What is cut off wavelength for a wave guide?

Cut-off Wavelength for a Waveguide

The cut-off wavelength of a waveguide is the maximum wavelength of light that can propagate down a waveguide mode. Beyond this wavelength, the mode becomes evanescent, meaning it decays exponentially along the propagation direction of the waveguide and cannot effectively transport energy.

Importance of Cut-off Wavelength

Understanding the cut-off wavelength is crucial for designing optical systems, as it determines the operational bandwidth of the waveguide. It is particularly important in telecommunications, sensors, and other photonic devices where precise control over light propagation is required.

Factors Affecting Cut-off Wavelength

• Waveguide geometry (e.g., width, height)
• Refractive index contrast between the core and cladding materials
• Waveguide material dispersion

Calculation of Cut-off Wavelength

The cut-off wavelength can be calculated using the waveguide's physical dimensions and the refractive indices of the core and cladding materials. The exact formula varies depending on the waveguide type (e.g., rectangular, circular) and the mode of interest (e.g., TE, TM).

Example

For a simple step-index fiber, the cut-off wavelength for the fundamental mode can be approximated by:

λ_c ≈ (2πa√(n₁² - n₂²))/V_c

where a is the core radius, n₁ and n₂ are the refractive indices of the core and cladding, respectively, and V_c is the cut-off V-number, a dimensionless parameter.

Conclusion

The cut-off wavelength is a fundamental parameter in the design and analysis of waveguides. It influences the waveguide's ability to guide certain wavelengths of light, impacting the device's performance in optical networks and systems.