Fresnel Number

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Yu N Makov - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear focal shift in medium Fresnel Number focused acoustic beams
    Internaltional Ultrasonics Symposium, 2010
    Co-Authors: F Camarena, Yu N Makov, V J Sanchezmorcillo, Silvia Adrian, Noe Jimenez
    Abstract:

    The study of the acoustic field characteristics generated by focusing sources, both in linear and nonlinear regime, is an active field of research as they are relevant in most of the ultrasonic applications in medicine and industry. Particularly, the linear focal shift phenomenon (i.e. the distance between the geometrical focus of the focused source and the on-axis maximum pressure position in linear regime, real focus) was explained in 1982 by Lucas and Muir. Also, the nonlinear focal shift phenomenon (the displacement of the pressure and intensity maxima position of focused acoustic beams under increasing driving voltages) has been related and interpreted in previous works. Nevertheless, till the moment it has not been published a specific experiment with the objective to study, experimentally and numerically, the focal region of medium Fresnel-Number transducers, and the magnitude of the this shift. This is the purpose of this work. The nonlinear focal shift phenomenon is presented for the case of a medium Fresnel-Number beam (N F =6). The experimental results show the existence of a short nonlinear shift in the position of the on-axis maximum pressure (6 mm). These results are coherent with numerical KZK model predictions. It is shown that in the nonlinear regime and for this focusing degree the position of the on-axis maximum pressure can surpassing the geometrical focal length. Contrary, the on-axis minimum pressure approaches the transducer under increasing driving voltages, and at high excitation the distance between on-axis maximum and minimum pressure is closer to 1 cm.

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    Ultrasonics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel Number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel Number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel Number NF = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.

  • nonlinear focal shift in focused ultrasonic transducers and its dependence on the Fresnel Number
    Journal of the Acoustical Society of America, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    In this work we present a systematic study of the on‐axis location of the maximum pressure and intensity points in the field radiated by a focused transducer. We report the motion of these characteristic points as the transducer voltage is increased. Different initial distributions, ranging from uniform to Gaussian cases, are considered. The numerical analysis is based on the solutions of the KZK equation with different initial conditions. Experimental results have been obtained for three different Fresnel Number focused transducers in linear and nonlinear regime in order to analyze the focal shift effect. An analytical expression of the initial (linear) shift of the maximum pressure position is given. This expression, and the results of the numerical simulations, shows a good agreement with the experimental data. As a main conclusion, we demonstrate that the axial range of the nonlinear shift of pressure is larger for strong initial focal shifts, occurring for small Fresnel Number transducers. Theoretica...

  • Fresnel Number concept and revision of some characteristics in the linear theory of focused acoustic beams
    arXiv: Fluid Dynamics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo
    Abstract:

    The advisability of the use of the Fresnel Number as the measure (characteristic) of the ratio of diffraction and focusing properties for ultrasonic transducers and its radiated beams is proposed and demonstrated. Althought this characteristic is more habitual in optics, in acoustics the equivalent (mathematically although not fully in its physical meaning) parameter of linear gain is used as a rule. However, the preference and the more accuracy of the Fresnel Number use is demonstrated here on the basis that the usual determination of the linear gain parameter ceases to correspond to the real value of the gain for low Fresnel Number acoustic beams. It connects with the linear effect of axial maximum pressure shift from the geometrical focus towards the transducer. This effect is known for a long time, but here the analytical formulas describing this shift with a high accuracy for arbitrary Fresnel Numbers are presented. As a consequence, also the analytical dependence of the real gain on the Fresnel Number is obtained.

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    arXiv: Fluid Dynamics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    Experimental results related with the movement of the position of pressure and intensity maxima along the axis of focused acoustic beams under increasing driving voltages and its interpretation are presented. It is shown that in the nonlinear regime the points of the pressure and intensity maximum are separated and move differently along the axis, contrary to the linear regime, where these points coincide. The considered effects are particularly strong in the case of low-Fresnel-Number beams.

V Espinosa - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    Ultrasonics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel Number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel Number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel Number NF = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.

  • nonlinear focal shift in focused ultrasonic transducers and its dependence on the Fresnel Number
    Journal of the Acoustical Society of America, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    In this work we present a systematic study of the on‐axis location of the maximum pressure and intensity points in the field radiated by a focused transducer. We report the motion of these characteristic points as the transducer voltage is increased. Different initial distributions, ranging from uniform to Gaussian cases, are considered. The numerical analysis is based on the solutions of the KZK equation with different initial conditions. Experimental results have been obtained for three different Fresnel Number focused transducers in linear and nonlinear regime in order to analyze the focal shift effect. An analytical expression of the initial (linear) shift of the maximum pressure position is given. This expression, and the results of the numerical simulations, shows a good agreement with the experimental data. As a main conclusion, we demonstrate that the axial range of the nonlinear shift of pressure is larger for strong initial focal shifts, occurring for small Fresnel Number transducers. Theoretica...

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    arXiv: Fluid Dynamics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    Experimental results related with the movement of the position of pressure and intensity maxima along the axis of focused acoustic beams under increasing driving voltages and its interpretation are presented. It is shown that in the nonlinear regime the points of the pressure and intensity maximum are separated and move differently along the axis, contrary to the linear regime, where these points coincide. The considered effects are particularly strong in the case of low-Fresnel-Number beams.

  • the strong effects of on axis focal shift and its nonlinear variation in ultrasound beams radiated by low Fresnel Number transducers
    INNOVATIONS IN NONLINEAR ACOUSTICS: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, 2006
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, V Espinosa, J Ramis, J Cruanes, F Camarena
    Abstract:

    On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on‐axis distribution and the corresponding temporal profiles for low‐FresnelNumber focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel Number, a strong initial (linear) shift of the main on‐axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on‐axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure poin...

  • strong on axis focal shift and its nonlinear variation in low Fresnel Number ultrasound beams
    Journal of the Acoustical Society of America, 2006
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, V Espinosa, J Ramis, J Cruanes, F Camarena
    Abstract:

    We examine the case of focusing transducers with a strong initial (in linear regime) shift of the main on-axis peak pressure maximum from the geometrical focal point toward the transducer. Such transducers are characterized, using the concepts introduced in this paper, by a low Fresnel Number. The displacement of this initially shifted on-axis pressure maximum point toward the geometrical focus, and its backward motion as the driving transducer voltage increases until highly nonlinear regimes, has been experimentally observed. The simultaneous monitoring of the temporal wave-form distortion determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of the on-axis pressure maximum. The numerical solution of the corresponding mathematical model confirms the physical interpretation of the observed phenomenon.

F Camarena - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear focal shift in medium Fresnel Number focused acoustic beams
    Internaltional Ultrasonics Symposium, 2010
    Co-Authors: F Camarena, Yu N Makov, V J Sanchezmorcillo, Silvia Adrian, Noe Jimenez
    Abstract:

    The study of the acoustic field characteristics generated by focusing sources, both in linear and nonlinear regime, is an active field of research as they are relevant in most of the ultrasonic applications in medicine and industry. Particularly, the linear focal shift phenomenon (i.e. the distance between the geometrical focus of the focused source and the on-axis maximum pressure position in linear regime, real focus) was explained in 1982 by Lucas and Muir. Also, the nonlinear focal shift phenomenon (the displacement of the pressure and intensity maxima position of focused acoustic beams under increasing driving voltages) has been related and interpreted in previous works. Nevertheless, till the moment it has not been published a specific experiment with the objective to study, experimentally and numerically, the focal region of medium Fresnel-Number transducers, and the magnitude of the this shift. This is the purpose of this work. The nonlinear focal shift phenomenon is presented for the case of a medium Fresnel-Number beam (N F =6). The experimental results show the existence of a short nonlinear shift in the position of the on-axis maximum pressure (6 mm). These results are coherent with numerical KZK model predictions. It is shown that in the nonlinear regime and for this focusing degree the position of the on-axis maximum pressure can surpassing the geometrical focal length. Contrary, the on-axis minimum pressure approaches the transducer under increasing driving voltages, and at high excitation the distance between on-axis maximum and minimum pressure is closer to 1 cm.

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    Ultrasonics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel Number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel Number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel Number NF = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.

  • nonlinear focal shift in focused ultrasonic transducers and its dependence on the Fresnel Number
    Journal of the Acoustical Society of America, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    In this work we present a systematic study of the on‐axis location of the maximum pressure and intensity points in the field radiated by a focused transducer. We report the motion of these characteristic points as the transducer voltage is increased. Different initial distributions, ranging from uniform to Gaussian cases, are considered. The numerical analysis is based on the solutions of the KZK equation with different initial conditions. Experimental results have been obtained for three different Fresnel Number focused transducers in linear and nonlinear regime in order to analyze the focal shift effect. An analytical expression of the initial (linear) shift of the maximum pressure position is given. This expression, and the results of the numerical simulations, shows a good agreement with the experimental data. As a main conclusion, we demonstrate that the axial range of the nonlinear shift of pressure is larger for strong initial focal shifts, occurring for small Fresnel Number transducers. Theoretica...

  • nonlinear change of on axis pressure and intensity maxima positions and its relation with the linear focal shift effect
    arXiv: Fluid Dynamics, 2008
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, F Camarena, V Espinosa
    Abstract:

    Experimental results related with the movement of the position of pressure and intensity maxima along the axis of focused acoustic beams under increasing driving voltages and its interpretation are presented. It is shown that in the nonlinear regime the points of the pressure and intensity maximum are separated and move differently along the axis, contrary to the linear regime, where these points coincide. The considered effects are particularly strong in the case of low-Fresnel-Number beams.

  • the strong effects of on axis focal shift and its nonlinear variation in ultrasound beams radiated by low Fresnel Number transducers
    INNOVATIONS IN NONLINEAR ACOUSTICS: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, 2006
    Co-Authors: Yu N Makov, V J Sanchezmorcillo, V Espinosa, J Ramis, J Cruanes, F Camarena
    Abstract:

    On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on‐axis distribution and the corresponding temporal profiles for low‐FresnelNumber focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel Number, a strong initial (linear) shift of the main on‐axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on‐axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure poin...

Kaifeng Huang - One of the best experts on this subject based on the ideXlab platform.

  • generation of structured beams in large Fresnel Number degenerate cavities and beam transformation with orbital angular momentum
    Proceedings of SPIE the International Society for Optical Engineering, 2010
    Co-Authors: Yueh Chin Lin, Yungfu Chen, Kaifeng Huang
    Abstract:

    We employ a large-Fresnel-Number laser system to demonstrate the three-dimensional optical coherent waves localized on Lissajous and trochoidal parametric surfaces with Lissajous and trochoidal transverse patterns in degenerate cavities. The coherent structured beams are verified to be composed of degenerate Hermite-Gaussian and Laguerre-Gaussian modes with different longitudinal indices resulted from longitudinal-transverse coupling. As well known, the Hermite- Gaussian modes can be converted into Laguerre-Gaussian modes possessing orbital angular momentum by use of a pair of cylindrical lens. Consequently, we make use of cylindrical lenses to transform the Lissajous structured beams superposed of degenerate Hermite-Gaussian modes into the intriguing trochoidal structured beam possessing optical orbital angular momentum.

  • observation of lasing modes with exotic localized wave patterns from astigmatic large Fresnel Number cavities
    Optics Letters, 2010
    Co-Authors: Y C Lin, H C Liang, Y J Huang, Yungfu Chen, Kaifeng Huang
    Abstract:

    We investigate the lasing modes in large-Fresnel-Number laser systems with astigmatism effects. Experimental results reveal that numerous lasing modes are concentrated on exotic patterns corresponding to intriguing geometries. We theoretically use the quantum operator algebra to construct the wave representation for manifesting the origin of the localized wave patterns.

  • observation and analysis of coherent optical waves emitted from large Fresnel Number degenerate cavities
    Optics Express, 2009
    Co-Authors: Y C Lin, Yungfu Chen, Kaifeng Huang
    Abstract:

    We demonstrate that the coherent optical waves emitted from large-Fresnel-Number degenerate cavities persistently display a sort of salient intensity variations. We use the representation of the coherent states to explore the origin of the salient intensity variations and find that these coherent laser waves arise from a quadrature superposition of two degenerate coherent states. With the analytical representation of the superposed coherent states, we verify that these coherent laser waves possess a large angular momentum per photon.

J M Guerra - One of the best experts on this subject based on the ideXlab platform.

  • Effect of the solvent viscosity on the local irregular intensity fluctuations in high Fresnel Number dye lasers
    IEEE Journal of Quantum Electronics, 1999
    Co-Authors: O.g. Calderon, Inmaculada Leyva, J M Guerra
    Abstract:

    We study the influence of the solvent viscosity in the local irregular intensity fluctuations characteristic of high Fresnel Number dye lasers. The relative amplitude of the fluctuations in a flashlamp-pumped dye laser is analyzed, We complete our previous work by using several solvents and different excitation energies above threshold. A decrease of the relative fluctuation amplitude is found as the solvent viscosity or the pumping energy increases. This effect is theoretically analyzed in the framework of the semiclassical Maxwell-Bloch equations, with a model based on the orientation of the dye molecules driven by the laser field in the solvent. These results point out the importance of the orientation of the dye molecules in the intensity fluctuation phenomenon.

  • local irregular intensity fluctuations in high Fresnel Number dye lasers
    High-power lasers and applications, 1998
    Co-Authors: J M Guerra, Inmaculada Leyva, O.g. Calderon
    Abstract:

    Local intensity fluctuations in a large aperture dye laser have been analyzed. We have studied the influence of solvent viscosity in the amplitude of these fluctuations. This experimental result provide a clear evidence of the role played by the molecular orientation in the spatio-temporal laser dynamics. The dependence of the average spectra of these fluctuations on the active laser medium length has been studied. The mean frequency of the spectra change with the active laser medium length.

  • weak turbulence in a high Fresnel Number dye laser
    International Journal of Bifurcation and Chaos, 1994
    Co-Authors: Victor M Perezgarcia, J M Guerra
    Abstract:

    Local spatiotemporal chaos found in a dye laser has been experimentally studied and characterized as a weak turbulent system. Furthermore, a new model based on a discrete version of the Maxwell-Bloch equations seems to agree with the experimental results. The dynamical system’s nonstandard behavior in the form of a new type of frequency locking and the analysis of the decay of the energy fluctuations are herein described from both the theoretical and experimental points of view.