Single-Frequency Laser Linewidth Characterization with Sigmoid Functions
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Solution Overview
Problem
Current techniques lack a widely accepted analytical expression to fully characterize the effective linewidth of single-frequency lasers against observation time, relying on cumbersome numerical methods for linewidth measurement.
Innovation Solution
The use of Sigmoid functions to represent the laser linewidth as a function of observation time, allowing for analytical characterization of laser spectral linewidths, including natural and technical linewidths caused by spontaneous emission and flicker noise.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical methods are used for linewidth measurement, then measurement precision can be achieved, but measurement complexity and time consumption increase
Solution Approach 1:
The patent replaces complex numerical computation methods with a simplified analytical Sigmoid function model. Instead of using cumbersome numerical methods to characterize laser linewidth, the invention uses an analytical expression (Sigmoid function) that can be easily fitted to measurement data, thereby substituting mechanical/computational complexity with a more efficient mathematical model that maintains measurement precision while reducing complexity
Solution Approach 2:
The patent changes the parameter representation of laser linewidth from traditional numerical computation to a Sigmoid function with specific parameters (amplitude, mid-point, slope). This parameter transformation allows the linewidth to be characterized by a few key parameters that capture the essential behavior across different observation times, simplifying the measurement and characterization process while maintaining accuracy
2Loss of information
If traditional linewidth characterization methods are used, then natural linewidth can be measured, but technical linewidth components (flicker noise, etc.) are not fully characterized
Solution Approach 1:
The patent segments the laser linewidth into different components (natural linewidth, technical linewidth from flicker noise, and other contributions) by analyzing the Sigmoid function parameters at different observation times. The short-time behavior captures natural linewidth while long-time behavior reveals technical linewidth components, effectively segmenting the total linewidth into physically meaningful parts that can be separately characterized and understood
Solution Approach 2:
The patent adds the dimension of observation time to the linewidth measurement, transforming it from a single-value parameter to a time-dependent function. By measuring linewidth across multiple observation times and fitting a Sigmoid function, the method captures dynamic characteristics that reveal different physical mechanisms (spontaneous emission at short times, flicker noise at long times), providing a more complete characterization without significantly increasing measurement difficulty
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables speedy assessment of laser coherence properties and facilitates the design of optical interferometer-based sensing devices by providing clear linewidth information and optimizing detection circuitry.
Implementation Method 1
an unbalanced optical interferometer involving a 3×3 coupler, a 2×4 multimode interference (MMI) coupler, or a 90° hybrid coherent receiver
Data Source
AI summary
The laser linewidth is an important parameter for characterizing the coherence properties of a single-frequency laser. The disclosure of this patent document provides techniques for characterizing laser spectral linewidths of single-frequency lasers in form of analytical formula in connection with the use of one or more Sigmoid functions of observation time by including various physical origins affecting the laser linewidths in addition to the natural linewidth caused by the spontaneous emission or quantum noise that can be described with an analytical expression known as the Schawlow-Townes-Henry formula. The disclosed methods for characterizing the laser linewidth caused by various factors in analytical formula can be advantageously used in various applications including designing an optical interferometer based sensing device using coherent laser light from a single-frequency laser.