1

Nonlinear optics continued-waveguides and parametric devices

Fredrik Laurell

Department of Applied PhysicsKTH – Royal Institute of Technology, Stockholm, Sweden

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Outline

• Optical waveguides – integrated optics

• Nonlinear integrated optics

• Introduction to parametric devices

• Optical parametric oscillators• Singly resonant OPOs vs. doubly resonant OPOs• Practical examples

• Summary

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Planar Waveguides: Overview

• Similar function as optical fibers• Easily fabricated on substrates with a mask

Image from NTT-AT (http://www.keytech.ntt-at.co.jp/optic2/prd_e0015.html)

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Uses for planar waveguides

• Routing Light• Devices

ModulatorsSplittersErbium Doped Planar Waveguide Amplifiers (EDWA) Resonators

http://www.ee.ic.ac.uk/optical/Optics.htmlhttp://www.netzartfedorov.com/clients/nanonics/newnanon/text-industry.html

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Couplers – grating devices - integration

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Maxwells Equations in Slab Waveguide

• Maxwell’s Equations

• Simplifications

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TE and TM modes

• Dispersion Curves

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Waveguide vs. Bulk for NLO

+ Waveguides provide high confinement and long interaction length – high efficiency + Fibers can be connected to the waveguide to provide robust sources- Additional fabrication steps to create a good waveguide- Power handling issues

SHG conversion efficiency for confocal focusing in the bulk

Conversion efficiency for SHG in waveguide

Normally 10 to 1000 X improvement in efficiency with waveguide vs. bulk

lPnncd

PP

FSHFF

eff

F

SHBulk 3

0

2216

222

0

228lP

ANNcd

PP

FOVLSHFF

eff

F

SHWG

OVLeff ANλl

2

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Why optical parametric devices?

• Very wide continuous tuning from a single device, via tuning of the phase-match condition

• High efficiency

• No heat input to the nonlinear medium

• No analogue of spatial-hole-burning as in a laser, hence simplified single-frequency operation

• Very high gain capability

• Very large bandwidth capability

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Oscillator(OPO) (2)

Nonlinear processes –optical parametric devices

PumpIdlerSignal(2)

Generator(OPG)

Seed

Amplifier(OPA)

(2)

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Optical parametric oscillation (OPO)

IdlerPumpSignal

Singel or double resonant OPO(SRO or DRO)

Pump

Signal and/or idler

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The Optical Parametric Oscillator

Pumpkpks

ki

Rp,s,iRs,i

Add feedback to OPG OPO

Three basic types of OPO depending on feedback:SRO - resonant signal or idler

DRO - resonant signal and idler

TRO - resonant signal, idler, and pump

pump power at threshold

stabilization requirements

practical interest

spectral quality

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Manley-Rowe relationsIntegrals of the coupled equations

n3|E3(z)|2/ω3 + n2|E2(z)|2/ω2 = const

n3|E3(z)|2/ω3 + n1|E1(z)|2/ω1 = const

n2|E2(z)|2/ω2 – n1|E1(z)|2/ω1 = const

Number of pump photons annihilated in the NL medium equals the number of signal photons created, which also equals the number of idler photons created

Imply

n3|E3(z)|2 + n2|E2(z)|2 + n1|E1(z)|2 = consti.e. conservation of power flow in propagation direction

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The resonance condition

DRO is an over-constrained system, where energy conservation, cavity resonance and phase matchinghave to be satisfied at the same time.

kpPump

ks

ki

s, ins,ni

L

Total cavity losses: s, i

Cavity finesses:

Free-spectral range:

ii

ss FF

,

iisspp

isp

nnn

,

Cavity resonance:

lnLcm

lnLcm

ii

ii

ss

ss )1(

,)1(

lnLc

jjj )1(

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The OPO threshold

If ∆k = 0 , threshold condition (assuming pump, signal & idler phases Φ3 – Φ2 – Φ1 = - /2 at input to crystal)

2/12

2/11

2/121 )(1coshRRRRL

Represent round-trip power loss by one cavity mirror having reflectance R1 (idler), R2 (signal)

Threshold → round-trip gain = round-trip loss

(for signal only, SRO, for signal and idler, DRO)

R1,2iisspp

isp

nnn

,

g g = gain coefficient

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OPO threshold: SRO vs DRO

1cosh 22 LR

222 1 RL

4/)1)(1( 1222 RRL

For SRO, R1 = 0

SRO

DRO

Advantage of DRO is low threshold:

Example:

DRO with R1 = 98%

If 1- R1,2 << 1

SROthreshold

DROthreshold

= 200 for 1 – R1 = 0.02

g

g

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Stability: comparison of SRO and DRO

SRO: No idler input. Gain does not depend on pump/signal relative phase.Signal frequency free to choose a cavity resonance;Idler free to take up appropriate frequency and phase. Signal frequency stability depends on cavity stability and pump frequency stability.

DRO: Cavity resonance for both signal & idler generally not achieved; OverconstrainedSignal/idler pair seeks compromise between cavity resonance and phase-mismatch;large frequency fluctuations

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Parametric gainPlane-wave, phase-matched

If gain is small, (gL << 1) , gain increment is

Note: incremental gain proportional to pump intensity

~ proportional to ω32

30321

32

2122 2cnnnId

L

proportional to d2 / n3 (NL Figure Of Merit)

g

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Optical parametric amplification (OPA)

Assume: high signal gain g >>k/2

k=0

gLgLG

ILI

s

s 2exp1sinh110 4

12

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

L

exp(

2gL)

p

i

s

p

0 L

s

g = gain coefficient, G = gain

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Typical OPO conversion efficiencies

Normally high conversion efficiency (>50%) obtained at 2-3x threshold

Initial slope efficiency >100% typical

Pumping appr. 3-4 x thresholdresults in reduced efficiency back-conversion of signal/idler to pump

Unlike lasers, OPOs do not have competingpathways for loss of pump energy

(ps is normalised pump threshold intensity)

Rosencher & Fabre, JOSA B, 19, 1107, 2002

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Quasi-phase matching for OPOs

+ Noncritical interaction+ Longer interaction length+ Engineerable spectral output+ Accessing the highest (2) over the

entire transparency region− Additional processing step (= cost)− deff =2/d33

6 9 12 15 18 21 24 27 30 33 36 39 420,51,01,52,02,53,03,54,04,55,05,5

pump

= 1064 nm

pump

= 800 nm

pump

= 532 nm

Sig

nal/

idle

r [

m]

Grating period [m]

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OPO configurations

Advantages with nanosecond QPM-OPOs

Low threshold

Increased interaction length

Spatial filtering => better M2 than the pump.

Easy tunability

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Quasi-Phase-MatchingOPO Tuning Techniques

Temperature tuning

Multigrating structures

Fanned grating

Non-collinear configuration

18T150 C

PumpSignal Idler

30 31 32 33 34 35 36 37 38

1,6

2,0

2,4

2,8

3,2

3,6

S

igna

l, id

ler (m

)

QPM period (m)

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Pump laser: (Mitsubishi Electric Corporation)Diode pumped, Q-switched, Nd:YAG laserfrep. rate = 15 kpps, 60 kHz, = 40 ns (FWHM), M2 = 1.1

60 mm

20 mm

w0 = 0.25 mm

R = 35 %, signal+idlerR = 100 %, pumpROC = -2 m

R = 99 %, signal+idlerAR for pumpFlat

0

5

10

15

20

25

0

0.1

0.2

0.3

0.4

0.5

10 20 30 40 50 60

Out

put p

ower

[W]

Conversion efficiency

Pump power [W]

High repetition rate DRO

= 48 %

Pout,max 24 W

3 mm thick PPKTP OPO pumped at 1064 nm, signal at 1.5 µm

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R = 64 %, signal, 10 kHzR = 64 %, signal, 20 kHzConversion efficiency20kHz = 28 %10kHz = 28 %

0

0.4

0.8

1.2

1.6

2

0 1 2 3 4 5 6 7 8

Tota

l out

put p

ower

[W]

Pump power [W]

Pout,max 2 W

deff 8.0 pm/V

SRO high repetition rate 3 mm PPKTP OPO pumped with ns pulses at 1064 nm,signal at 1.5 µm

-5 0 5 10 15 20-1

0

1

2

3

4

Ampl

itude

(a.u

.)

Time (ns)

Depletion of the pump

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Intracavity CW-SRO

• 50 mm PPLN, w=70 µm• M2 – HR for pump• M2 - M3 – Hi-Q cavity for signal

[D.J.M. Stothard etal Opt. Lett 23, 1895 (1998) ]

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Tuning singly-resonant OPOs

Noncollinear interaction+ Wider tuning range+ Fast tuning+ Separable signal, idler

and pump beams+ Truly singly resonant+ Reduces back-conversion+ Single period grating– Shorter interaction length

Manipulating the QPM-crystal

• Temperature

• Multigrating structures

• Fanned gratings

• Rotation

• Noncollinear interaction

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0 5 10 15 20 251500

2000

2500

3000

3500

Sign

al a

nd id

ler w

avel

engt

hs

s,i (

nm)

Rotation angle (°)

The pump laserNd:YAG, 6 ns, 10 Hz, M2 = 1.1

The PPKTP sample 2.1 mm diameter, = 35.0 mpoled area 10 by 10 mm2, thickness 0.5 mm,

= 17.3%, at = 26°. Etot = 74 JEpump = 430 J

Widely tunable OPO with circular PPKTP

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Volume Bragg gratings

Optical•

•

•

Material• Period, • Thickness, d• Strength, n1

• Narrowband reflection peak• Performance can be tailored to suit needs• Made in durable and cheap glass

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Cavity element – volume Bragg grating

777 874 971 1068 11650,0

0,1

0,2

0,3

0,4

0,5

Wavelength [nm]

Ref

lect

ivity

, %

973 974 975 976 9770,0

0,1

0,2

0,3

0,4

0,5

Wavelength [m]

Ref

lect

ivity

, %

= 0.16 nm (50 GHz) @ 975nm

= 3.0 nm (950 GHz) @ 975nm

conventional mirror 150 nm

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Narrowband OPO at 975 nm

spectrum

0.4 mJ signal limited by pump

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Angle tuning

tuning spectra

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Angle tuning improved

tuning spectra

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OPO with transversely chirped Bragg grating

tuning spectra

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Linewidth narrowing - OPO

• Conventional techniques1

• Folded cavity with grating • Inserting etalon – Increased cavity length– Higher thresholds

1. S. Brosnan and R.L. Byer, IEEE J. Quantum Electron. 15, 415 (1979)

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Tools for NLO

SNLO . Public Domain Software for non-linear opticshttp://www.sandia.gov/imrl/XWEB1128/xxtal.htm

SNLO – a public domain software

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OPO with focussed Gaussian beam.

• Seminal paper:

‘Parametric interaction of focussed Gaussian light beams’Boyd and Kleinman, J. Appl. Phys. 39, 3597, (1968)

• Extension to non-degenerate OPO. Relates treatments for plane-wave, collimated Gaussian and focussed Gaussian:‘Focussing dependence of the efficiency of a singly resonant OPO’

Guha, Appl. Phys. B, 66, 663, (1998)

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Summary: Attractions of OPOs

• Very wide continuous tuning from a single device, via tuning the phase-match condition

• High efficiency

• No heat input to the nonlinear medium

• No analogue of spatial-hole-burning as in a laser, hence simplified single-frequency operation

• Very high gain capability

• Very large bandwidth capability