**7. Conclusion**

392 Acoustic Waves – From Microdevices to Helioseismology

wavelength—to decrease of pressure. In the course of medium relaxation, stress amplitudes and, correspondingly, spot wavelength shifts should have been reduced. At ≈50ns delay (twisted lines, Fig.16) spots have noticeable wavelength shifts which correspond to high stress amplitudes. Structures at moments over 300 ns after pump (Fig.14) correspond to a smoothed picture of *n*(*r*) profile. Note, that structures recorded with such big delays indicate the continued acoustic "ringing" in the medium. Estimated from Fig. 11, 14, 16 (at *k* = 20) period of stress spatial oscillations in YAG and glass varies from 15 to 40 μm and is in a qualitative agreement with the calculations (Sharma & Rieckhoff, 1970). Acoustic vibrations frequencies corresponding to these values constitute 108–109 Hz. Attenuation of phonons at these frequencies at a room temperature for YAG is smaller than 0.1 db/μs and for glass about 10 cm–1 (Dutoit, 1974; Zhu et al., 1991). These data confirm that "ringing" of the unloading medium in the focal region in YAG and glass may continue over several μs. The Yb:YAG line spectra near 1,03 μm were registered usually with 10÷50 ns delays after the end of ccl pulse and even together with the trailing edge of the ccl pulse. Observations of line spectra near 1,03μm, emitted soon after the pump pulse, like Fig.11, reveal noticeable inclination of spectral lines. This bending means that the wavelength of lasing at the same longitudinal mode (the number of nodes is preserved) changes from the centre to periphery of the excited region in the active medium. This corresponds to the development of lasing in some sites of the medium with a pressure (refractive index) gradient from the beam centre to its periphery. It can be easily shown that *λg* shifts to the blue if the refractive index gradient decreases from the beam axis to its periphery, Fig. 11. The pressure drop *ΔP* in the medium after the end of pump can be estimated from this line spectral shift. The frequency

*<sup>q</sup>* of the longitudinal mode of the resonator with the number of wavelengths *λq* over the

<sup>0</sup> ( ) () *<sup>q</sup> cq L ln l nr* π

where *Δl* is the longitudinal size of the optical inhomogeneity of radius *r*; n0 is the averaged refractive index outside the nonlinearity region; and *n(r)* is the refractive index in the

> [( ) ( )][( ) ( )] *<sup>q</sup> cq l n r n r L ln l nr L ln l nr*

1 2 01 02 [ ( ) ( )]

> ( ) *<sup>q</sup> L ln l nr*

λ*r*

<sup>0</sup> ( ) *<sup>q</sup> q*

λ

Here, *Δλq(r)* is the wavelength shift along the radius. For *Δλq(r)* ≈ 1.4 ×10-7 cm, *λ<sup>q</sup>* ≈ 10-4 cm, L ≈ 2 cm, *n0* ≈ 1, and *Δl* ≈ 10-2 cm, the change in the index is *Δn* ≈ 0.28. By assuming that the change in the index is produced only by the change in pressure along the radius and using

Δ Δ =

λ

*r Ln*

*l*

<sup>=</sup> −Δ +Δ ⋅ (2)

−Δ +Δ ⋅ −Δ +Δ ⋅ (3)

−Δ +Δ ⋅ <sup>=</sup> into (3) and assuming that

Δ (4)

ω

*<sup>q</sup>* during the

resonator length *2L* equal to *q* is described by the expression

displacement along the radius from *r1* to *r2* is

ω

By substituting the expression for 0 2[( ) ( )]

ω

nonlinear region. It follows from (2) that the change in the mode frequency

Δ − Δ =

*q*

π

*Δln(r)<Ln0*, we obtain the dependence of the change in the refractive index, *Δn* on *r*

*n*

ω

The study of the interaction of powerful ns pulses of low-coherence radiation of the LiF: F2 + color center laser (ccl) with optical materials (Yb:YAG, glass, et al.) was carried out. Efficient SBS of low-coherence pump, accompanied by SRS and formation of hypersonic waves reaching the intensity of shock waves were found. A physical model of excitation of SBS and hypersonic waves at scattering of ultrashort pulses of low-coherence pump at stationary inhomogeneities in optical materials is presented. It is shown that ns laser pulse, whose duration is much higher than its inverse spectral width, causes SBS much more efficient than a pulse of high coherence with the same duration and energy. Unlike SBS of a coherent radiation caused by a pressure fluctuation, scattering of low-coherence pump may be caused by any stationary inhomogeneities in a medium: cracks, dislocations, microinclusions, or just by a plane back surface of a sample. An effective energy contribution of light pulses into hypersonic waves on a small coherence length near the input surface of a sample leads to their transformation into a periodic succession of high-pressure shock waves, which results in structure changes of a crystal lattice (phase transition) in that region. The appearance of structural changes in optical materials that are specific to the interaction of powerful pulses of low coherence radiation with matter was found. The mechanisms of structural changes based on the action of intense hypersonic waves were considered.

Excitation of Periodical Shock Waves in Solid–State Optical Media (Yb:YAG, Glass)

*Science* Vol.124, №10, pp.1607-1611 *ISSN*: 0021-9533

Koechner, W. (2006). *Solid State Laser Engineering*, 6th ed., Springer, Berlin.

*Usp*. Vol.50, pp.771-791*,* ISSN: 0038-5670.

*Lett*., Vol.18 (4), pp.152-155, ISSN 0003-6951.

Mak, A & Soms, L. (1990). *Nd:Glass Lasers,* Nauka, Moscow.

Vol.148, pp.104–122*.* ISSN: 0038-5670.

Vol.37, pp.1939-1941, ISSN 0021-8979.

Vol.102, pp.207-220, ISSN 0038-1098.

p.90-92, ISSN: 0021-3640.

*Electron*., Vol.6 (6), pp.1287 – 1296, ISSN1077-260X.

26, pp.1061- 1064, ISSN 0368-7147.

pp.335–340, ISSN 0368-7147.

3640.

432, ISSN 0368-7147.

at SBS of Focused Low–Coherent Pump Radiation: Structure Changes, Features of Lasing 395

Bykovsky, N.E. & Senatsky, Yu.V. (2010). Twisted lines and small-scale structures in

color center laser. *Laser Physics* Vol.20, No.2, pp. 478-486, ISSN 1054-660X. Bykovsky, N.E. (2005). *Preprint FIAN* No. 16. (http://ellphi*.*lebedev*.*ru*/*12*/*pdf16*/*pdf*).* Bykovsky, N.E. (2006). *Preprint FIAN* No. 36. (http://ellphi.lebedev.ru/17/pdf36/pdf). Conners, G. & Thompson, R. (1966). A Continuum Mechanical Model for Laser-Induced

Dutoit, M. (1974). Microwave phonon attenuation in yttrium aluminum garnet and gadolinium gallium garnet. *J. Appl. Phys*. Vol.45, pp.2836-2841, ISSN 0021-8979. Galbraith, C. & Galbraith, J. (2011). Super-resolution microscopy at a glance *Journal of Cell* 

Gordienko,V., Mikheev P. & Potemkin F. (2010). Generation of coherent terahertz phonons

Gorelik, V. (2007). Optics of globular photonic crystals. *QuantumElectron*, Vol.37(5), pp. 409-

Kanel, G., Fortov, V. & Razorenov, S. (2007). Shock waves in condensed-state physics. *Phys.* 

Katarkevich, V., Kurstak V., Rubinov, A., & Efendiev T. (1996). Kinetics of the operation of a

Kogelnik, H., & Shank, C. (1971). Stimulated emission in a periodic structure. *Appl. Phys.* 

Koldunov, M., Manenkov, A. & Pokotilo, I. (2002). Mechanical damage in transparent solids

Krupke W.F. (2000). Ytterbium solid-state lasers. The first decade *IEEE J. Sel. Top. Quantum* 

Manenkov, A. & Prokhorov, A. (1986). Laser-induced damage in solids. *Sov. Phys. Usp*.,

Martinelli, J. (1996). Laser-Induced Damage Thresholds for Various Glasses. *J. Appl. Phys.*,

Merlin R. (1997). Generating coherent THz phonons with light pulses. *Solid State Commun*.,

Nelson K.A., Miller R.J.D. & Fayer M.D., (1982). Optical generation of tunable ultrasonic

Polyakova A.L. (1968). Elastic Nonlinearity in Stimulated Mandel'shtam-Brillouin

Polyakova, A. (1966). Nonlinear Effects in a Hypersonic Wave. *JETP Letters,* Vol.4, Iss. 4,

waves. *J. Appl. Phys*., Vol.53, pp.1144-1149, ISSN 0021-8979.

Scattering. *JETP Letters,* Vol. 7, Iss. 2, pp. 57-59, ISSN: 0021-3640.

Ready, J. F. (1971). *Effects of High Power Laser Radiation,* Academic, New York, London.

generation spectra of Yb-doped media excited by focused radiation of LiF:F 2+

Fracture in Transparent Media. *J. Appl. Phys*. Vol.37, pp.3434-3441, ISSN 0021-8979.

by sharp focusing of a femtosecond laser beam in the bulk of crystalline insulators in a regime of plasma formation.*JETP Letters,* Vol.92, No.8, pp.502-506, ISSN 0021-

distributed-feedback dye laser with nanosecond excitation. *Quantum Electron*.,Vol.

caused by laser pulses of different durations. *Quantum Electron*., Vol.32. No.4,

Nanosecond pulses of Yb lasing in the region 1.00-1.06 μm with the spectral width up to 20 nm in Yb :YAG and 50 nm in the Yb: glass samples were observed. The divergence of the broadband laser radiation (10-3 -10-4 rad) was one or two orders of magnitude smaller than the diffraction limit respectively to the source of Yb radiation in a sample. The mechanism of generation of broadband laser pulses of short duration and high directivity in the spatial structure of thin layers with inversion produced in the region of the propagation of intense hypersonic waves in the medium is discussed. The interpretation of experimental data is based on a new concept of the spatial distribution of the electromagnetic field of a photon not in the form of a "traveling" wave but with the field structures located in fixed positions along the photon propagation direction. The new approach allows the existence of light beams of an aperture *d ≈ λ* and with a "sub-diffraction" angle of divergence. Such beams must consist of groups of phase-synchronized photons with a small phase difference distanced by an interval ≈ *λ*. This synchronized group is no longer a "traveling" wave, its angle of divergence is defined by the phase difference of photons in a group.

Spectral lines in 1.03–1.05 μm region structured by 50–200 μm spots as well as lines with inclinations were found at Yb lasing in a resonator. Structures of multiple spots in spectra reflect the specific spatial configuration of the field of thermo-elastic stresses in the unloading region of ccl pulse focusing after the end of the pump. Inclinations of spectral lines reflect the pressure gradient from the center to the periphery of the region of ccl focusing. Basing on inclinations of spectral lines the pressure in the region of shock hypersonic wave propagation was estimated. Estimations show that for some of the studied media the pressure values may exceed the phase transition threshold.

### **8. Acknowledgment**

Authors thank O. Yaremchuk for the help in preparing this article for publication.

### **9. References**


Nanosecond pulses of Yb lasing in the region 1.00-1.06 μm with the spectral width up to 20 nm in Yb :YAG and 50 nm in the Yb: glass samples were observed. The divergence of the broadband laser radiation (10-3 -10-4 rad) was one or two orders of magnitude smaller than the diffraction limit respectively to the source of Yb radiation in a sample. The mechanism of generation of broadband laser pulses of short duration and high directivity in the spatial structure of thin layers with inversion produced in the region of the propagation of intense hypersonic waves in the medium is discussed. The interpretation of experimental data is based on a new concept of the spatial distribution of the electromagnetic field of a photon not in the form of a "traveling" wave but with the field structures located in fixed positions along the photon propagation direction. The new approach allows the existence of light beams of an aperture *d ≈ λ* and with a "sub-diffraction" angle of divergence. Such beams must consist of groups of phase-synchronized photons with a small phase difference distanced by an interval ≈ *λ*. This synchronized group is no longer a "traveling" wave, its

Spectral lines in 1.03–1.05 μm region structured by 50–200 μm spots as well as lines with inclinations were found at Yb lasing in a resonator. Structures of multiple spots in spectra reflect the specific spatial configuration of the field of thermo-elastic stresses in the unloading region of ccl pulse focusing after the end of the pump. Inclinations of spectral lines reflect the pressure gradient from the center to the periphery of the region of ccl focusing. Basing on inclinations of spectral lines the pressure in the region of shock hypersonic wave propagation was estimated. Estimations show that for some of the studied

angle of divergence is defined by the phase difference of photons in a group.

media the pressure values may exceed the phase transition threshold.

No.3 (August 2002), pp. 1630-1643, ISSN 0021-8979.

No.12, pp. 1138-1142, ISSN 0368-7147.

*Electron.,* 22 (8), 1524-1533. ISSN: 0018-9197.

*Phys*. Vol.37, pp.2283-2288 , ISSN 0021-8979.

Vol.5, Iss. 9. pp. 664–670, ISSN 1612-2011.

813-822, ISSN 0368-7147.

Authors thank O. Yaremchuk for the help in preparing this article for publication.

Alcock, R. & Emmony, D. (2002). Sensitivity of reflection transducers *J. Appl. Phys*., Vol. 92,

Basiev, T. et al. (1982). Solid-state tunable lasers based on color centers in ionic crystals *Bulletin of the Academy of Sciences of the USSR*, *ser. phys.,* Vol. 46, No.8, pp.145-154. Basiev, T.T, Bykovsky, N.E, Konyushkin, V.A & Senatsky, Yu.V. (2004). Use of a LiF colour

Bor, Z. & Muller, A. (1986). Picosecond distributed feedback dye lasers *IEEE J. Quantum* 

Bullough, R. & Gilman, J.J. (1966). Elastic Explosions in Solids Caused by Radiation. *J. Appl.* 

Bykovsky, N. & Senatsky, Yu. (2008a). Broadband collimated generation in YAG:Yb crystal

Bykovsky, N.& Senatsky, Yu. (2008b). Spectra, temporal structure, and angular directivity of

centre laser for pumping an Yb:YAG active medium. *Quantum. Electron*. Vol.34,

and ytterbium glass under LiF:F2+color center laser pumping. *Laser Phys. Lett*.

laser radiation of a Yb:YAG crystal and ytterbium glass pumped by low-coherence radiation from a F2+:LiF colour centre laser. *Quantum Electron*. Vol.38, No.9, pp.

**8. Acknowledgment** 

**9. References** 


**18** 

Adam Brański

*Poland* 

**An Optimal Distribution of Actuators** 

**– Some Aspects, Theoretical Considerations** 

The reduction of the effects of mechanical vibration fall into the of vibration isolation, design for vibration or vibration control (de Silva, 2000). The vibration control is subdivided into two group: passive control and active one. The core of the vibration control is to detect the level of vibration in a system and to counteract the effects of the vibration, so it needs two devices. Hence, the passive devices do not require external power for their operation. Hence, passive control is relatively simple, reliable and economical. But it has limitations namely, the control force depends entirely on the natural dynamics and it may not be adjust on line. Furthermore, in a passive device, there is no supply of power from an external source. It

The shortcomings of passive control can be overcome using an active one. In this case, the system response is directly sensed on line and on that basis, the specific control actions are applied to any locations of the system. But the active control needs external power, namely to apply control forces to vibrating system through actuators and to measure vibration

Two different types of actuators can be applied (Shimon et al., 2005). The first, inertial actuators, make up a piezoelectric material to vibrate large masses. Their vibrations are used to counteract the vibrations of the structure (Jiang et al., 2000). The advantages and

The second type of actuators is a layer of smart or intelligent materials. The sensors also belong to these materials; together they are well−known as piezoelectric elements (Tylikowski & Przybyłowicz, 2004). It was shown that these elements can offer excellent potential for an active vibration reduction of the structure vibrating with low frequencies (Croker, 2007; Fuller at al, 1997; Hansen & Snyder, 1997; Kozień, 2006; Przybyłowicz, 2002; Wiciak, 2008). As a general, piezoelectric elements are glued to the host structure. It makes the advantage, namely their incorporating into the structure is that the actuating mechanism becomes part of the structure. Both sensors and actuators are relatively light, compared to the structure, and can be made in arbitrary shape. The disadvantage is that they once bonded and they cannnot be used again. In recent years the measure of the vibration with the sensors are replaced by touch less measures. For this reason, hereafter in research the sensors are omitted and only second type actuators will be considered. Nowadays actuators

leads to the incomplete control, particularly in complex and high-order systems.

**1. Introduction** 

response using sensors.

disadvantages are enumerated in above reference.

**in Active Beam Vibration** 

*Rzeszow University of Technology* 

