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The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

100%
Ayadi S., Haeberlé O.
Open Physics
|
2014
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vol. 12
|
issue 3
203-214
EN
We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ℘ is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C P”[7], close to the second laser threshold “2C 2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.
2
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Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation

81%
Vertu S., Flügge J., Delaunay J.-J., Haeberlé O.
Open Physics
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2011
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vol. 9
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issue 4
969-974
EN
Tomographic Diffractive Microscopy is a technique, which permits to image transparent living specimens in three dimensions without staining. It is commonly implemented in two configurations, by either rotating the sample illumination keeping the specimen fixed, or by rotating the sample using a fixed illumination. Under the first-order Born approximation, the volume of the frequency domain that can be mapped with the rotating illumination method has the shape of a “doughnut”, which exhibits a so-called “missing cone” of non-captured frequencies, responsible for the strong resolution anisotropy characteristic of transmission microscopes. When rotating the sample, the resolution is almost isotropic, but the set of captured frequencies still exhibits a missing part, the shape of which resembles that of an apple core. Furthermore, its maximal extension is reduced compared to tomography with rotating illumination. We propose various configurations for tomographic diffractive microscopy, which combine both approaches, and aim at obtaining a high and isotropic resolution. We illustrate with simulations the expected imaging performances of these configurations.
3
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Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space

81%
Vertu S., Delaunay J.-J., Yamada I., Haeberlé O.
Open Physics
|
2009
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vol. 7
|
issue 1
22-31
EN
Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives morphological information only, diffraction microtomography makes it possible to obtain the complex optical refractive index of the observed sample by mapping a three-dimensional support in the spatial frequency domain. The technique can be implemented in two configurations, namely, by varying the sample illumination with a fixed sample or by rotating the sample using a fixed illumination. In the literature, only the former method was described in detail. In this report, we precisely derive the three-dimensional frequency support that can be mapped by the sample rotation configuration. We found that, within the first-order Born approximation, the volume of the frequency domain that can be mapped exhibits a missing part, the shape of which resembles that of an apple core. The projection of the diffracted waves in the frequency space onto the set of sphere caps covered by the sample rotation does not allow for a complete mapping of the frequency along the axis of rotation due to the finite radius of the sphere caps. We present simulations of the effects of this missing information on the reconstruction of ideal objects.
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