Source: arXiv

Understanding Laser Linewidth and Noise

Introduction to Laser Linewidth

Lasers are coherent light sources with applications ranging from telecommunications to medical devices. A critical parameter in laser performance is the linewidth, which is a measure of the spectral width of the laser output. The narrower the linewidth, the more coherent the laser light.

The Schawlow-Townes Linewidth

Before the first practical laser was built, Schawlow and Townes calculated the fundamental quantum limit of laser linewidth. This calculation resulted in the Schawlow–Townes equation, which has become a cornerstone in laser physics. The equation describes how the linewidth is inversely proportional to the output power and directly proportional to the resonator bandwidth.

Key Equation

The original Schawlow–Townes equation is given by:

Δν_laser = (4πhν(Δν_c)²) / P_out

Where h is Planck’s constant, ν is the frequency of light, Δν_c is the resonator bandwidth, and P_out is the output power.

Refinements and Generalizations

Melvin Lax later refined this understanding, showing that the actual linewidth during laser operation is half of that predicted by Schawlow and Townes, leading to a modified equation. Further generalizations account for additional factors such as resonator losses and spontaneous emission.

Advanced Equation

A more generalized form of the equation is:

Δν_laser = (hνθl_totT_oc) / (4πT_rt²P_out)

Here, θ is the spontaneous emission factor, T_oc is the output coupler transmission, l_tot is total resonator losses, and T_rt is the resonator round-trip time.

Phase Noise and Quantum Fluctuations

The Schawlow–Townes linewidth is influenced by quantum noise, which causes fluctuations in the optical phase. This quantum noise arises equally from the laser gain medium and the resonator’s linear losses, meaning that even with ideal conditions, the linewidth cannot be reduced to zero.

Challenges in Achieving Minimal Linewidth

In practice, achieving the theoretical minimum linewidth is challenging due to technical noise sources. Solid-state lasers can achieve linewidths in the kilohertz range, but this is still far above the Schawlow–Townes limit due to excess noise.

Semiconductor Lasers

Semiconductor lasers typically have larger linewidths due to factors like amplitude-to-phase coupling and carrier fluctuations. These effects can be quantified by the linewidth enhancement factor, which can significantly increase the linewidth.

Applications to Mode-locked Lasers

The Schawlow–Townes formula is also applicable to mode-locked lasers, which produce ultra-short pulses of light. For actively mode-locked lasers, the formula uses the total average power, while for passively mode-locked lasers, it provides an estimate for the linewidth near the center of the spectrum.

Conclusion

Understanding laser linewidth is crucial for optimizing laser performance across various applications. While theoretical models provide a baseline, practical implementations must consider additional noise sources and operational conditions to achieve desired laser characteristics.

Source: ResearchGate
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