Max-Born Institutefor Nonlinear Optics and

Short Pulse Spectroscopy

Optical Transistor: From Optical Event Horizonsto Rogue Waves

Ayhan Demircan Günter Steinmeyer1 Shalva Amiranashvili2

Weierstrass Institute forApplied Analysis and

Stochastics

1 MBI, Max-Born-Str. 2A,12489 Berlin, 2 WIAS, Mohrenstr. 39, 10117 Berlin

Abstract

We demonstrate that the properties for the concept of an optical eventhorizon are naturally given in the supercontinuum (SC) generation processwhen fundamental solitons (FS) interact with surrounding dispersive waves(DW). Under certain conditions this interaction leads to strongly acceleratedsolitons with extremely high peak powers. Using the underlying mechanismin a deterministic way makes an all-optical control of light pulses possible.This can be done in a very efficient and versatile manner with the opportu-nity to overcome the main limitations for realizing an optical transistor.

Emergence of a giant soliton

Non-envelope propagation model for ultrashort pulses with dispersion andKerr nonlinearity provides the minimum set of optical effects necessary forthe formation of rogue waves

i∂zEω + |β(ω)|Eω +3ω2χ(3)

8c2|β(ω)|(|E|2E)ω = 0

Pulse electric field E(z, t) = Re[E(z, t)].

SC generation by soliton fission

0

1

2

3

4

5-500 0 500 1000 1500 2000 2500

Pow

erHa

rb.u

.L HaL

-500 0 500 1000 1500 2000 25000

2

4

6

8

Time delay HfsL

Pro

paga

tion

dist

anceHc

mL 1

0

HbL

A

A'

B

Typical temporal SC evolutionin a photonic crystal fiber withone ZDW.

One wave is exceeding the av-erage wave crest by more thana factor of three.

Parabolic trajectory of one FSwith strong increase of thepeak power between A and B.

A, A’: FS-DW interaction withconditions for an optical eventhorizon.

Isolation of the energy transfer between the DWs and the champion soliton

I1,2 are finite and proportionalto the time-averaged photon fluxand power, respectively:

I1 =X

ω

n(ω)

ω|Eω |

2

I2 =X

ω

n(ω)|Eω |2

Development of λ0(z) (red line),pulse energy ∝ I2 (black line),and peak power P0(z) (dashedline). Energy content of the dis-persive wave (dotted line).

Energy, peak power (arb. u.)

0 0.5 1 1.5 2 2.5

z (

cm

)

1.5

2

2.5

3.5

4

3

4.5

Soliton center wavelength (nm)

980 10601020

A

B

x5

A‘

-600

2000-200-400

Deviation from undisturbed soliton path (fs)

2

3

4

z (

cm

)

A

A‘

B

Po

we

r (a

rb.u

.)

A‘

A

x5

(a)

(b)

Collaborations

Fedor Mitschke, Christoph Mahnke (University of Rostock)

Carsten Bree (WIAS, MBI, Berlin), Jens Bethge (MBI, Berlin)

Supported by: Sh. A. by the DFG Research Center MATHEON (projectD 14), C. M. and F. M. by DFG, and G. S. by the Academy of Finland(project grant 128844).

Key conditions for optical Event Horizon

Group velocity dispersion β2 and relative group delay β1 of fluoride glass.

0.5 1.0 1.5 2.0

-0.6

-0.4

-0.2

0.0

3.77 2.69 2.09 1.71 1.45 1.26 1.11 0.99 0.9

4.20

4.22

4.24

4.26

angular frequency H PHz L

Β2H

fs2 Μ

mL

Λ H Μm L

Β1H

fsΜ

mL

Β2<0

Β2>0Β2HΩL

Β1HΩL

Soliton

Pulse 1

Pulse 2

Nonlinear refractive indexchange due to an intensesoliton.

Frequency combinationsfor a soliton and a controlpulse with nearly equalgroup velocities.

=> Extending the interaction length for an enhanced XPM

All-optical control with an Event Horizon

Manipulation of a strong soliton signal by a much weaker control pulse

-200 0 200 4000

2

4

6

8

10

time delay HfsL

prop

agat

ion

dist

anceHc

mL

0.0

0.03

HaL

0.0 0.5 1.0 1.5 2.0 2.50

2

4

6

8

10

angular frequency HPHzL

prop

agat

ion

dist

anceHc

mL

-10

-6

HbL

-300 -200 -100 0 100 200 3000

2

4

6

8

10

time delay HfsL

prop

agat

ion

dist

anceHc

mL

0.0

0.04HaL

0.0 0.5 1.0 1.5 2.0 2.50

2

4

6

8

10

angular frequency HPHzL

prop

agat

ion

dist

anceHc

mL

-10

-6HbL

Faster control pulseRedshift of the signal; energyfrom signal to control pulse.=> Switch Off

Manipulation of the solitonstrongly depends on the in-duced frequency shift whichcan be adjusted by the controlpulse parameter

Faster signal pulseBlue shift of the signal, signalis compressed.=> Switch On

Concept for an optical Transitor fulfilling all Miller criteria

Experimental verification

Wavelength switch induced for a FS and a DW with a power ratio 4:1

!

Variation of the time delay between a faster control pulse and a signal.Strong blue shift for the control pulse and a small red shift for the signal.

Publications

• A. Demircan, Sh.Amiranashvili, G. Steinmeyer ’Controlling light by lightwith an optical event horizon’. Phys. Rev. Lett. 16,163901 (2011).

• A. Demircan, Sh. Aminarashvili, C. Bree, Ch. Mahnke, F. Mitschke, G.Steinmeier ’Soliton acceleration by dispersive waves: a contribution torogue waves?’, Phys. Rev. Lett. (2011), submitted.

• Sh.Amiranashvili, A. Demircan ’Hamiltonian structure of propagationequations for ultrashort optical pulses’. Phys. Rev. A 82, 013812 (2010).