Mode locking theory of the Nyquist laser

Area of Science:

• Laser Physics
• Nonlinear Optics
• Quantum Optics

Background:

• Mode-locked lasers are crucial for generating ultrashort optical pulses.
• Nyquist lasers offer unique spectral properties for pulse generation.
• Generating specific pulse shapes like sinc functions is challenging.

Purpose of the Study:

• To derive a master equation for mode-locked Nyquist lasers capable of emitting sinc function pulses.
• To investigate the role of optical filters in shaping laser output.
• To provide a theoretical framework for understanding sinc pulse generation.

Main Methods:

• Derivation of a master equation using exponential perturbative expressions for gain, loss, and amplitude modulation.
• Incorporation of a flat-top optical filter with edge enhancement.
• Analysis of the integral equation and introduction of a differential equation operator.

Main Results:

• A master equation was successfully derived for mode-locked Nyquist lasers.
• A sinc function pulse with a flat-top spectral profile was generated.
• The sinc function solution was shown to satisfy spherical wave propagation and Bessel equation properties.

Conclusions:

• The derived master equation accurately describes sinc pulse generation in Nyquist lasers.
• The optical filter design is critical for achieving the desired sinc pulse shape.
• The theoretical framework supports the direct derivation of sinc function solutions.