Control of Laser Radiations in the Systems of Sun Power Engineering
The use of laser technologies provides to create optical concentrators and photovoltaic solar cells of the next generation with high energy effectiveness. In the next article it was shown how laser radiations propagate in natural and artificial materials and how the parameters of radiations (phase intensity, polarization) can be controlled and manipulated by various means.
Modulation of quality (Qswitching) of resonator. In order to multiply the number of atoms, which take part in strengthening of light flux, it is necessary to detain the beginning of generation and accumulate the maximal amount of the excited atoms by means of reduction of quality factor of a resonator. This mode of operation can be attained by the use in a resonator of a cell with variable in time absorption (fig.4,a). When the quality factor of the system will provide the beginning of generation, population inversion of levels will be enough considerable. Therefore power of radiation of laser grows strongly. Such method of control by the generation of laser is called the modulation of quality or Qswitching method.
Duration of pulse relies on many factors and usually is equal about 10^{7} 10^{8} s. Modulation of quality factor can be attained, for example, by means of prism, the frequency of rotation of which makes the ten and, even, hundreds of cycles per second. The pulses of laser radiations have the same frequency. Greater frequency of pulses is achieved by the use of the Kerr cell and polarizer, placed in a resonator. Polarizer provides the generation of radiation of certain polarization, and Kerr cell is oriented thus, that under action of electrical voltage the light with this polarization does not pass through the cell. In the process of pumping of the laser the voltage is taken off in the moment of time corresponding to the maximal value of generation.
Common picture of modes of radiations. In the stationary mode of radiation of laser the standing waves appear in the resonator. In the more general case a standing wave can be represented as superposition of simple standing waves, which are called the mode of oscillations. The radiations of laser, corresponding to the given modes of oscillations, are called the modes of radiations of laser. The modes of oscillations are determined by geometrical parameters of resonator, coefficient of refraction of active medium and conditions on the boundary surfaces of resonator. Consider for an example the two types of resonators: one with flat rectangular mirrors, second – with spherical mirrors.
The origin of standing waves in a rectangular resonator is determined by terms (fig.5,a): mλ_{с} = 2L; k'_{x}a = m_{x}π; k'_{у}b = m_{y}π; k'_{z}L = m_{z}π, where: a, b, L  sizes of resonator in direction of axes X, Y, Z; k'_{x}, k'_{у}, k'_{z}  wave numbers.
Axial modes. The modes are characterized by the set of numbers (m_{x}, m_{y}, m_{z}). The main mode of resonator is a mode (0, 0, m_{z}). It has not of nodes (knots) in a plane, normal to the axe Z, and describes a standing wave that is a superposition of light waves, traveling parallel to the axe of laser. In the theory of waveguides this mode is called a transversal electromagnetic mode and is marked as TEM00m_{z}. Taking into account a fig.5, for frequencies of radiations of this mode we get correlation: ω_{mz} = k'_{z}c/n = cπm_{z}/(Ln).
Not all frequencies are generated by a laser, but only those, fulfilling the conditions of threshold of generation. These frequencies are found within the defined values of ω_{1} and ω_{2} on the equal distances one from other. The amount of the excited frequencies, lying in this interval, relies on concrete terms. For a heliumneon  laser this number is equal to 510, for a ruby laser – several hundreds, and for lasers on dyes – a few thousands.
Each emitted line is not strictly monochromatic; it has an eventual width Δν that can be calculated on general conditions: (Δν)τ ≈ 1, where τ – duration of radiations.
In Qswitching lasers τ ≈ 10^{8}s and, accordingly, Δν = 10^{8} Hz. Uncontrolled fluctuations of index of refraction, vibration change of length of resonator (distance L), thermal broadening of bases etcetera, result in expansion of lines. For example, from the equations described before flows out: Δν/ν =  ΔL/L. Therefore the small change of ΔL = λ/50 at L =
Lateral modes. The values of a_{m} and m_{у} characterize the number of knots of standing wave in a plane XY. At m_{х} = 0, m_{у} = 0 the knots are absent, and on the output of laser an axial mode (0, 0, m_{z}) gives distribution of intensities without knots (fig.6,a). Modes with m_{х} ≠ 0 and m_{у} ≠ 0 are called lateral modes. The distribution of intensities of radiations of these modes on the output of laser is characterized by the presence of lines of zero intensity, corresponding to the knots of standing waves at m_{х} ≠ 0 and m_{у} ≠ 0. On fig.6,a the distribution of intensity of radiation on the output of laser in the first lateral modes is shown.
For standing waves in the cylinder resonator the surfaces of mirrors are the surfaces of equal phase. In other words, a waveform is changed along the axe Z on mirrors and coincides with the surface of mirrors (fig.6,b). At the equal radiuses of curvature of mirrors into a resonator the waveform is flat. For one cycle, during which a wave is twice reflected from mirrors and twice is passed through a resonator, all characteristics of each of waves – reflected and transmitted – are to get back to the initial values.
A calculation shows that the condition of recurrence for the reflected waves can be written as follow: [m_{z} + (1/π) (2р + q + 1) arccos(1  L/p)]λ_{c} = 2L, where m_{x}, p, q – integers, characterizing a mode.
Synchronization of Modes. Short pulses (~10^{12}s)^{ }are got by synchronization of modes. The essence of this method consists in the following. Multimode laser radiates the spectrum of frequencies. An interval between axial modes is equal Δω. If all modes are added in an identical phase, an amplitude of total wave is equals to the sum of amplitudes of modes (fig.7,a). Through the time interval of Δt a phase of waves is changed on a value of ΔωΔt, 2ΔωΔt, ..., (Nl)ΔωΔt. N is a number of modes, which take part in forming of amplitude. The picture of superposition of complex amplitudes through Δt is shown on fig.7,b. At the subsequent increase of Δt an amplitude is diminished, and then begins to grow. An initial situation, when amplitudes summarized in an identical phase, will repeat oneself through the interval of time Т = 2π/(Δω) = 2nL/c, where T  duration of cycle.
Thus, a situation, at which the phases of different modes become equal to each other, is repeating through a cycle.
The concordance of phases of different modes is named synchronization of modes. In the moment, when the amplitudes of modes are superposed in an identical phase, the intensity of laser radiation grows; the pulse of radiations occurs (fig. 7,c). The pulses arise up one after the other with a frequency 1/Т = c/(2nL).
The duration of pulse is determined with transformation into a zero of total amplitude. Marking ΔТ – duration of pulse, N  number of modes, which take part in synchronization, the condition of transformation into zero of total amplitude is writhed so: ΔТ = 2π/(ТΔω) = 2Ln/(cN) = T/N.
The greater is a number of the synchronized modes, the smaller is duration of pulse. For example, for n ≈ 1; L = 10^{1}м; N = 10^{3} we get ΔТ ≈ 0,6х10^{12}s.
Thanking to synchronization of modes, practically all energy of radiations, corresponding to a time interval T = 2Ln/c, is emitted in a pulse by duration ΔТ = T/N. It means that power in a pulse is increased in Т/(ΔТ) times.
Synchronization of modes can arise up arbitrary. For reduction of duration of pulses, in particular, a modulation of quality factor is used, with the cycle period of 2Ln/c. Nonlinear effects are used for this purpose. Taking into account the nonlinear effects, between different modes a bound is established. So these modes can not be examined, as independent. As an example consider the case using in the resonator of filter, the coefficient of admission of which is multiplied with growth of intensity of light passing through the filter. If strengthening of intensity came as a result of synchronization of small quantity of modes, these synchronized modes will be less than other weakened at passing through the filter. So these modes will get advantage in comparison with other modes that pass through the filter in other intervals of time at less intensity of the field. Thus, only synchronized modes are amplified. Thanking that, duration of pulse is diminished, and its power is increased. Pulse’s duration presently got is less than 10^{12}^{ }s.
Written by Vasil Sidorov on August 07,
Technopark QUELTA,
Nizhyn Laboratories of Scanning Devices
References
1. Rebrin Y.K., Sidorov V.I. // Optical Deflectors.
2. Rebrin Y.K., Sidorov V.I. Optical mechanical and holographic deflectors // Results in science and technology. Radio engineering. Vol. 45. 
3. Rebrin Y.K., Sidorov V.I. Holographic devices of control of an optical ray. –
4. Rebrin Y.K., Sidorov V.I. Piezoelectric multielement devices of control of an optical ray. –
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