RamanMediated Pulse Amplification in Silicon Wires

1
Raman-Mediated Pulse Amplification in Silicon
Wires
Fiber on a chip
2
Outline

• Introduction
• Characteristics in SOI nanowire waveguide
• Waveguide structure and supported propagation
  mode
• Dispersion effect in silicon nanowire waveguide
• Third order nonlinearity in silicon
• Theoretical modeling of Raman amplification in
  silicon
• Coupled mode equations that models stimulated
  Raman scattering in nanowire
• Numerical simulation results
• Conclusions

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Raman Emission in Si Nanowires(collaboration
with Yuri Vlasov and Sharee McNab, IBM)

• Silicon exhibits Raman effect
• nR 15.6 THz Dn105 GHz
• Si/SOI advantages for Raman emission
• SRS-gain coefficient of silicon 104? larger than
  silica
• High-index-contrast/confinement ? high intensity

Smaller Raman amplifier in SOI waveguides!
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Nanowire waveguides
Nanowire waveguide support E11x mode.
x-component dominant. Most energy (90)
confined in waveguide
The input facet is in the (110) surface of
silicon. Red arrow points to 100 direction.
Waveguide w0.45µm, h0.22µm.

• Properties of the nanowire waveguide
• Ultrasmall waveguide cross-section (0.1 µm2),
  tight optical confinement
• High power density, enhanced nonlinearity

with Y. Vlasov, S. McNab, IBM
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Dispersion can be engineered in nanowire
waveguides!

• Waveguide dispersion dominates material
  dispersion.
• First-order dispersion determines
  pulse-interaction length (walk-off)
• Second-order material dispersion positive in
  C-band, while can be either positive or negative
  for nanowires. Dispersion-free nanowire can be
  realized for specific ?.

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Third order nonlinear processes in silicon

• Electronic
• Raman

Parametric processes (SPM, XPM)
real
?e(3)
imaginary
4th rank tensor
TPA
Energy transfer between pump and Stokes pulse
?R(3)
4th rank tensor
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Free-carrier (FC) effects in Silicon

• Carrier generation by two-photon absorption
• Free-carrier-induced optical properties (Drude
  Model)

• Additional loss mechanism
• Four processes possible but absorption of two
  pump photons dominates.
• Is described by imaginary part of ?(3)

• Free-carrier absorption (FCA) through interaction
  between FC and incoming field
• Dielectric constant changes because of FC phase
  shift

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Modeling SRS in SOI nanowire

• Start with coupled Maxwells equations
• Perturbations SRS, Kerr effect, TPA, and
  dielectric-constant change.
• Linear loss and free-carrier generation included
• Response time of different interactions
• 10(s)fs for electronic and 10ps for Raman

• Additional assumptions
• Slowly varying envelope for all fields
• Keep dispersion term to second order
• Include only third-order nonlinearity.
  (second-order nonlinearity vanishes due to
  inversion symmetry)

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Normalized Coupled Mode Equations for long pulse
(gt10ps)
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Noise-seeded Raman generation in SOI nanowire
waveguide (no loss)
Time domain
Frequency domain
Pp 0.1mW Ps10-8W L5LR1.92cm T0 30ps ain
0
80

• Verify the generation of Raman signal from noise
• When Raman signal is strong, its interaction
  with the pump causes the temporal profile
  modulation for the pump pulse

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Noise-seeded Raman generation in Silicon nanowire
(with loss) build-up in laser
Time domain
Frequency domain
Pp 0.1mW Ps10-8W L5LR53.83mm T0
30ps ain 3.5dB/cm
15

• Pump attenuation due to loss, amplification is
  smaller for signal
• Signal is not strong enough to significantly
  change pump profile

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Raman amplification vs. pump power in nanowire
waveguide
Ps10-8W L2.0cm T0 30ps
0.5dB/cm
0dB/cm
3.5dB/cm

• Threshold increases with the intrinsic loss
• Amplification saturates at high pump power

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Free Carrier Density for the previous two cases

• FCD change in time is determined by pump
• Strong Raman signal contributes to the free
  carrier generation
• With loss, the FCD decreases along the waveguide
• At these power levels ?n lt 10-9, ?a lt 10-5,
  FC effects not important

Nanowires have short recom times!!
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Raman interaction of large signal and long pulse
(30ps) in SOI nanowire Raman Amplifier
Time domain
Frequency domain
Pp 0.1mW Ps0.05mW L5LR1.92cm T0 30ps ain
3.5dB/cm

• Pump depletes fast due to energy transfer to the
  signal and loss
• Signal amplification and loss balanced to define
  a optimum amplification length

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Raman interaction of large signal and short pulse
(2ps) in SOI nanowire Raman Amplifier
Time domain
Frequency domain
Pp 0.1mW Ps0.05mW L16LR 6.13cm Lw4.76cm T
0 2ps ain 0 dB/cm

• Walk-off length is comparable to waveguide
  length, significant asymmetric depletion and
  pulse reshaping for the pump
• Energy transferring mostly happens in the first
  few Raman lengths

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Conclusions

• Rigorous coupled-mode analysis of SRS in Silicon
  nanowire waveguide Raman signal generation and
  amplification pulse shaping
• Waveguide dispersion dominates material
  dispersion significant dispersion engineering
  possible!
• TPA and FCA effects are not prominent in the
  silicon nanowire waveguide
• Raman-mediated pulse interaction show different
  dynamic behavior for long and short pulses