# A Simple Coupled-Bloch-Mode Approach To Study Active Photonic Crystal Waveguides and Lasers

## TL;DR

This paper introduces a simplified coupled-Bloch-mode method to analyze active photonic crystal waveguides and lasers, providing physical insights into coupling mechanisms, dispersion effects, and laser threshold behavior with implications for designing efficient photonic devices.

## Contribution

The paper presents a new, simplified coupled-Bloch-mode approach for analyzing active photonic crystal waveguides and lasers, highlighting the impact of distributed feedback and gain on device performance.

## Key findings

- Coupled-Bloch-mode approach accurately predicts transmission properties.
- Gain-induced feedback limits slow-light enhancement.
- Active regions without back reflections can lase effectively.

## Abstract

By applying a coupled-Bloch-mode approach, we have derived a simple expression for the transmission properties of photonic crystal (PhC) line-defect waveguides with a complex refractive index perturbation. We have provided physical insights on the coupling mechanism by analyzing the frequency dependence and relative strength of the coupling coefficients. We have shown the impact of the perturbation on the waveguide dispersion relation and how the gain-induced distributed feedback limits the maximum attainable slow-light enhancement of the gain itself. We have then applied our approach to analyze the threshold behaviour of various PhC laser cavities and proved the significant impact of coherent distributed feedback effects in these lasers. Importantly, our approach also reveals that a structure simply consisting of an active region with zero back reflections from the passive output waveguides can achieve lasing oscillation with reasonable threshold gain.