final!year!project2018!physics.ucc.ie/fyp2018/masoud_seifikar_fyp_presentation...mutually!delay[coupled!lasers!...
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Final Year Project 2018
The numerical inves9ga9on of the Lang Kobayashi equa9ons for coupled
semiconductor lasers
Masoud Seifikar,
Mo9va9on • Around 54% of the world popula4on has an internet connec4on today (was 40% in 2014).
• An adult in the US spends 10h 39min a day online.
2 www.internetlivestats.com
Mo9va9on
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Mo9va9on
• Data centres consume ~ 3% of the global electricity supply, accoun4ng for ~ 2% of total greenhouse gas emissions.
• Internet consumes ~ 10% of total electricity consump4on.
4 hLps://yearbook.enerdata.net
World power consump4on
Photonic Integrated Circuits • Photonic integrated circuits (PICs) are devices on which several components are integrated.
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• The main advantages of PICs:
o Smaller size, weight, lower power consump4on -‐ Lower CO2 emission
o Lower cost o Improved reliability o …
• We are interested in mutually Coupled lasers in a PIC.
What is Laser?
• Principles of Lasers o Spontaneous Absorp4on o Spontaneous Emission o S4mulated Emission o Popula4on Inversion
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Absorp9on
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Spontaneous Emission
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S9mulated Emission
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Popula9on Inversion
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Op4cal pumping
S9mulated emission
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LASER (Light Amplifica9on by S9mulated Emission of Radia9on)
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• Using PheT Laser simula4on, a laser is produced. thanks PhET, for the awesome simula4on tool.
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How a Laser works?
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The characteris9cs of laser
• The Important characteris4cs of laser are Monochroma4city, Coherence, Direc4onality and Sharp focus
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Coupled Lasers
Synchroniza4on of Mechanical Oscillators
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Synchroniza9on of Metronomes
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Pendulum Waves
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Mutually Delay-‐coupled Lasers Laser 1 Laser 2 &me delay, τ = d/c
• We are looking at the development of mutually coupled lasers for integra4on in a PIC.
• Interes4ng laser dynamics • It is of importance in the crea4on of advanced modula4on formats within a PIC.
• We study the dynamic of the system for finite small τ.
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Two mutually delay-‐coupled lasers
• The lasers are coherently coupled via their op4cal fields E1 and E2, where the 4me delay τ (= d/c), arises from the propaga4on 4me of the light from one laser to the other one.
• Yanchuk used the rate equa4on models to predict one colour symmetric states for very small delays [1].
• Erzgraber et. al. used DDE-‐BIFTOOL and studied the dependence of behaviour of this system, to coupling phase and detuning of two lasers [2].
• Clerkin and Amann studied this this system for zero delay 4me [3]. • We study the dynamic of two mutually coupled lasers for finite small
delays, to account for non-‐zero separa4ons of the lasers.
[1] Yanchuk et. al. Phys. Rev. E 69 056221 (2004) [2] Erzgraber et. al. SIAM J. Appl. Dyn. Sys. 5, 30 (2006) [3] Clerkin et. al. Phys. Rev. E 89 032919 (2014)
d
Laser 1 Laser 2
𝜏=0 𝜏≠0
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Rate Equa9on Model • Lang-‐Kobayashi Eqs, in nondimensional form:
Our main parameters: o N1,2 are normalized inversions o E1,2 are normalized complex slowly varying envelope of the op4cal fields.
o Coupling phase, Cp o Coupling rate 𝜅, frac4on of the photons coupled into the other laser. o Here we assume zero detuning Δ=0. o Time is measured in units of photon life4me, 𝜏p (~5ps) ! d= 𝜏c=1.5-‐3 mm
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𝑑𝐸1(𝑡)/𝑑𝑡 =(1+𝑖𝛼)𝑁1(𝑡)𝐸1(𝑡)+𝜅𝑒↑−𝑖𝐶↓𝑝 𝐸2(𝑡−𝜏)−𝑖Δ𝐸1(𝑡) 𝑑𝐸2(𝑡)/𝑑𝑡 =(1+𝑖𝛼)𝑁2(𝑡)𝐸2(𝑡)+𝜅𝑒↑−𝑖𝐶↓𝑝 𝐸1(𝑡−𝜏)+𝑖Δ𝐸2(𝑡) 𝑇𝑑𝑁1(𝑡)/𝑑𝑡 =𝑃−𝑁1(𝑡)−(1+2𝑁1(𝑡))|𝐸1(𝑡)|↑2 𝑇𝑑𝑁2(𝑡)/𝑑𝑡 =𝑃−𝑁2(𝑡)−(1+2𝑁2(𝑡))|𝐸2(𝑡)|↑2
Solve the DDE • Separate the real and imaginary parts of E1,2, and solve system of six DDEs for given values of κ, Cp and 𝜏.
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Ini4al condi4on: ℜ(E1(t=0))=0.4 ℜ(E2(t=0))=0 ℑ(E1(t=0))=-‐0.4 ℑ(E2(t=0))=0 N1(t=0)=0.05 N2(t=0)=0.05
𝜏 =0.5, κ=0.1, Cp=0.1π,
Cp =0.1𝝅
Cp =0.2𝝅
Cp =0.2𝝅
Cp =0.3𝝅
Cp =0.513𝝅
Symmetric 1-‐colour
Symmetric 1-‐colour
Sym. Broken 2-‐colour
Sym. Broken 2-‐colour
Symmetric 2-‐colour
Symmetric and Symmetric Broken 𝜏=0.5; κ=0.1
ℜ(E2(t = 0)) = −0.39, N2(t = 0) = −0.05
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time (ns) time (ns) frequency (GHz)
Fixed point
Periodic orbit
Final Year Project
• We want to inves4gate the effect of the material parameters like carrier life4me, linewidth enhancement factor and pumping parameters in the behaviour of the lasers, especially their frequency.
• If you are interested please contact me by mseifikar@cc.ie
• My office is located in 1.01C
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