Generation of Terahertz waves

Abstract

A method of THz photon generation comprising: providing a magnon gain medium; wherein the magnon gain medium supports generation of nonequilibrium magnons; and injecting nonequilibrium electrons into the magnon gain medium. Propagation of nonequilibrium electrons in the magnon gain medium causes generation of nonequilibrium magnons. Interaction between nonequilibrium magnons causes generation of THz photons.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

FIG. 1 illustrates process of strong electron-magnon interaction (comparatively with electron-electron or with electron-phonon interaction) wherein a nonequilibrium electron put in the upper subband with spin down rapidly emits a magnon with a large wave vector for the purposes of the present invention.

FIG. 2 shows a diagram that illustrates the method of magnon generation of the present invention in terms of a four-level laser effect.

FIG. 3 illustrates the apparatus of the present invention for generation of THz photons.

BEST MODE FOR CARRYING OUT THE INVENTION

Reference now will be made in detail to the preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with the preferred embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, numerous specific-details are set forth in order to provide a thorough understanding of the present invention. However, it will be obvious to one of ordinary skill in the art that the present invention may be practiced without these specific details. In other instances, well known methods, procedures, components, and circuits have not been described in detail as not to unnecessarily obscure aspects of the present invention.

Some portions of the detailed descriptions which follow are presented in terms of particles and quasi-particles interactions, procedures, equations, blocks, diagrams, and other symbolic representations of physical processes. These descriptions and representations are the means used by those skilled in the art of physics of condensed matter to most effectively convey the substance of their work to others skilled in the art.

I. General Idea

The electrons in a ferromagnetic semiconductor can be divided into two groups: free electrons, which determine the electrical conductivity of the semiconductor, and electrons localized at the ions (d- or f-electrons), which determine its magnetic properties.

The main interaction between these two groups of electrons is the exchange interaction, which lift the spin degeneracy of the electrons. The conduction (valence band) splits into two subbands with spin up (along the magnetization) and spin down, with an exchange gap Δ=2I<S_z>, where I is the exchange energy of the conduction electrons and the localized spins, and <S_z> is the mean value of the localized spins. At temperatures much lower than the Curie temperature, Tc, the mean value of the localized spins <S_z> is temperature independent: <S_z>=S.

The exchange gap Δ is usually larger than 0.1 eV. For example, for EuO the exchange gap is: Δ=0.6 eV. For the reference, please see: J. Lascaray, J. P. Desfours, and M. Averous, Sol. St. Corn. 19, 677 (1976).

If the exchange energy is positive, I>0, then the bottom of the subband with spin up 12 is located below the bottom of the subband with spin down 14 (FIG. 1). Usually in ferromagnetic semiconductors the gap Δ 16 (of FIG. 1) is much larger than the maximum of {Tc, E_f}, where E_f is the Fermi energy of the electrons. Therefore, only the states in the lower subband are occupied in equilibrium, i.e. the electrons are fully polarized.

A nonequilibrium electron 20 put in the upper subband with spin down rapidly emits a magnon 18, with a large wave vector q≈⁻¹ (2 mΔ)^1/2, where m is the electron effective mass. It follows from the energy and momentum conservation laws that if the energy of this electron, ε_p, measured from the bottom of the spin down subband is much smaller than Δ, the wave vector of the emitted magnon, q lies in the interval q₁≦q≦q₂, where q_1,2=⁻¹ (p₀±p), p₀=(2 m Δ)^1/2, p=(2 m ε_p)^1/2<<p₀. The frequency of these magnons may be in the Terahertz region.

For EuO, the values of electron mass m are inconsistent according to different references. According to one reference, (J. Shoenes and P. Wachter, Phys. Rev. B 9, 3097 (1974)), m=0.35 m₀, m₀ is the free electron mass, and the wave vector of the exited magnons q≈q₀=⁻¹ p₀=2.6 10⁷ cm⁻¹. The spin-wave stiffness D=10.8 10⁻¹⁶ mev·cm². (Please, see L. Passel, O. W. Dietrich and J. Als-Nielsen, Phys. Rev. B 9, 3097, 1974). This gives the energy of the exited magnons ω=Dq²=0.73 meV, and the frequency f_m=ω/2π=0.19 THz. Merging of two magnons with frequency f and wave vectors {right arrow over (q)} and (−){right arrow over (q)} generates a photon with frequency 2f (for the reference, please see M. I. Kaganov and V. M. Tsukernik, Sov. Phys. -JETP 37, 587 (1960)). Thus, in the above given example, the frequency of the emitted radiation is: f_r=2f_m=0.38 THz.

On the other hand, according to another reference (I. Ya. Korenblit, A. A. Samokhvalov and V. V. Osipov, in Sov. Sc. Rev. A, Physics, 8, 447. Harwood Ac. Publ., UK, 1987), the electron mass value in EuO is quite different: m=1.5 m₀. If this is the case, one obtains a quite different value for the radiation frequency: f_r=1.6 THz.

More generally, consider a ferromagnetic semiconductor with Δ≈0.2 eV, and m=0.3 m₀. Then we have q₀=1.4 10⁷ cm⁻¹. The magnon frequency ω(q₀)≈kTc (q₀a)², where k is the Boltzman constant, and α is the lattice constant. With Tc≈100-300 K and α≈3-5×10⁻⁸ cm, the magnon frequency is f_m≈1.6 THz, and the radiation frequency f_r≈2.0 THz.

The ratio of the magnon generation rate, Γ_e({right arrow over (q)}), to the rate of Γ_m({right arrow over (q)}), their relaxation (in collisions with equilibrium magnons) is a function of the wave vector {right arrow over (q)}. Therefore the nonequilibrium magnon distribution function, N({right arrow over (q)}) has a maximum at some wave vector {right arrow over (q)}={right arrow over (q)}*. N({right arrow over (q)}) increases with the increase of the electron pumping, and because of the simulated emission of magnons, the function N({right arrow over (q)}) grows most rapidly at {right arrow over (q)} close to {right arrow over (q)}*. When the pump reaches some critical value, N({right arrow over (q)}*) starts to increase very fast with the increase of the electron pumping. At some conditions the generation of magnons with {right arrow over (q)}={right arrow over (q)}* becomes avalanche-like, and the magnon system becomes unstable. For more details, please see references: I. Ya. Korenblit and B. G. Tankhilevich, Sov. Phys. -JETP, 46, 1167 (1977); I. Ya. Korenblit and B. G. Tankhilevich, Sov. Phys. -JETP Lett. 24, 555 (1976); I. Ya. Korenblit and B. G. Tankhilevich, Phys. Lett. A 64, 307 (1977), and equations below. As a result an intense Terahertz radiation can be obtained.

II. Basic Equations for Magnon Generation.

The system of equations which govern the behavior of the electron, f_↓({right arrow over (p)}), and magnon, N({right arrow over (q)}) distribution functions were obtained in the following paper: I. Ya. Korenblit and B. G. Tankhilevich, Sov. Phys. -JETP, 46, 1167 (1977). They read

[1+N({right arrow over (q)})]Γ_e({right arrow over (q)})]−[N({right arrow over (q)})−N⁽⁰⁾({right arrow over (q)})]Γ_m({right arrow over (q)})=0

f _↓({right arrow over (p)})γ_em({right arrow over (p)})=g(ε_p).  (Eqs. 1)

Here Γ_e({right arrow over (q)})] is the rate of relaxation of magnons in collisions with electrons

Γ_e({right arrow over (q)})=4π⁻¹I²Sv₀∫d³p(2π)⁻³δ(γ_↑({right arrow over (p)}−{right arrow over (q)})|ε_{{right arrow over (p)}↓}−ω_{{right arrow over (q)}}−ε_{{right arrow over (p)}−{right arrow over (q)},↑})f_↓({right arrow over (p)}),  (Eq. 2)

where v₀ is the unit cell volume.γ_em is the electron-magnon relaxation rate:

γ_em({right arrow over (p)})=4π⁻¹I²Sv₀∫d³q(2π)⁻³δ(γ_↑({right arrow over (p)}−{right arrow over (q)})|ε_{{right arrow over (p)}↓}−ω_{{right arrow over (q)}}−ε_{{right arrow over (p)}−{right arrow over (q)},↑})(1+N({right arrow over (q)})),  (Eq. 3)

The “smeared” δ-function, δ(γ|ε), takes into account the finite lifetime of the electrons in the final state, caused by the interaction with optical phonons, which may be strong in ferromagnetic semiconductors, with an essential ionicity contribution to the chemical bonds. We have

$\begin{array}{cc}\delta \left(\gamma |\varepsilon \right)=\frac{1}{\pi }\frac{\mathrm{\hslash \gamma }}{\left({\varepsilon }^2+{\hslash }^2{\gamma }^2\right)}& \left(\mathrm{Eq}.4\right)\end{array}$

The rate γ_↑(p, ε_p) is the known electron damping rate due to the emission of longitudinal optical phonons (22 of FIG. 1). For electrons with energy ε_p close to Δ, this rate is given by

γ₁(ε_p)=(π/2)αΩ(Ω/Δ)^1/2ln(4Δ/Ω)<<Δ.  (Eq. 5)

Here Ω is the energy of an optical phonon, and α is the strength of the electron-phonon interaction.

The function g(ε) is the generation function of electrons, with spin down. We shall treat it as a δ-function

g(ε_p)=g_0εδ(ε−ε_p).  (Eq. 6)

We suppose in what follows that the energy ε is small, ε<<Δ.

The second term in the l.h.s. in the first of Eqs. (1) describes the relaxation of non-equilibrium magnons in collisions with equilibrium ones, under the assumption that N({right arrow over (q)}), is close to its equilibrium value,

N ⁽⁰⁾({right arrow over (q)})=[e^(ωq/kT)−1]⁻¹.  (Eq. 7)

Γ_m({right arrow over (q)}) is the magnon-magnon relaxation rate. From Eqs. (1) we obtain the following integral equation for N({right arrow over (q)}),

N({right arrow over (q)})=(N⁰({right arrow over (q)})+Γ_e({right arrow over (q)})/Γ_m({right arrow over (q)}))(1−Γ_e({right arrow over (q)})/Γ_m({right arrow over (q)}))⁻¹,  (Eq. 8)

where

Γ_e({right arrow over (q)})=g_0ε∫d³pδ(γ_↑(γ_↑({right arrow over (p)}−{right arrow over (q)})|ε_{{right arrow over (p)}↓}−ω_{{right arrow over (q)}}−ε_{{right arrow over (p)}−{right arrow over (q)},↑})δ(ε−ε_p)Z⁻¹({right arrow over (p)}),  (Eq. 9)

and

Z({right arrow over (p)})=∫d³qδ(γ_↑({right arrow over (p)}−{right arrow over (q)})|ε_{{right arrow over (p)}↓}−ω_{{right arrow over (q)}}−ε_{{right arrow over (p)}−{right arrow over (q)},↑})(1+N({right arrow over (q)})).  (Eq. 10)

Eq. (8) is formally reminiscent of the expression for the magnon distribution function under conditions of parametric pumping. The difference is that here the rate Γ_e is itself a functional of N({right arrow over (q)}), since the number of the emitted magnons depends on the distribution function of the electrons with spin down, f_↓, which according to Eqs. (2) and (3) is in its turn determined not only by the pump g(ε_p) but also by a certain average (10) over the magnon distribution function. The behavior of N({right arrow over (q)}) is therefore different from that in the case of parametric pumping.

III. N({right arrow over (q)}) for Strong Pumping

A. Isotropic Magnons

Let us assume for simplicity that the magnon and electron spectra are isotropic. Then F_e(q) and F_m(q) do not depend on the direction of {right arrow over (q)}.

The relaxation rate Γ(q) is usually a power function of q, and it can be written as

Γ_m(q)=Γ_m(p₀)(q/p₀)^t.  (Eq. 11)

More specifically, if Γ_m(q) is determined by magnon-magnon exchange scattering, then t=4 for magnons, with energy ω(q₀) larger than kT, and t=3 for magnons, with energy ω(q₀) smaller than kT.

The strong pumping regime sets in, when g₀ exceeds a critical value G_c. If the damping of electrons by optical phonons is less than (ΓΔ)^1/2, this critical value is given by

G _c=2gc/(t+1),

g _c=(Δ/ε)^3/2Γ_m(q₀)[1+N⁽⁰⁾(q₀)].  (Eqs. 12)

At g₀>G_c the function N(q) increases exponentially with pumping

N(q)=[1+N⁽⁰⁾(q₀)](p₀/2p_ε(t+1))exp(g₀/G_c),  (Eq. 13)

if q falls into the smooth region

p ₀ −p _ε≦q≦p₀−p_ε+δq,

δq=2p_εexp(−g₀/G_c),  (Eqs. 14)

while N(q) with wave vectors outside of the above-given range does not depend on the pump.

Thus, under sufficiently strong pumping the magnon distribution function has a sharp peak at q≈p₀−p_ε.

Let us define the number of electrons, ε, pumped per second per unit cell as:

ε=v₀(2π)⁻³∫d³pg(ε_p).  (Eq. 15)

One gets for the pumping given by Eq. (6)

β=(v_0ε^3/2m^3/2g₀/2^1/2π²³)  (Eq. 16)

and the critical pumping β_c, with g₀=G_c is

β_c=(v₀q³₀/(2(t+1)π²))Γ_m(q₀)[1+N⁽⁰⁾(q₀)].  (Eq. 17)

Since we are interested in high-frequency magnons, we suppose that their relaxation is mainly due to four-magnon exchange interaction. Using the expressions for Γ_m given in the following reference (V. G. Vaks, A. I. Larkin and S. A. Pikin, JETP 53 (1967)), we estimated for T/Tc≈0.2, and ω(q₀)>kT, N⁽⁰⁾(q₀)<<1: Γ_m≈10⁸-10⁹ sec⁻¹.

Thus, it follows from Eq. (17) the estimate β_c≈10⁵-10⁷ sec⁻¹, and we took into account that N⁽⁰⁾(q₀) is small.

To get a sense of these estimates, we consider a model, in which the spin-down electrons are emitted into their active region across the surface area 1 cm². The lattice constant α of EuO is approximately 5×10⁻⁸ cm, i.e. the unit cell volume is approximately v₀≈10⁻²² cm³. The critical value N_e≈β_c×v₀≈10²⁸-10²⁹ cm⁻³ sec⁻¹. This is the number of electrons, which should cross the edge in one second to achieve the critical number of emitted magnons in a volume of 1 cm³. However, electrons will emit magnons at a short distance from the edge, which can be estimated in the following way.

The electron-magnon frequency γ_em is of order 3×10¹²-10¹³ sec⁻¹. The velocity of electrons with energy of order of 10⁻²Δ is 5×10⁶-10⁷ cm×sec⁻¹. This gives the mean free path of electrons with respect to magnon emission as: l≈10⁻⁶ cm. Thus, all electrons entering a sample (including a magnon gain medium) across a selected side will emit magnons at this distance from that side. Therefore, only the region of width l is active, and we get for the current density j=N_e×1 electrons/sec×cm². The charge of an electron is 1.6×10⁻¹⁹ Q. Taking into account that 1×Q/sec=1 A, we finally get: j=10⁴-10⁵ A/cm². Current densities of order 10⁵-10⁶ A/cm² are easy to achieve in semiconductors. In a pulse regime one can obtain current densities j as high as: j=10⁹ A/cm.

The physical meaning of the critical pumping G_c can be understood as follows. The ratio Γ_e/Γ_m of the rate of generation of the magnons to the rate of their relaxation reaches its maximum value at q=p₀−p_ε and has its minimum at q=p₀+p_ε, i.e. there is an excess generation on the left end of the interval in comparison with the right end. Stimulated emission causes the increase of this asymmetry. Nonlinear generation begins when the difference between the number of non-equilibrium magnons at the ends of the generation interval becomes equal to the number of equilibrium magnons, if N⁽⁰⁾>1. On the other hand, nonlinear generation begins when the difference between the number of non-equilibrium magnons at the ends of the generation interval becomes equal to 1, if the opposite inequality (N⁽⁰⁾<1) holds.

FIG. 2 shows a diagram 30 that illustrates the method of magnon generation of the present invention in terms of a four-level laser effect. Indeed, the valence band corresponds to the lowest laser level 38. These electrons should be pumped into the spin-down subband, which corresponds to the laser's highest level 34. Then the electrons move into the lower energy states in the spin-up subband 36, each electron emitting a magnon. These last electron states correspond to the intermediate state in lasers. Electrons in the spin-up subband 36 move into the bottom of the spin-up subband 32 by emitting optical phonons.

If the electron damping due to optical phonon scattering is large, _γ↑>>(εΔ)^1/2, the critical pumping, G′_c is smaller than gc given by Eq. (12).

G′ _c =πg _cγ_↑/Δ.  (Eq. 18)

The function N (q) in the critical region increases as g₀², and the wave-vector interval of generated magnons decreases as 1/g₀:

N(q)=[1+N⁽⁰⁾(q)](q₀/G′_c)².  (Eq. 19)

One should stress that only the main generation regimes are taken into account herein. More details can be found in the following reference: I. Ya. Korenblit and B. G. Tankhilevich, Sov. Phys. -JETP, 46, 1167 (1977).

B. Effect of Anisotropy. Instability of the Magnon System.

If the ratio of the generation rate Γ_e({right arrow over (q)}) to the relaxation rate Γ_m({right arrow over (q)}) depends on the direction of the wave vector {right arrow over (q)}, then in the nonlinear regime the stimulated emission of magnons results in the strong anisotropy of magnon distribution function. As an example, one can consider the anisotropy of Γ_e ({right arrow over (q)})/Γ_m({right arrow over (q)}) caused by the anisotropy of the magnon spectrum. The spectrum of magnons with q close to p₀/ can be written as

ω_q=Dq²(1+Λ sin² θ),  (Eq. 20)

where

Λ=2gμ_BM_s/ω_p0<<1,  (Eq. 21)

M_s is the magnetization, θ_{{right arrow over (q)}} is the angle between the vectors {right arrow over (q)} and {right arrow over (M)}_s. If the inequality ω(q₀)<kT holds, then the anisotropy of Γ_e({right arrow over (q)})/Γ_m({right arrow over (q)}) implies that the generation is the largest at some angle θ.

Consider the situation, when the damping is large, i.e. γ_↑>>(εΔ)^1/2. Since the anisotropy is small (Λ<<1), the anisotropy becomes effective only at sufficiently strong pumping, larger than the critical one, Eq. (18). At g=G_c given by this equation, the number of magnons starts to increase as in the isotropic case. If one assumes that the basic equations (Eqs. 1), describing the generation of magnons close to equilibrium, are valid also beyond the critical pumping, one can reveal the role of small anisotropy.

As shown in the following reference: I. Ya. Korenblit and B. G. Tankhilevich, Sov. Phys. -JETP, 46, 1167 (1977), the maximum generation takes place for magnons with θ close to zero and q close to p₀. If the pumping reaches the critical value g*

g*=π ² γ_↑g_c/2Λ^1/2Δ,  (Eq. 22)

the function N({right arrow over (q)}) becomes

$\begin{array}{cc}\begin{array}{c}N\left(\overrightarrow{q}\right)=N^{\left(0\right)}\left(\overrightarrow{q}\right)\\ {\left[1+\Lambda {\sin }^2\left(\theta \right)-\frac{{\hslash }^2{\gamma }_{\uparrow }^2}{\left({\left(\Delta -{\varepsilon }_q\right)}^4+{\hslash }^2{\gamma }_{\uparrow }^2\right)}{\left(\frac{p_0}{\hslash q}\right)}^2\right]}^{-1}\end{array}& \left(\mathrm{Eq}.23\right)\end{array}$

where ε_q=²q²/2 m.

We get at q=p₀, i.e. at ε_q=Δ

N({right arrow over (q)})=N⁽⁰⁾({right arrow over (q)})/Λ sin² (θ_{{right arrow over (q)}})  (Eq. 24)

At θ=0 the denominator of this expression goes to zero. The steady solution of Eqs. (1) exists only at pumping levels below g*. When the pumping level reaches the critical value g*, an avalanche-type growth of the number of magnons occurs, whereas the wave vectors of these non-equilibrium anisotropic magnons are directed along the magnetization and are equal to p₀.

Note, that at sufficiently low temperatures the three-magnon dipole scattering may be more important then the discussed above four-magnon exchange scattering. However, the three-magnon scattering probability, as opposed to the four-magnon exchange scattering probability, is a highly anisotropic one and is proportional to sin^{2 θ cos2} θ. If this is the case, one should expect an instability of magnons with θ=0 and θ=π/2.

IV. Generation of THz Radiation.

The interaction of magnons with electromagnetic radiation was considered in the following reference: M. I. Kaganov and V. M. Tsukernik, Sov. Phys. -JETP 37, 587 (1960). Merging of two magnons with wave vectors q and q′ generates a photon with wave vector

{right arrow over (k)}={right arrow over (q)}+{right arrow over (q)}′  (Eq. 25)

and with frequency v_k equal to

ω_q+ω_q′=v_k=ck,  (Eq. 26)

where c is the light velocity.

It follows from these conservation laws that k is much smaller than q, i.e. {right arrow over (q)}=−{right arrow over (q)}′.

Using the results of the same reference: M. I. Kaganov and V. M. Tsukernik, Sov. Phys. -JETP 37, 587 (1960), one can derive the rate of the change of the photon distribution function, n(v) in the following way:

$\begin{array}{cc}\begin{array}{c}n\left(v\right)/t=W\int \theta ·{\sin }^5\theta [N^2\left(v/2,\theta \right)·\left(n\left(v\right)+1\right)\\ -n\left(v\right){\left(N\left(v/2,\theta \right)+1\right)}^2]-\frac{n\left(v\right)-n^{\left(0\right)}\left(v\right)}{{\tau }_{\mathrm{ph}}},\end{array}& \left(\mathrm{Eq}.27\right)\end{array}$

Here

$\begin{array}{cc}W=\frac{{\mu }^2q_0^3}{2\hslash }·{\left(\frac{4\pi g\mu M_s}{\hslash v}\right)}^2,& \left(\mathrm{Eq}.28\right)\end{array}$

where μ is the Bohr magneton. The last term in the (Eq. 27) describes the relaxation of generated photons, and τ_ph is the photon relaxation time.

For EuO, with q₀=2.6×10 cm⁻¹, v=1.5 meV, and 4πM_s=24×10³ Gs, one obtains W≈2×10⁷ sec⁻¹.

If the magnon distribution function is isotropic, one can perform the integration in Eq. (27) and one gets the following equation:

$\begin{array}{cc}\begin{array}{c}n\left(v\right)/t=\left(16/15\right)·W·[N^2\left(v/2\right)-2n\left(v\right)·\\ N\left(v/2\right)-n\left(v\right)]-\frac{n\left(v\right)-n^{\left(0\right)}\left(v\right)}{{\tau }_{\mathrm{ph}}}.\end{array}& \left(\mathrm{Eq}.29\right)\end{array}$

By analyzing this equation, it is clear that at the initial stage of generation, when n is smaller than N, the number of photons increases as N², provided the photon relaxation is sufficiently small. With the increase of n, the negative terms in Eq. (29) become significant, and the photons reach a steady state, with dn/dt=0. If this is the case, we have the following expression for the number of photons n at the steady state:

$\begin{array}{cc}n=\frac{n^{\left(0\right)}+w{\tau }_{\mathrm{ph}}N^2}{1+\left(2N+1\right)w{\tau }_{\mathrm{ph}}},& \left(\mathrm{Eq}.30\right)\end{array}$

where w=16W/15.

If wτ_ph is large, wτ_ph>>1/N, the number of photons is as follows:

$\begin{array}{cc}n=\frac{N^2}{2N+1}\approx \frac{N}{2}.& \mathrm{Eq}.\left(31\right)\end{array}$

If, on the other hand, 1/N²<<wτ_ph<<1/N, the number of photons is as follows:

n=wτ _ph N ²,1<<n<<N.  Eq. (32)

Finally, if the relaxation of photons is very fast, wτ_phN²<<1, the pumping is inefficient, and

n≈n⁽⁰⁾.  Eq. (33)

V. Applicable Materials.

The magnon gain medium of the present invention can be implemented by selecting any material that supports generation of substantial number of nonequilibrium magnons that by merging into photons generate THz photons. For example, ferromagnetic semiconductors (europium chalcogenides and chalcogenide spinels), and/or ferromagnetic isolators, can be used to implement the magnon gain medium of the present invention.

VI. Pumping Methods.

Any method that can generate substantial number of nonequilibrium electrons that could rapidly emit nonequilibrium magnons could be used for the purposes for the present invention. For example, laser pumping of polarized electrons, injection of polarized electrons, etc. In addition, injection of non-polarized electrons can be also used for the purposes for the present invention.

VII. Apparatus for Generation of THZ Waves.

In one embodiment of the present invention, FIG. 3 illustrates the apparatus 60 for generation of THz waves having the following elements: a magnon gain medium 64 including a material that supports generation of substantial number of nonequilibrium magnons, a pumping source 62 configured to pump nonequilibrium electrons into the magnon gain medium 64, an optical resonator 74-76 configured to accumulate generated THz photons, and configured to release the generated THz photons exceeding the threshold photon density, and a THz waveguide 78 configured to output the generated THz photons.

In one embodiment of the present invention, the optical resonator 74-76 comprises polished surfaces of magnon gain medium 76 and 74, or additional mirrors (not shown) configured to contain THz photons up to the threshold density of THz photons. At the threshold density, the THz photons are released from the magnon gain medium 64 into the THz waveguide 78.

In one embodiment of the present invention, the THz photons released from the magnon gain medium 64 into the THz waveguide 78 can be accumulated in the optical cavity 82.

In one embodiment of the present invention, the optical cavity comprises an optical resonator. In one embodiment of the present invention, the optical resonator comprises a Fabry-Perot cavity, a distributed feedback (DFB) cavity, or a distributed Bragg reflector (DBR).

In one embodiment of the present invention, the magnon gain medium 64 is placed in a thermostat 80 that keeps the operational temperature T below the critical temperature T_c. For instance, for EuO, the thermostat 80 keeps the EuO sample at temperature T below its Curie temperature: T<T_c=70K.

VIII. Method for Generation of THz Waves.

In one embodiment, the steps of the method of the present invention for THz photon generation can be performed by using the above-disclosed apparatus 60 (of FIG. 3) of the present invention.

In one embodiment, the method of the present invention for photon generation comprises the following steps (not shown): (A) providing a magnon gain medium; wherein the magnon gain medium supports generation of nonequilibrium magnons; and (B) generating the nonequilibrium magnons in the magnon gain medium; wherein interaction between the nonequilibrium magnons causes generation of photons.

In one embodiment of the present invention, the step (A) further comprises: (A1) placing the magnon gain medium 64 in the thermostat 80 to maintain temperature of the magnon gain medium below a critical temperature. This step is herein illustrated by using the apparatus 60 (of FIG. 3) of the present invention.

In one embodiment of the present invention, the step (A) further comprises: (A2) selecting the magnon gain medium from the group consisting of: {ferromagnetic semiconductor; ferromagnetic isolator; and ferromagnetic material}.

In one embodiment of the present invention, the step (A2) further comprises: (A2, 1) placing the magnon gain medium comprising the selected ferromagnetic material in the thermostat to maintain temperature of the selected ferromagnetic material below its Curie temperature.

Indeed, in general, to achieve the generation of photons, it is sufficient to generate nonequilibrium magnons in a magnon gain medium, and to merge the generated nonequilibrium magnons.

More specifically, in one embodiment of the present invention, the step (B) of generating the nonequilibrium magnons in the magnon gain medium comprises: (B1) injecting nonequilibrium electrons into the magnon gain medium; wherein propagation of the nonequilibrium electrons in the magnon gain medium causes generation of the nonequilibrium magnons. Please, see the given above detailed equations Eqs. (1-24) that describe how the propagation of the nonequilibrium electrons in the magnon gain medium causes generation of nonequilibrium magnons.

In one embodiment of the present invention, the step (B1) further comprises pumping nonequilibrium electrons by using the source of electrons 62 (of FIG. 3).

In another embodiment of the present invention, the step (B1) further comprises pumping substantially sufficient number of polarized nonequilibrium electrons into the magnon gain medium to cause generation of the nonequilibrium magnons in the magnon gain medium. In one more embodiment of the present invention, the step (B1) further comprises pumping a threshold number of polarized nonequilibrium electrons into the magnon gain medium, wherein the threshold number of pumped polarized nonequilibrium electrons is substantially sufficient to generate a magnon avalanche effect in the magnon gain medium. Please see Eqs. (12-14).

In one embodiment of the present invention, the step (B1) further comprises changing a maximum frequency of the generated photons by changing critical temperature of the magnon gain medium; wherein the critical temperature of the magnon gain medium depends on an external parameter; and wherein the external parameter is selected from the group consisting of: {an external pressure; and a concentration of impurities in the magnon gain medium}.

Indeed, for instance, the Curie temperature of EuO can be changed by applying an external pressure, and/or by doping EuO with certain impurities. Please, see M. W. Shafer and T. R. McGuire, J. Appl. Phys., 39, 588 (1968).

In one embodiment of the present invention, the step (B1) further comprises changing a n operating frequency of the generated photons; wherein the operating frequency of the generated photons depends on an external parameter; and wherein the external parameter is selected from the group consisting of: {energy of the injected electrons; and an operating temperature of the thermostat}.

From the given above equations Eqs. (1-24) one can deduct that an operating frequency of the generated photons depends to some extent on the energy of the injected electrons. In addition, an operating frequency of the generated photons also depends on operating temperature of the thermostat according to the according to the following relationship ω=Dq²=2D⁻¹ mΔ and according to the following equation Eq. (34):

Δ=2I<S_z>.  Eq. (34)

In one embodiment of the present invention, the step (B1) further comprises: (B2) generating THz photons by using a merging process between the nonequilibrium magnons in the magnon gain medium.

The given above detailed equations Eqs. (25-34) describe the generation of THz photons by using the merging of two nonequilibrium magnons, and the properties of generated THz photons.

In one embodiment, the method of the present invention further comprises: (C) manipulating photon reflection coefficient of the generated photons at surface area of the magnon gain medium by using reflective and transmission means attached to the surface area of the magnon gain medium. Please, see the apparatus 60 (of FIG. 3) of the present invention.

In one embodiment of the present invention, the step (C) further comprises: (C1) selecting the reflective and transmission means from the group consisting of: {an optical cavity; and a Fabry-Perot cavity}.

In one embodiment of the present invention, the step (C) further comprises: (C2) accumulating the generated photons in the magnon gain medium by using the reflective and transmission means attached to the surface area of magnon gain medium. Please, see the apparatus 60 (of FIG. 3) of the present invention.

In one embodiment of the present invention, the step (C2) further comprises accumulating a threshold number of the generated photons in the magnon gain medium, wherein the threshold number of accumulated photons is substantially sufficient for nonlinear photon-photon interaction process. If this is the case, and if the nonequilibrium magnons generate photons having basic frequency v_basic, the nonlinear photon-photon interaction process can lead to generation of photons having v_2basic, v_3basic, v_4basic, and so on.

In one embodiment, the method of the present invention further comprises: (D) utilizing a waveguide (78 of FIG. 3) attached to the magnon gain medium (64 of FIG. 3) to output the generated photons outside the magnon gain medium.

In one embodiment of the present invention, the step (D) further comprises: (D1) accumulating the generated photons in an outside optical cavity (82 of FIG. 3) attached to the waveguide.

In one embodiment of the present invention, the step (D) further comprises: (D2) accumulating a threshold number of generated photons in the outside optical cavity attached to the waveguide, wherein the threshold number of accumulated photons is substantially sufficient for nonlinear photon-photon interaction process (not shown).

The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents

Claims

1. A method of photon generation comprising: (A) providing a magnon gain medium; wherein said magnon gain medium supports generation of nonequilibrium magnons; and(B) generating said nonequilibrium magnons in said magnon gain medium; wherein interaction between said nonequilibrium magnons causes generation of photons.

2. The method of claim 1, wherein said step (A) further comprises: (A1) placing said magnon gain medium in a thermostat to maintain temperature of said magnon gain medium below a critical temperature.

3. The method of claim 1, wherein said step (A) further comprises: (A2) selecting said magnon gain medium from the group consisting of: {ferromagnetic semiconductor; ferromagnetic isolator; and ferromagnetic material}.

4. The method of claim 3, wherein said step (A2) further comprises: (A2, 1) placing said magnon gain medium comprising said selected ferromagnetic material in said thermostat to maintain temperature of said selected ferromagnetic material below its Curie temperature.

5. The method of claim 1, wherein said step (B) further comprises: (B1) injecting nonequilibrium electrons into said magnon gain medium; wherein propagation of said nonequilibrium electrons in said magnon gain medium causes generation of said nonequilibrium magnons; and wherein interaction between said nonequilibrium magnons causes generation of photons.

6. The method of claim 5, wherein said step (B1) further comprises: (B1, 1) pumping nonequilibrium electrons into said magnon gain medium.

7. The method of claim 5, wherein said step (B1) further comprises: (B1, 2) pumping polarized nonequilibrium electrons into said magnon gain medium.

8. The method of claim 5, wherein said step (B1) further comprises: (B1, 3) pumping substantially sufficient number of polarized nonequilibrium electrons into said magnon gain medium to cause generation of said nonequilibrium magnons in said magnon gain medium.

9. The method of claim 5, wherein said step (B1) further comprises: (B1, 4) pumping a threshold number of polarized nonequilibrium electrons into said magnon gain medium, wherein said threshold number of pumped polarized nonequilibrium electrons is substantially sufficient to generate a magnon avalanche effect in said magnon gain medium.

10. The method of claim 5, wherein said step (B1) further comprises: (B1, 5) changing a maximum frequency of said generated photons by changing critical temperature of said magnon gain medium; wherein said critical temperature of said magnon gain medium depends on an external parameter; and wherein said external parameter is selected from the group consisting of: {an external pressure; and a concentration of impurities in said magnon gain medium}.

11. The method of claim 5, wherein said step (B1) further comprises: (B1, 6) changing an operating frequency of said generated photons; wherein said operating frequency of said generated photons depends on an external parameter; and wherein said external parameter is selected from the group consisting of: {energy of said injected electrons; and an operating temperature of said thermostat}.

12. The method of claim 1, wherein said step (B) further comprises: (B2) generating THz photons by using a merging process between said nonequilibrium magnons in said magnon gain medium.

13. The method of claim 1 further comprising: (C) manipulating photon reflection coefficient of said generated photons at surface area of said magnon gain medium by using reflective and transmission means attached to said surface area of said magnon gain medium.

14. The method of claim 13, wherein said step (C) further comprises: (C1) selecting said reflective and transmission means from the group consisting of: {an optical cavity; and a Fabry-Perot cavity}.

15. The method of claim 13, wherein said step (C) further comprises: (C2) accumulating said generated photons in said magnon gain medium by using said reflective and transmission means attached to said surface area of magnon gain medium.

16. The method of claim 15, wherein said step (C2) further comprises: (C2, 1) accumulating a threshold number of said generated photons in said magnon gain medium, wherein said threshold number of accumulated photons is substantially sufficient for nonlinear photon-photon interaction process.

17. The method of claim 16, wherein said step (C2, 1) further comprises: (C2, 1, 1) changing the frequency of said generated photons by using said nonlinear photon-photon interaction process.

18. The method of claim 1 further comprising: (D) utilizing a waveguide attached to said magnon gain medium to output said generated photons outside said magnon gain medium.

19. The method of claim 18, wherein said step (D) further comprises: (D1) accumulating said generated photons in an outside optical cavity attached to said waveguide.

20. The method of claim 18, wherein said step (D) further comprises: (D2) accumulating a threshold number of said generated photons in said outside optical cavity attached to said waveguide, wherein said threshold number of accumulated photons is substantially sufficient for nonlinear photon-photon interaction process.

21. The method of claim 20, wherein said step (D2) further comprises: (D2, 1) changing the frequency of said generated photons by using said nonlinear photon-photon interaction process

22. An apparatus for photon generation comprising: (A) a magnon gain medium; wherein said magnon gain medium supports generation of nonequilibrium magnons; and(B) a means for generating said nonequilibrium magnons in said magnon gain medium; wherein interaction between said nonequilibrium magnons causes generation of photons.

23. The apparatus of claim 22 further comprising: (C) a thermostat, wherein said magnon gain medium is placed in said thermostat, and wherein said thermostat is configured to maintain temperature of said magnon gain medium below a critical temperature.

24. The apparatus of claim 22, wherein said means (B) further comprises: (B1) a means for injecting nonequilibrium electrons into said magnon gain medium; wherein propagation of said nonequilibrium electrons in said magnon gain medium causes generation of said nonequilibrium magnons; and wherein interaction between said nonequilibrium magnons causes generation of photons.

25. The apparatus of claim 24, wherein said means (B1) further comprises: (B1, 1) a means for pumping nonequilibrium electrons into said magnon gain medium.

26. The apparatus of claim 24, wherein said means (B1) further comprises: (B1, 2) a means for pumping nonequilibrium polarized electrons into said magnon gain medium.

27. The apparatus of claim 22 further comprising: (D) a reflective and transmission means attached to surface area of said magnon gain medium, wherein said reflective and transmission means are configured to manipulate said reflection coefficient of said generated photons at said surface area of said magnon gain medium, and wherein said reflective and transmission means are selected from the group consisting of: {said optical cavity; and said Fabry-Perot cavity}.

28. The apparatus of claim 22 further comprising: (E) a waveguide attached to said magnon gain medium, said waveguide configured to output said generated photons outside said magnon gain medium.

29. The apparatus of claim 22 further comprising: (F) an outside optical cavity attached to said waveguide, wherein said outside optical cavity is configured to accumulate said generated photons.

30. The method of claim 1, wherein said step (A) further comprises: (A3) providing said magnon gain medium; wherein said magnon gain medium includes a conduction (valence band) that splits into two subbands, and wherein said first subband is configured to be populated by electrons having spin up, and wherein said orientation of spin up is an orientation directed along a direction of a magnetization of said magnon gain medium; and wherein said second subband is configured to be populated by electrons having spin down, and wherein said orientation of spin down is an orientation directed opposite to said direction of said magnetization of said magnon gain medium.

31. The method of claim 1, wherein said step (A) further comprises: (A4) providing said magnon gain medium; wherein said magnon gain medium includes said conduction (valence band) that splits into said two subbands, and wherein said first subband is configured to be populated by electrons having spin up; and wherein said second subband is configured to be populated by electrons having spin down; and wherein said two subbands with said spin up and said spin down are separated by an exchange gap.

32. The method of claim 1, wherein said step (A) further comprises: (A5) providing said magnon gain medium; wherein said magnon gain medium includes said conduction (valence band) that splits into said two subbands, and wherein said first subband is configured to be populated by electrons having spin up; and wherein said second subband is configured to be populated by electrons having spin down; and wherein said two subbands with said spin up and said spin down are separated by said exchange gap; and wherein if an exchange energy is positive then a bottom of said subband with said spin up is located below a bottom of said subband with said spin down.

33. The method of claim 1, wherein said step (A) further comprises: (A6) providing said magnon gain medium; wherein said magnon gain medium includes said conduction (valence band) that splits into said two subbands, and wherein said first subband is configured to be populated by electrons having spin up; and wherein said second subband is configured to be populated by electrons having spin down; and wherein said two subbands with said spin up and said spin down are separated by said exchange gap; and wherein if said exchange energy is positive then said bottom of said subband with said spin up is located below said bottom of said subband with said spin down; and if said gap Δ is much larger than the maximum of {Tc, Ef}, wherein Tc is a Curie temperature of said magnon gain medium, and wherein Ef is a Fermi energy of electrons, then only the electron states in said lower subband with spin up are occupied in equilibrium, i.e. the electrons are fully polarized.

34. The method of claim 1, wherein said step (A) further comprises: (A7) providing said magnon gain medium; wherein said magnon gain medium includes said conduction (valence band) that splits into said two subbands, and wherein said first subband is configured to be populated by electrons having spin up; and wherein said second subband is configured to be populated by electrons having spin down; and wherein said two subbands with said spin up and said spin down are separated by said exchange gap; and wherein if said exchange energy is negative then said bottom of said subband with said spin up is located above said bottom of said subband with said spin down.