Dielectric Resonator Antenna E field absolute open cavity 1.8 GHz

Video animation of the absolute value of the electric field at 1.8 GHz of a cylindrical DRA placed within an open metallic cavity.

Tutorial: Mode Analysis of Isolated Dielectric Resonator


Mode analysis is a vital step during the design stage and later at the the laboratory experimentation stage of a resonant microwave structure. Acquiring information about the internal and external E and H fields of a structure gives an understanding of its resonant properties. For new RF designers, this mode identification process can be confusing and sometimes too difficult to perform on the first attempt.

It is important to understand that a dielectric resonator can support an infinite number of modes. Each mode corresponds to a unique resonant frequency and a unique E and H field pattern is generated. At resonance, the power utilised at the device is maximised, this is shown in practice by observing e.g. its S11 response on a Network Analyzer. The 'low' or 'deep' curve in the S11 response indicates a resonance. For high-Q (Q=Qualitify Factor) structures the width of the 'deep' in the S11 response is narrow and sharp - indication of highly resonator structure. Alternatively, for low-Q structures such as the antenna studied here the resonance is characterised by observing the wide 'deep'in the S11 response. Furthermore, the lower Q factor indicates higher losses in the structure - for an antenna such losses are mainly due to radiation (spread of travelling waves in the open space). Additional losses include dielectric and conductor loss, but normally these are unwanted since the EM power is dissipated in the form of heat.

At each resonant frequency there is a unique interior electromagnetic (EM) field configuration (or mode). For Dielectric Resonators (DRs) standing waves are formed within the structure, with the EM waves being trapped at the resonator's volume. Of course some power leakage (radiation) out of the dielectric also co-exists due to the dielectric-non dielectric interface resulting in the distortion of the ideal confined EM wave nature of the resonator. However, to a good approximation, for most DRs such an assumption is helpful for first order analysis.

Nowadays, there are many commercial simulation packages available that analyse 2-D and 3-D EM problems, using various numerical techniques such as FDTD, FIT, Transmission Line method, etc. Among other calculations, they can help you to study and visualise the EM field configurations and based on those, it can assist on the assignment of the mode order for each resonant frequency, e.g. TE01, TM02, HEM21 and so on. Literature information about mode nomenclature is generally a confusing topic and publications are not always following the same methodology. Especially, in some complex geometries mode identification can be almost impossible. Even for simple geometries, such as rectangular or cylindrical waveguiges and resonators, mode assignment requires careful observation of E and H fields at various cutting planes and at several instances of the field's phase shift.

For cylindrical resonators there are three possible group of modes that can be excited: TE, TM and HEM modes. On the other hand, rectangular resonators can only support TE and TM modes. In between other advantages, knowing the mode patterns allows DR designers to:


For advanced analysis, please check my references to guide you through the literature survey of the DR properties.

In the text to follow it is aimed to provide a introduction to mode characterisation for an isolated cylindrical dielectric resonator (CDR) by an example [E.20]. Such structure behaves as an antenna in the open space, too. This analysis can be used to understand the procedure for mode behaviour for similar structures, such as waveguides or rectangular geometries. Simulation results below are compared with the findings published in [E.20] and their similarity is discussed.


Isolated cylindrical dielectric resonator antenna modes meshing simulation

Meshing of the structure, prior to simulation. Cylinder's parameters:


The cylinder is suspended in free space. At the boundary of the surrounding free space a magnetic wall approximation was assumed. It takes around 3 min to simulate this structure and calculate the first 6 resonant modes, shown on the table below:

Resonant Frequencies of the Isolated Dielectric Resonator

Mode #

Mode type

Resonant Frequency (Kajfez [E.20])

Resonant Frequency (simulation)



4.829 GHz

4.773 GHz



6.333 GHz

6.247 GHz



6.638 GHz

6.679 GHz



7.524 GHz

7.523 GHz



7.752 GHz

7.742 GHz



(not considered)

8.296 GHz


Mode Identification

E and H field plots of the first main modes of the isolated cylidrical DR are shown below, just click a tab on the panel below to select a mode. Resonant frequency of each mode is as shown on the table above.

=> Notice that TE011 mode requires careful consideration, since there are two half-waves along z-direction. This means that the investigation of the E-field needs to be studied close to the top or bottom surface of the dielectric cylinder, since it vanishes at cylinder's mid-way plane (the maximum intensity of E-field is 'shifted' away from cylinder's center along z-axis, compare the plots with TE01 mode and observe the absolute E-field of TE011 in the colour plot).

  • TE01δ
  • HEM11δ
  • ΗΕΜ12δ
  • ΤΜ01δ
  • ΗΕΜ21δ
  • TE011δ H-field
  • TE011δ E-field

TE01, E-field

TE01 E field isolated dielectric resonator Kajfez



HEM11, H-field

HEM11 mode isolated dielectric resonator antenna

Perspective view of the first hybrid mode of the structure. This is the magnetic field of mode HEM11 at 6.25 GHz.

Mode HEM12, E-field

Isolated cylindrical DR


Mode TM01, H-field

TM01 H isolated cyl DR


Mode HEM21, H-field

HEM21 isolated cyl DR


ΤΕ011δ, H-field

TE011 H isolated cyl DR


TE011, E-field

TE011 E-field isolated DR

TE011 E-field abs colour isolated cyl DR

Note: Red colour indicates maximum field strength. Green colour indicates minimum field strength.


Video Animation: HEM11 mode H-field

For educational purposes, below is shown a video animation of the H-field for HEM11 mode. Compare this with HEM11 mode on the tabbed images above.