Slow light in photonic crystal waveguides

Slow light in photonic crystal waveguides

Nikolay Primerov

Doctoral program in photonics “Photonic crystals” by Romuald Houdré

• Why do we need slow light?• What is slow light?• Possibilities to make a slow light• Slow light in photonic crystals waveguides• Conclusions

Outline

Nikolay Primerov


1. Nonlinearities2. Optical switching 3. Optical storage4. Delay lines5. Quantum optics

T.F. Krauss, J. Phys. D: Appl. Phys. 40 (2007) 2666-2670Z. Zhu et al., Science, 318 (2007) 748-750F. Morichetti et al., Opt. Express, 16 (2008) 8395-8405

Nikolay Primerov

Why do we need slow light?


What is a slow light?

Nikolay Primerov


=++++

( , ) ej k z tS z t A

Pulse signal

Nikolay Primerov



d d n z td d c

The peak of the pulse propagates at the Group Velocity.

1 0dnn z tc d

or 0 g

z tV

( , ) ej k z tS z t A

Pulse signal

Nikolay Primerov



gdnn nd

1

gg

dk cVdw n

Thus, in a material and/or structure with large first order dispersion coefficient, Vg can be drastically increased

Nikolay Primerov

Group index

Group velocityWhat is a slow light?


Possibilities to make a slow light

Stimulated Brillouin Scattering (SBS)Stimulated Raman Scattering (SRS)Electromagneticaly induced transparency (EIT)Coherent population oscillation (CPO)Coupled ring resonatorsPhotonic crystals and others

Nikolay Primerov

Doctoral program in photonics “Photonic crystals” by Romuald Houdré Nikolay Primerov

Periodically structured medium

Free space

Medium with constant n

k

ω

c= ω/k

c/n= ω/k

wVk

gdwVdk

k

ω

π/a

0gdwVdk

Band edge

Band gap

Slow light: Science and application / editors, J.B. Khurgin and R. Tucker, 388 p.


g

VS

V

2g

g g

d c cVdk n n a

Slow down factor Maximum bandwidth



1)BackscatteringStanding wave Slow mode optical mode is close to a resonance with the structure

2) Omnidirectional reflectionNo cut-off angle, mode at k≈0 slow modes of for k=0 standing wave

T. F. Krauss, J. Phys. D: Appl. Phys. 40 (2007) 2666-2670

The band edge is the most obvious place for the slow light


But there are some problems:

1) Dispersion curve near the gand edge is typically parabolic strong group velocity dispersion (GVD)

2) Band edge presents a cut off point propagation mode turns to evanescence mode

3) Fabrication tolerance

It’s not the best region for the slow light to operate

Dispersion engineering


J.Li, T.P. White, et al. Opt. Express, 16(9) (2008), 6227-6232


Section of constant group velocity over approximately 20% of Brillouin zone low GVD

Ng= 30, 50, 80


GVD handling


Enhancement of the linear interaction

Δφ=ΔkL=π

Optical switching devices (for example, Mach-Zehnder configuration)

Δk= Δnk0

We have to distinguish between nmat and neff

Slow light regime Δk1 > fast light regime Δk2

T. F. Krauss, J. Phys. D: Appl. Phys. 40 (2007), 2666-2670D. M Beggs, et al., Opt. Lett., 33 (2008), 147-149

0 matg

VkL k n L

V

Slow light regime yields a large Δk for a given Δnmat

Slow light coupler 5 um length with Δnmat = 4×10^-3. Conventinal coupler 200 um long


Problems to overcome1) Signal distortion by GVD2) Reflection losses due to modal mismatch between incident wave and guided wave3) Losses due to disordering in the structure4) Other loss sources5) Tunability

Solutions:

1. Chirping the waveguide properties, changing the waveguide width, changing the hole size and position of the photonic lattice close to the waveguide.

2-4. Many different effects involved. Need of transition region to build up to reduce the mode-matching problem Slow light operation away from the band-edge

5. ??

Conclusions


Conclusions


Main Advantages:- Relatively large bandwidth from GHz up to few THz- Room temperature operation- Availability to tune the wavelength, slowdown factor and bandwidth with the structural design

Main Disadvantages:- Tunability of the slowdown factor in given structure- Reflection and injection losses


Thank you for attention!

Slow light in photonic crystal waveguides

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