June 12-17 2005 Morten Bache 1

The Cavity Soliton Laser

M. Bache*, F. Prati, G. Tissoni, I. Protsenko, L. LugiatoDipartimento di Fisica e Matematica, Università dell’Insubria, Como (Italy)

M. BrambillaDipartimento di Fisica Interateneo, Università e Politecnico di Bari (Italy)

*Current address: Research Center COM, Technical University of Denmark

CLEO-EQEC Europe (Munich) June 12-17 2005

VCSEL with saturable absorber Cavity solitons and the cavity soliton laser The model Exciting the solitons Deleting the solitons

June 12-17 2005 Morten Bache 2

Motivation: Cavity soliton laser?

What is a cavity soliton laser? Compact tunable laser Spatial solitons are supported

Excitation pulse: turn-on Deleting pulse: turn-off

Bistability required Saturable absorber included in

the model

Important: no holding beam needed to keep soliton alive!!!

field

inte

nsity

bifurcation parameter

June 12-17 2005 Morten Bache 3

The model: Broad area VCSEL with saturable absorber

We use semiconductor rate equations with adiabatic elimination of the polarization, describing an active region where radiative recombination dominates and a passive region where nonradiative recombination dominates.

Major bifurcation parameters: injected currents μ and γ. We fix γ=0.5. The detuning does not play any role except fixing the frequency of the field.

N.G. Basov, IEEE J. Quant. Electr. QE-4, 855 (1968); C.H. Henry, J. Appl. Phys. 51, 3051 (1980); S.V. Fedorov et al., PRE 61, 5814 (2000). See also M. Yamada, IEEE J. Quant. Elec. 29, 1330 (1993).

nFsbn

NFbN

FiFniNiiF

n

N

2

2

2

1

1

111

Optical field

Absorber carrier density

Amplifier carrier density

linewidth enhancement factors

loss rates injected currents, note the signsaturation parameter

detuning

June 12-17 2005 Morten Bache 4

1.35 1.40 1.45 1.50 1.55

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45 =0.5, s=10, =2, =0bN=0.01, bn=0.005

|F|2

Exciting a solitonA soliton may bemay be excited in the regime where the stable trivial solution coexists with a modulational instability (gray area). A suitably sized (space/time/duration/phase) Gaussian pulse is injected, and after turn-off the dynamics are followed.

possible soliton area

The soliton converges to a steady state after roughly 104 t.u. (app. 100 ns)

current value

June 12-17 2005 Morten Bache 5

Exciting a soliton Exciting a soliton is possible if

Peak field intensity inside certain regime Beyond regime no soliton is created Injected profile has proper width Injected field phase not important!!

1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

0.1

1

10

Dpe

ak(t=

inj)

|Finj

||F

peak

(t= in

j)|2

soliton is excited

Soliton excited

Soliton not excited

0 100 200 3000.0

0.5

1.0

1.5

2.0

|Fpe

ak|2

timeInjected field on

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Existence of the solitonsThe solitons exist in a certain range of the injected current of the active material

Region 1 the soliton starts oscillating and eventually breaks down

Region 2 the solitons oscillate, but are eventually stable

Region 3 the soliton becomes modulationally unstable

Region 4 does not support solitons because the background is unstable

1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.520.91.01.11.21.31.41.5

N

-0.5

-0.4

-0.3

-0.2

-0.1

n

0.00.10.20.30.40.50.6

|F|2

-15 -10 -5 0 5 10 15

0.91.01.11.21.31.41.5

x

-0.5-0.4-0.3-0.2-0.10.00.00.10.20.30.40.50.6

profile for μ=1.461 2 3 4

June 12-17 2005 Morten Bache 7

Deleting the solitons Field frequency ω0+Ω depends

on the field intensity

The field phase is random Impossible to “engineer” an

injected field with a given phase and frequency to delete the soliton

Soliton can be deleted nonetheless!!

21)(

Fs

Strong field: the soliton is deleted

Weaker field: the soliton survives

June 12-17 2005 Morten Bache 8

Deleting the solitons Deleting a soliton

Peak field intensity beyond the regime found before Thus, if the field is too too weak, soliton is not destroyed

-5 0 5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

|F(y

=0,t=

inj)|2

x

Increasing injected field strength

Soliton deleted

Soliton not deleted

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.5

1.0

1.5

0.1

1

Dpe

ak(t=

inj)

|Finj

|

Soliton excited Soliton not excited Soliton deleted Soliton not deleted

|Fpe

ak(t=

inj)|2

soliton survives

June 12-17 2005 Morten Bache 9

Exciting and deleting more solitons Neighbor solitons may be excited as well as deleted. The existing ones are not affected as long as a certain

distance between them is kept.

June 12-17 2005 Morten Bache 10

Model parameters Linewidth enhancement factors

α=2 (active material) β=0 (passive material) For larger β solitons appear to become unstable

Loss rates Carrier dynamics (much) slower than field dynamics If carriers are too slow, solitons become oscillatory and

eventually unstable For faster carrier dynamics solitons can be excited

spontaneously

The solitons are stable due to a balance between field-matter interaction

June 12-17 2005 Morten Bache 11

Conclusions and outlook Excite and delete a soliton in broad area VCSEL with

saturable absorber existence regime in bistable region does not depend on phase excitation and deletion threshold several solitons excited and deleted individually

Cavity Soliton Laser can be realized No holding beam (no thermal problems) Soliton has maximum contrast Beam entirely determined by the radiation-matter interaction

and not the boundary conditions

M. Bache et al., submitted to Applied Physics B - Lasers and Optics (special issue on saturable absorbers)