Paper Review IEEE Journal of Quantum Electronics, Feb 1985 Special - - PowerPoint PPT Presentation

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Paper Review

IEEE Journal of Quantum Electronics, Feb 1985

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Contents

 Semiconductor laser review  High speed semiconductor laser  Parasitic elements limitations  Intermodulation products  Intensity noise  Large signal effects  Conclusion

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Interaction between light and matters

+

• ℎ𝜉

<Photon interacting with an hydrogen atom> Three interaction processes are possible Absorption Spontaneous Emission Stimulated Emission

𝑆12 = 𝐶12 ∙ 𝑂1 ∙ 𝜍 𝑆𝑡𝑞 = 𝐶𝑡𝑞 ∙ 𝑂2 𝑆21 = 𝐶21 ∙ 𝑂2 ∙ 𝜍

𝜍 : photon density, 𝑂1,2: electron density at 𝐹1,2 𝐶12,21,𝑡𝑞: constants

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Interaction between light and matters

Absorption Spontaneous Emission Stimulated Emission

𝑆12 = 𝐶12 ∙ 𝑂1 ∙ 𝜍 𝑆𝑡𝑞 = 𝐶𝑡𝑞 ∙ 𝑂2 𝑆21 = 𝐶21 ∙ 𝑂2 ∙ 𝜍

𝜍 : photon density, 𝑂1,2: electron density at 𝐹1,2 𝐶12,21,𝑡𝑞: constants

𝑆12 = 𝑆𝑡𝑞 + 𝑆21 : Equilibrium condition

𝑂2 𝑂1 = exp − 𝐹2−𝐹1 𝑙𝑈

: Statistical mechanics 𝜍 ℎ𝜉 =

8𝜌ℎ𝜉3 𝑑3{exp ℎ𝜉

𝑙𝑈 −1} : Black-body radiation

𝐶21 𝐶12 = 1, 𝐶𝑡𝑞 𝐶12 = 8𝜌ℎ𝜉3 𝑑3

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Optical amplifier

Amplifier

𝑄𝑗𝑜 𝑄𝑝𝑣𝑢 = 𝐻 ∙ 𝑄𝑗𝑜

Stimulated emission should be dominant Pumping 𝑂2 > 𝑂1(Population Inversion)

Special Topics in Optical Engineering II (15/1) Minkyu Kim

LASER

LASER : Light Amplification by Stimulated Emission of Radiation LASER = Optical amplifier + Mirrors

• Use initial photon produced by spontaneous emission
• Recycle photons produced by stimulated emission
• Use mirrors for recycling photons
• Condition for sustaining photons in laser

⑴𝑓𝑕𝑀 =

1 𝑆 (Gain > mirror loss)

⑵𝑓−𝑘2𝑜𝑙0𝑀 = 1 (No loss after one round trip)

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Conditions for lasing

Lasing conditions : ⑴𝑓𝑕𝑀 =

1 𝑆  𝑕𝑢ℎ = 1 L ln 1 𝑆

⑵𝑓−𝑘2𝑜𝑙0𝑀 = 1𝜇

𝑜 = 2𝑀 𝑛 (𝑛 = 1,2,3, … )

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Semiconductor laser

Absorption Spontaneous Emission Stimulated Emission

𝑆12 ℎ𝜉 = 𝐶12 ∙ 𝑂1(𝐹1) ∙ 𝑄2(𝐹2) ∙ 𝜍(ℎ𝜉) 𝑆𝑡𝑞 ℎ𝜉 = 𝐶𝑡𝑞 ∙ 𝑂2(𝐹2) ∙ 𝑄

1(𝐹1)

𝑆21 ℎ𝜉 = 𝐶21 ∙ 𝑂2(𝐹2) ∙ 𝑄

1(𝐹1) ∙ 𝜍(ℎ𝜉)

For population inversion,

𝑂2∙𝑄1 𝑂1∙𝑄2 > 1 Electron & hole should be injected

(Forward bias in PN junction)

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Semiconductor laser structure

Special Topics in Optical Engineering II (15/1) Minkyu Kim

High speed semiconductor laser

⑴

𝑒𝑂 𝑒𝑢 = 𝐾 𝑓𝑒 − 𝑂 𝜐𝑡 − 𝐵 𝑂 − 𝑂𝑝𝑛 𝑄

⑵

𝑒𝑄 𝑒𝑢 = 𝐵 𝑂 − 𝑂𝑝𝑛 𝑄 − 𝑄 𝜐𝑞 + 𝛾 𝑂 𝜐𝑡

𝑂: carrier density 𝑂𝑝𝑛: carrier density for transparency 𝑄: photon density 𝐾: pump current density 𝑒: thickness of active layer 𝜐𝑡: spontaneous recombination lifetime of carriers 𝜐𝑞: photon lifetime 𝐵: optical gain coefficient 𝛾: fraction of spontaneous emission entering to lasing mode

Rate equations

Small signal & linearization 𝑔

𝑈 𝑠𝑓𝑚𝑏𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑡𝑑𝑗𝑚𝑚𝑏𝑢𝑗𝑝𝑜 𝑔𝑠𝑓𝑟𝑣𝑓𝑜𝑑𝑧 = 1

2𝜌 𝐵𝑞0 𝜐𝑞

𝐁 ↑, 𝐪𝟏 ↑, 𝛖𝐪 ↓  high speed semiconductor laser

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Parasitic elements limitation

Substrate

n doped confining layer p doped confining layer active layer

• xide insulator

𝐽 𝐽

Circuit modeling Semiconductor laser 𝜃 = 𝑑𝑣𝑠𝑠𝑓𝑜𝑢 𝑔𝑚𝑝𝑥𝑗𝑜𝑕 𝑗𝑜𝑢𝑝 𝑢ℎ𝑓 𝑗𝑜𝑢𝑠𝑗𝑜𝑡𝑗𝑑 𝑒𝑗𝑝𝑒𝑓 𝑤𝑝𝑚𝑢𝑏𝑕𝑓 𝑝𝑔 𝑢ℎ𝑓 𝑡𝑗𝑕𝑜𝑏𝑚 𝑡𝑝𝑣𝑠𝑑𝑓 = 1 𝑡2 𝜕0

2 +

𝑡 𝜕0𝑅 + 1 𝜕0 = 50 + 𝑆 𝑀𝑆𝐷 , 𝑅 = 𝑀𝑆𝐷(50 + 𝑆) 𝑀 + 50𝑆𝐷 Second-order low pass filter type

Intrinsic diode Contact resistance Parasitic capacitance Bonding wire

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Parasitic elements limitation

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Parasitic elements limitation

Circuit modeling 𝑎 = 𝑎0

1+𝑓−2𝑙𝑋 1−𝑓−2𝑙𝑋, W : width of top contact

𝑎0 = 𝑆𝑒𝑗𝑡𝑢 𝑘𝜕𝐷𝑒𝑗𝑡𝑢 , 𝑙 = 𝑘𝜕𝑆𝑒𝑗𝑡𝑢𝐷𝑒𝑗𝑡𝑢 Higher frequency  higher propagation constant(k) electric field cannot penetrate far beyond laser junction

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Intermodulation products

Third order intermodulation can be a problem in multichannel frequency division transmission Third order intermodulation

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Intensity noise

𝑆𝑓𝑚𝑏𝑢𝑗𝑤𝑓 𝐽𝑜𝑢𝑓𝑜𝑡𝑗𝑢𝑧 𝑂𝑝𝑗𝑡𝑓 𝑆𝐽𝑂 = < Δ𝑄 >2 < 𝑄0 >2

𝑄0: average light output power < Δ𝑄 >2: mean square intensity fluctuation spectral density of the light output

With rate equations, 𝑆𝐽𝑂 ~

1 𝑞0 𝜕3

𝜕2 𝜕𝑆 2−1 2

+ 𝜕2

𝜕𝑆 4 𝜐𝑆 2

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Large signal effects

Non-linearity problem for large signal

<Effects of increasing optical modulation depth>

Optical modulation depth for high speed below ~70 percent

Special Topics in Optical Engineering II (15/1) Minkyu Kim

Conclusion

𝑔

𝑈 = 1

2𝜌 𝐵𝑞0 𝜐𝑞

A ↑, p0 ↑, τp ↓  high speed semiconductor laser

• Parasitic elements limitations
• Intermodulation products
• Intensity noise
• Large signal effects

⑴

𝑒𝑂 𝑒𝑢 = 𝐾 𝑓𝑒 − 𝑂 𝜐𝑡 − 𝐵 𝑂 − 𝑂𝑝𝑛 𝑄

⑵

𝑒𝑄 𝑒𝑢 = 𝐵 𝑂 − 𝑂𝑝𝑛 𝑄 − 𝑄 𝜐𝑞 + 𝛾 𝑂 𝜐𝑡

𝑂: carrier density 𝑂𝑝𝑛: carrier density for transparency 𝑄: photon density 𝐾: pump current density 𝑒: thickness of active layer 𝜐𝑡: spontaneous recombination lifetime of carriers 𝜐𝑞: photon lifetime 𝐵: optical gain coefficient 𝛾: fraction of spontaneous emission entering to lasing mode

Rate equations