed for this
[ purpose [8], but difficulties in synchronization have pre-
Historically the focus has been on spatial CSs, i.e.,

vented experimental realization. This represents a ma-
1 non-diffractinglocalizedbeamsoflighttrappedinplanar
jor shortcoming, since the potential to be independently
v cavities [2–4]. More recently experiments performed in
9 optical fiber loops [5, 8–10] have stimulated interest in erased is widely regarded as a defining characteristic of
8 CSs, underpinning many of their proposed functionali-
theirtemporalcounterparts: recirculatingnon-dispersive
2 ties [4, 16, 17].
pulses of light [7]. Such temporalCSs do not suffer from
5
0 material defects that hinder the performance of spatial Here, we implement another method for temporal CS
. cavities [11], although somewhat analogous impairments excitation that alleviates these deficiencies. Our tech-
1
canariseduetoelectrostriction-mediatedinteractions[9]. nique relies on the phase modulation that is typically
0
5 These interactions can however be overcome by phase applied to the cavity driving field to trap CSs into spe-
1 modulating the continuous wave (cw) laser driving the cific time-slots[5]. Byapplying localboostsinthe phase
v: cavity; the CSs are then trapped to the peaks of the modulation, we are able to write CSs into corresponding
i ensuing intracavity phase profile [2, 5]. In parallel with empty slots. Significantly, similar boosts also allow us
X
investigationsinmacroscopic fibercavities,temporalCSs to demonstrate selective erasure of CSs already trapped
r
havealsoattractedattentioninthecontextofmonolithic in the cavity. This technique minimizes the complexity
a
microresonators [12,13]. Inthesedevices,CSscanunder of CS systems, since the same components enable writ-
certainconditions correspondto the temporalstructures ing, trapping, anderasure. It could also representa step
underlying broadband “Kerr” frequency combs [14, 15], towards controlled pulse generation in optical microres-
suggesting applications in metrology and high repetition onators [19].
rate pulse train generation.
The ability to switch dispersive cw bistable devices
Excitation of CSs requires that the resonator cw through appropriate changes of the phase of the driv-
steady-state is suitably perturbed [6, 16–18]. For tem- ing field was first proposed by Hopf et al. [20], and an-
poral CSs two techniques have been demonstrated. Ex- alyzed theoretically in the context of CSs by McDonald
periments in fiber resonators have used an incoherent and Firth [18]. Phase modulation has also been used
“writing” scheme [5, 8–10], where an optical “address- recently to excite localized topological phase structures
ing” pulse perturbs the cw steady-state via nonlinear in a laser with external forcing and feedback [21]. For
cross-phasemodulation (XPM). In microresonators,sta- a better understanding of our experiment, we first illus-
2
trate the phase-induced switching dynamics of temporal 2.17 rad
CSs by means of numerical simulations. To this end, we
model the evolutionof the field envelope E(t,τ) inside a 0.52 rad
high-finesse fiber resonator using the well-known mean-
A(t)
field equation [7, 8, 14]: 10
W)
∂E 2 β2L ∂2 wer ( 5
tR ∂t =(cid:18)−α+iγL|E| −iδ0−i 2 ∂τ2(cid:19)E(t,τ) Po 0
400
+√θS(t,τ). (1)
−50 300
Here, t is a slow time variable that describes evolution 0 200 Roundtrip
over consecutive roundtrips and τ is a fast time that de- 50 100
Fast time
scribes the temporal profile of the field envelope. tR is 0
the cavity roundtriptime, α is half the fractionof power
Figure 1. Numerical results of CS writing and erasing by
lost per roundtrip, γ is the nonlinearity coefficient, L
means of abrupt changes in the phase of the cavity driving
is the cavity length and β2 is the group-velocity disper- field. The phase modulation amplitude A(t) is shown as the
sion coefficient. The parameter δ0 describes the phase curve on the left. The numerical parameters are similar to
detuning of the driving field S(t,τ) from the nearest the experiments that follow: Pin = 908 mW, tR = 0.48 µs,
cavity resonance and θ is the power transmission co- L = 100 m, θ = 0.1, α = 0.146, γ = 1.2 W−1km−1, β2 =
efficient used to couple light into the resonator. The −21.4 ps2/km, δ0 =0.4426 rad, and τ0 =43 ps.
driving field is cw with power Pin, periodically phase-
modulated with a one-bit pattern synchronized to the
cavity free-spectral range, S(t,τ) = P1/2exp[iφ(t,τ)], ferent phase sequences. The blue curve corresponds to
in
where φ(t,τ) = A(t)exp( τ2/τ2). Our simulations use the successful writing procedure in Fig. 1, whereby the
0
−
parameters similar to the experiments that follow (see phase modulation amplitude is first boosted to 2.17 rad
caption of Fig. 1), (thecorrespondingrotationislabeledasstep1)andthen
Figure1illustrateshowCSwritinganderasingcanbe reducedbackto0.52radafter10roundtrips(step2). As
achieved by dynamically controlling the phase modula- can be seen, the field eventually spirals to the stable CS
tionamplitudeA(t). Startingwithacoldcavity,weturn solution (this spiraling represents the transient oscilla-
on the driving field with a weak Gaussian [70 ps full- tions seen in Fig. 1). In contrast, if the phase modula-
width at half maximum (FWHM)] phase modulation, tion amplitude during the 10-roundtrip boost is slightly
A = 0.52 rad, which mimics that used in our experi- lower (2.00 rad, red curve), no writing takes place; the
ments to overcome soliton interactions [5, 9]. As can be field remainsin the basinofattractionofthe originalcw
seen, this weak phase modulation alone does not lead to solution. Similar behavior is observed when the modu-
CSexcitation. Instead,aftersometens ofroundtripsthe lation amplitude is only boosted but never returned to
fieldconvergestoacwsteady-state. After100roundtrips its original value, and the green curve in Fig. 2 shows
we abruptly boost the phase modulation amplitude to a trajectory for this case. We note, however, that these
A = 2.17 rad for 10 roundtrips. This leads to a broad dynamicsareparticulartoourchoiceofparameters,and
peak in the optical intensity which evolves and settles for others, writing can be achieved even with a single
into a 2.6 ps wide (FWHM) CSin about100roundtrips.
TheCSthenpersistsuntilweagainboostthephasemod-
ulation amplitude to 2.17 rad for 15 roundtrips, which Im[E(t,τ=0)]
erases the CS after a brief transient. 2.00rad,10roundtripphasepulse
The ability to write and erase using phase modula- 2.17rad,10roundtripphasepulse
CS
tion can be understood by noting that an abrupt step in
2.40radphasestep
thedrivingphaseisequivalenttorotatingtheintracavity
fieldincomplexphase-spacearoundtheorigin[20]. Writ-
ing (erasing) occurs if the sequence of rotations, com-
bined with the intervening nonlinear evolution, is such
step2
thatthe fieldfalls within the basinofattractionofa sin-
Re[E(t,τ=0)]
gle CS (lower-state cw). This of course implies that not cw Unstable CS
all phase operations lead to switching, as is illustrated
forCSwriting inFig.2. Here weplotthe simulatedevo- step1
lution of the amplitude E(t,τ =0) in the complex plane
(withphasecalculatedrelativetothatofthedrivingfield Figure2. Simulatedphase-spacedynamicsduringattemptsof
at τ = 0), starting from the cw solution, for three dif- CS writing with three different phase-modulation sequences.
3
phase-step [18]. In fact, the precise dynamics depends FWHM electronic pulses, are synchronised by a single
quite sensitively on the parameters involved. This may externalclock, suchthat the repetition rate of their out-
be linked to the metastable nature of the unstable CS putpatternscoincidewiththecavityfree-spectralrange.
solution (which exists for the same parameters [8]), and Oneofthem[topinFig.3(b)]issettoselectivelyproduce
to which the emerging soliton field is initially attracted pulses whose amplitude is 3 times larger than those
∼
to (see blue curve in Fig. 1), as well as to the associated from the other. The low-amplitude pattern is fed to the
non-critical slowing [18]. We find that, for given param- EOM at all time; this gives rise to an intracavity phase
eters,sometrialanderrorisrequiredtodeterminephase profile that allows CSs to be trapped [5], but not writ-
sequences suitable for writing and erasing. Fortunately ten or erased. In contrast, the high-amplitude pattern is
this task is quite effortless; whilst the precise dynamics controlled by an electronically gated switch. When the
may somewhat differ, switching nevertheless occurs over switch is activated, the outputs of both pattern genera-
a wide range of conditions. We must remark that CS tors are combined for about 10 roundtrips. In this way
switching can also be realized with abrupt changes to the amplitudes of those electronic pulses that are con-
other parameters, even with a static phase profile. Such tained in the high-amplitude pattern can be selectively
changescanbeinducedby,e.g.,mechanicallyperturbing boosted to 4 times their original level.
∼
the cavity. For a particular experimental demonstration, we set
To experimentally demonstrate CS writing and eras- the low-amplitude pattern generator to produce a se-
ing, we use the set-up schematicallyillustratedin Fig. 3. quence of 5 electronic pulses separated by 300 ps (the
The optical cavity is similar to that used in [5, 9], con- whole pattern repeats once per cavity roundtrip). We
sisting of 100 meters of single-mode fiber (SMF) closed then explore complex writing and erasing sequences by
on itself with a 90/10fiber coupler. The cavity is driven selectively boosting some of the amplitudes as described
with a narrow linewidth cw laser at 1550 nm whose out- above. Experimental results are shown in Fig. 4. The
put is phase-modulated with an electro-optic modulator density map concatenates successive oscilloscope traces
(EOM) and then amplified with an erbium-doped fiber recorded at the cavity output, illustrating how the opti-
amplifier (EDFA). An electronic feedback controlloop is cal intensity inside the resonator is affected by abrupt
used to actively lock the laser frequency near a cavity changes in phase modulation amplitude (the bit se-
resonance. The cavity also hosts a fiber isolator, used quences on the right indicate which electronic pulses are
to suppress stimulated Brillouin scattering, as well as a boostedinamplitude). Duringthefirst5secondsofmea-
99/1 tap-coupler, through which the intracavity dynam- surement no CSs are excited, confirming that the low-
ics are monitored with a 12 GHz real-time oscilloscope. amplitude modulation itself is insufficient for this pur-
Before detection, the cavity output is filtered using a pose. At t = 5 s all five electronic pulses are boosted
narrow (0.6 nm width) bandpass filter (BPF) centered for 10 roundtrips, resulting in the creation of five CSs.
at 1551 nm. This improves the signal-to-noise ratio by After excitation, the CSs remain trapped to the peaks
removing the cw component [8].
The abrupt phase changes that enable switching are Boosted pattern
achievedbymanipulatingtheelectronicsignalthatdrives 100 0 0 1 0 0 1
the EOM [see Fig. 3(b)]. Two programmable pattern 90
0 1 0 1 0
generators, capable of producing approximately 70 ps 80 1 0 0 0 1 0.8
0 1 1 0 0
70 O
s) p
(a) Optical cavity Fiber coupler 99/1 Output ory time ( 5600 100 110 110 111 100 0.6 tical inten
Isolator Fiber coupler 90/10 908 mW Laborat 3400 010 000 101 000 010 0.4 sity (a.u.)
EDFA
1550 nm cw laser 20 0 0 0 1 0 0.2
100 m SMF EOM 0 0 1 0 0
Controller 10 0 1 0 0 0
1 1 1 1 1
(b) Electronic configuration 0 0
−500 0 500 1000 1500 2000
Electronic Fast time (ps)
switch
pattern
generators Directional Figure 4. Experimental density map showing successive os-
coupler cilloscope tracesof theopticalintensityat thecavityoutput.
All the traces were acquired at 1 frame/s with a 40 GSa/s
real-time oscilloscope. The bit sequences on the right indi-
Figure 3. Schematic illustration of the (a) optical and (b) cate which of the five phase pulses are boosted to achieve
electronic segments of theexperimental setup. writing and erasing.
4
of the low-amplitude phase modulation [2, 5]. We then
demonstrate erasure of individual CSs, by boosting se- u.) 1 (a) Phase modulation
a.
lected phase pulses alreadytrapping a CS, and highlight e ( 0.5
s
the flexibility of the scheme by performing complex si- ha
P 0
multaneous writing and erasing operations. In this con-
text we remark that we are experimentally able to write u.) 1
atunddeearpaspelieudsinovgerthtehesasmameeopneurmatbioerno(fsarmouendpthraipses)a.mTphliis- sity (a. 0.5 (b) Writing
n
should be contrasted with simulations of Fig. 1, where nte 0
I
different number of roundtrips were required for writing
and erasure. We believe this discrepancy arises due to u.) 1
a. (c) Erasing
eentevrisrodnumrienngtatlheflumcteuaasutiroenmsetnhta.tTahltiesrntohteiosnysistesmupppaorratmed- nsity ( 0.5
e
by the fact that we do not achieve 100% fidelity, but in- nt 0
I
stead several attempts are occasionally required for suc- 0 10 20 30 40
cessful switching. Slow time (µs)
The above experiment demonstrates that direct phase
Figure 5. Real-time dynamicsof CS writing and erasing. (a)
modulation allows temporal CSs to be written and
ElectronicsignalfedtotheEOM.(b,c)Experimentallymea-
erased. However, the acquisition rate in this measure- suredroundtrip-to-roundtripdynamicsof(b)writingand(c)
ment was limited to 1 frame/s, which is too slow to erasing. The green curves show results from numerical simu-
capture the switching transients. To gain more insights, lations.
we havethus alsotaken real-time measurements that re-
solve the roundtrip-to-roundtrip dynamics of the optical
and could enable controlled pulse train generation in
intensity at the cavity output together with the elec-
monolithicmicroresonators. Inthiscontext,wemustem-
tronic signal that drives the EOM. As above, we use
phasize that writing is achieved with phase pulses that
the same phase operation for both writing and erasing
have a much longer duration than the CSs (70 ps ver-
(except that we use here only one electronic pulse per
sus 2.6 ps). Our work also reports the first experimental
roundtrip), and Fig. 5(a) shows the corresponding elec-
demonstration of temporal CS erasure. This highlights
tronic signal. Experimental results for transient writing
that temporal CSs are truly independent entities, and
and erasing dynamics are shown in Figs. 5(b) and (c),
constitutes a step towards their use as fully addressable
respectively. During writing, the field displays ringing
bits in optical buffers.
similartothatobservedduringopticalexcitation[8]and
numerical simulations (Fig. 1), and stabilizes in about
100roundtrips after the momentof addressing. Erasure,
onthe otherhand,appearsto takeplacealmostimmedi-
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(2009).
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