Pentagonal active laser interferometer "Dulkyn" Optical scheme of pentagonal gravitational detector and principle of its operation Reference and signal resonators The gravitationalwave detector "Dulkyn", designed for the detection and investigation of lowfrequency periodic gravitational radiation (GR) is based on the pentagonal configuration of optical laser resonator with two contours of light circulation. Optical scheme of the circular twocontour resonator with the main reflecting elements being placed at the corners of regular pentagon, is presented at fig.1. Along with standard mirrors 1,2,4 the basic resonator elements are the holographic diffractional reflecting elements 3 and 5, presenting the thick phase transmitting gratings recorded on the photosensitive layer coating the mirror surface. These elements fulfil the function of division of the light falling on them into two beams with orthogonal azimuths of polarization. They work as standard mirrors of zeroth order of diffraction, providing the circulation of light with TMpolarization (the electric field vector lies in the plane of the figure) over the external contour 123451, and the radiatiton of the first order of diffraction forms the internal contour 12314251 of the circulation of the light with TEpolarization (the electriá field vector being perpendicular to the figure plane), therewith the sections between the elements 5,1,2,3 are common for both contours. Here the active medium AM (gasdischarge tube without Brewster windows) providing the light generation in both contours is situated. The coefficients of reflection of the holographic elements and for the mirrorreflected wave with TMpolarization and the diffracted wave with TEpolarization will be equal correspondingly at optimal depth of modulation of dielectrical permeability inside thick phase transmitting gratings (at generation on the wavelength 0.6328 ). So due to diffractional reflecting elements 3 and 5 spational and polarizational outcome of optical radiations, circulating in the external and the internal contours is achieved. A small amount of radiation (few percents) of the opposite polarization penetrating into "another" contour is extracted from the resonators by means of P_{TE} and P_{TM} polarizators, which present themselves the polarization prisms of Glantype and transmit correspondingly the linearilypolarized light of TE and TM polarizations only. Resonator in which the light circulates in the external contour is the reference one, and radiation circulating in the internal contour forms the signal resonator. Calculation of longitudinal eigenfrequences Let periodical gravitational wave (with frequency ) be described in TTcalibration by metrics
where  the amplitudes of two GR polarizations, propagating along Z axis, and the pentagonal twocontour resonator lies in XOY plane. As the relaxation time of the electromagnetic field amplitude in resonator ( being of the order of , where rad/sec is the width of resonator band), one may consider the gravitationalwave field to be specified when calculating the longitudinal eigenfrequences and when solving the equations of generation. As a consequence of the fact, that the reference and the signal resonators are simple ones, one can find the spectrum of their longitudinal eigenfrequences from the condition of multiplicity of the total phase incursion to at the full bypass over the closed contour:
Here  are eigenfrequences, d_{1,2}  the thicknesses of polarizators with refraction indexes n,  total phase changing at reflections, N_{1,2}  modes numbers, and  rectilinear kth sections of perimeter in the signal and reference resonators correspondingly, which form the angle with the principle direction of the first polarization of GR. In the absence of GR field
where l  is the pentagon side. One may adjust the generation frequences symmetrically in reference to the centre of amplification line or make them equal by means of varying the optical thickness of P_{TE} and P_{TM} polarizators. In consequence of the fact that all the reflecting elements providing the light circulation over two contours and the active medium belong simulteneously to the reference and signal resonators, the technical fluctuations of the generation frequences conditioned by all types of the mechanical effects on the mirrors, instability of the discharge current, the gas pressure variation, the electron density etc. will appear in both contours simulteneously, i.e. they will be correlated. As for the natural fluctuations conditioned by spontaneous radiation of the atoms of active medium they are found to be minimal, if one works in the synchronization band, when the generation in the reference and the signal resonators occurs at the same frequency. The GRfield causes the additional phase variation
where  is the generation wavelength. By symmetry of the external contour g_{2}=0 in the reference resonator. To facilitate the calculation of g_{1} let us assume that is counted from the section 21. In this case
(If the principle direction of the first GR polarization is shifted by 45º in reference to 21 section, then h_{+} should be replaced with h_{X}). Therefore in the field of GR the eigenfrequency of optic radiation in reference resonator will remain unchanged , while in the signal one it will become equal to
i.e. it will get the increment :
Hence the GRdetector creation on the basis of the pentagonal configuration of the optic twocontour resonator allows to form two informational channels when processing the signalresponse: in the first (reference) channel useful signal is absent, but the noise signals are present, conditioned by the technical and natural fluctuations of generation frequency, and in the other (signal) one the additive mixture of useful and noise signals is present, the noise signals in both channels being correlated. GRAVIMETRIC LASER INTERFEROMETRIC COMPLEX Geologic medium status monitoring is one of the most urgent problems of modern science about Earth. To realize the monitoring programme it is necessary, in particular, to develop gravimetric devices of new generation, capable to perform longterm and continuous measurements, accumulate their results and analyze
To solve all these problems we studied theoretically the phenomenon of gravitationallyinduced shift of laser generation frequency. Theoretical analysis prompted the way of developing the measurer of the Terrestrial gravity potential first, second and third derivatives using this phenomenon. Whereat we use optical radiation itself as a sensitive element. Gravitationallyinduced laser generation frequency shift The analysis of phenomenon of gravitationallyinduced laser generation frequency shift is based on the following statements:
We are solving the problem of gravitationallyinduced laser generation frequency shift registration by the laserinterferometric method. The working formula for calculating the generation frequency of horizontally arranged laser is as follows:
where W_{0} is the resonator eigenfrequency, w_{0} is the laser operating medium atomic transition eigenfrequency, independant on gravitational potential, d is stabilization parameter (approximately equal to resonator mode line width / Doppler line width radio). If potential j varies along the resonator axis line, for example, at the vertical arrangement of resonators, then it can be demonstrated that in this case some efficient potential value should be substituted into the given above formula, being numerically equal to the value j in some internal  "middle"  resonator point. Limiting case of small stabilization parameters When d > 0, what corresponds to the real case of gaseous lasers (d ~ 10^{2}10^{3}), the generation frequency is determined by the resonator eigenmode frequency w_{0}:
Limiting case of large stabilization parameters At d > infinity the resonator line width is significantly greater than the Doppler line width, and the laser generation frequency is defined by the active medium atoms eigenfrequency w_{0}:
Formula (2) may be used for the case, when the absorbing cell with extremely small spectral line width, its absorption line center frequency being very close or exactly equal to the amplification line center frequency, is introduced in the laser resonator. Gravity field potential j occurs in the formulae (1) and (2) with different coefficients. Hence generation frequency w_{2} of the laser containing the absorbing cell will differ from the generation frequency w_{1} of the similar laser without absorbing cell. Let us assume that the absorbing cell is arranged to provide equal potential values in the formulae (1) and (2). The frequences difference for these two lasers being next to each other
depends on the gravity field potential value in the corresponding "middle" point. It is just the circumstance that allows to create the device sensitive to the gravitational potential. Solving the last formula with respect to j, we obtain:
The second addend in this formula is a constant value, determined by the device construction only. Potential is defined at accuracy of an arbitrary additive constant, and only potentials difference is of sense, hence the second addend vanishes in the final formulae. Besides, in all real cases W_{0}=o_{0} is met with high accuracy, then disregarding an additive constant we obtain:
One can estimate the terrestrial gravity potential value in the "middle" point by measuring the generated frequences difference Dw using the phase method. The abovementioned approach allows to create the laserinterferometric device for measuring the finite difference of Terrestrial gravity field potentials. The proposed instrument basic diagram is presented on fig. 1. Laserinterferometric gravimeter To get a gravimeter some changes should be introduced into design of laserinterferometric measuring instrument of gravity field potential, namely: to introduce the absorption cell in the left resonator to provide the absorption cells of the right and left resonators location in the points with different gravitational potential values in the case of the device vertical position (fig. 2). Let the potential in the point of the left absorption cell location be equal to j_{1}, and in the point of location of the right one  to j_{2}, the distance between the absorption cells centres being equal to h. In this case, according to formula (2), the left and right resonators will generate optical radiation with different frequences, therewith the frequences difference Dw will be determined by the gravity potentials difference Dj:
It is easy to obtain the free fall acceleration value g from this formula:
Using of two lasers instead of one allows to create a device for measuring the first, second anf third derivatives of the gravity potential, or a device for measuring the potential finite difference and its first and second derivatives. The scheme of the latter device is presented at figure 3.

