# A High Optical Waveguide Confinement Factor Indicates Low Optical Losses

### Key Takeaways

• The objective of an optical waveguide is to transmit electromagnetic waves through guided paths.

• The optical waveguide confinement factor is uniform when the electromagnetic fields are completely confined to the core.

• The optical waveguide confinement factor is found by the ratio of the electromagnetic field within the core region to the electromagnetic field within the entire waveguide structure.

A high optical waveguide confinement factor produces low optical losses

The objective of an optical waveguide is to transmit electromagnetic waves through guided paths. An efficient optical waveguide ensures that all electromagnetic fields are confined to the guided path. The optical waveguide confinement factor describes the ratio of electromagnetic waves confined to the guided path to the entire propagation through the waveguide. In this article, we will take a closer look at how the optical waveguide confinement factor impacts optical losses.

## The Optical Waveguide Confinement Factor

In an ideal waveguiding structure, electromagnetic waves are confined to the core and guided to their target location. However, the non-idealities of the waveguiding structure can cause electromagnetic waves to spread out of the core region and follow a Gaussian profile.

When the thickness of the core is less than the wavelength of the electromagnetic signal, the spread of electromagnetic waves from the core will be greater. The electromagnetic fields are not only confined to the core but also the cladding region. The optical waveguide confinement factor represents how well electromagnetic fields are confined to the core. It is found by the ratio of the electromagnetic fields within the core region to the electromagnetic fields within the entire waveguide structure.

## The Ideal Optical Waveguide Confinement Factor

The optical waveguide confinement factor is represented by the symbol Γ, which is found between zero and one. So, the optical waveguide confinement factor is a unitless quantity. It can be derived from Maxwell’s equations corresponding to the mode propagation in the waveguide, either transverse electric mode (TE) or transverse magnetic (TM) mode.

### How Core Thickness Influences the Optical Waveguide Confinement Factor

When the core's thickness is larger than the wavelength of the electromagnetic signal, the wave propagation remains confined to the core, and the electromagnetic fields are not leaked into the cladding. So, the optical waveguide confinement factor is uniform when the electromagnetic fields are completely confined to the core.

As the core thickness decreases, electromagnetic fields spread from the core, leading to a low optical waveguide confinement factor. The optical waveguide confinement factor completely depends on the core thickness dimension and the refractive index profile of the core and cladding.

## The Transverse Mode Confinement Factor

Consider a dielectric slab waveguide with a core of refractive index n2, surrounded by cladding material of refractive index n1, let the core thickness be d, and the core width be w. Assume the refractive index of the core changes from n2 for n2+Δn2. The core refractive index variation causes a change in the value of the propagation vector, Δβ.

The change in propagation vector Δβ depends on variables including:

• The speed of the electromagnetic signal.
• The electromagnetic signal’s frequency.
• The group index of the waveguiding mode.
• The material group index of the waveguiding core.
• The transverse mode confinement factor.

When the refractive index of the core material changes, the transverse electromagnetic components experience perturbations and start to spread from the core to the cladding. This causes variations in the modal electromagnetic energy confined in the core of the waveguide. The factor that dictates the transverse electromagnetic field to spread in any mode of wave propagation is called the transverse mode confinement factor.

The optical waveguide confinement factor indicates how efficiently electromagnetic waves propagate through a waveguide without any leakage. When designing an optical waveguide, the optical waveguide confinement factor is required to be close to uniform to avoid optical losses. Cadence software can help design low-loss optical waveguides.