tf krauss romme 2014 no.1/45 photonic crystal cavities...tf krauss romme 2014 no.17/45 t i→f 2π h...

TF Krauss Romme 2014 No.1/45

Thomas F Krauss Department of Physics, University of York

[email protected]

Photonic Crystal Cavities

TF Krauss Romme 2014 No.4/45 Photonic Crystal cavities

What is so special about photonic crystal cavities ?

Nonlinearity, Bistability Notomi et al., Opt. Express 13, 2678 (2005)

Trapping,Optomechanics Houdre et al., PRL 110, 123601 (2013)

Strong coupling, QIP Vuckovic et al., Opt Express 17, 18652 (2009)


Source: Wikipedia "Optical coatings"

The reflectivity of a metal mirror

R ≈ 95-98%


π/a!

ω!

k!

Photonic crystal bandstructure!

0! 0.05! 0.1! 0.15!0.2! 0.25! 0.3! 0.35! 0.4! 0.45! 0.5!0!0.05!0.1!0.15!0.2!0.25!0.3!0.35!

k (multiples of 2π/a)!

frequency !(multiples of c/a) [a/λ]!

W1 waveguide!

€

vg =dωdk

Operating point

n=1

vφ =c0nφ=ωk

Cross-section


How can I make a cavity that confines light in all three directions if I only have a bandgap available in two ?

Answer: Fourier space engineering. Light line control.

+ ?

Photonic Crystal cavities

TF Krauss Romme 2014 No.8/45 Light line in 2D

In 1 dimension, the light line corresponds to the line of total internal reflection. Modes with neff>1 lie to the right, modes with neff<1 lie to the left and can radiate out.

k

ω$

kx ky

ω$ In two dimensions, one can think of this line as a cone (“light cone”). For a given frequency ω0 and in an isotropic medium, this cone becomes a circle.

kx

ky

ω0$ €

ω =cneff

k


High Q (low loss) comes from lack of radiation within light cone. The cavity mode is designed such that it carries very little light in the light cone.

High Q cavity

Real space

Fourier space

FT explanation

TF Krauss Romme 2014 No.10/45 Fourier transform explanation

FT => x k

a) Harmonic oscillation -> delta function

FT => k

€

2π nmodeλ

€

2π ncladdingλ

k

€

2π nmodeλ

€

2π ncladdingλ

FT =>

If the mode is confined by a Gaussian envelope, its Fourier transform has minimum amplitude inside the light cone -> so very little light is lost.

b) Top hat confinement -> convolution with sinc

c) Gaussian confinement -> reduced extent in k-space


S. Noda et al., “High-Q photonic nanocavity in a two-dimensional photonic crystal” Nature 425, p. 944 (2003).

The recipe for high Q cavities: Gaussian mode profile. Approximated here by adjusting mirror boundaries

High Q cavity

How does the Q-factor relate to reflectivity ?

TF Krauss Romme 2014 No.12/45 Q-factor vs Reflectivity

Q = 2π Energy storedEnergy lost per cycle

Q = 2π Ucav

2(1− R)Ucav

Q =π1− R

Q =mπ1− R

Assume R->1,m=1 (single mode) Assume only mirror loss Loss per single pass=1-R

for m>1 (multimode)

F = Qm=

π1− R

“Finesse”

What is the reflectivity for our cavity of Q=45,000 ?

m=3

TF Krauss Romme 2014 No.13/45 The heterostructure cavity

S. Noda et al., “Ultra-high-Q photonic double-heterostructure nanocavity”, Nature Materials 4, 207-210 (2005) Time dependence


€

Q = 2π Energy storedEnergy lost /cycle

Q = 2π Energy stored

Energy lost ×TCycleΔt

The cavity Q (“Quality factor”) describes how well the cavity can store energy. High Q cavities can store a lot of light in a small space, hence increase nonlinearities; this also means that the light is stored for a long time.

Q = 2π Ucav

−dUcav

dt×TCycle

⇔−dUcav

dt=

2πQ TCycle

UcavExpress the same as a differential equation with U as the energy, and -dU/dt as the energy lost,

Ucav (t) =Ucav,0 exp−tτ

τ =Q TCycle2π

This yields the following time-dependence,

Example:, λ=1.5 µm, Q=1.2M, τ= ?

Storing light in a cavity

TF Krauss Romme 2014 No.15/45 Ultrahigh high Q cavities

€

Q =λΔλ

=1555nm

1.3×10−3nm=1.2M

€

τ =Q TCycle2π

=1.2 ×106 × 5 ×10−15

2π≈1ns

M. Notomi et al., “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity” Nature Photonics 1, pp. 49-52 (2007)

TF Krauss Romme 2014 No.16/45 Extreme Q factor cavities


Ti→ f =2πh

f H i2ρ f

FP =34π 2

λn!

"#

$

%&3QV

τ rad,Purcell =τ radFP

The Purcell effect is based on Fermi’s Golden Rule

The strength of the transition from an initial state to a final state is the product of the matrix element < f | H | i > and the density of states in the final state ρf.

Translated into the cavity situation, a high Purcell effect can be achieved in a cavity with a high Q/V factor.

The radiative lifetime in a cavity is accordingly reduced by the Purcell factor.

Purcell effect


λ$

Δλ$

€

Q =λΔλ

emitter

Assumptions: Cavity linewidth dominates. Emitter smaller than cavity mode Cavity and emitter are spectrally aligned.

In very simple terms, the Q/V argument is one of spectral and spatial overlap.

quantum dot

FP =34π 2

λn!

"#

$

%&3QV

Purcell effect


“….with an estimated Purcell enhancement of 2.4 at room temperature, and 11 to 17 at cryogenic temperatures.”

Purcell effect in Er-doped overlayer

Luca Dal Negro et al., “Linewidth narrowing and Purcell enhancement in photonic crystal cavities on an Er-doped silicon nitride platform” OpEx 18, 2601 (2010)


2) A quantum dot is placed inside a photonic crystal cavity. Why do you cool it down ?

3) An organic light emitter is placed inside a high Q cavity. Do you observe Purcell enhancement ?

Review questions

FP =34π 2

λn!

"#

$

%&3QV

4) The radiative lifetime of an emitter placed in a cavity is reduced by the Purcell effect. Does that mean the radiative efficiency improves by the same factor ?

1) Why are photonic crystal cavities better for Purcell enhancement than microring resonators ?


M Galli et al. Opt. Express 18, 26613 (2010).

Nonlinear effects (here: Second and third harmonic generation) observed due to high intensity buildup (Icav~ Q) and far-field engineering.

Harmonic Generation

Intensity enhancement


Icav (1-R) Icav

R Icav

R I0

I0

R(1-R) Icav

Intensity enhancement: The reflection at the first mirror RI0 and the transmission of the cavity light at the same mirror cancel out on resonance: No light is reflected back. The magnitude of the two signals has to be equal for complete destructive interference.

RI0 = (1− R)Icav ⇔ Icav =1

1− RI0

I0 Input intensity. Icav Intensity circulating in the cavity. R1=R2=R, R->1

Intensity enhancement

TF Krauss Romme 2014 No.23/45 THG and SHG in Si cavities

M Galli et al. Opt. Express 18, 26613 (2010).

TF Krauss Romme 2014 No.24/45 Silicon light source


SOITEC website

Hydrogen in SOI

Hydrogen implantation


Silicon Indirect band-gap gives low radiative recombination

Energy

K

Si

Si

Si Si

Si

Si

Si Si e-

h+

Defect emission mechanism


Hydrogen implantation creates defects that overcome Δk.

Energy

K

Si

Si

Si Si

Si

Si

Si X

e-

h+

Homewood et al., �An efficient room-temperature silicon-based light-emitting diode��Nature 410, 192-194 (2001)



TEM: Stefania Boninelli, Catania

Hydrogen incorporation creates line defects (“platelets”) that give rise to a compressive strain field. Compressive strain field localises carriers.

Weman & Monemar, PRB 42, 3109 (1990)



So now we have a lightsource…. What can photonic crystals do to help ?

Noda et al. Nature 2003

TF Krauss Romme 2014 No.30/45 Cavity enhanced light emission

R. Lo Savio et al., Appl. Phys. Lett. 2011

x300

300-fold enhancement observed x 12 (Purcell) x 25 (Extraction)


H2 Plasma (RIE)

Hydrogen Plasma

Bulk defects (SOITEC process)

Surface defects (Plasma process)

TF Krauss Romme 2014 No.32/45 Photonic Crystal after H2 Plasma

TEM: S. Boninelli, P. Cardile, Catania

TF Krauss Romme 2014 No.33/45 PL for cavity + H2 Plasma

Hydrogen plasma treatment considerably increases defect PL emission. Cavity enhancement again adds a factor 300.

A Shakoor et al, Laser&Photonics Reviews, Jan 2013

TF Krauss Romme 2014 No.34/45 Electroluminescent device

TF Krauss Romme 2014 No.35/45 Electroluminescent operation


TF Krauss Romme 2014 No.36/45 Electroluminescent operation



Stimulated emission from PbS-quantum dots in glass matrixF. Yue, J. W. Tomm, D. Kruschke, and P. Glas

LASER & PHOTONICSREVIEWS

www.lpr-journal.org Vol. 7 No. 1 January 2013

ISSN 1863-8880 Laser Photonics Rev., Vol. 7, No. 1 (January), 1–140 (2013)Now open fo

r Lette

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Original A

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Laser & Photonics Review

sV

olume 7

2013 N

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All-silicon photonic crystal nanocavity LED

A. Shakoor et al.

LASER & PHOTONICSREVIEWS

www.lpr-journal.org Vol. 7 No. 1 January 2013

ISSN 1863-8880 Laser Photonics Rev., Vol. 7, No. 1 (January), 1–140 (2013)Now open fo

r Lette

rs and

Original A

rticles

F. Priolo, T. Gregorkiewicz, M. Galli and T.F. Krauss , “Silicon Nanostructures for Photonics and Photovoltaics” Nature Nanotechnology January 2014

Cavity enhanced light emission


IBM website

Optical Interconnects

TF Krauss Romme 2014 No.40/45 Photonic crystal modulators

K. Debnath et al., Opt Exp 20, 27420 (2012)


2"cascaded"PhC"p"i"n"junc.on"modulators"Modulate"each"channel"individually"Q~10,000"∆n~4e?4"

0V 2v

Cavity 1 Cavity 2

Cavity 1 Cavity 2

Photonic crystal modulators

TF Krauss Romme 2014 No.42/45 WDM Transmitter architecture

Very small Very low power consumption (fJ/bit)


Cav1 Cav2 Cav3 Cav4 Cav5

Multichannel operation


!500 Mbit/s, 0.6 fJ/bit

Comb laser source

Multichannel modulation

K. Debnath et al., Opt Exp 20, 27420 (2012)


Novel interconnect architecture – low power modulation

Defect-based light emission

Conclusion Photonic crystals offer enhanced light-matter interaction for a number of applications; their unique advantage is the high Finesse and resulting Purcell-factor.

Enhanced harmonic generation – mW pump !!

FP =34π 2

λn!

"#

$

%&3QV

Finesse = π1− R


2) A quantum dot is placed inside a high Q photonic crystal cavity. Why do you cool it down ? At room temperature, the qdot emission is thermally broadened (kT≈25meV), which gives an equivalent Q-value for the emitter below 100; Since the Purcell factor refers to the larger of the two linewidths (emitter or cavity), using a high Q cavity on such a relatively broad emitter is pointless.

3) An organic light emitter is placed inside a high Q cavity. Do you observe Purcell enhancement ? No. Organic light emitters typically have broadband transitions. The argument is similar as in 2). Some people have referred to wavelength-selective Purcell enhancement in this case, which is true, but since the cavity suppresses the emission off-resonance, the overall enhancement is very low.

Review questions - answers

4) The radiative lifetime of an emitter placed in a cavity is reduced by the Purcell effect. Does that mean the radiative efficiency improves by the same factor ? Not necessarily. The radiative efficiency is given by

1) Why are photonic crystal cavities better for Purcell enhancement than microring resonators ? Microrings may achieve the same Q-factor, but photonic crystal cavities achieve a much smaller volume, which leads to the higher density of states.

ηrad =τ non−rad

τ rad +τ non−radThe radiative efficiency therefore depends on the balance between radiative and non-radiative lifetimes τrad >> τnon-rad: The emitter is inefficient, but Purcell enhancement has a large impact. τrad << τnon-rad: The emitter is very efficient already, and Purcell enhancement makes little difference.

tf krauss romme 2014 no.1/45 photonic crystal cavities...tf krauss romme 2014 no.17/45 t i→f 2π h...

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