overview of ultrafast and nonlinear optics

www.bilkent.edu.tr/~ilday

Overview of Ultrafast and NonlinearOptics

F. ÖMER İLDAY

Physics Department


Optical Nonlinearity, Pulse

Propagation and Solitons


For sufficiently high intensities, theinduced polarization in any medium hasa linear + a nonlinear part.

EEPPeezyxDielectric unit volumeElectromagneticlight wave

χ(1) Linear susceptibility

Classical optical effects(reflection, absorption)

χ(3)

Third order susceptibility

Optical Kerr effect, THG,Raman effect

SHG, parametric processes,electro-optic effect

χ(2)

Second order susceptibility

This slide was adapted from Aggarwal et al.

Nonlinear Optics

P = ε0(χ(1)E + χ(2)E2 + χ(3)E3 +…)


Basic Pulse Physics

Nonlinear Schrödinger Eqn.

Wave equation from Maxwell Equations


Dispersive propagation (linear)

dispersive medium:

index of refraction depends on frequency

t (time delay) tt

n = n(ω)

→ →

Pulse spreads due to (group-velocity) dispersion (GVD)

z


New frequency components are created

t

I

t

n

t

Φt

n = n0 + n2I nonlinear medium:

index of refraction depends on intensity

ωins

Nonlinear propagation (χ(3))


Soliton-like pulse shaping

Anomalous dispersion & nonlinearity cancel exactly for correct pulse shape

Pulse is self-guided

∆Φ

t

dispersion ∆Φ

t

nonlinearity

(blue leads red)


Pulse Formation in Lasers


Pulse Generation in a Cavity - 1

Pulse builds up from noise within the cavity (ns-ps domain):• A saturable absorber (SA) imposes lower loss to higher power

• A noise spike is shortened and grown roundtrip after roundtrip…

SA

T

I

SA

Frequency domain picture: Emergence of coherence

(Nearly) all modes are initially incoherent

Coherence develops because modes locked in phase experience higher gain.

Onset of mode-locking is a 1st order phase transition



anom. GVD, NL, & gain SA

In the sub-ps regime, dispersion and nonlinearity dominate pulse shaping:

Dispersion is strong: length scale ~ 0.1 m for 100 fs pulses

Nonlinear phases are large: length scale ~ 0.1 m for 10 kW peak power

Material lengths are long: typically ~ 5 m (for fiber lasers)



SA + gain & loss + periodicity=> non-Hamiltonian, dissipative (attractors can exist)

(here, periodicity is “hidden” in the parameters,can also be imposed explicitly => Haus’ Master Equation)


Mode-locking in the frequency domain

Math picture: Represent the pulse in your favorite basis (Hermite-Gaussian, etc.)Physical pictures: Think modes of the cavity.

A lot of modes (N >> 1) !!! Dispersive and nonlinear phase changes dominate the pulse shaping

N cavity modes/degrees of freedom:


Generating short pulses = “mode-locking” (Taken from Rick Trebino)

Locking the phases of the laser frequencies yields an ultrashort pulse.


Soliton lasers

anomalous dispersion & nonlinearity → solitons need fast SA to start and stabilize

anom. GVD, NL, & gain SA

overview of ultrafast and nonlinear optics

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