Chapter 2. Optical Fibers

Chapter 2. Optical Fibers • Geometrical Optics & Wave Optics in Fiber • Loss • Dispersion • Nonlinearity

2.1 Geometrical Optics & Wave Optics in Fiber 2.1.1 Geometrical Optics suited for a >> λ • Multimode Step-Index Optical Fiber weak-waveguided fiber

2.1.1 Geometrical Optics

2.1.1 Geometrical Optics • Multimode Graded-Index Optical Fiber

2.1.1 Geometrical Optics

2.1.2 Wave Optics suited for a ~λ, wave theory

2.1.2 Wave Optics 2. Basic Concepts • Normalize Frequency • Mode Index n1 n1 > n2 n2 n2

2.1.2 Wave Optics • Birefringence 双折射 HE11 → two orthogonally polarized fiber modes x, y Uniform: Degeneracy! Nonuniform: y x linear → elliptical → linear 线偏 → 椭圆 → 线偏 modal birefringence beat length

2.1.2 Wave Optics

2.1.2 Wave Optics PMF: Polarization —Maintaining Fiber Small random birefringence fluctuations do not affect the light polarization significantly Spot Size w: field radius 1.2<V<2.4 Confinement Factor V=2, Γ≈75% V=1, Γ=20% 2<V<2.4

2.2 Fiber Loss 2.2.1 Attenuation Coefficient Pin Pout integrating

2.2.2 Loss Mechanism 1. Absorption (light energy → heat energy, 能量转移) • Intrinsic absorption • Impurity absorption Infrared (λ>7μm): vibrational resonances ultraviolet (λ< 0.4μm): electronic resonances 0.8~1.6 μm : < 0.1dB/km 400nm Transitional metal (Fe, Cu, Co, Ni):

2.2.2 Loss Mechanism 2. Scattering (方向偏折，能量不转移) Rayleigh Scattering → Intrinsic, on a scale smaller than λ Mie scattering → Waveguide Imperfection, on a scale larger than λ 3. Bending (模式泄漏，能量不转换) Macro－bending Installing Micro－bending Cabling

课堂作业 • 某光纤通信线路长80km，使用的光纤芯层折射率为1.45，相对折射率差为0.3％，截止波长为1m，光纤损耗只于瑞利散射有关。工作在1310nm时，输入功率为1mW，接收到功率为－28.5dBm。请计算：（1）该光纤在1550nm处的模场半径为多少？（2）光纤在1550nm处的损耗系数为多少dB/km? • 如果模拟信号的带宽为3.1kHz，信噪比大于30dB，则转化数字信号后要求传输速率至少为：（） A、31kb/s； B、31Mb/s； C、93kb/s； D、91Mb/s。 • 请简要描述固定电话使用者是如何通过点对点光纤通信系统实现通话的？

Bit 2 Bit 1 Bit 2 Bit 1 Bit 2 Bit 1 2.3 Dispersion in SMF SMF Inter-symbol interference !!!

2.3 Dispersion in SMF • Chromatic Dispersion (CD) • Group Velocity Dispersion (GVD) • Intra-modal Dispersion • High-order Dispersion • Polarization Mode Dispersion (PMD)

2.3.1 Group Velocity Dispersion 1. Dispersion parameter L T= L /Vg

2.3.1 Group Velocity Dispersion D: Dispersion Parameter, ps/(nm·km) 2. D ~ λ

2.3.1 Group Velocity Dispersion n2g: the group index of the cladding material

2.3.2 Material Dispersion Sellmeier equation:

2.3.3 Waveguide Dispersion

①: ② : 2.3.3 Dispersion Compensation ① SMF ② DCF D=16ps/(nm ·km) L1=50km D’=-100ps/(nm ·km) L2=?

Dispersion Shifted Fiber Refractive Index Profile of Optical Fiber

l l long short ChirpedBragg grating • • • Dispersion Compensation G.652: Positive Dispersion@1550nm

2.3.4 High－Order Dispersion Really?

Ey nx ny Ex Pulse As It Enters the Fiber Spreaded Pulse As It Leaves the Fiber 2.3.5 PMD

statistic modal birefringence

2.3.5 PMD A limiting factor for high bit rates lightwave systems

2.4 Dispersion－Introduced Limitations Optical pulse: T0: half-width at 1/e intensity point C: frequency chirp

2.4 Dispersion－Introduced Limitations When the source spectrum is Gaussian with the RMS spectral width σw : dispersion-introduced broadening of Gaussian input pulses L: fiber length σ0: RMS width of the input Gaussian pulse

2.4 Dispersion－Introduced Limitations 1. Optical Sources with a Large Spectral Width • non-zero-dispersion wavelength

2.4 Dispersion－Introduced Limitations • zero-dispersion wavelength 2. Optical Sources with a Small Spectral Width • non-zero-dispersion wavelength

2.4 Dispersion－Introduced Limitations • zero-dispersion wavelength

2.5 Nonlinearities in Optical Fiber 2.5.1 Stimulated light scattering • Rayleigh Scattering － not to generate new frequency • Raman Scattering － photon → stokes photon + optical phonon both directions, frequency shift is large 能量大，频移大，单个原子振动 • Brillouin Scattering － photon → stokes photon + acoustic phonon backward directions, frequency shift is small 能量小，频移小，多原子振动

2.5.1 Stimulated light scattering 1. SRS SRS 影响小

Figure 2.18: (a) Raman gain spectrum of fused silica at λp = 1μm and (b) energy levels participating in the SRS process.

2.5.1 Stimulated light scattering 2. SBS Note: frequency shift < 10GHz, channel spacing ~ 100GHz, not to generate crosstalk, but the loss of signal power

Figure 2.17: Brillouin-gain spectra measured using a 1.525-μm pump for three fibers with different germanium doping: (a) silica-core fiber; (b) depressed-cladding fiber; (c) dispersion-shifted fiber. Vertical scale is arbitrary.

2.5.2 Phase Modulation Power dependence of refractive index 1. SPM • nonlinear refraction • propagation constant

2.5.2 Phase Modulation 1. SPM • nonlinear phase shift

2.5.2 Phase Modulation 2. XPM assuming equal channel power SPM → distortion of optical pulse ? How to solve XPM → intensity noise Solution: Corning: Large Effective Area Fiber (LEAF)

2.5.3 Four-Wave Mixing Also originates from the three-order nonlinear susceptibility Easily to realize phase-matching at zero-dispersion wavelength ! DWDM: large effective area non-zero dispersion-shifted fiber YOFC: LAPOSH

2.5.4 Evolvement of Fiber • 1. G.651 MMF 2. G.652 SMF 3. G.653 DSF 4. G.655 NZDSF 5. LEAF LAPOSH 6. Dry fiber, All-wave fiber 7. DCF: D=－100ps/(nm·km), RDCF: SMF, D’=16ps/(nm·km) reverse • C band: 1530 ~ 1570 nm S band: 1490 ~ 1530 nm L band: 1570 ~ 1610 nm O band & E band: 1260 ~ 1490 nm Problems: 2.5, 2.8, 2.11, 2.13, 2.16, 2.19

Fiber evolution G.651 G.652 Dry fiber DCF Module G.653 DCF RDCF G.654 G.655 LEAF G.656 C+L+S fiber

Connector • Cable Optical fibers Tube Strain relief(e.g., Kevlar) Inner jacket Sheath Outer jacket

Chapter 2. Optical Fibers