A theoretical investigation of the quarter-wavelength model-part 2: verification and extension

Abstract

The quarter-wavelength model states that the reflection of microwaves is minimized if the thickness of the film is mλ/4 where m is an odd integer and λ is the wavelength within the film . In part 1 of this work, published previously, it was shown that the theory behind this model is flawed and that it needs to be replaced using a wave superposition approach involving principles not beyond physics at college level. Through the verification of the results from formulae familiar to material scientists, it is shown here that many other concepts in current mainstream microwave absorption theory are used inappropriately including that reflection loss RL has been used to characterize microwave absorption from material instead of film and also that the results have been rationalized incorrectly by impedance matching theory. Impedance matching theory is developed from transmission-line theory for scattering parameter s 11 but cannot be applied to RL which is an innate property only for metal-backed film.

Microwave absorption of film explained accurately by wave cancellation theory

“…However, RL(x 1 -)/dB is not a monotonic function of d thus it cannot be used to characterize the absorption of material. The multipeaks RL(x 1 -)/dB originate from the fact that the phase of beam t is a function of d and thus the peaks of RL(x 1 -)/dB are due to the fact that the phase difference φ of beams t and 1 r is periodically out of phase by π as d increases [7,8]. This provides a good example of the observation that the property of a portion of material is different from that of the material itself.…”

“…Relevant expressions are fully derived in the Appendix. It is first demonstrated from numerical calculations [7] and then proved theoretically from angular effects [8] that the most efficient absorption takes place when φ = (2n + 1)π resulting in full wave cancellation and the least absorption takes place where φ = 2nπ, where n is an integer. Since the absorption of film is characterized by the cancellation of beams 1 r and t, films providing efficient absorption can be composed of poor absorption material and at absorption peaks, films can absorb more microwaves than can the material alone.…”

“…As a result, it is commonly speculated that a weaker beam t provides greater absorption [10]. But these arguments are flawed, being a result of confusion between a film and the material [7,11,12].…”

“…The back-and-forth reflection cycles within film are related to energy conservation and the wave superposition of beams 1 r and t. Thus, in contrast to material, the number of reflection cycles in film are responsible for its unique absorption property [7,11]. These new results are derived from physics and can be proved by numerical calculations on the amplitude of beam t [8,11,12], which contrasts with the commonly accepted previous proposals [10] based on speculation where film and material have not been distinguished.…”

“…They consider a block of material making up a film to have the same properties as the material in general. However, while permittivity ε r and permeability µ r can be properties of material [13], scattering parameters such as reflection loss RL are parameters for devices and not for material [7,8,11,13]. Film, which has thickness, is a device made of material but thickness obviously cannot be a general property of material.…”