Comprehensive Notes on Photonic Integrated Circuits (PIC) – Concepts, Equations, Design Methods, and Applications

Context and Strategic Orientation

  • Vision of the University: "To be globally recognized as a Centre of Excellence for Research, Innovation, Entrepreneurship and disseminating knowledge by providing inspirational learning to produce professional leaders for serving the society."

  • Mission statements (University):

    • M1: Provide world-class infrastructure, renowned academicians, and environment for Research, Innovation, Consultancy, and Entrepreneurship relevant to society.
    • M2: Offer programs & courses aligned with national policies for nation-building and global challenges.
    • M3: Design curriculum to match international standards, industry needs, civil society, and inculcate Creative Thinking, Critical Analysis, as well as Human and Ethical values.
    • M4: Ensure student delight through blended learning, corporate mentoring, professional grooming, flexible curriculum, and co-/extra-curricular activities.
    • M5: Create a scientific, transparent exam/evaluation system for ideal certification.
    • M6: Establish strategic relationships with national/international corporates and universities for collaborations.
    • M7: Contribute to a healthy, sustainable society via Institutional Social Responsibility (ISR) activities (rural development, welfare of senior citizens, women empowerment, health and hygiene awareness, environmental protection).

  • Vision and Mission of the Department (Engineering/ECE):

    • Department Vision: Be a leading department through effective teaching practices and excellence in research and innovation to create competent professionals with ethics, values, and entrepreneurial attitude for service to society and global industry standards.
    • Department Mission (M1–M3):
    • M1: Provide practical knowledge with state-of-the-art technology for experiential learning.
    • M2: Provide industry-recommended curriculum and transparent assessment for quality learning.
    • M3: Create global linkages for interdisciplinary learning and research.

  • Program-level objectives and outcomes (Summary):

    • PEOs (Program Educational Objectives):
    • PEO 1: Produce xxx graduate engineers who can comprehend and provide sustainable solutions for real-life problems under disruptive technologies.
    • PEO 2: Inculcate life-long learning and ability to work in changing environments and multi-disciplinary teams to be globally employable.
    • POs (Program Outcomes, 12+):
    • PO1 Engineering Knowledge
    • PO2 Problem Analysis
    • PO3 Design/Development of Solutions
    • PO4 Conduct Investigations of Complex Problems
    • PO5 Modern Tool Usage
    • PO6 The Engineer and Society
    • PO7 Environment and Sustainability
    • PO8 Ethics
    • PO9 Individual and Team Work
    • PO10 Communication
    • PO11 Project Management and Finance
    • PO12 Life-long Learning
    • PSOs (Program Specific Outcomes):
    • PSO1: Capability to analyze and apply modern tools for integrating electronics hardware and software.
    • PSO2: Attitude to design and develop electronics & communication systems with embedded technologies, fabrication, and IoTs for contemporary needs.

  • Academic calendar and program administration (Chandigarh University, Session 2025-26, Odd Semester):

    • Key dates (illustrative subset):
    • 01.07.2025: Start of Registration (2nd Year onwards, All Programs) for Odd Semester (01.07.2025 to 14.07.2025).
    • 15.07.2025: Start of Odd Semester for 2nd and 4th Year (All Programs) Except MBA 2nd Year.
    • 16.07.2025: Start of Odd Semester for 3rd and 5th Year (All Programs).
    • 23.07.2025: Orientation & Induction for 1st Year Batch I (23.07.2025 to 29.07.2025).
    • 24.07.2025: Start of Odd Semester-1st Year Batch I; MBA 2nd Year starts for USB & MBA APEX.
    • 11.10.2025: Academic Day (All Years) [Note: second marking/academic day event].
    • 26.07.2025: Academic Day for 1st Year Batch I & MBA 2nd Year (USB & MBA APEX) – Sat.
    • Various other dates cover orientation, tests, festivals, practical MSTs, last teaching day, end-semes, convocation, and registration for even semester (details in calendar).

  • Course context and schedule (Electrical & Computer Engineering, ECE, Chandigarh University)

    • Program/course code: B.Tech ECE (example: EC 201, 7th Semester) with industry-aligned outcomes and project-based learning.
    • Credits: Optical Fiber course listed with L (Lecture), T (Tutorial), P (Practical) credits: 3 L, 0 T, 0 P, Total Cr = 3.

  • Course Information and prerequisites (Optical Fiber/Integrated Photonics):

    • Prerequisites: None specified beyond foundational optics and electromagnetics; depth in waveguides and photonics topics is assumed.
    • Core focus: Photonic Integrated Circuits (PIC), materials for integrated optics, waveguide design, coupling, passive/active devices, fabrication, and applications.

  • Text, references, and learning resources summary

    • Core textbooks and references (selected):
      1) Saleh & Teich, Fundamentals of Photonics, Wiley-Interscience, 2nd Ed., 2007.
      2) Hunsperger, Integrated Optics: Theory and Technology, Springer, 6th Ed., 2009.
      3) Bhattacharya, Semiconductor Optoelectronic Devices, Pearson, 2nd Ed., 1997.
      4) Agrawal, Fiber-Optic Communication Systems, Wiley, 4th Ed., 2010.
      5) Lipson & Coldren, Integrated Photonics, Wiley, 2019.
      6) Vivien & Pavesi, Handbook of Silicon Photonics, CRC Press, 2013.
    • E-learning links: NPTEL Integrated Photonics, MIT OCW Photonic Materials and Devices, edX Fundamentals of Photonics, Coursera Introduction to Photonics, and industry/tutorial resources (VPIphotonics, Lumerical, etc.).

  • Content Beyond Syllabus and Industry context

    • Theme areas: Silicon Photonics, Hybrid Integration, Photonic Crystals, Quantum Photonics, and Advanced Modulation & Multiplexing Techniques (Coherent optical communication, WDM, PDM).
    • Fabrication and design tools: Lumerical, COMSOL, BeamPROP, VPI Photonics; layout tools such as KLayout, IPKISS, Nazca Design.
    • Assessments and delivery: MST (Mid-Semester Tests), assignments, quizzes, attendance, and lab/experiential exercises; problem-solving and design exercises included in lectures (as provided by the instructor).

  • Photonic Integrated Circuit (PIC) fundamentals – key ideas

    • PIC integrates multiple photonic functions on a single chip; advantages include compact size, low power, high speed; applications span Telecom, LIDAR, sensing, optics, and data processing.
    • Core devices and building blocks commonly listed:
    • Waveguides, Couplers/Splitters, Lasers, Modulators, Photodetectors, Filters, Amplifiers, Multiplexers/Demultiplexers.
    • Evolution timeline highlights (selected):
    • 1865–1969: Maxwell’s equations and guiding concepts; early waveguide concepts, and the first transistor.
    • 1989–1993: Invention of integrated optics and photonic integration; early PICs on InP; WWW foundation (Tim Berners‑Lee).
    • 2008–2017: Rapid growth in PIC architectures, silicon photonics, and large-scale integration; self-driving cars, medical devices, 5G deployment.
    • 2020–2025: MPW (multi-project wafer) in InP and silicon photonics; enhanced integration densities and neural photonics research.

  • Core topics covered in this course (Unit-wise overview)

    • Unit 1: Introduction & Material Technology for Integrated Optics
    • PIC components, dispersion, phase velocity, group velocity, anisotropic media, polarization in anisotropic media.
    • Guided wave optics: waveguide structures, modal design, boundary-value formulation, perturbation methods.
    • Unit 2: Coupling Light in a Waveguide and Photonic Devices
    • Coupled mode theory, directional couplers, Y-splitters, MMI (multimode interference) devices, MZI, micro-ring resonators, light-chip and end-fire coupling.
    • Passive and active devices, electro-optic modulators, semiconductor light sources and photodetectors, transport phenomena.
    • Unit 3: Material Engineering & Fabrication and Applications
    • Semiconductor lasers, photodetectors, detector noise, fabrication processes, PIC technology, and PIC applications (telecom, sensing, bio-photonics).

  • Key theoretical concepts and equations (selected, representative springs and notes)

    - Maxwell’s equations (source-free, linear media):

    • Wave equations and boundary conditions: tangential E and H continuity, D normal jump equals surface charge density, B normal continuity.
    • Wave propagation in guided structures:
    • Assume field dependence of the form extbfE(x,y,z)=extbfE(x,y)e−jβzextbf{E}(x,y,z) = extbf{E}(x,y) e^{-j\beta z} and obtain an eigenvalue problem for eta.
    • TE/TM/hybrid mode classifications in dielectric guides; TEM modes in two-conductor systems.
    • Phase and group velocities:
    • vp=ildeβextω=extωβext(phasevelocity)v_p = \frac{ ilde{\boldsymbol{\beta}}}{ ext{ω}} = \frac{ ext{ω}}{\beta} ext{ (phase velocity)}
    • vg=dextωdβv_g = \frac{d ext{ω}}{d\beta}
    • In non-dispersive media: v<em>p=v</em>gv<em>p = v</em>g; in dispersive media, v<em>p≠v</em>gv<em>p \neq v</em>g; group velocity is the relevant speed for energy/information transfer.
    • Group velocity dispersion and dispersion parameter (typical notation):
    • D(ildeextλ)ext(chromaticdispersionparameter)=ildeextλcd2βdildeextλ2D( ilde{ ext{λ}}) ext{ (chromatic dispersion parameter)} = \frac{ ilde{ ext{λ}}}{c} \frac{d^2\beta}{d ilde{ ext{λ}}^2}
    • (Often expressed in ps/(nm·km) with appropriate unit conversions.)
    • Gaussian pulse broadening due to dispersion (example):
    • For a Gaussian input pulse with initial width A<em>t0A<em>{t0} and spectral width A</em>extλA</em> ext{λ} and dispersion coefficient DD over length LL, the output pulse width is
    • A<em>t=extsqrt(A</em>t02+(DimesAextλimesL)2)A<em>t = ext{sqrt}\big(A</em>{t0}^2 + (D imes A_ ext{λ} imes L)^2\big)
    • Example: λ = 1550 nm, Aextλ=0.2extnmA_ ext{λ} = 0.2 ext{ nm}, D=17extpsextnmext⋅kmD = 17 \frac{ ext{ps}}{ ext{nm} ext{·km}}, L=50extkmL = 50 ext{ km} → dispersion-induced broadening ≈ DimesAextλimesL=17imes0.2imes50=170extpsD imes A_ ext{λ} imes L = 17 imes 0.2 imes 50 = 170 ext{ ps}
    • The transmitted pulse width becomes A<em>t=extsqrt(A</em>t02+(170extps)2)A<em>t = ext{sqrt}\big(A</em>{t0}^2 + (170 ext{ ps})^2\big) depending on the initial width.
    • Material vs waveguide dispersion:
    • Material dispersion arises from the wavelength dependence of the refractive index n(λ).
    • Waveguide dispersion arises from the geometry and confinement (how mode propagation depends on the fiber cross-section).
    • Polarization and anisotropy concepts:
    • Optical anisotropy: refractive index depends on propagation direction and/or polarization.
    • Birefringence (Δneo): difference between extraordinary and ordinary refractive indices: rianglen=n</em>e−noriangle n = n</em>e - n_o.
    • Optical axis: direction in a crystal along which light experiences no birefringence; uniaxial crystals have one optical axis; biaxial have two.
    • Types of crystals and axes (brief summary): isotropic (no axis), uniaxial (one axis with indices n<em>o,n</em>en<em>o, n</em>e), biaxial (three indices nextα,n<em>β,n</em>extγn_ ext{α}, n<em>\beta, n</em> ext{γ}).
    • Polarization concepts:
    • Linear, Circular, Elliptical polarization; polarization states change upon propagation in anisotropic media.
    • Malus’ Law for polarizers: Iout = Iin cos^2 θ for an ideal linear polarizer with transmission axis rotated by θ relative to the input polarization.
    • Waveguide geometries and classifications:
    • Slab (planar): one-dimensional confinement; Channel (2D confinement); Rib/Ridge (partially etched channel).
    • Based on refractive-index profile: Step-index (abrupt change) and Graded-index (GRIN: gradual change).
    • Based on material: Dielectric waveguides (e.g., silica, polymers, semiconductors); Metallic/plasmonic waveguides (surface plasmon polaritons).
    • Based on mode propagation: Single-mode (supports only fundamental mode, V < 2.405 for fibers); Multi-mode (V > 2.405).
    • Dimensional confinement: 1D (slab), 2D (channel/fiber), 3D (complex PICs, photonic crystals).

  • Design and analysis methodology (Waveguide theory and BVP)

    • Preliminaries: field equations and notation
    • General approach from Maxwell: derive vector Helmholtz equations (for E or H).
    • Mode types: TE (no Ez), TM (no Hz), hybrid (both E and H have components along propagation).
    • Boundary conditions: tangential components of E and H are continuous; normal components of D and B follow appropriate boundary rules (charges/surface currents as applicable).
    • Waveguide Analysis – general workflow
      1) Define geometry and material distribution e(r), μ(r).
      2) Write the governing PDE (vector Helmholtz) with boundary conditions.
      3) Solve eigenvalue problem to obtain mode fields and propagation constants β.
      4) Normalize modes (power through z) and compute derived quantities (group velocity, effective index, confinement).
      5) Validate with numerical solvers and compare to analytic approximations.
    • Worked example (symmetric slab, TE case)
    • Core region (−a ≤ x ≤ a): solution for Ey is sinusoidal; in cladding (|x| > a) Ey decays exponentially.
    • Even TE modes satisfy a transcendental dispersion relation; odd TE modes satisfy a complementary relation.
    • Use boundary conditions to relate transverse wavenumbers to β and solve for allowed modes.
    • Normalize forms and express via normalized frequency (slab V-number):
      V=k<em>0a extsqrt(n</em>12−n22)V = k<em>0 a \, ext{sqrt}(n</em>1^2 - n_2^2)
      with relationships between u = k a, w = α a, and dispersion equations for even/odd modes.
    • Effective Index Method (EIM)
    • Reduces a 3D problem to a sequence of 2D problems by splitting geometry into vertical and lateral slabs; obtain neff,vert(y) and then solve for lateral modes using the resultant effective index, neff.
    • Use as a fast starting point for design; accuracy depends on weak coupling and moderate index contrast.
    • Perturbation theory for waveguides (first-order)
    • For a small perturbation Δε(r) of the permittivity, the first-order change in propagation constant is given by an overlap integral with the unperturbed mode: Δβ ≈ (ω / (2 P)) ∫ Δε(r) |E(r)|^2 dA, where P is power flow along z.
    • Practical use: sensitivity analysis, index sensors, fabrication tolerances, slowly varying losses.

  • Mode classification and dispersion considerations

    • Modes in waveguides can be classified by:
    • Polarization content: TE, TM, HE/EH (hybrid) modes; TEM in multi-conductor (not typical in single-dielectric guides).
    • Confinement: bound (guided) modes with real β and evanescent tails in cladding; leaky modes with complex β; radiation modes (continuous spectrum).
    • Dimensionality: planar slab (1D confinement), channel/rib (2D confinement), optical fibers (cylindrical), slot/pic-based waveguides, photonic crystal waveguides.

  • Dispersion and its practical consequences in optical communications

    • Consequences of dispersion: pulse broadening, ISI (inter-symbol interference), degradation of signal fidelity, limits on max bit-rate and distance.
    • Dispersion management techniques:
    • Use of single-mode fibers to eliminate modal dispersion.
    • Graded-index fibers to reduce modal dispersion in multimode fibers.
    • Dispersion-shifted fibers (zero-dispersion near operating wavelength).
    • Chirped Fiber Bragg Gratings (CFBG) for dispersion compensation.
    • Electronic equalization (DSP-based) at the receiver.
    • Optical phase conjugation for mid-link compensation of nonlinear and dispersive effects.

  • Concrete formulas and examples (Gaussian pulses and dispersion)

    • Gaussian pulse broadening equation (example):
      A<em>t=extsqrt(A</em>t02+(D Aextλ L)2)A<em>t = ext{sqrt}\big(A</em>{t0}^2 + (D \, A_ ext{λ} \, L)^2\big)
    • Where:
      • At: output pulse width, A{t0}: input pulse width, D: dispersion coefficient, A_ ext{λ}: spectral width, L: fiber length.
    • Example for dispersion broadening:
    • Source wavelength λ = 1550 nm, A_ ext{λ} = 0.2 nm, D = 17 ps/(nm·km), L = 50 km
    • Dispersion-induced broadening term: D A_λ L = 17 × 0.2 × 50 = 170 ps

  • Optical anisotropy, birefringence and optical axis (crystal optics)

    • Optical anisotropy: refractive index depends on propagation direction and/or polarization; isotropic materials have the same index in all directions.
    • Birefringence (Δη = ne − no): extraordinary vs ordinary rays; uniaxial crystals have one optical axis (no birefringence along the axis); biaxial crystals have two optical axes.
    • Optical axis determination and crystal types:
    • Isotropic: no optical axis (e.g., glass, NaCl).
    • Uniaxial: one optical axis; principal indices: no (ordinary), ne (extraordinary).
    • Biaxial: two optical axes; three principal indices nα < nβ < n_γ.
    • Measurement techniques: conoscopic interference in polarized light microscopy, ellipsometry, interferometry, birefringence compensators.

  • Polarization physics and devices

    • Polarization definitions: linear, circular, elliptical; natural light is often unpolarized.
    • Polarization control methods:
    • By reflection (Brewster’s law): reflected light can be completely polarized at the Brewster angle; tan(θB) = n2/n_1.
    • By transmission (Polaroids): absorbs one polarization component and transmits the orthogonal component.
    • By scattering (e.g., sky light): partial polarization due to scattering.
    • By birefringence (double refraction): split into orthogonally polarized ordinary and extraordinary rays.
    • By dichroism: selective absorption of one polarization component.
    • Polarization devices and applications:
    • Polaroid filters, wave plates (half-wave plate for polarization rotation, quarter-wave plate for converting linear to circular/elliptical), Nicol prism.
    • Applications: LCDs, 3D glasses, polarization-division multiplexing, stress analysis (photoelasticity), polarization-based imaging.
    • Malus’ Law and polarization analysis:
    • If a linear polarizer is followed by an analyzer with relative angle φ, transmitted intensity I = I_0 cos^2 φ.

  • Photonic waveguides: practical and design considerations

    • Slab vs channel vs rib/ridge vs photonic crystal guides; based on dimension and geometry.
    • 1D vs 2D confinement; mode profiles (even/odd) in symmetric structures; field distribution inside the core and cladding (sinusoidal in core, exponential decay in cladding for guided modes).
    • Effective-index method (EIM) as a quick design tool; limitations in strongly confined, high-contrast or strongly coupled regimes.

  • Loss mechanisms in photonic circuits (overview)

    • Material absorption (intrinsic): attenuation related to imaginary part of refractive index; nepers/m or dB/m conversions.
    • Scattering loss: from surface/sidewall roughness; scales with roughness and perturbations.
    • Bending/radiation loss: increases with tighter bends; dependence on bend radius.
    • Coupling loss: mode mismatch at interfaces (e.g., fiber-to-waveguide); quantified by overlap integrals.
    • Radiation/leaky modes: incomplete total internal reflection; loss channels to substrate.
    • Nonlinear-induced loss (at high power): two-photon absorption (TPA), free-carrier absorption in semiconductors.

  • Practical takeaways for exam and project work

    • Distinguish phase velocity vs group velocity and their relevance to signal transmission (group velocity governs information transfer).
    • Use D parameter to gauge dispersion; know how to compute from β(ω) or β(λ) data (central differences for numerical estimation).
    • For a given waveguide, determine whether it is single-mode or multimode with the V-number criterion and corresponding dispersion considerations.
    • Apply boundary-value problem (BVP) formulation to set up mode problems and extract eigenvalues/beta; use EIM for rapid initial estimates.
    • Recognize and classify PIC components and architectures; map applications to devices (e.g., MZI, micro-ring resonators, MMIs).