# Judiciously distributing laser emitters to shape the desired far field patterns

## TL;DR

This paper explores how to optimally distribute laser emitters in a one-dimensional array to achieve desired far-field patterns, revealing that successful beam shaping can occur even with poorly scaled system matrices, simplifying design constraints.

## Contribution

It introduces a novel insight that effective far-field pattern shaping is possible despite non-ideal matrix scaling, based on an inequality involving optical distances between emitters.

## Key findings

- Successful beam shaping occurs with poorly scaled matrices.
- An inequality defines the functional range of optical distances.
- The approach simplifies the design and optimization of photonic systems.

## Abstract

The far-field pattern of a simple one-dimensional laser array of emitters radiating into free space is considered. In the path of investigating the inverse problem for their near fields leading to a target beam form, surprisingly we found that the result is successful when the matrix of the corresponding linear system is not well-scaled. The essence of our numerical observations is captured by an elegant inequality defining the functional range of the optical distance between two neighboring emitters. Our finding can restrict substantially the parametric space of integrated photonic systems and simplify significantly the subsequent optimizations.