rus
A radically new approach to self-organization in a system collective of fields + molecular gas of an ensemble of optically active electron-ion nanoparticles on a prepared magnetomultipole transition is substantiated. Laser generation is self-excited in the nanoparticle ensemble at the magnetomultipole transition frequency. This radiation has a high-order coherence, σ-polarized vertex field, and large orbital angular momentum.
Теги: coherence laser molecular optics optically active medium orbital angular momentum vertex field вихревое поле когерентность лазер молекулярная оптика оптически активная среда угловой орбитальный момент
As is well known [1], basic elements of an electric dipole (ED) laser are a medium comprising molecules (atoms), a resonator, and a pump. Laser radiation generation is self-excited at the moment of time when the threshold inversion of the population density is reached between the states of the ED transition of molecules (atoms) of the medium at the frequency of one of the resonator modes due to a positive feedback (PFB) between the photons of stimulated radiation and the medium. The characteristics and properties of ED laser radiation depend on those of the medium, the resonator, and the pump.
Basic elements of a magnetomultipole (MM) laser are a collective of fields and a molecular gas comprising molecules and broadening particles (molecules or atoms). The molecules have low-frequency ED and high-frequency magnetic multipole rovibrational transitions united by the lowest state according to the V-scheme
(1)
The collective of fields consists of the electric, , and magnetic components, , of the field of elastic collisions of molecules with broadening particles, the p-polarized biharmonic pumping light wave (BLW), and the Rayleigh scattering [2, 3].
The two-dimensional parametrical energy resonance between the V-scheme of transitions and the difference and summed BLW frequencies engenders the two-dimensional spatiotemporal PFB between energies of the quadratic Stark and Zeeman effects [3] in the BLW coherence volume of the system collective of fields + molecular gas (referred to as the system below). The molecules accumulate the threshold diamagnetic susceptibility along the Z BLW axis in the process of a single elastic collision with particles and hence, the threshold diamagnetic energy in the V-scheme of transitions to the highly excited magnetic multipole state. In this system: 1) the ensemble of optically active electron-ion nanoparticles on the prepared (mixed) MM nonrigid transition and 2) the complex refractive index of the nanoparticle ensemble are self-organized into a multi-cylindrical optical “solenoid-resonator.” Generation of MM laser radiation is self-excited at the MM transition frequency. The MM radiation characteristics and properties depend on those of nanoparticle ensemble and BLW pumping field [4].
The present work is aimed at substantiation of a radically new approach to self-organization of the electron-ion nanoparticle ensemble on the nonrigid prepared MM transition and generation of MM radiation at its frequency.
FROM INITIAL EXPERIMENTS
TO A CONCEPTUAL MODEL
In the absorption [5] and re-radiation spectra [6] of Н2О molecules obtained with participation of ruby laser radiation and broadening particles (N2 molecules) at atmospheric pressure there was something extraordinary. The absorption spectrum of Н2О molecules [5] contained ten lines (rather than one well-known line) obtained by the classical technique examined/reference beam of BLW p-polarized ruby laser radiation. The absorption coefficient in the center of 9 lines appeared greater by four orders of magnitude than its value corresponding to the intensity of these lines [7]. In [6] the well-known Н2О line was recorded with a polychromatic ruby ICL spectrometer for the same molecular gas parameters. The well-known absorption line decreased the population density inversion in the ruby laser radiation circuit, and a high-power signal of monochromatic radiation was recorded near the center of the absorption line. These results fell beyond the scope of the ED approximation and semiclassical theory of laser radiation interaction with molecular gas having the preset parameters of the medium and pumping.
Two specially performed experiments with the well-known line gave the following results. The nonlinear absorption of p-polarized laser radiation was manifested in the anomalous region of the known Н2О line profile more strongly, than that of σ-polarized radiation [8]. The absorption coefficient in the anomalous region of the well-known line profile recorded with the ICL spectrophotometer depended significantly on the frequency of the Stark modulation of Н2О states [9].
An analysis of the role of system parameters in the formation of the anomalous region of the well-known absorption line profile allowed three conclusions to be drawn. First, the probabilities of ED and weak rovibrational magnetic multipole transitions can change radically during one elastic collision of molecules with particles for definite parameters of the collective field and molecular gas.
Second, we can go beyond the scope of the ED approximation and semiclassical theory by means of control over quantum events of intra- and intermolecular dynamics of energy states in the V-scheme of transitions.
Third, internal sign-variable amplitude-phase modulation of the pumping BLW in the V-scheme of transitions described by Eq. (1) can correct the process of origin of the two-dimensional PFB between energies of the quadratic Stark and Zeeman effects [3, 4].
TWO-DIMENSIONAL CONSTRUCTIVE FEEDBACK
The physical reason for the origin of the two-dimensional PFB is the two-dimensional parametrical energy resonance (interference between the intramolecular field and the collective field) between the V-scheme of transitions given by Eq. (1) and the difference, , and summed frequencies, , in the BLW coherence volume:
, (2)
where and are the coherence length and the diameter of the BLW pumping beam. Here is the serial number of the step of the BLW field at time moments of amplitude modulation sign change (±) in the direction orthogonal to the Z axis and at time moments of phase modulation sign change () along the Z axis of BLW propagation.
The field of elastic collision, breaking the symmetry of electronic shells of the molecule, induces in them the electric, , and magnetic, , dipole moments, and also their components characterizing the fields gradient and the gyration tensor g. These components create diamagnetic traps for the electron, , and ion, , of the molecule that run away under the action of the Lorentz and Coriolis forces. Here and are fluctuations of the electric polarizability perpendicular to the Z axis and of the diamagnetic susceptibility along the Z axis of the BLW.
To implement the BLW phase modulation and to create the two-dimensional PFB, it is necessary to have a sufficient degree of field asymmetry and a sufficient number of broadening particles, BLW pumping photons, and molecules in the volume given by Eq. (2). The sign-variable BLW amplitude-phase modulation corrects running away of charges and , respectively, and hence, the frequency of fluctuations of the dipole moments and .
As a “trigger” mechanism for the origin of the two-dimensional PFB, the amplitude-phase step serves, where fluctuations of he moments and at the frequencies of V-scheme (1) are locked by the BLW frequencies and in the two-dimensional parametrical resonance. The size of the BLW step must be less than the valence electron memory [10] of molecules (here is the energy of molecule ionization). As a consequence, the nonlocality radius of the electron response between the time moments and increases regularly in the anomalous region of the weak magnetic multipole transition given by Eq. (1) due to electron orbit deformation in the process of the elastic collision.
The collective field components and are overlapped on transitions (1), the quadratic nonlinearity arises in molecules, and the diamagnetic energy of coupling of charges and increases under the action of the Lorentz and Coriolis forces when they run away. As a consequence, the two-dimensional PFB arises between energy fluctuations of the Stark effect at the frequency perpendicular to the Z axis and of the Zeeman effect at the frequency along the Z axis in volume (2) at the time moment. Here and are radius-vectors emanating from the origin of coordinates of the molecule perpendicular the Z axis and along the Z axis at the points of electron localization at the time moments and .
SELF-ORGANIZATION OF THE NANOPARTICLE ENSEMBLE AND SELF-EXCITATION OF GENERATION
The two-dimensional PFB controls over the velocity of charges and running away in the V-scheme of transitions of molecules and over the transformation of diamagnetic traps into an amplitude-phase profiled zone plate so that the even and odd Frenel zones in volume (2) “act in phase.” The amplitude-phase zone plate is the magneto-optical analog of the “phase” zone plate [11] having different thicknesses of the even and odd zones of the microlens system. The magneto-optical analog allows the phase of the outgoing light wave to be varied smoothly within each Fresnel zone. In this case, in the anomalous region of the weak magnetic multipole transition the velocity of energy transfer of the collective field decreases down to the electron velocity , and the BLW phase velocity increases. As a consequence, the steepness of the real component and the absolute value of the imaginary component (susceptibility ) of the complex refractive index increase on the magnetic multipole transition .
Since the molecular relaxation times s (at atmospheric pressure) is greater than the time of their elastic collision s [12] and, the more so, than the step of energy changes and in the V-scheme, by the end of the cycle
(3)
the energy of motion of molecules is frozen down to the lowest state in Eq. (1), and the energy of the collective field is transformed into the diamagnetic energy of the highly excited magnetic multipole state, which increases the probability of transition by several orders of magnitude. In this case, the ensemble of optically active electron-ion nanoparticles in the system is self-organized on the prepared nonrigid MM transition described by Eq. (1). The ensemble of nanoparticles acquires multi-cylindrical shape (according to the number of the Fresnel zones) of the optical “solenoid-resonator” with the electric, magnetic, and mechanical spatiotemporal ordering. The nanoparticle ensemble possesses:
the complex refractive index
the property of circular birefringence;
the built-in projections of the angular orbital nanoparticle momentum along the field vector of the standing s±-polarized wave (SEPW) in the “solenoid-resonator.”
The collective field components and in the “solenoid-resonator” are shifted in time by , and the spatial distribution of their amplitudes are displaced by , so that the maxima (antinodes) coincide with zero (nodes) and vice versa. At the point of space the phases of the fields (at the time moment ) and (at the time moment ) coincide, which demonstrates the presence of the Umov–Pointing vector for the SEPW field in the ensemble of nanoparticles.
The coincidence of the nodes and antinodes (as in the ED laser resonator) of SEPW fields affects the motion of charges and at each perpendicular to the Fresnel zones at the frequency of amplitude modulation and along the Fresnel zones at the carrier frequency of phase modulation .
By the moment of cycle (3) termination:
the mode of the two-dimensional PFB is transformed into the mode of energy self-oscillations (the spin-flip mode) between the ensemble of electron-ion nanoparticles and the SEPW;
the nanoparticle ensemble transforms resonantly the p-polarized BLW field into the solenoidal (vertex) vector field of σ-polarized MM radiation in the closed cycle “emission-absorption.”
ESTIMATION OF THE RADIATION CHARACTERISTICS
It is expedient to start estimation of the characteristics and properties of MM radiation from the characteristics of the state of molecule and electric and magnetic photons. The state of molecule is characterized by the angular momentum J and parity . The transition of the molecule between states is regulated by the selection rules for the momentum J and parity [13]. The molecule emits on the radiative transition the quantum of energy (photon) of the vector field with spin S = 1. The total angular momentum of the photon is the vector sum , where L is the rank of the spherical functions entering into the photon wave function.
The photons with orbital momentum and parity are called electric or EJ-photons. Photons with the orbital momentum and parity are called magnetic or -photons. Thus, ED laser radiation is a set of electric photons each of which carries the energy . MM laser radiation is an ensemble of magnetic photons each of which carries energy corresponding to the quantum of the magnetic flux [J/A] along the Z axis.
The transition of molecules between natural states of the ED transition is regulated by selection rules for the electric dipole moment oriented perpendicularly to the Z axis [12]. The transition of the ensemble of electron-ion nanoparticles between the states of the prepared MM transition is regulated by selection rules for the magnetic dipole moment oriented along the Z axis. At the frequency of the prepared MM transition, σ-polarized magnetomultipole radiation is generated in the spin-flip mode with orbital angular momentum along the Z axis.
MONOCHROMATICITY
We estimate the monochromaticity of MM radiation based on the photon lifetime in the coherence volume for the given resonator -factor [1]. The volume represents the multi-cylindrical optical “solenoid-resonator” with regular nonradiative losses [7] in the V-scheme. The reason of losses is the deceleration of molecule polarizability fluctuations on the ED transition with frequency and acceleration of the diamagnetic susceptibility fluctuations with accumulation (absorption,) of the diamagnetic energy on weak magnetic multipole transition with the frequency .
The resonator Q-factor [1] can be estimated as – the ratio of the resonant frequency of the mode (the Fresnel zone with allowance for ) to the resonator linewidth or as (stored energy) / (energy lost for the period). Hence, the monochromaticity of MM radiation can be expressed in the form
(4)
Conditions of experiment [6] where the re-radiation signal was recorded led to the following estimate of the monochromaticity of MM radiation. The diamagnetic energy stored by the nanoparticle ensemble and by the σ-polarized standing wave field in is equal to erg (S “ 0.8 cm2 and )). In this case, the MM radiation power at the frequency stored for the period s will be equal to .
From Eq. (4) it follows that the threshold monochromaticity of MM radiation is .
COHERENCE ORDER [14]
We now estimate the coherence order of MM radiation from the number of molecules mD taking part in self-organization of the nanoparticle ensemble and filling of the optical “solenoid-resonator” described by Eq. (2).
The criterion of radiation coherence in a gas is the relationship [15]. Since , the question about coherence of stimulated oscillations of molecules in the dispersion theory is reduced to a comparison of with . Here and are the velocity and the mean free path time of the molecule, respectively; and are the free path length and the Rayleigh scattering cross section under atmospheric conditions for ; and is the polarizability of unabsorbing () isolated molecules.
The molecules absorbing on the magnetic multipole transition () and interacting via the collective of fields and form the relationship that has the meaning of the coherence criterion for MM radiation. Since , the question about the coherence of MM radiation in volume (2) is reduced to a comparison of changes in and during time (3). Since the fluctuations and of molecules in each step s in the fields and are synchronized, and change in volume (2) perpendicular and along the Z axis of the BLW pumping field. Here and are the velocity of molecules at the moment of time and their free path time in the medium comprising broadening particles .
Photons of MM radiation arise in the volume at time at which the coherent displacement of the electron with respect to the ion in each molecule mD can create by the time the anisotropic configuration and of the electron orbit perpendicular and along the Fresnel zone. The time moment indicates the onset of self-organization of molecules into diamagnetic traps that, holding charges and inside of the height/thickness of the Fresnel zone , are self-organized into the nanoparticle ensemble during time (3). The nanoparticle ensemble forms the “flat microlens system” arranged perpendicular to the Z axes with the step and along the Z axis with the step for nanoparticle spacing and , respectively.
Thus, the condition and also the time moments and limit the number of water vapor molecules in the coherence volume given by Eq. (2) to in the initial state of the V-scheme of transitions. This number of molecules participating in generation of MM radiation defines the mD th coherence order at spatiotemporal points of the Fresnel zones. For molecules of other types, the coherence order will be different.
ORIENTATION
We now estimate the orientation of MM radiation considering that the ensemble of electron-ion nanoparticles interacts through the collective fields and and has the th order of spatiotemporal coherence in the multi-cylindrical optical “solenoid-resonator.”
Pumping p-polarized BLW radiation with the diameter and Gaussian cross sectional intensity distribution at the input of the “solenoid-resonator” will create a beam of output σ-polarized MM radiation
(5)
whose divergence will be less than the diffraction divergence of laser radiation by a factor of . Here is the factor characterizing spatiotemporal electric, magnetic, and mechanical ordering of the electron-ion nanoparticles on the prepared MM nonrigid transition in volume (2).
The correlation function of the running MM wave with the mDth order coherence is
.
BRIGHTNESS
The brightness of the beam of ММ radiation with the diameter and divergence angle is
(6)
which is greater than the brightness of ED laser radiation by a factor of because of the divergence. Here is the power of the MM radiation beam at the output from the “solenoid-resonator.” The energy of MM radiation depends on the energy of the p- polarized BLW, coherence length , cross section of the maximum Fresnel zone , and concentration of nanoparticles (molecules) as follows:
.
Since the electric photons of p-polarized BLW are transformed into the magnetic photons of σ-polarized MM radiation in the closed cycle “emission-absorption,” the quantum efficiency of energy conversion reaches .
STABILITY WITH RESPECT TO NOISE
The stability with respect to noise of MM radiation in the atmosphere is caused, first, by the fact that the information (and energy) transfer in the atmosphere is determined by the magnetic component whose range of action is assigned by the Biot–Savart law on the axis of the optical “solenoid-resonator” (as in solenoid [16]). Here and are the serial number of the Fresnel zone and the electron current on its surface, respectively. The absence of a dependence of the field on the “resonator” axis in the Fresnel zones on the distance r between the charges and for the orbital momentum along the Z axis predetermines the stability of the wave front of MM radiation with respect to turbulent inhomogeneity of the complex refractive index of the atmosphere on the macroscale of the Biot–Savart law. The orbital angular momentum on the Z axis provides an increase in the stability with respect to noise of the wave front of MM laser radiation in the atmosphere by factors of ~106–1010 compared to ED laser radiation.
Second, the probability of magnetodipole transitions of molecules (atoms) is by a factor of ~106 less than the probability of ED transitions; therefore, the intensity of MM radiation in the atmosphere will be attenuated less by the same factor compared to the intensity of ED laser radiation. These two characteristics of MM radiation allow MM lasers to be used in various optical systems irrespective of weather conditions.
Third, the MM radiation is recorded with photodetector based on the electro-optical principle and on the magneto-optical principle. In the second case, the photodetector S/N ratio does not depend on the time of day, which provides round-the-clock noise-proof operation of optical systems based on the MM laser in the atmosphere.
CONCLUSIONS
In the foreign and domestic literature there are no data on generation of MM radiation. As a rule, results of formation of spiral beams in the anisotropic medium of the resonator of the laser generating radiation on ED transition are presented. The wave front of ED radiation “is splitted” (loses its stability) into small vertex fluxes in the process of ED radiation propagation in the outdoor atmosphere. The process of “splitting” is caused by interference of primary and secondary waves on dislocations generated by the atmospheric turbulence [17].
Within the limits of classical electrodynamics, it is impossible to obtain MM laser radiation. To generate MM radiation, it is necessary to solve theoretical problems within the framework of quantum electrodynamics and to approve the conceptual model on modern technological base. The Open Joint-Stock Company “Superposition” at IAO SB RAS has successfully solved theoretical and experimental problems in stage “0” of R&D Project of Skolkovo Foundation. Stage “1” suggests creation of a theoretical basis and of an MM laser prototype and excitation of generation of MM radiation.
Basic elements of a magnetomultipole (MM) laser are a collective of fields and a molecular gas comprising molecules and broadening particles (molecules or atoms). The molecules have low-frequency ED and high-frequency magnetic multipole rovibrational transitions united by the lowest state according to the V-scheme
(1)
The collective of fields consists of the electric, , and magnetic components, , of the field of elastic collisions of molecules with broadening particles, the p-polarized biharmonic pumping light wave (BLW), and the Rayleigh scattering [2, 3].
The two-dimensional parametrical energy resonance between the V-scheme of transitions and the difference and summed BLW frequencies engenders the two-dimensional spatiotemporal PFB between energies of the quadratic Stark and Zeeman effects [3] in the BLW coherence volume of the system collective of fields + molecular gas (referred to as the system below). The molecules accumulate the threshold diamagnetic susceptibility along the Z BLW axis in the process of a single elastic collision with particles and hence, the threshold diamagnetic energy in the V-scheme of transitions to the highly excited magnetic multipole state. In this system: 1) the ensemble of optically active electron-ion nanoparticles on the prepared (mixed) MM nonrigid transition and 2) the complex refractive index of the nanoparticle ensemble are self-organized into a multi-cylindrical optical “solenoid-resonator.” Generation of MM laser radiation is self-excited at the MM transition frequency. The MM radiation characteristics and properties depend on those of nanoparticle ensemble and BLW pumping field [4].
The present work is aimed at substantiation of a radically new approach to self-organization of the electron-ion nanoparticle ensemble on the nonrigid prepared MM transition and generation of MM radiation at its frequency.
FROM INITIAL EXPERIMENTS
TO A CONCEPTUAL MODEL
In the absorption [5] and re-radiation spectra [6] of Н2О molecules obtained with participation of ruby laser radiation and broadening particles (N2 molecules) at atmospheric pressure there was something extraordinary. The absorption spectrum of Н2О molecules [5] contained ten lines (rather than one well-known line) obtained by the classical technique examined/reference beam of BLW p-polarized ruby laser radiation. The absorption coefficient in the center of 9 lines appeared greater by four orders of magnitude than its value corresponding to the intensity of these lines [7]. In [6] the well-known Н2О line was recorded with a polychromatic ruby ICL spectrometer for the same molecular gas parameters. The well-known absorption line decreased the population density inversion in the ruby laser radiation circuit, and a high-power signal of monochromatic radiation was recorded near the center of the absorption line. These results fell beyond the scope of the ED approximation and semiclassical theory of laser radiation interaction with molecular gas having the preset parameters of the medium and pumping.
Two specially performed experiments with the well-known line gave the following results. The nonlinear absorption of p-polarized laser radiation was manifested in the anomalous region of the known Н2О line profile more strongly, than that of σ-polarized radiation [8]. The absorption coefficient in the anomalous region of the well-known line profile recorded with the ICL spectrophotometer depended significantly on the frequency of the Stark modulation of Н2О states [9].
An analysis of the role of system parameters in the formation of the anomalous region of the well-known absorption line profile allowed three conclusions to be drawn. First, the probabilities of ED and weak rovibrational magnetic multipole transitions can change radically during one elastic collision of molecules with particles for definite parameters of the collective field and molecular gas.
Second, we can go beyond the scope of the ED approximation and semiclassical theory by means of control over quantum events of intra- and intermolecular dynamics of energy states in the V-scheme of transitions.
Third, internal sign-variable amplitude-phase modulation of the pumping BLW in the V-scheme of transitions described by Eq. (1) can correct the process of origin of the two-dimensional PFB between energies of the quadratic Stark and Zeeman effects [3, 4].
TWO-DIMENSIONAL CONSTRUCTIVE FEEDBACK
The physical reason for the origin of the two-dimensional PFB is the two-dimensional parametrical energy resonance (interference between the intramolecular field and the collective field) between the V-scheme of transitions given by Eq. (1) and the difference, , and summed frequencies, , in the BLW coherence volume:
, (2)
where and are the coherence length and the diameter of the BLW pumping beam. Here is the serial number of the step of the BLW field at time moments of amplitude modulation sign change (±) in the direction orthogonal to the Z axis and at time moments of phase modulation sign change () along the Z axis of BLW propagation.
The field of elastic collision, breaking the symmetry of electronic shells of the molecule, induces in them the electric, , and magnetic, , dipole moments, and also their components characterizing the fields gradient and the gyration tensor g. These components create diamagnetic traps for the electron, , and ion, , of the molecule that run away under the action of the Lorentz and Coriolis forces. Here and are fluctuations of the electric polarizability perpendicular to the Z axis and of the diamagnetic susceptibility along the Z axis of the BLW.
To implement the BLW phase modulation and to create the two-dimensional PFB, it is necessary to have a sufficient degree of field asymmetry and a sufficient number of broadening particles, BLW pumping photons, and molecules in the volume given by Eq. (2). The sign-variable BLW amplitude-phase modulation corrects running away of charges and , respectively, and hence, the frequency of fluctuations of the dipole moments and .
As a “trigger” mechanism for the origin of the two-dimensional PFB, the amplitude-phase step serves, where fluctuations of he moments and at the frequencies of V-scheme (1) are locked by the BLW frequencies and in the two-dimensional parametrical resonance. The size of the BLW step must be less than the valence electron memory [10] of molecules (here is the energy of molecule ionization). As a consequence, the nonlocality radius of the electron response between the time moments and increases regularly in the anomalous region of the weak magnetic multipole transition given by Eq. (1) due to electron orbit deformation in the process of the elastic collision.
The collective field components and are overlapped on transitions (1), the quadratic nonlinearity arises in molecules, and the diamagnetic energy of coupling of charges and increases under the action of the Lorentz and Coriolis forces when they run away. As a consequence, the two-dimensional PFB arises between energy fluctuations of the Stark effect at the frequency perpendicular to the Z axis and of the Zeeman effect at the frequency along the Z axis in volume (2) at the time moment. Here and are radius-vectors emanating from the origin of coordinates of the molecule perpendicular the Z axis and along the Z axis at the points of electron localization at the time moments and .
SELF-ORGANIZATION OF THE NANOPARTICLE ENSEMBLE AND SELF-EXCITATION OF GENERATION
The two-dimensional PFB controls over the velocity of charges and running away in the V-scheme of transitions of molecules and over the transformation of diamagnetic traps into an amplitude-phase profiled zone plate so that the even and odd Frenel zones in volume (2) “act in phase.” The amplitude-phase zone plate is the magneto-optical analog of the “phase” zone plate [11] having different thicknesses of the even and odd zones of the microlens system. The magneto-optical analog allows the phase of the outgoing light wave to be varied smoothly within each Fresnel zone. In this case, in the anomalous region of the weak magnetic multipole transition the velocity of energy transfer of the collective field decreases down to the electron velocity , and the BLW phase velocity increases. As a consequence, the steepness of the real component and the absolute value of the imaginary component (susceptibility ) of the complex refractive index increase on the magnetic multipole transition .
Since the molecular relaxation times s (at atmospheric pressure) is greater than the time of their elastic collision s [12] and, the more so, than the step of energy changes and in the V-scheme, by the end of the cycle
(3)
the energy of motion of molecules is frozen down to the lowest state in Eq. (1), and the energy of the collective field is transformed into the diamagnetic energy of the highly excited magnetic multipole state, which increases the probability of transition by several orders of magnitude. In this case, the ensemble of optically active electron-ion nanoparticles in the system is self-organized on the prepared nonrigid MM transition described by Eq. (1). The ensemble of nanoparticles acquires multi-cylindrical shape (according to the number of the Fresnel zones) of the optical “solenoid-resonator” with the electric, magnetic, and mechanical spatiotemporal ordering. The nanoparticle ensemble possesses:
the complex refractive index
the property of circular birefringence;
the built-in projections of the angular orbital nanoparticle momentum along the field vector of the standing s±-polarized wave (SEPW) in the “solenoid-resonator.”
The collective field components and in the “solenoid-resonator” are shifted in time by , and the spatial distribution of their amplitudes are displaced by , so that the maxima (antinodes) coincide with zero (nodes) and vice versa. At the point of space the phases of the fields (at the time moment ) and (at the time moment ) coincide, which demonstrates the presence of the Umov–Pointing vector for the SEPW field in the ensemble of nanoparticles.
The coincidence of the nodes and antinodes (as in the ED laser resonator) of SEPW fields affects the motion of charges and at each perpendicular to the Fresnel zones at the frequency of amplitude modulation and along the Fresnel zones at the carrier frequency of phase modulation .
By the moment of cycle (3) termination:
the mode of the two-dimensional PFB is transformed into the mode of energy self-oscillations (the spin-flip mode) between the ensemble of electron-ion nanoparticles and the SEPW;
the nanoparticle ensemble transforms resonantly the p-polarized BLW field into the solenoidal (vertex) vector field of σ-polarized MM radiation in the closed cycle “emission-absorption.”
ESTIMATION OF THE RADIATION CHARACTERISTICS
It is expedient to start estimation of the characteristics and properties of MM radiation from the characteristics of the state of molecule and electric and magnetic photons. The state of molecule is characterized by the angular momentum J and parity . The transition of the molecule between states is regulated by the selection rules for the momentum J and parity [13]. The molecule emits on the radiative transition the quantum of energy (photon) of the vector field with spin S = 1. The total angular momentum of the photon is the vector sum , where L is the rank of the spherical functions entering into the photon wave function.
The photons with orbital momentum and parity are called electric or EJ-photons. Photons with the orbital momentum and parity are called magnetic or -photons. Thus, ED laser radiation is a set of electric photons each of which carries the energy . MM laser radiation is an ensemble of magnetic photons each of which carries energy corresponding to the quantum of the magnetic flux [J/A] along the Z axis.
The transition of molecules between natural states of the ED transition is regulated by selection rules for the electric dipole moment oriented perpendicularly to the Z axis [12]. The transition of the ensemble of electron-ion nanoparticles between the states of the prepared MM transition is regulated by selection rules for the magnetic dipole moment oriented along the Z axis. At the frequency of the prepared MM transition, σ-polarized magnetomultipole radiation is generated in the spin-flip mode with orbital angular momentum along the Z axis.
MONOCHROMATICITY
We estimate the monochromaticity of MM radiation based on the photon lifetime in the coherence volume for the given resonator -factor [1]. The volume represents the multi-cylindrical optical “solenoid-resonator” with regular nonradiative losses [7] in the V-scheme. The reason of losses is the deceleration of molecule polarizability fluctuations on the ED transition with frequency and acceleration of the diamagnetic susceptibility fluctuations with accumulation (absorption,) of the diamagnetic energy on weak magnetic multipole transition with the frequency .
The resonator Q-factor [1] can be estimated as – the ratio of the resonant frequency of the mode (the Fresnel zone with allowance for ) to the resonator linewidth or as (stored energy) / (energy lost for the period). Hence, the monochromaticity of MM radiation can be expressed in the form
(4)
Conditions of experiment [6] where the re-radiation signal was recorded led to the following estimate of the monochromaticity of MM radiation. The diamagnetic energy stored by the nanoparticle ensemble and by the σ-polarized standing wave field in is equal to erg (S “ 0.8 cm2 and )). In this case, the MM radiation power at the frequency stored for the period s will be equal to .
From Eq. (4) it follows that the threshold monochromaticity of MM radiation is .
COHERENCE ORDER [14]
We now estimate the coherence order of MM radiation from the number of molecules mD taking part in self-organization of the nanoparticle ensemble and filling of the optical “solenoid-resonator” described by Eq. (2).
The criterion of radiation coherence in a gas is the relationship [15]. Since , the question about coherence of stimulated oscillations of molecules in the dispersion theory is reduced to a comparison of with . Here and are the velocity and the mean free path time of the molecule, respectively; and are the free path length and the Rayleigh scattering cross section under atmospheric conditions for ; and is the polarizability of unabsorbing () isolated molecules.
The molecules absorbing on the magnetic multipole transition () and interacting via the collective of fields and form the relationship that has the meaning of the coherence criterion for MM radiation. Since , the question about the coherence of MM radiation in volume (2) is reduced to a comparison of changes in and during time (3). Since the fluctuations and of molecules in each step s in the fields and are synchronized, and change in volume (2) perpendicular and along the Z axis of the BLW pumping field. Here and are the velocity of molecules at the moment of time and their free path time in the medium comprising broadening particles .
Photons of MM radiation arise in the volume at time at which the coherent displacement of the electron with respect to the ion in each molecule mD can create by the time the anisotropic configuration and of the electron orbit perpendicular and along the Fresnel zone. The time moment indicates the onset of self-organization of molecules into diamagnetic traps that, holding charges and inside of the height/thickness of the Fresnel zone , are self-organized into the nanoparticle ensemble during time (3). The nanoparticle ensemble forms the “flat microlens system” arranged perpendicular to the Z axes with the step and along the Z axis with the step for nanoparticle spacing and , respectively.
Thus, the condition and also the time moments and limit the number of water vapor molecules in the coherence volume given by Eq. (2) to in the initial state of the V-scheme of transitions. This number of molecules participating in generation of MM radiation defines the mD th coherence order at spatiotemporal points of the Fresnel zones. For molecules of other types, the coherence order will be different.
ORIENTATION
We now estimate the orientation of MM radiation considering that the ensemble of electron-ion nanoparticles interacts through the collective fields and and has the th order of spatiotemporal coherence in the multi-cylindrical optical “solenoid-resonator.”
Pumping p-polarized BLW radiation with the diameter and Gaussian cross sectional intensity distribution at the input of the “solenoid-resonator” will create a beam of output σ-polarized MM radiation
(5)
whose divergence will be less than the diffraction divergence of laser radiation by a factor of . Here is the factor characterizing spatiotemporal electric, magnetic, and mechanical ordering of the electron-ion nanoparticles on the prepared MM nonrigid transition in volume (2).
The correlation function of the running MM wave with the mDth order coherence is
.
BRIGHTNESS
The brightness of the beam of ММ radiation with the diameter and divergence angle is
(6)
which is greater than the brightness of ED laser radiation by a factor of because of the divergence. Here is the power of the MM radiation beam at the output from the “solenoid-resonator.” The energy of MM radiation depends on the energy of the p- polarized BLW, coherence length , cross section of the maximum Fresnel zone , and concentration of nanoparticles (molecules) as follows:
.
Since the electric photons of p-polarized BLW are transformed into the magnetic photons of σ-polarized MM radiation in the closed cycle “emission-absorption,” the quantum efficiency of energy conversion reaches .
STABILITY WITH RESPECT TO NOISE
The stability with respect to noise of MM radiation in the atmosphere is caused, first, by the fact that the information (and energy) transfer in the atmosphere is determined by the magnetic component whose range of action is assigned by the Biot–Savart law on the axis of the optical “solenoid-resonator” (as in solenoid [16]). Here and are the serial number of the Fresnel zone and the electron current on its surface, respectively. The absence of a dependence of the field on the “resonator” axis in the Fresnel zones on the distance r between the charges and for the orbital momentum along the Z axis predetermines the stability of the wave front of MM radiation with respect to turbulent inhomogeneity of the complex refractive index of the atmosphere on the macroscale of the Biot–Savart law. The orbital angular momentum on the Z axis provides an increase in the stability with respect to noise of the wave front of MM laser radiation in the atmosphere by factors of ~106–1010 compared to ED laser radiation.
Second, the probability of magnetodipole transitions of molecules (atoms) is by a factor of ~106 less than the probability of ED transitions; therefore, the intensity of MM radiation in the atmosphere will be attenuated less by the same factor compared to the intensity of ED laser radiation. These two characteristics of MM radiation allow MM lasers to be used in various optical systems irrespective of weather conditions.
Third, the MM radiation is recorded with photodetector based on the electro-optical principle and on the magneto-optical principle. In the second case, the photodetector S/N ratio does not depend on the time of day, which provides round-the-clock noise-proof operation of optical systems based on the MM laser in the atmosphere.
CONCLUSIONS
In the foreign and domestic literature there are no data on generation of MM radiation. As a rule, results of formation of spiral beams in the anisotropic medium of the resonator of the laser generating radiation on ED transition are presented. The wave front of ED radiation “is splitted” (loses its stability) into small vertex fluxes in the process of ED radiation propagation in the outdoor atmosphere. The process of “splitting” is caused by interference of primary and secondary waves on dislocations generated by the atmospheric turbulence [17].
Within the limits of classical electrodynamics, it is impossible to obtain MM laser radiation. To generate MM radiation, it is necessary to solve theoretical problems within the framework of quantum electrodynamics and to approve the conceptual model on modern technological base. The Open Joint-Stock Company “Superposition” at IAO SB RAS has successfully solved theoretical and experimental problems in stage “0” of R&D Project of Skolkovo Foundation. Stage “1” suggests creation of a theoretical basis and of an MM laser prototype and excitation of generation of MM radiation.
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