Nonlinear Photonics for All-Optical Signal Processing

Nonlinear Photonics for

All-Optical Signal Processing

Part A: Introduction, Integrated Photonics, Optical

Cavities, Materials

FIP module, IOGS

February 5th -12th, 2019

Alfredo De Rossi

Thales Research and Technology

1 av. Augustin Fresnel, 91767 Palaiseau

I. Confinement of light and lightwave technologies

• Introduction: Integrated Photonics

• Integrated Nanophotonics

• optical cavities and micro-cavities

• Beyond Silicon: novel photonic platforms

II. Confinement in sub-wavelength structures

• Interactions in cavities

• Photonic Crystals

• Novel Device Concepts

• Small Lasers

• Integration

III. All-Optical Signal Processing

IV. Optical Nonlineartities in Integrated Photonic Circuits

• Third Order NL and related effects in Semiconductors

• Free Carriers

• Nonlinear Semiconductor Resonator

• All-Optical Gating

• Application: All-Optical sampling

1 / 136

This lecture: preamble

• Aim: to provide a technology-centric view of nonlinear

photonics, with a strong emphasis on the integrated optics

(just celebrating its 50 years!)

• Device Physics rather than Fundamental Aspects

Topics:

• brief introduction to integrated optics, cavities and methods

• Materials for nonlinear Integrated Photonics, specifically

semiconductors

• Sub-wavelength Structures, particularly Photonic Crystals and

their Nonlinear Properties

• Examples of novel NL Photonic Structures

• All-optical Signal Processing with Photonic Nanostructures

2 / 136

Integrated Photonics and future of Computing

• Development of the internet and computing (and artificial

intelligence) linked to the improvement of energy efficiency

• Photonic communication layer for short range high-capacity

comm. (CPU-CPU, CPU-MEM)

• Concepts of reservoir, neuromorphic, and hybrid

Analog/Digital Computing (IBM)

On-chip photonic interconnect developed by IBM (2015)

Prof. K Bergman, Columbia U., NY

High Performance Computing with Optics

https://lightwave.ee.columbia.edu

Need for miniature and energy-efficient photonic components3 / 136

Optical Signal ProcessingTHALES: about 60000 employees worldwide: complex electronic

systems, critical signal processing, ...

Khilo, et al., Opt. Expr. 2011

MLL clock

RF input signal

linear photonic linear sampler circuit

Ana lo g wo rld :

C o ntinuo us sig na ls in

the p hysic a l wo rld

Dig ita l wo rld :

Fo rm a t fo r d a ta p ro c e ssing

(b y c o m p ute rs.. .)

Analog to

Digital

Converter

• New Paradigm: Photonic Front-End between communication

layer (optics) and computing (electronics)

• Analog Computing4 / 136










• Small Lasers

• Integration




• Free Carriers




5 / 136

From the Light Fountain to Integrated Nanophotonics

(see: J. Hecht, City of Light, and plenary talk in Ecoc2010)

Daniel Colladon's "Light Fountain"

Comptes Rendus 1842

Light source water

Light beam

The light follows the bend of the water

beam: TOTAL INTERNAL REFLECTION

The ancestor of the optical fibre.

6 / 136

Historical notes: guiding light

applications ?

Luminous fountain, Gaston Menier, 1889

7 / 136

One century later, integrated optics

1969

8 / 136

Guided wave modes

resonance

Total internal reflection in a waveguide

total internal reflection

9 / 136

Optical Waveguides

An optial waveguide is based on Total Internal Reflection

Confinement in-plane or in a channel.

A contrast in the refractive index is all what is needed.

10 / 136

Planar lightwave circuits

A kind of fibre... some applications

11 / 136

Then, after year 2000, something happened

Implications of using the Internet:

R. Tucker, OFC 2014

Need to have energy-efficient telecommunications

12 / 136

The Silicon Photonic Foundry

• Idea: recycle old microelectronics fabs must be compatible

with the CMOS process IMEC, CEA-Leti, IME/A-star

• Still, It is hard to generate light with Silicon...

13 / 136

III-V Integrated Photonic Foundries

Telecomm Semiconductor lasers are based Indium Phosphide:

Jeppix foundry [Europe]

Combination with other materials, specifically Silicon Nitride.

14 / 136










• Small Lasers

• Integration




• Free Carriers




15 / 136

Scaled-down integrated photonics

• Integrated photonics is mostly based on design concepts

dating back to the 70’s

• but huge efforts in materials and fabrication have turned it into

an industrial platform

• take exemple from VLSI, scaling down to improve speed and

energy efficiency

16 / 136

Modern computer: Power issue, again!

modern processors are multi-core

most of the energy is used to communicate between cores

Idea: use on-chip photonic network

17 / 136

Photonic Network on a Chip

Research cluster at Cornell University, Columbia U., HP, MIT, IBM

Image:IBM, around 2010

Use photons to move data around and to synchronize data

18 / 136

Convergence of Electronics and Photonics

Left: Artist’s view of a CMOS photonic chip, right: SEM image combining electric and

photonic (blue) paths. IBM 2014.

Photonic circuits need to be as small as possible to fit in CMOS

electronics.

19 / 136

Silicon nano-Photonics

Integrated optics nano-photonics

Photonic wire

Photodetector

CMOS-photonics

IBM, J.Watson laboratory. Y. Vlasov group

λ

Scaling down to the diffraction limit: λ/2n

20 / 136










• Small Lasers

• Integration




• Free Carriers




21 / 136

Electromagnetic Resonators

• A resonance of the electromagnetic field involves the periodic

exchange of electric∫

ε|E|2/4 and magnetic∫

µ|H|2/4energy

• The LC (inductance-capacitance) resonator is the iconical

representation of this concept

l0

gb

d

b bEH

k

L L

C

from: Withayachumnankul, Opt. Expr. 18,25912 (2010)

• LC circuit can be much smaller than the wavelength. e.g. at 3

GHz λ ≈10 cm

• However, loss increases at optical frequencies22 / 136

Resonators at optical frequencyIssues with sub-wavelength resonators based on metal.

khurgin, Nat. Nanotech. 10, 2, 2015

Cavity lifetime ≈ electron scattering time: 10 − 100fs

23 / 136

Optical Dielectric Cavities

Mirror Mirror

Fabry-Pérot Resonator

In Out

phase = 2π n

Micro sphere

"wispering gallery" modes

Micro disk

"wispering gallery" modes

Micro-pillar

distributed Bragg reflector

micro-ring

Confinement by total internal reflection

24 / 136

The Fabry-Perot as the emblematic resonator

Mirror ResonancesMirror

Field

• resonance: reflected waves interfere constructively

• 2 Lλm

n = m [n refractive index]

• mode spacing δν =vg

2L ∝ L−1. → small cavity less modes.

25 / 136

The Fabry-Perot as the emblematic resonator

Mirror Mirror

Fabry-Pérot Resonator

In Outphase = 2π m

Transm

issio

n (

%)

Wavelength (nm)

m m+1 m+2 m+3

R<1

τc

τ0

scattering

• resonance: reflected waves interfere constructively

• 2 Lλm

n = m [n refractive index]

• mode spacing δν =vg

2L ∝ L−1. → small cavity less modes.

• Cavity decay rate 1/τcav [s−1], related to absorption (α) and

out-coupled power (1 − R).

• i.e. 1/τcav = vg(α − 1/L ln R) or

• with τ−1 = τ−10 + τ−1

c

25 / 136

Properties of optical cavities 1/2

• Resonator with motion equation:ddtA = (−iω0 − 1

2τ )A + (τc)−1/2S

• the energy in the cavity |A|2decays as exp(−t/τ)

• the power lost by the cavity is

− ddt |A|2 = |A|2/τ = P

• in the spectral domain:

A(ω) = S (τc)−1/2τ1/2−iτ(ω−ω0)

• hence |A(ω)|2 is a Lorentzian

lineshape ∆ωF W HM = τ−1

• the Q factor is

ω0/∆ω = τω0 = ω |A|2/P

−2 −1 0 1 20

0.2

0.4

0.6

0.8

1

Detuning τ(ω−ω0)

Am

plit

ud

e |A

|2

Lorentzian

FWHM

remember coupled mode theory, H. Benisty lecture

26 / 136

Properties of optical cavities 2/2

|s|2

ω0

τ0τc

|A|2

Consider the case of a cavity coupled to a waveguide with

incoming power |S|2At resonance, ω = ω0, the energy in the cavity is |A|2 = 4τ2

τc|S|2

and the reflection is R = |S|2(2ττc

− 1)2

at critical coupling τ0 = τc = 2τ

• |A|2 = τc|S|2 and R = 0

• All the incoming power |S|2 is transferred to the cavity and lost

through internal losses τ0

• In electronics, that is the case of adapted load

conversely, if the cavity is lossless (1/τ0 = 0, hence τ = τc), then

R = 1. Total reflection.

27 / 136

Resonant filterConsider now one cavity with two ports (input + output):

|si|2

ω0

τ0

τc

|A|2

τc

|so|2

In-line cavity configuration

|si|2 ω0

τ0|A|2

τc|so|

2

Side-coupled cavity configuration

|sr|2

|sr|2

−2 −1 0 1 20

0.2

0.4

0.6

0.8

1


Norm

aliz

ed p

ow

er

|sr,

o|2

/|s

i|2

In−line cavity

T+RR

T

−2 −1 0 1 20

0.2

0.4

0.6

0.8

1


Norm

aliz

ed

pow

er

|sr,

o|2

/|s

i|2

T+R

R

T

side-coupled cavity

(τ/τc)2

( τ/τc)2

2

Limit of no loss: τ−1 = 1τ−10 + 2τ−1

c = 2τ−1c

in-line: R = 0, T = 1. side-coupled: R = 1, T = 0

28 / 136

Increasing complexity

a variety of functionalities can be obtained

four-ports drop filter

|s4|2 |s3|

2

|s1|2

|s2|2

multi-channel drop filter

|s1|2

|si|2

|s2|2 |s3|

2

|s4|2

just a matter of topology

29 / 136

Optical microresonator on silicon platform

Disk or ring resonators are widely used in silicon-photonics

micro-disk micro-ring

silicon-nitride or silicon

photonic wire

roughness scattering

bend loss

Ming C. Wu, Berkeley

Hosseini, Georgia Tech

light circles inside the structure

limitations: bend-lossess and scattering

30 / 136

Application: High-order optical filters

The combination of multiple resonators and waveguides on a

silicon platform also includes electric controls in order to tune the

device

2nd order

5th order

tunable filter for microwave photonics

bandwidth = 1 GHz (1.7 pm) [Kotura/Telcordia, USA]

31 / 136










• Small Lasers

• Integration




• Free Carriers




32 / 136

Materials in Photonics

Silicon Photonics is extremely popular because it represents an

industrial-grade fabrication platform existing since a decade.

However, some intrinsic limitations of the material have motivated

the developement of alternative platforms, sometimes still

compatible with Silicon Photonics, in order to:

• access to broader transparency window: visible, UV, or mid-IR

• second harmonic generation (non-centro symmetric crystals)

• electro-optic effects (idem)

• piezo electric (idem)

• suppress of nonlinear absorption

• achive ultra low loss

33 / 136

Ultra high-Q resonatorsLimitations of Silicon, nonlinear and free-carrier absorption,

transparency window (λ > 1.1µm)

Novel emerging technologies: SiN3 Photonic Foundry.

Lionix BV

Optical beamforming network

Triplex SiN3 process

delay ~ 1 ns

Propagation Losses

Rrefle

cti

on

Heck, Laser Phot. R. 8, 667 (2014)

Very low propagation losses (reduced index contrast)34 / 136

Silicon Nitride and Silica: ultra low loss

chemical mechanical polishing

roughness

= 0.08 nm

Ji, et al. Optica 4, 619 (2017)

Silicon Nitride

Silica

Yang, et al., Nat. Phot., 12, 297 (2018)

Q is about 200 M! Integrated Optical Combs with low pump power

35 / 136

Record high QSingle crystalline MgF2, CaF2 polished resonators based on

whispering gallery modes

EPFL T. Kippenberg group

FEMTO-ST

Y. Chembo groupOEWaves (Maleki, Matsko et al.)

Polished Crystals

CaF, MgF

Highest Q. Spectrally ultra-pure microchip lasers

36 / 136

Wafer Bondingcombine a III-V active laser with a passive Silicon Photonic Circuit

Roelkens, Günther, et al., Materials Today 10, 36 (2007)

Adhesive wafer bonding

Niklaus, F. et al., J. of appl. physics 99, 2 (2006)

III-V/Si photonics by die-to-wafer bonding

also other techniques, molecular adhesion and direct growth on Si

37 / 136

AlGaAs on Glasssmaller effective area = much larger nonlinear coefficient γdispersion control demonstrated

Pu, M. et al., Optica 3, 823 (2016)

negative dispersion

optical parametric oscillation, SHG, all-optical signal processing,data comm. [Hu, et al. Nat. Phot. 12, 469(2018)]

38 / 136

Gallium Phosphidezinc-blende, Eg = 2.26eV (550 nm), n = 3.05 (1550 nm), very

good thermal conductivity, suppressed TPA with pump in telecom

spectra

Mitchell, APL 104, 141104 (2014) Wilson et al. ArXiv 1808,03554 (2018)

Photonic Crystals (SHG)

Rivoire et al., Opt.Expr. 17, 22609 (2009)

GaP on Silicon Oxide

on-chip comb generation, SHG, optomechanics

39 / 136

Indium Gallium Phosphidezinc-blende, Eg = 1.9eV (630 nm), n = 3.17 (1550 nm),

suppressed TPA. Grown lattice-matched on GaAs, used for

high-power electronics and diode lasers

1 um

Dave et al, Opt. Expr, 23, 4650 (2015)

NL photonic crystals, super continuum generation, SHG, etc...40 / 136

Gallium Nitridewurtzite (zinc-blende possible) usually grown on Sapphire,Eg = 3.4eV (360 nm), large thermal conductivity. Direct bondingtechnique: [Stassen, et al. CLEO 2018]

Alternative techniques:

Electrochemically sliced low loss optical microresonators

Bruch, et al. , APL 110, 021111 (2017)

Annealing termperature °C

lower NL but allows access full visible and UV bandAluminum Nitride, Eg = 6.2eV . Sputtered on silica, cristalline

Q=4 × 105[Pernice, et al. Opt. Expr. 20, 12261 (2012)]

41 / 136

Lithium NiobateMaterial of fundamental importance for electro-optic conversion

(e.g. modulators)

Lithium Niobate Photonic Wires H. Hu, et al., OX 17, 24261(2009)

Air milling, 10 dB/cm

LiNbO3 bonded on Silica

Zhang et al., OPTICA 4, 1536 (2017) Wang et al., OPTICA 5, 1438 (2018)

SHG and low Vπ EO modulators 42 / 136

Diamondvery large thermal conductivity and very broad transparency

Burek, et al. Optica 3, 1404 (2016)

Haussman, et al. Nat Phot 8, 364 (2014)

particularly suited for optomechanics (low mechanical losses)

43 / 136

What else?

• Hydrogenated Silicon: larger gap, almost TPA free (at 1.5µm)

parametric amplification (pulsed) Kuyken et al, OL 36, 552 (2011)

large figure of merit Grillet et al, OX, 20, 22609 (2010)

• Silicon-rich Nitride: much larger n2 than stoichiometric SiN

Kruckel et al, OX 23, 25827 (2015)

• Strained silicon: breaks symmetry, allows EO effect

Jacobsen et al, Nature 441, 199 (2006)

allows SHG Cazzanelli et al., Nat. mat. 1, 148 (2012)

• Silicon with Silicon nano crsytals, All optical switch

Martinez et al, Nanolett. 10, 1506 (2010)

• Chalcogenides: low TPA, large NL

Eggleton et al., Nat. Phot. 5, 141 (2011)

44 / 136

Mid Infrared NL Photonicstransparency of Silica in the mid IR is an issue. Replacing Silica

with other substratesSilicon on Sapphire

Baehr-Jones et al., Opt. Expr. 18 12127(2010)

Pedestal

Lin et al., Opt. Lett. 38 1031 (2013)

Silicon GermaniumL=7cm

Sinobad et al., Optica 5, 360 (2018)

spectroscopy and remote sensing

45 / 136










• Small Lasers

• Integration




• Free Carriers




46 / 136










• Small Lasers

• Integration




• Free Carriers




47 / 136

Implications of reducing the size

R R

L

W: densiy of the EM energy

Fabry-Perot: L = 1 cm, d = 0.1 mm, V =10-4 cm3 I = 0.05 mW/cm2

d

IoptFabry-Perot resonator

Total energy =

n

power flux

What is the power flux in a cavity containing 1 photon?

VCSEL: L = 3 μm, d = 10 μm, V =3 10-10 cm3 I = 5 W/cm2

"Nanocavity": V=0.25(λ/n)3 = 2 10-14 cm3 I =10 kW/cm2

power flux in the cavity increases by 8 orders of magnitude!

Electric field -> 0.5 V/μm

48 / 136

And increasing the Quality Factor Q

R R

Iopt n

steady state

What is the power required to keep 1 photon in the cavity?

Popt Popt(out)Photon lifetime

Low-Q cavity (10):

f=240THz (1um)

High-Q cavity (106):

49 / 136

Optical confinement is important!

• Large optical field can be generated with a very weak input.

• strong light-matter interaction

• implications for lasers, detectors, sensing and nonlinear

devices

• next: how to make very small cavities

50 / 136










• Small Lasers

• Integration




• Free Carriers




51 / 136

Nano-scale photonic structures

Advances in fabrication techniques (e-beam, direct laser writing,..)

Thiel, et al. Adv. Mat. 2009

Chiral Photonic Structure Amorphous and Cristalline Diamond structure

Edagawa et al., Phys. Rev. Lett. 2008

"Woodpile" Photonic Crystal

Ogawa, et al. Science 2004

Active Layer

"defect"

Very complex structures the λ scale. Huge parameter space!

52 / 136

Alfredo D

e Rossi, T

HA

LE

S R

&T

Light in patterned dielectrics

Modern fabrication technologies enable the accurate fabrication of

structures with nanometer accuracy.

Waves in a periodic structure, X-rays propagating through a crystal or

PHOTONS in a PERIODIC DIELECTRIC, behave similarly:

● wavelength λ comparable to the atomic spacing d

● Scattered waves interfere CONSTRUCTIVELY

● when: 2 d sin θ = n λ is satisfied, the wave is reflected

Bragg reflection

Alfredo D

e Rossi, T

HA

LE

S R

&T

X-ray diffraction

Photonic structures in the Nature

Scanning Electron Microscope

seen at the wavelenth scale

Morpho Rhetenor(a butterfly)

Bio-inspired technological applications?

53 / 136

Optical Density of States

Yablonovitch, JOSAB 10, 283 (1993)

total Density of Optical States (DOS)Forbidden!

spontaneous recombination

frequency

wavevector DOS (arb. u.)

yablonovitch,

PRL 61, 2546 (1988)

K.Bush, S.John, PRE 58, 3896 (1998)

Forbidden band DOS=0

54 / 136

Alfredo D

e Rossi, T

HA

LE

S R

&T

localisation

fre

qu

en

cy

wavevector

Perfect periodic structure

fre

qu

en

cy

wavevector

periodic structure with disorder

Pseudo gap

localisation

Bloch waveLocalised radiation

Localized states

mobility

Yablonovitch, PRL 67, 3382 (1991)

deterministic defect

55 / 136

Alfredo D

e Rossi, T

HA

LE

S R

&T

Photonic crystal cavities and waveguides

Local perturbation

Line defect waveguide

Linear chain of defect states

Fabrication

e-beam patterning SiO2 mask etchingDeep RIE ecthing

wet etchingremoval ofthe sacrificiallayer

GaAs

GaInP

GaAs

SiO2 mask

resistSiO2 mask

56 / 136

Optimisation

non optimized process

Etching GaAs/GaInP

optimized process

Combrie' 2006

control of nanoscale pattering is tricky! 2D patterned slab are

much easier to fabricate. Is the forbidden band preserved?57 / 136

2D PhC

x

yz

x

y

z

Johnson, PRB 60 5751 (1999)

Srinivasan and Painter, OX 11 579 (2003)

Implication of 2D periodicity:

the band gap is not complete

intrinsic radiative loss

58 / 136

PhC cavities: the beginning

optical cavity in PhC, 2001Q~800MIT Group

f2

f1

Noda Group, 2000

Painter et al, 2000

Imperfect confinement of optical modesOut of plane scattering

Q-factor is low, why?

the PhC cavity mode is a combination of truly confined and radiating modes

Proper design should minimizeradiatiating modes

59 / 136

High-Q PhC cavities

Further optimisation

Q>107, limited by absorbtion

Spatial reshaping of the optical

mode modifies the content of

leaky modes

Akahane, et al. Nature 425, 944 (2003)

Song et al., Nat. Mat. 4, 207 (2005)

Asano et al., OX 25, 1769 (2017)

60 / 136

Improvement of PhC cavities

H. Benisty, 2006

61 / 136

Design of high Q/V cavities (NL and Quantum Optics)

Nakamura, et al., Opt. Expr. 24, 260172 (2016)

Fourier Transform Optimisation

Dharanipathy et al., 2014; Minkov, Savona Sci Rep 4, 5124 (2014)

Automatic Optimisation (Genetic Alg.)

Topologic Optimisation, Borel et al, Opt. Expr. 200462 / 136

Consequences of the Fabrication ImperfectionsFabrication disorder limits the Q factor and induces fluctuations of

the resonance

Y. Taguchi et al., OX 19, 11916 (2011)

40 GHz

• Current limit (Silicon) is σ ≈ 0.6nm, leading to δν ≈ 40GHz

• Wealth of experiments and theory:

H. Hagino et al, PRB 79, 085112 (2009), D. Fussel et al., PRB 78, 144201 (2008),

Minkov et al., OX 21, 28233 (2013)

63 / 136

Harnessing and controlling Disorder

Vasco and Hughes, arXiv 2018

Long-distance correlated disorderLocalisation induced by disorder

Thyrrestrup, et al, PRL 2012

Compensating Disorder

Yuce et al, 2018

64 / 136










• Small Lasers

• Integration




• Free Carriers




65 / 136

Photonic Crystal Cavities in Science and Technology

novel concept: Fano Laser

Yu, et al, Nat Phot 2016

Optical RAM

Light-Matter Interaction

Voltz et al.,Nat. Phot 2012

Nozaki et al.,Nat. Phot 2012

Ultra-Efficient Nanolaser Diode

Crosnier et al., Nat. Phot. 2017

achieving confinement to the diffraction limit enables new science

and new devices

66 / 136

Sensing

• to detect small amount of matter (e.g. a molecule),

concentrate into a tiny volume

• then use a small resonator (or waveguide) which would

change resonance (transmission)

Erickson, opt. lett 2006

67 / 136










• Small Lasers

• Integration




• Free Carriers




68 / 136

Why making small lasers?

• Remind: Scaling down transistors: from cm to (< 1µm): faster

and less power consumption.

69 / 136




• Laser: L ≈ 1m (first device), scaled down to semiconductor

lasers (L < 1 mm), and so-called NanoLasers (L ≈ λ).

69 / 136




• Laser: L ≈ 1m (first device), scaled down to semiconductor

lasers (L < 1 mm), and so-called NanoLasers (L ≈ λ).

• Photonic interconnects will enter in future computer at the

chip scale! Laser sources will have to be small

• and consume little power

69 / 136

The semiconductor Laser Diode

Resonator: Fabry - Perot cavity, reflection at the cleaved facets.

Gain: population inversion the p-n junction.

R R

The current at threshold depends on the volume Vg of the gain

material: Ith ∝ Vg(Nth − Ntr), and this must be commensurate to

the volume of the optical field V .

70 / 136

Improvement of the active material

Threshold Current

From Z. Alferov. Nobel Lecture 2000

First Laser diode 1962

From C. Townes. Nobel Lecture

71 / 136


Threshold Current



Double-Heterostructure ≈1970

From Z. Alferov. Nobel Lecture

71 / 136


Threshold Current



Double-Heterostructure ≈1970

Quantum Dot VCSEL [TU Berlin]

From Z. Alferov. Nobel Lecture

71 / 136

The first Photonic Crystal Laser

• main idea: use the small volume of a PhC resonator to use

very little optical power

r'

r

a

y

x

Painter, Science 284, 1819 (1999)

• Optical Pumping (electric is difficult): pump at threshold 7 mW

• pulsed operation at 150 K

• power density very large, heating issues.

72 / 136

Efficient PhC laser

• efficient pumping of a very small active region: 0.2µm3

• needs advanced fabrication technology

InGaAsP (λg=1.35μm)

InGaAsP (λg=1.35μm)

InP substrate

InGaAs sacrif cial layer

InP

InP photonic crystal

Pumping waveguide

Gain media (InGaAsP)

Pumping region

Gain media (InGaAsP) =Pumping region

InP region

InGaAsP BH

SQW active region

Air

InP

Matsuo, Nat. Phot. 4, 628 (2010)

• Threshold 1.5µW (optical pumping), RT, CW

• energy efficiency → less heat, no thermal issues

73 / 136

Photonic Crystal Laser Diode

• First electric pump Kim et al. 2004 (pulsed, fab challenging)

Park, Science, 305, 1444 (2004)

74 / 136



• ultra efficient PhC laser (NTT) ≈ 10 fJ/bit, 2013.

InGaAsP MQWs: confined carriers

doped InP re-grown InP

Optical Cavity

Takeda, Nat. Phot. 2013

p

n

74 / 136




• Confinement of photons,

Vmode ≈ 2(λ/n)3 = 0.15µm3 InGaAsP MQWs: confined carriers


Optical Cavity


p

n

74 / 136




• Confinement of photons,

Vmode ≈ 2(λ/n)3 = 0.15µm3

• and confinement of carriers:

Vg = 3×0.3×0.2µm3 ≈ Vmode.

Good overlap. Minimizes Jth

and also heating.

• injected through a planar PN

junction

• Ith ≈ 4µA direct modulation

about 10 GHz.

InGaAsP MQWs: confined carriers


Optical Cavity


p

n

74 / 136










• Small Lasers

• Integration




• Free Carriers




75 / 136

Integrated Nanophotonics

Shen et al., Nat. Phot. 11, 441 (2017)

machine learning with photonic circuits

Sun, et al. Nature 528, 534 (2015)

76 / 136

Hybrid III-V nanostructures on Silicon Photonics:

fabrication

technology developed at Centrre de Nanosciences et de

Nanotechnologies (C2N), Paris-Saclay

2 µm

1 µm

300 µm2 c m

III-V: InP, InGaP, GaInAsP, ...

77 / 136

Hybrid III-V nanostructures on Silicon Photonics: design

Design of a Silica-Encapsulated Nanobeam CavityBazin et al., JLT 32, 952 (2014)

Crosnier et al., OL 41, 579 (2016)

principle of "gentle confinement"

Song, Nature 2005

tapered lattice period

Measured Q-factor

evanesent coupling

Q0=106 (theory)

105 (exp.)

78 / 136










• Small Lasers

• Integration




• Free Carriers




79 / 136

Helping Electronics

Electrons good for processing, photons deliver signals efficiently

• Optical Interconnects to reduce energy consumption in

transmission lines in CPU and between CPUs.

80 / 136

Helping Electronics




• One step further: minimizing signal conversion from the

optical to the electric domain

80 / 136

Helping Electronics




• One step further: minimizing signal conversion from the

optical to the electric domain

Highly idealized architecture

CPU

CLOCK

“Processing” CPUE/O

optics

E/O

Electronics

Keep electronics but add some simple all-optical operations

80 / 136

Bistable Electronic Circuit

CMOS NOT Gate

Bistable Gate

[latch]

Set

Reset

R=(∞,0)

R=(0,∞)

NAND

T,F

F,T

Feedback

Once set or reset, the circuits keeps the prescribed state owing to

positive feedback.

81 / 136

Use of an optical ”flip-flop”

Dorren, JLT 2003

out λ1

out λ2

time (us) time (ns)0 1 2

An optical flip flop is a bistable laser controlled all-optically by the

input header of the data signal. It decides which wavelength

channel the output will go. Eventually a memory is necessary.

82 / 136

Optical Bistability

• Bistability = nonlinear response + feedback

• nonlinear f(x): f(αx) 6= αf(x)

• CMOS gate is highly nonlinear

In optics

• feedback: optical cavity

• nonlinear response: intensity-dependent refractive index:

n = n0 + n2I

83 / 136

Optical Bistability

|si|2

ω0

τ0

τc

|A|2

τc

|so|2

|sr|2

|s|2

|A|2

nonlinear resonance

Two stable states

cubic equation in |A|2

Kerr NL

(unstable)

84 / 136

Optical Bistability: H. Gibbs

Gibbs

Bistable Etalon

85 / 136

Undergraduate experiment

ONOFF

Input

Output

86 / 136

The very first experiment

R R

Na cell

Nonlinear Fabry Perot Interferometer

Pi

detuning (MHz)

Gibbs, 1976

Pmax=10 mW

L=11 cm

time scale: μs

87 / 136

Optical Bistability: what is the trouble?

• using resonant NL response (Na): time > µs SLOW!

• bulky and unpractical: λ = 588nm, Na D-lines

Use nonlinear response in semiconductors. New experiment by

Gibbs, 1982

• I = 1mW/µm2 = 0.1MW/cm2: that is fine

• timescale 20 ns. Data at 50 Mb/s... too late!

basically we are here:

Point-contact Transistor Bardeen Shockley Brattain

Bell Labs 1947 [Nobel Prize]

88 / 136

Bistable laser

• A laser is an extremely nonlinear system.

two coupled ring laser (InP)

10 μm

Hill, "A fast low-power optical memorybased on coupled micro-ring lasers", 2004

5fJ

20ps

• mutually injected lasers have two stable states

• still, heat dissipation is an issue for stability

89 / 136

Optical Memory based on passive devices

Efficient NL interactions:

1) strong nonlinearities

2) resonant enhancement

3) optical confinement

The next part will be about how to harness the nonlinear response

from a material!

90 / 136










• Small Lasers

• Integration




• Free Carriers




91 / 136










• Small Lasers

• Integration




• Free Carriers




92 / 136

Concepts

idea: to associate intensity-dependent refractive index with an

interferometer 93 / 136

Nonlinear Absorption

TPA (β) is the imaginary part of the third order susceptibility χ(3)

94 / 136

Universal Scaling of Nonlinear Absorption in Solids

TPA scaling: β = K

√Ep

n2

0E3

gF2(2~ω/Eg)

fitting parameter K is material independent, close to theoretical

prediction, F2(x) from band theory

95 / 136

Universal Scaling of bound electronic nonlinearity

• n2 tied to Two Photon Absorption β through Kramers-Kronig

eq., no fitting parameters

• K fitted from TPA

• strong scaling with the electronic band gap Eg

96 / 136

III-V Compound Semiconductors

• TPA vanishes when 2~ω < Eg

Adapted from C.G. Fonstad, MIT Course

6.772/SMA5111 Compound Semiconductors

Zinc-Blende

C-band

Telecom

O-band

(x2)

• III-V SC is a mature technology offering bandgap tuning

• Telecom bands are TPA free with Eg > 2eV , but C-band only

requires Eg > 1.6eV

97 / 136

Optimized NL response

Ioffe database

NL index Two Photon Absorption

et al

theory

Large bound-electronic (ultra-fast)

n2 = 2.5 × 10−17m2/W ≈ n2(SiO2) × 103 with T < 1

98 / 136










• Small Lasers

• Integration




• Free Carriers




99 / 136

NL response due to Free Carriers

Van Stryland et al.

Nonlinear propagation

FC absorption cross section

FC dispersion

linear abs.

TPA

Said, et al. JOSAB 5 405 (1992)

−2 0 2 40

0.2

0.4

0.6

0.8

1

Time

τcar >Tpulse

N

I

Wherret, 1982

FC refraction: plasma +

other effects

Free Carrier Abs. αF CA = σexN linked to FCD (Dispersion)

100 / 136

Free Carriers Refraction (advanced model)

(Burstein-Moss effect)

(plasma effect)

the effective NL response can be large, example:

101 / 136

Residual Absorptionmainly due to surface states, defects

Grillanda, Morichetti, Nat. Comm. 6, 8182 (2015)

Surface Carrier absorption

• in Silicon narrow photonic waveguides this is not negligible

• combined with free carrier absorption, this leads to a much

stronger effective TPA

102 / 136

Photothermal effect

Temperature dependence of the Absorption

Johnson Tiedje, JAP 78, 5609 (1995)

60 °C

630 °C

and related change of the refractive index

GaAs

thermal resistance

thermal relaxation

W

T

R

T0

C

effective thermal NL

example: GaAs photonic crystal nanocavities. Rth = 105K/W ,

V = 10−19m3, dn/dT ≈ 10−4K−1, α = 300/m gives an effective

n2,th ≈ 10−16m2/W .

103 / 136

Non instantaneous Kerr response

Q=10^8

Sillica Toroidal Resonator

pump

MZM

probe

Lock-in

probe

Ker and Thermal 3rd order NL

(insulating delectrics)

Free-Carrier and gain dynamics

(active semiconductor devices)

Roskari Vahala, OL 30, 426 (2005) Bilenca et al. PTL 15, 563 (2006)

SOA

FOUR WAVE MIXING

pump

probe

thermal: ms to µs, free carriers: ns to ps, bound electronic: fs.

104 / 136

Example: AlGaAs Nonlinear Directional Coupler

Villeneuve et al., APL 62, 147 (1992)

NL directional

Coupler

issue: peak power about 1 kW

105 / 136

AlGaAs on Glasssmaller effective area = much larger nonlinear coefficient γdispersion control demonstrated

Pu, M. et al., Optica 3, 823 (2016)

negative dispersion

optical parametric oscillation, SHG, all-optical signal processing,data comm. [Hu, et al. Nat. Phot. 12, 469(2018)]

106 / 136










• Small Lasers

• Integration




• Free Carriers




107 / 136

Scaling of Optical Power with Size

R R

L

Energy density matters!

|S|2

Bistability equation

"threshold"

moreover...

input power scales as:

W

GaAs : n2 = 10-17W-1m-2 [Kerr]

τ=10 ps Power in =600 GW/cm3 Vmode !

FP cavity: L = 1cm, W = 0.1 mm, V =10-4 cm3 P = 60 MW !

Micro-pillar: L = 3μm, W = 1μm, V = 3 10-12 cm-3 P = 1.8 W

VCSEL: L = 3μm, W = 10μm, V = 3 10-10 cm-3 P = 180 W

PhC cavity: V = 3 10-14 cm-3 P = 20 mW

energy in thecavity

108 / 136

Small dielectric optical cavities

Foresi, 1997

"Nanobeam" cavity1D PhC

Ladder cavity

Notomi, 2008

H0 2D PhCno missing hole - 2 displaced holes

Zhang and Qiu, 2004

Diffraction limit @ 1550nm, free space:

limited by bend lossesR > 1.5 μm

Ring resonator

Xu,Fattal,Beausoleil 2008

109 / 136

Optical Bistability at microWatt power

Q ~ 250000

V ~ (λ/n)3

off

resonance

On

resonance

Weidner et al., APL 90 101118 (2007)

Thermal nonlinearity, τ ≈ 1µs (th. capacitance Cth is small. 1)

1 discussion in Part 1

110 / 136

Scaling Devices Down: CMOS technology

scaling

volume 1/K3

delay 1/Kpower dissipation 1/K2

power-delay product 1/K3

Table: source: R. Dennard,

IEEE JSSC, 1974

Weste Harris, VLSI design, 4th edition

In Photonics, volume of the optical mode V

• Laser threshold ≈ V ∝ 1/K3. → Nanolasers

• Optical Memories and gates operating power 1/V ∝ 1/K3

• Waveguide modulators driving power 1/K2.

111 / 136

Optical Bistability based on carrier NLSilicon PhC: [Notomi et al. OX 13, 2678 (2005)]

high-Q (>105) cavity

V = 0.16μm3

GaInAsP (Eg λ=1.3 μm)

Theor. threshold for bistability

TPA + FCD= 5th order NL

Shinya et al., OX 16, 19382 (2008)

• Quaternary Indium Phosphide optimized for NL response112 / 136

Optical Bistability based on carrier NL

Silicon PhC: [Notomi et al. OX 13, 2678 (2005)]

hysteresis cycle vs detuning Memory operation

Pth = 10uWthermal

Shinya et al., OX 16, 19382 (2008)

• Quaternary Indium Phosphide optimized for NL response

• Need to reduce heating, which drives the cavity off-resonance.

112 / 136

Nonlinear Cavity Detuning

n2=1.6x10-17m2.W-1

Tra

nsm

issio

n

Wavelengthλc

“cold” cavityKerr (fs)

Free Carrier

Dispersion (ps)

Wavelengthλc

Kerr (fs)

Thermo-optic (>>µs)

n2=-3x10-15m2.W-1

• Free Carrier Dispersion : blue shift (usually)

• Thermal : red shift (always)

• Kerr : red shift (usually)

113 / 136

Optimized bistable cavity

carriers confined here (InGaAsP)

InP

Pth (min) = 30 nW

[consistent with estimate]

Switching energy = 2 fJ

Nozaki, et al. Nat. Phot. 6, 248 (2012)

Mbit optical RAM possible!100 nW

114 / 136

optical memory

Nozaki, 2012

Transm

issio

n

OFF ON

0 2 4 60

0.2

0.4

0.6

0.8

1

Input Power (arb.u.)

En

erg

y in

th

e c

avit

y (

arb

. u

n.)

OFF

ON

bias

set

reset

115 / 136

Application: optical storage

Nozazi, 2012

power consumption (static) : 50nW/bit: 1 Mbit= 50 mW

dynamic: 2.5fJ * 10Gb/s = 25µW - size: 10 µm2 × 106 = 10mm2

116 / 136










• Small Lasers

• Integration




• Free Carriers




117 / 136

All-Optical Gates 1/2

• Based on Telecom-grade

components : Low-loss

transmission(fibres),

low-cost and advanced

modules . . .

• Very fast: gate opening time

< 1 ps

• 50 pJ/pulse →100 mW avg.

pump [with rep rate 2 GHz]

• Processing optical signals

up to 5 Tb/s [Oxenlowe,

DTU]

• length about 100 m

Nonlinear Op�cal Loop Mirror

Doran and Wood, Opt. Let . 1988

ON

OFF

118 / 136

All-Optical Gates 2/2

• Semiconductor Optical Amplifiers (SOA) used for compact

All-Optical Gates

• Gain saturation induces a phase shift, but recovery is about

100 ps at least

• Gate opening time reduced to about 1 ps using differential

mode

C. Schubert, PhD thesis, TU Berlin, 2004

Gate: 1 ps

SOA1

SOA2

Differen�al-mode opera�on

Nonlinear MZ interferometer

SOA

Still, repetition rate is limited to a few GHz (by the recovery time)119 / 136

Resonant All-Optical Gating

Transmission

Wavelengthλcλs

“cold” cavity

Signal

Resonator

• more energy-efficient

• signal bandwidth must fit the resonance, however

• dominant NL effect: induced Free Carrier Dispersion

120 / 136

Resonant All-Optical Gating

Transmission

Wavelengthλcλs

“cold” cavity

Signal

ResonatorPump

Pump

“excited” cavity

Signal

• more energy-efficient

• signal bandwidth must fit the resonance, however

• dominant NL effect: induced Free Carrier Dispersion

120 / 136

Ultra-fast response in GaAs NL Resonators

• all-in plane configuration

• H0 cavity → smallest modal volume for dielectric cavity[1] →

large enhancement of NL

1. Z. ZHANG et al. Opt. Exp. 12 (2004), (2009), p. 021111 121 / 136

Ultra-fast response in GaAs NL Resonators

• all-in plane configuration

• H0 cavity → smallest modal volume for dielectric cavity[1] →

large enhancement of NL

• All optical modulation with low energy (≈ 100fJ ) and

• ultra-fast recovery (≃ 6 ps)[2]

• inferred effective carrier lifetime τcar ≃ 1 ps

• consistent with previous experiments in PhC4

Bulk GaAs:

carrier lifetime ≫ 1ns

diffusion length

≫ 1µm

1. Z. ZHANG et al. Opt. Exp. 12 (2004),

p. 3988

(2009), p. 0211114

121 / 136

Probing the dynamical response

pump-probe technique allow probing with very high time resolution

122 / 136

Dynamical response of a NL PhC cavityTransmission

Resonance

excitation

Time

Pump Probedelay

wavelength

Spectra

Free carrier index change n4<0

Blue shift

123 / 136

Fano Gate

Fano interference → asymmetric lineshape → larger modulation

contrast

Yi Yu, et al, APL 105, 061117 (2014)

124 / 136

Fano GateFano interference → asymmetric lineshape → larger modulation

contrast

Yi Yu, et al, APL 105, 061117 (2014)

much faster response, error-free 10 Gbit/s modulation with low

pump energy[3]

3. Y. YU et al. Optics letters 40 (2015), pp. 2357–2360124 / 136

Fano LaserThe fano gate can be used as a dynamical mirror closing a

Fabry-Perot laser cavity

Mork, J., et al., PRL 113 163901,(2014)

cavity

=

mirror

gain

It can behave as a saturable absorber. Self-pulsing observed 125 / 136










• Small Lasers

• Integration




• Free Carriers




126 / 136

All-optical sampling

Optical Sampling OscilloscopeYOKOGAWA- AQ7750Wavelength range : 1530 to 1625nm Bandwidth : 700 GHz , Time resolution : 600 fsJitter : < 100 fs

• Fastest electronic oscilloscope limited to 80 GHz [2014]

• all-optical sampling has been demonstrated up to 1 THz!

• the technology need to be miniaturized

127 / 136

Processing Radar Signals

• key operation is to go move the signal to the base band

[down-conversion]

• the detection chain need to be simplifiedLO

ADCIF

IF

Filter S/H DSP

RFBande de base

Time

Sig

na

l (V

)

Sampling

instant

Sampling (Nyquist band)

Fréquence

DSP

LOIF

128 / 136

Processing Radar Signals

• key operation is to go move the signal to the base band

[down-conversion]

• the detection chain need to be simplified

ADCS/H DSP

Bande de baseRF

Brique te c hno . c ritique

Time

Sig

na

l (V

)

Sampling

instant

Sampling (Nyquist band)

Fréquence

DSP

LOIF

Fréquence

DSP

sub-sampling

LO

LO

• removing one conversion stage128 / 136

Importance of the exact timing

• sub-sampling: same rate, but signals are much faster

dV

dt(clock jitter)

Time

Sig

nal Sampling Point

Sampling (Nyquist band) sub-Sampling

Time

Sig

nal

• requires more accurate timing

129 / 136

Optical Clocks

T. K. Kim et al, Opt. Let . 2011

Ji�er < 0.1 fs

Fiber Mode Locked Lasers (MLL)

Doped-glass chip

H. Byun, Phot. Tech. Let . 2009

Typical ji�er: 100fs – 1ps

Electronics

A. M . Ali, Solid-State Circuits,

IEEE Journal, 2006

80 fJ reported recently

Fibre Laser

Compact Low-jitter (≈ 20fs) ML laser available.

130 / 136

All-photonic sampling

Photonic Assisted Sampling: use optical clock to control an

electronic gate

ADC

RF

Filter DSPS/H

Photonic assisted sampling

Simplified radar receiver architecture

clock

(Mode-Locked Laser)

131 / 136



electronic gate

• Other advantages of light: transport of the signal

• Bandwidth, immunity to EM disturbances, lightweight

ADC

RF

Filter DSPS/H

Photonic assisted sampling

Simplified radar receiver architecture

clock

(Mode-Locked Laser)

131 / 136



electronic gate

• Other advantages of light: transport of the signal

• Bandwidth, immunity to EM disturbances, lightweight

• Implication:

• All-Photonic Sampling: light to control light, which combines

the benefits above

• Still, this requires an All-Optical (nonlinear) gate.

ADC DSPS

All-optical sampling front-endclock

Full-photonic linkSignal on optical carrier

EDFA

(Mode-Locked Laser)

Photo

diode

131 / 136

All-photonic sub-sampling using an AOG

Time Domain

Frequency Domain

Signal

Clock

fs

fdif

n x f0,c

fdif

GATE

BP filter

BP filter

Clock

Signal

po

we

r

t

po

we

r

t

po

we

r

f

po

we

r

f

po

we

r

f

0

0

0

0

0

GATE

po

we

r

t

132 / 136

Wavelength conversion of optical data

Wavelength conversion

Silicon/III-V Hybrid:InP nonlinear resonatorSilicon photonic circuit

Bit error rate

Bazin 2014

linear absorptionSurface Quantum Wellτcar = 30 ps

133 / 136

AOG with analog signals: preliminary measurement

Clock: MLL at 2 GHz (Ts = 500 ps), signal frequency 20 GHz

Time (ps)

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

Time (ps)

-100 0 100 200 300

Response (

norm

.)

0

0.2

0.4

0.6

0.8

1

-60 -40 -20 0 20 400

0.5

1

20 ps

10 dB

Large modulation contrast, necessary for signal processing

134 / 136

AOG with analog signals: preliminary measurement

Clock: MLL at 2 GHz (Ts = 500 ps), signal frequency 20 GHz

Gate

open:

18

mV

Nois

e:

2.2

mV

RF ON (40 GHz)

RF OFF

14 ps

Gate

clo

sed:

2.8

mV

5 m

V

20 ps

9 m

V

Large modulation contrast, necessary for signal processing

134 / 136

Reconstructed signals

sub-sampling: work with a window in the RF spectrum

0 50 100 150

−1

0

1

Time (ns)

Sig

nal (V

)

[ 3f] −36.3

[2f]

−37.8

fin = 38.023 GHz

−0.5 0 0.5 10

500

1000

[y−y(t)]

counts

residuals (noise)

σ = 0.371

0 50 100 150−1

0

1

Time (ns)

Sig

nal (V

)

[ 2f] −30.6

[ 3f] −41.0

−0.6 −0.4 −0.2 0 0.2 0.4 0.60

500

1000

0 50 100 150

−0.5

0

0.5

1

Time (ns)

Sig

nal (V

) [ 2f] −20.2

[ 3f] −45.8

−0.4 −0.2 0 0.2 0.40

500

1000

0 50 100 150

−0.5

0

0.5

1

Time (ns)S

ignal (V

) [ 2f]

−16

[ 3f]

−33

−0.2 −0.1 0 0.1 0.20

500

1000

[y−y(t)]

counts

σ = 0.078

[y−y(t)]

counts

σ = 0.119

[y−y(t)]

counts

σ = 0.189

fin= 28.023 GHz

fin = 18.023 GHz fin = 8.023 GHz

135 / 136

Summary

• photonic integrated technologies are becoming very important

• trend towards the miniaturization of devices

• implications of reducing the size of the optical field

• novel lasers

• novel devices (optical memories)

• all-optical signal processing

136 / 136

Nonlinear Photonics for All-Optical Signal Processing

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