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Dielectric Slab Waveguide Modes: TE and TM Guided Modes

Key Takeaways

  • The dielectric slab waveguide is the simplest waveguiding structure used in optical applications.

  • The guided modes in a dielectric slab are dependent on the thickness of the film, wavelength, and refractive indices. 

  • When n2  = n3, the waveguide structure turns into a symmetric dielectric slab waveguide. 

Optical interconnects

Waveguide technology is often used in optical interconnects

In optical devices such as modulators, semiconductor lasers, and optical interconnects,  waveguide technology is often utilized. In optoelectronic devices, metallic and dielectric waveguides allow electromagnetic waves to travel from one point to another without obstruction.

The dielectric slab waveguide is the simplest waveguiding structure used in optical applications. This waveguide offers guided and radiation modes with simple geometry. Understanding dielectric slab waveguide modes is important to understanding wave propagation in other complicated waveguiding structures

Dielectric Slab Waveguides

A three-layer dielectric slab waveguide includes a substrate, film, and superstrate layer. The substrate layer has a refractive index n2, and above the substrate, the core region formed by the film is placed. The film is a material of refractive index n1. The superstrate forms the cladding on the film and is of refractive index n3.

If the longitudinal dimension of the layers is greater than the dimension in the transverse direction, then there are no variations in material and fields in the y-direction of the dielectric slab waveguide. This type of dielectric slab waveguide supports guided modes of wave propagation as well as radiation modes of wave propagation. The only difference is that the number of guided modes is finite, whereas the radiation modes are infinite in number. The guided modes in a dielectric slab are dependent on the thickness of the film, wavelength, and refractive indices. 

Symmetric and Asymmetric Dielectric Slab Waveguides

For mode guidance, the condition to be followed is as follows:

n1  > n2  ≥ n3  

When n2 = n3, the waveguide structure turns into a symmetric dielectric slab waveguide. In these types of waveguides, the guided modes are either even or odd in their field distributions.

When n2 ≠ n3, then the structure is an asymmetric dielectric slab waveguide. A symmetric dielectric slab waveguide is considered a special case of asymmetric dielectric slab waveguides. 

Dielectric Slab Waveguide Modes

Assume a dielectric slab waveguide is uniform in the y-direction and extends infinitely in the same direction. This assumption makes the electric field uniform in the y-direction as well. There is no variation of fields in the y-direction. The wave equation of a dielectric slab waveguide can be written as the following equation, where β is the longitudinal propagation constant, k0 is the free space wavenumber, and ni is the refractive indices:

d2Edx2+(k02ni2-2)E=0

Solving this equation gives the fields present in the dielectric slab waveguide. These fields follow two guided dielectric slab waveguide modes, transverse electric guided mode and transverse magnetic guided mode.

Transverse Electric Guided Mode

In transverse electric (TE) guided mode, the field components to pay attention to are Hx, Ey, and Hz. In guided modes, the power is confined to the core region and no power loss exists. To achieve no power loss guided modes, the longitudinal propagation constant β should be within the range given below:

k0n1≥≥k0n2≥k0n3

Transverse Magnetic Guided Mode

The field components of interest in transverse magnetic (TM) guided mode are Ex, Hy, and Ez. The solution for TM  modes is obtained by applying boundary conditions to the magnetic fields parallel to the interfaces in y and z directions. The TM guided mode transforms to TM radiation mode when the value of β becomes:

 0<<k0n3

Understanding the basics of dielectric slab waveguide modes is helpful when designing the desired waveguiding modes in complicated dielectric waveguides of different geometries. Luckily, Cadence’s software can help you design optical devices utilizing dielectric slab waveguides.

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