TF Krauss Romme 2014 No.1/45 Photonic Crystal Cavities...TF Krauss Romme 2014 No.17/45 T i→f 2π h...
Transcript of 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
Photonic Crystal Cavities
TF Krauss Romme 2014 No.2/45
TF Krauss Romme 2014 No.3/45
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)
TF Krauss Romme 2014 No.5/45
Source: Wikipedia "Optical coatings"
The reflectivity of a metal mirror
R ≈ 95-98%
TF Krauss Romme 2014 No.6/45
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
TF Krauss Romme 2014 No.7/45
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
TF Krauss Romme 2014 No.9/45
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
TF Krauss Romme 2014 No.11/45
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
TF Krauss Romme 2014 No.14/45
€
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
TF Krauss Romme 2014 No.17/45
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
TF Krauss Romme 2014 No.18/45
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
TF Krauss Romme 2014 No.19/45
“….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)
TF Krauss Romme 2014 No.20/45
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 ?
TF Krauss Romme 2014 No.21/45
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
TF Krauss Romme 2014 No.22/45
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
TF Krauss Romme 2014 No.25/45
SOITEC website
Hydrogen in SOI
Hydrogen implantation
TF Krauss Romme 2014 No.26/45
Silicon Indirect band-gap gives low radiative recombination
Energy
K
Si
Si
Si Si
Si
Si
Si Si e-
h+
Defect emission mechanism
TF Krauss Romme 2014 No.27/45
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)
Defect emission mechanism
TF Krauss Romme 2014 No.28/45
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)
Defect emission mechanism
TF Krauss Romme 2014 No.29/45
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)
TF Krauss Romme 2014 No.31/45
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
A Shakoor et al, Laser&Photonics Reviews, Jan 2013
TF Krauss Romme 2014 No.36/45 Electroluminescent operation
A Shakoor et al, Laser&Photonics Reviews, Jan 2013
TF Krauss Romme 2014 No.37/45
TF Krauss Romme 2014 No.38/45
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
rs and
Original A
rticles
Laser & Photonics Review
sV
olume 7
2013 N
umber 1
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
TF Krauss Romme 2014 No.39/45
IBM website
Optical Interconnects
TF Krauss Romme 2014 No.40/45 Photonic crystal modulators
K. Debnath et al., Opt Exp 20, 27420 (2012)
TF Krauss Romme 2014 No.41/45
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)
TF Krauss Romme 2014 No.43/45
Cav1 Cav2 Cav3 Cav4 Cav5
Multichannel operation
TF Krauss Romme 2014 No.44/45
!500 Mbit/s, 0.6 fJ/bit
Comb laser source
Multichannel modulation
K. Debnath et al., Opt Exp 20, 27420 (2012)
TF Krauss Romme 2014 No.45/45
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
TF Krauss Romme 2014 No.46/45
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.