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The amplification of microwaves in
*n*-GaAs films has been widely studied. On the other hand, using nonlinear parametric effects in microwave, millimeter, and THz ranges has a large potential. In this paper the resonant nonlinear phenomena are investigated in active
*n*-GaAs semiconductor and in films on its base. The phenomena are the nonlinear interactions of space charge waves, including the frequency multiplication and mixing, and the three-wave interaction between two THz electromagnetic waves and a single space charge wave. This three-wave interaction results in the superheterodyne amplification of THz waves. The electron velocity in GaAs is the nonlinear function of an external electric field. If the bias electric field is more
*E*_{0}>*E*_{crit} ≈3KV/cm , it is possible to obtain a negative differential mobility (NDM and space charge waves). The space charge waves have phase velocity of electrons equal to
*v*_{0}*=v(E*_{0}*), E*_{0}*=V*_{0}*/L*_{z} , where
*V*
_{0} is the voltage, producing the bias electric field
*E*
_{0 }in GaAs film. The superheterodyne amplification and the multiplication of microwaves are very promising for building active sensors in telecommunications system, radiometers, and radio telescopes. The superheterodyne mechanism has an advantage related to decreasing noise because of increasing of frequency in the process of amplification. It is used in the process of amplification of longitudinal space charge waves that in turn causes the transfer of energy from longitudinal wave into transverse one with increasing frequency. This is realized due to parametric coupling of two transverse waves and a single space charge wave in GaAs.

Very high frequencies including gigahertz range are very promising for building active devices [

There are different effects of nonlinear interaction of electromagnetic waves which caused the increase of frequency. More frequently it is using the terminus superheterodyne mechanism for increasing the frequencies. It is useful to show how works all mechanisms on simplest case with analytical demonstration of superheterodyne amplification in case of GaAs thanks parametric connection of two transversal waves and charge wave. It is necessary to explain the role of space charge wave. Amplification of traveling space charge waves (SCW) of the microwave range in n-GaAs has been under investigations for many years [

In order to obtain a negative differential mobility (NDM), the bias electric field

Let’s consider el crystal GaAs In order to obtain a negative differential mobility (NDM) in GaAs, the bias electric field

There are the two electromagnetic waves of THz range with frequencies and wave numbers _{,}

The wave synchronism is realized at the frequencies:

where

and hydrodynamic equation of the motion for the electrons

where

with plasma frequency

(

It is necessary to use

where

rential mobility

where

obtain the equation for longitudinal variable wave

where the right part is calculated like resonance part of longitudinal part,

tivity negative if field is more critical.

For transverse waves (

The right parts of (7) and (8) describe the nonlinear interaction of waves which is resonance (1) with respect to the wave equation.

The nonlinear interactions of waves are with longitudinal wave and transversal electromagnetic waves

where

The nonlinear right parts in (7) and (8) were calculated using Bloembergen’s method [

where_{. }From (8) we have two nonlinear equations for transverse waves:

where

tain the nonlinear equation for longitudinal wave

We analyze amplification by means of using constant pumping wave

tions

and the conditions

decisions

For

And

The superheterodyne amplification is characterized by coefficients

If we have negative differential mobility

where

centration of electrons

the plasma frequency_{o} is the mass of electron,

for the case of superheterodyne interaction.

The amplification is more perspective for integrated system so it is necessary to analyze amplification and multiplication for obtain increase of frequencies in GaAs films with space charge waves. It is possible by means of computer simulation and consideration of the parametric interaction of space charge waves with matching conditions is realized:

The electron velocity in GaAs is the nonlinear function of an external electric field [

The Equations (15), (16) are added by boundary conditions:

Here

The output antenna is in

For a small monochromatic input signal (

In the case of NDM (

Simulations of wave mixing in GaAs films demonstrate a possibility to get the

signal at sum frequency under a wide range of amplitudes of input signals. The spectral distributions of output signal

A comparison of simulations with experiment on wave mixing in GaAs films [

It is shown that superheterodyne amplification is realized by negative differential mobility in GaAs and nonlinear interaction two transversal and longitudinal waves. The pumping wave of very small amplitude helps to move the energy of battery to microwave. Usually level of noise is low in high of frequency and absent of domains. The advantage to use of transversal waves is in moving very easy from crystal. The pumping wave may be very low amplitude. The value of amplification is very big on the length

The mechanism of the mixing and the multiplication is a transition of instability into an essentially nonlinear regime. There exists the optimal width of input antenna for observing wave parametric and multiplication effects.

Comparison of simulations with experiment on wave mixing in GaAs films is to show a coincidence on frequency interval and possible levels of input signals.

It is possible future work to investigate some other crystal having negative differential mobility which it is realized now. For another hand it is possible to use the strongly nonlinear material like

Koshevaya, S., Grimalsky, V., Kotsarenko, Y., Tecpoyotl, M. and Escobedo, J. (2017) Superheterodyne Amplification for Increase the Working Frequency. Journal of Electromagnetic Analysis and Applications, 9, 43-52. https://doi.org/10.4236/jemaa.2017.93005