Overview of Ultrafast and Nonlinear Opticsilday/courses/2006/577/lecture_1.pdf · 2006-02-03 ·...

www.bilkent.edu.tr/~ilday

Overview of Ultrafast and NonlinearOptics

F. ÖMER İLDAY

Physics Department


Schedule

TODAY (seminar style)

Basics of nonlinear optics, pulse propagation, mode-locked lasersOver the weekend: Check the web for your first mini assignment

WEDNESDAY (seminar style)

Dynamics of ultrafast lasers, nonlinear optics, special topics 1, 2, 3

AFTERWARDS

We need to make up for this week’s Wednesday: Monday 5:40 PhysDept Seminar Room

Start with the regular course material


Goals of the Course

Broad overview of ultrafast and nonlinear optics

Intuitive grasp of the key concepts

Development of tools and recipes for some real calculations

Introduction to certain technologically important developments

Introduction to recently “hot” research areas

Introduction to real-world academic practices (paper writing, talkpreparation, etc)


Administrative

Lectures: Wednesday 16:40-18:40 and Friday 9:40-10:40

Lecturer: F. Ömer ILDAY, [email protected], ARL-Z04Office hrs: To be announced soon and by appointment

TA: Askin KOCABAS, [email protected], ARL-101TA office hours: To be announced soon

Problem sets: There will be at least 6 assignments (announced electronically) 25%Collaboration recommended.

Exams: There will be 1 midterm 15% and 1 final 25%“Adults” treatment policy in place

Project: A paper and a talk required, you may form small groups for the paper but “one man, one talk” policy applies. 35%


Outline of the Course

Pulse propagation and optical solitons (weeks 2, 3)

Origins of optical nonlinearity (week 4)

Lasers: cw, Q-sw, mode-locked and dynamics of lasers (weeks 5-9)No class on week 8: April 23-29, I am in Japan

Nonlinear optics (weeks 10, 11)

Special topics (weeks 12, 13, 14)

Project presentations (week 15)


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:

Overview of Ultrafast and Nonlinear Opticsilday/courses/2006/577/lecture_1.pdf · 2006-02-03 ·...

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Transcript of Overview of Ultrafast and Nonlinear Opticsilday/courses/2006/577/lecture_1.pdf · 2006-02-03 ·...