ENEE 684 Lecture 13 | Passive Photonic Components (Part 1)

Overview

Ergun Simsek explains how passive photonic components control light on-chip, focusing on directional couplers, Y-junctions, multimode-interference (MMI) splitters, and the Mach–Zehnder interferometer (MZI). He connects device behavior to coupled-mode theory, phase differences, fabrication trade-offs, and insertion-loss calculations—including a 1:32 splitter budget of 22.6 dB with 1.5 dB excess loss per stage—and shows how MZIs convert phase changes into measurable output power.

Key takeaways

For identical, lossless coupled waveguides, power transfers as sin²(κL): equal splitting occurs at κL = π/4, and complete transfer occurs at κL = π/2.
A 3 dB directional coupler gives equal output powers but also imposes a 90-degree relative phase, which must be accounted for when designing interferometers.
Propagation-constant mismatch limits a directional coupler’s peak transfer to κ²/(κ² + δ²); increasing mismatch can broaden bandwidth while reducing efficiency.
MMI splitters create multiple images through interference among modes, and their approximate beat length scales as 4n_effW_eff²/(3λ).
A five-stage 1:32 splitter has about 15.1 dB ideal division loss; adding 1.5 dB excess loss per stage produces approximately 22.6 dB total insertion loss.
An MZI converts a phase difference into output power, allowing lithium-niobate electro-optic index changes to modulate light and environmental changes to be sensed.

Chapters

0:00 Passive Photonic Components: Lecture Scope

The lecture introduces directional couplers, Y-junctions, and multimode-interference (MMI) splitters.
The planned follow-up topics include Mach–Zehnder interferometers, optical isolators, circulators, and fiber Bragg gratings.
The central design challenge is routing and dividing light with passive structures rather than electrical-style interconnects.

2:00 Directional Couplers Transfer Light Between Nearby Waveguides

A directional coupler places two dielectric waveguides close enough for their optical fields to overlap.
The evanescent tails let light transfer from the excited guide to the neighboring guide and later transfer back.
Choosing the coupling-region length controls the output split; a 3 dB coupler sends half the input power to each output.

6:00 Evanescent Coupling Enables Sensors and Multilayer Connections

Coupling strength depends on mode overlap, waveguide spacing, coupling length, and how closely the guides’ effective indices match.
A cited sensing arrangement uses selected wavelengths near chemical absorption peaks to detect low-concentration molecules.
Couplers can also connect waveguides on different chip layers, serving as photonic interconnects.

9:00 Even and Odd Supermodes Set the Coupling Length

For identical, lossless waveguides, the combined field can be represented as symmetric even and antisymmetric odd supermodes.
Their propagation constants are approximately β + κ and β − κ, where κ is the coupling coefficient.
The accumulated relative phase is 2κz; full transfer occurs at the critical length Lc = π/(2κ), while equal power occurs at Lc/2.

13:00 Coupled-Mode Theory Models Exchange Between Guides

Coupled-mode theory starts from Maxwell’s equations and approximates each guide’s field with a slowly varying amplitude.
For weakly overlapping, identical guides, each amplitude’s evolution depends on the other guide through the coupling coefficient κ.
The same framework applies to coupled waveguides and to a ring resonator coupled to a bus waveguide.

17:00 A 3 dB Coupler Produces Equal Powers with a 90° Phase Offset

In the ideal symmetric case, the guide powers vary as cos²(κL) and sin²(κL), so the total power remains conserved.
At κL = π/4, each output carries half the input power; at κL = π/2, transfer to the second guide is complete.
The coupled output has a 90-degree phase relationship to the through output, an essential property for interferometers.

23:00 Index Mismatch Limits Coupling and Creates a Bandwidth Trade-Off

Real waveguides can have different propagation constants; their difference acts as a detuning parameter in coupled-mode theory.
With detuning δ, maximum transfer is limited to κ²/(κ² + δ²), so mismatched guides cannot achieve complete power transfer.
Increasing detuning can broaden a coupler’s operating bandwidth, but lowers its peak transfer efficiency; wavelength-dependent mode overlap also changes κ.

34:00 Y-Junction Geometry Trades Footprint Against Loss

A Y-junction divides one input into two branches, with a gradual transition intended to split light efficiently.
Unequal branch widths can create ratios such as 10:90; a smaller branching angle generally needs a longer transition.
Making the angle larger can reduce footprint but increase loss, while fabrication asymmetry can add roughly 0.5 dB or, in poorer cases, 2–3 dB.

40:00 MMI Splitters Use Self-Imaging in a Multimode Region

An MMI splitter launches a single-mode input into a wider region that supports multiple modes.
The modes accumulate different phases and interfere constructively or destructively, producing repeated images of the input field.
By placing output guides at the appropriate image locations, one MMI can produce 1:2, 1:3, or other splits.

46:00 MMI Beat Length Predicts Output Image Positions

The propagation constants of MMI modes depend on mode number, effective index, wavelength, and effective—not just physical—width.
The approximate beat length Lπ is 4n_eff W_eff²/(3λ), providing a starting point for selecting device length.
Approximate self-imaging rules help estimate splitter dimensions before full-wave simulation.

52:00 MMIs Simplify Fabrication and Scale to Multiple Outputs

Compared with a Y-junction, an MMI can use a straightforward rectangular multimode region, avoiding sensitivity to branch angles and symmetry.
MMIs can be cascaded or designed for several images to build 1:N splitters.
Designers commonly use analytical estimates first, then validate structures with numerical solvers or beam-propagation methods.

59:00 A 1:32 Splitter Accumulates 22.6 dB of Loss

A balanced 1:32 cascade needs log₂(32) = 5 splitter stages and has an ideal division loss of about 15.1 dB per output.
At 1.5 dB excess loss per 1:2 stage, the five stages add 7.5 dB, bringing total insertion loss to about 22.6 dB.
The example shows why splitter-stage losses must be included in signal-to-noise and link budgets.

1:01:18 Free-Space and Integrated Mach–Zehnder Interferometers

A free-space MZI splits light into two paths, recombines them, and converts their phase difference into an interference pattern measurable with cameras or photodetectors.
An integrated MZI uses two 3 dB couplers around separate waveguide arms; phase differences determine the bar and cross outputs.
MZIs can serve as sensors, communication components, and building blocks for programmable photonics.

1:08:06 MZI Phase Control Enables Electro-Optic Modulation

The phase difference between arms depends on their effective indices and lengths: each arm accumulates phase proportional to 2πn_effL/λ.
A phase shift of π swaps bright and dark interference outputs; small environmental changes can therefore become detectable power changes.
Applying an electric field to lithium niobate changes its refractive index and effective index, enabling electro-optic control of MZI output.

1:12:00 Beam-Splitter Matrices Relate MZI Input and Output Fields

An MZI transfer calculation combines two 3 dB coupler matrices with the propagation phases accumulated in the two arms.
For an ideal coupler, the reflected and transmitted field components have a relative phase shift; the lecture notes that the precise phase convention depends on the matrix representation.
The resulting output fields vary sinusoidally with phase difference, with sine- and cosine-dependent outputs and corresponding sine-squared and cosine-squared powers.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Ergun Simsek.