Mode-locked Lasers

How are ultrashort pulses generated?

Mode-locked lasers are most common

Other (rarer) techniques include E-O modulation, modulation instability and compression

An ultrashort pulse requires large bandwidth, this is obtained by having many longitudinal

modes in the cavity lasing simultaneously

However, multi-mode lasing just generates noise unless there is a fixed phase relationship

among the modes, thus the term “mode-locking”.

Generic Elements of Modelocked Lasers

1) Broadband gain medium

2) Cavity

mirrors, provide feedback

3) Output coupler

partially transmissive mirror, provides output

4) Anomalous dispersive element

Compensate normal dispersion in other elements

5) Modelocker

Active: phase modulator

Passive: saturable absorber

gD ML

For the basics of lasers see, for example, Verdeyen “Laser Fundamentals”

Gain Medium

g

Must be supplied with energy – the “pump”

Typical ultrafast lasers are pumped by another laser

Amplifies light by stimulated emission

Requires inversion – more atoms/molecules in the excited state – so that

stimulated emission overcomes absorption

Two categories:

3-level

Inferior – require strong pumping

Example: erbium, ruby

4-level

Preferred

Examples: ti:sapphire, organic dyes

The gain medium always operates in saturation

Gain: Ti:sapphire(the ultrafast work horse)

Titanium substitutes for an Al atom in the sapphire

(Al2O3) host crystal

There is a single optically active electron, levels are

split by crystal fields.

Effective 4 – level system due to Jahn-Teller effect:

Minimum in electronically excited state is shifted from

ground state with respect to a configuration coordinate

Relaxation occurs due to vibronic transitions

Yields very broad emission/gain spectrum

Excited state lifetime ~ 3.9 ms

Sapphire has excellent thermal & hardness properties

Other Gain Media

Material Gain Pump Comments

Dyes Various Excimer, Nd: YAG

SH, flashlamp

Messy, limited

lifetime,

toxic/carcinogenic

Diodes Various (~850

best)

Electrical Gain dyanmics

limit minimum

duration

Cr:LiSAF,

Cr:LiCAF

820-880 670 nm diode Poor thermal

properties

Cr:Forsterite 1300-1400 Nd:YAG

Cr:YAG 1500-1600 Nd:YAG Crystals rare

Erbium 1530-1560 980 or 1480 nm

diode

3 - level

General Saturation

General form for saturation of absorption

Propagation through an absorbing material with absorption coefficient a [cm-1]:

Idz

dIa

(gain is simply a < 0)

IIIdz

dI

S

1

0a

Where Is is the “saturation intensity”, i.e. the intensity for which the absorption is reduced to ½

its small signal value.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

aa

0

I/Is

For absorption, Is depends on number of atoms, cross-section and relaxation rate

For gain, it also depends on pump rate

Output coupling

0.00 0.02 0.04 0.06 0.08 0.10

0.00

0.01

0.02

0.03

0.04

0.05

Ou

tpu

t p

ow

er

rela

tive

to

Is

Output coupler transmission

For a CW laser, the optimum output coupling is a trade off between

1) Extracting the power (increasing transmission); and

2) Decreasing the intracavity power because increased loss means gain less saturated

where To is the output coupler transmission, g0 is

small signal gain and L is other losses in the cavity

In the case of a passively mode-locked laser, one must also consider the issue of pulse stability, i.e.

maintaining high enough peak power, this depends on details of the mode-locking mechanism

1

0

0

TL

gTII osout

20

0

LgII

LgLT

smaxout

opto

g0 = 0.1

L = 0.01

The maximum is

In the situation of high cavity Q (low net loss), the output power is approximately

ABCD (Ray) Matrices(lightspeed review)

Represent propagation through optical elements

system matrix is simply product of matrices for individual elements

10

1n

d Propagation through a distance d in a medium with

index of refraction n. [Take care to not double count n.]

11

01

f

A thin lens with focal length f

12

01

R

Reflection from a spherical mirror with radius R. R > 0 for

center of curvature in positive propagation direction

Ray Optics: represent ray by vector:

Gaussian beams: describe transformation of beam parameter

r

r

Propagation of Gaussian beams through optical elements

Characterize a beam by

0izzq

Propagation through an element characterized by matrix is

DC

BA

DCq

BAqq

1

12

znwi

zRzz

zi

zz

z

izzq 2

0

22

0

22

0

111

00

1

12

Lqq

Check for free space1

0 1

L

Beam in resonator must be self-consistent, i.e., the same after one round trip.

Determine the ABCD matrix for one round trip in the resonator

matrix depends on starting point

Solve equation

DCq

BAqq

which gives 2 solutions (using fact that AD-BC =1 for ABCD matrices)

21 1

12 2

D A A D

q B B

Then construct the proper matrix to propagate to other points inside or outside the cavity

Cavity: Basics of Stability I

Cavity: Basics of Stability II

Use ABCD matrices, resonator stable if round-trip matrix satisfies

stable conditionally stablerequires perfect alignment

unstable

20 1

4

A D

Flat mirrors, just free space, A = D = 1, gives conditionally stable

Equality conditionally stable

Astigmatism correctionBrewsters angle is used to minimize loss entering the gain medium 2

1

tann

n

At the same time, the beam is focused into the crystal

Net result is astigmatism [focus different for the two transverse directions]

Use an angled mirror to compensate

cos,

cosff

ff yx

y

x

For Brewster plate of thickness d and index n between two curved mirrors with RoC R

cos

sin112 2

4

24

n

nn

R

dFor 9 mm Ti:Sapph and R = 10 cm, = 9.5o

Kogelnik, Ippen, Dienes and Shank, J. Quantum Electr. 8, 373 (1972)

For dye lasers, full compensation impossible,

cancellation between two astigmatic focii is used

Dispersion Compensation

D

We have discussed the following dispersion compensation elements that can be used in a bulk optics

laser cavity:

Prisms

Dispersion compensating mirrors

In a fiber laser at 1550 nm, the dispersion of the fiber itself can be engineered

Standard “lore”: the net “cold cavity” GVD needs to be slightly anomalous cancels chirp due to

nonlinearity

Not true: “stretched pulse” designs, works when dispersion is “managed”

Mode locker

Active

Electooptic or Acoustooptic

Passive Saturable absorption

Real vs. effective

Slow vs. fast

Active Modelocking

Modulation at cavity repetition rate, either

Amplitude

or

Phase

works…amplitude is fairly intuitive, but phase?

Think in frequency domain, modulation at frequency wm puts sidebands on spaced by wm

If wm matches mode spacing

feed energy from initial CW mode into sidebands, with fixed phase

W

Cavity modes

Limit to minimum pulse duration

mf

g 122ln2 41

2

0

Where

fm is modulation frequency

n is gain bandwidth

is the modulation index

Note bandwidth dependence

Real Saturable Absorption

CW: Atoms relax and can continue to absorb subsequent photons

Pulse: Saturate medium, some photons pass through

Front edge of the pulse preferentially absorbed

Back edge unaffected

Operating intensity depends on saturation of both absorption and gain:

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

aa

0, 0

I/Is

Intensity will increase to upper crossing point

Fluctuation required to start lasing

Modelocking with Real Saturable Absorption

The pulse itself modulates the loss

Time window asymmetric

Rise: integral of pulse

Fall: life time of absorber

Limited pulse shortening

Use gain depletion in concert with saturable absorption

Gain depletion acts on trailing edge of pulse

Combination results in short window with net positive gain

Requires gain and absorber recovery short compared to

round-time

Real saturable absorbers are “slow”

Dynamics slower than pulse

0

1A

mp

litud

e

Lo

ss

Time

0

1

0

1

Gain

Am

plitu

de

Loss

Time

Examples of Real Saturable Absorbers1) Dyes – usually a jet

2) Semiconductors – usually incorporated into a mirror

Known as “saturable Bragg reflector” (SBR) or “semiconductor saturable absorber mirror” (SESAM)

Effective Saturable Absorption: Kerr lens

CW

Modelocked

Kerr Lens & Aperture gives increased transmission at high intensity

Increased transmission at high intensity = saturable absorption

Requires biasing alignment away from optimum CW

Misalign cavity, Kerr lens realigns it

Output beam become intensity dependent

GaussianLaser Beam

High Intensity

Gaussian Beam =Gaussian Index Profile =Gradient Index Lens

GaussianLaser Beam

Low Intensity

Kerr Mediumn = n0 + n2I

Effective Saturable Absorption: Nonlinear Polarization Rotation

The nonlinear phase shift from the Kerr effect rotates elliptically polarized light

Due to differential phase shift between components with different

amplitude does not occur for linearly or circularly polarized light

Most easily observed in fiber

Can be used as modelocking mechanism: effective saturable absorber

“Elliptical

Polarizer” -p

late

Nonlinear medium (fiber)

Low IntensityHigh intensity

Initiating Modelocking

Both active modelocking and real saturable absorbers are self starting

Effective (fast) saturable absorbers are not in general

Requires starting mechanism perturbation noise spike

builds up

Stronger self-amplitude modulation makes it easier to start

Almost self starting in some cases (any miniscule perturbation is sufficient)

Can be automated

Or add weak real saturable absorber as starter

Prototypical modelocked Ti:sapphire laser

Put all the pieces together….

Output

coupler High reflectorPump

Ti:Sapphire

crystal

Prisms(Dispersion compensation)