The 15 reference contexts in paper P. Loiko A., V. Savitski G., K. Yumashev V., N. Kuleshov V., A. Pavlyuk A., П. Лойко А., В. Савицкий Г., К. Юмашев В., Н. Кулешов В., А. Павлюк А. (2015) “ОПРЕДЕЛЕНИЕ ПАРАМЕТРОВ ТЕРМИЧЕСКОЙ ЛИНЗЫ В АНИЗОТРОПНЫХ ЛАЗЕРНЫХ КРИСТАЛЛАХ В УСЛОВИЯХ ДИОДНОЙ НАКАЧКИ // THERMAL LENSING MEASUREMENTS IN THE ANISOTROPIC LASER CRYSTALS UNDER DIODE PUMPING” / spz:neicon:pimi:y:2012:i:1:p:62-68

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    1919
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    Introduction As optical pumping of the laser crystal results in the volumetric heat deposition that leads to the complicated refractive index distribution, the active medium can act as a lens (thermal lens)
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    [1–4]
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    . It results in dropping of output power, decreasing of output beam quality and poorer laser cavity stability [1, 2]. In general, thermal lensing restricts substantially the laser power scaling capabilities.
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    2041
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    Introduction As optical pumping of the laser crystal results in the volumetric heat deposition that leads to the complicated refractive index distribution, the active medium can act as a lens (thermal lens) [1–4]. It results in dropping of output power, decreasing of output beam quality and poorer laser cavity stability
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    [1, 2]
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    . In general, thermal lensing restricts substantially the laser power scaling capabilities. Optimization of laser cavity in order to eliminate the influence of thermal lensing effects requires information about thermal lens properties.
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    2586
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    Similarly to a conventional lens, the thermal lens is characterized by the sign (focusing or defocusing action). However, its optical power is a linear function of pump power (the corresponding slope is usually denoted as the sensitivity factor M)
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    [3]
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    . The M value indicates the change in optical power of thermal lens due to 1W variation of the pump power. Thermal lensing can be measured by monitoring changes in the laser output [1, 2], or by introduction of an additional probe beam [5, 6].
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  4. Start
    2793
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    The M value indicates the change in optical power of thermal lens due to 1W variation of the pump power. Thermal lensing can be measured by monitoring changes in the laser output
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    [1, 2]
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    , or by introduction of an additional probe beam [5, 6]. In both cases, the possibility to determine the beam spatial profile as a function of pump power is available. In addition, during laser operation the influence of thermal lensing on laser mode can be detected from rollover of the output power at high pump powers when the cavity becomes unstable [2, 7].
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  5. Start
    2849
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    The M value indicates the change in optical power of thermal lens due to 1W variation of the pump power. Thermal lensing can be measured by monitoring changes in the laser output [1, 2], or by introduction of an additional probe beam
    Exact
    [5, 6]
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    . In both cases, the possibility to determine the beam spatial profile as a function of pump power is available. In addition, during laser operation the influence of thermal lensing on laser mode can be detected from rollover of the output power at high pump powers when the cavity becomes unstable [2, 7].
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  6. Start
    3177
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    In addition, during laser operation the influence of thermal lensing on laser mode can be detected from rollover of the output power at high pump powers when the cavity becomes unstable
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    [2, 7]
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    . The second scenario suffers by two reasons: a possibility for multimode operation and influence of mode matching. Indeed, switching to the multimode operation and corresponding output power increase can mask the moment when the laser cavity becomes unstable.
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  7. Start
    4152
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    Thus, under diode-pumping conditions the analysis of the output beam spatial profile should be selected as a simple tool for thermal lensing measurements. Thermal lens in the anisotropic crystals can be substantially astigmatic
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    [1]
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    (i.e., its optical power depends on the meridional plane). It leads to elliptic profile of the output beam. The idea of preset paper was to extract the information about astigmatism of the thermal lens from measurements of divergence of the output beam performed for different meridional planes.
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    5965
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    variation of the pump intensity M = dD/dIin; 4) the difference of the sensitivity factors for principal meridional planes S = |MB – MA| (thermal lens astigmatism degree) is determined. The key point is the correct ABCD-modeling of the laser cavity, which suffers from the uncertainty in the distances between all optic elements that form the laser cavity
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    [2]
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    . Indeed, for the real laser scheme these distances can be measured with some precision (typically not better than 0.5 mm). The increase of the element number results in the increase of the overall error.
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  9. Start
    10680
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    On the contrary, when the inner surface of the output coupler is concave and the outer one is flat (as it is drawn in figure 1), it acts as a lens with focal length f = –R2/(n2 – 1) (where n2~1.5 is the refractive index of the glass)
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    [2]
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    . Thus, such a mirror affects significantly the beam divergence. Another factor that should affect the beam diameters is the M2 parameter of the beam. For real laser systems, it is close to 1 (typically within the range of 1,1–1,2).
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  10. Start
    15751
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    Experimental By means of the described approach, thermal lensing was characterized in the diode-pumped monoclinic Nd(3at.%)-doped potassium gadolinium tungstate laser crystal (Nd:KGd(WO4)2, or Nd:KGdW). The crystal was cut for light propagation along the Np optical indicatrix axis (that coin- cides with crystallographic axis b)
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    [6]
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    . The laser cavity was formed by a concave back mirror (R1 = = 50 mm, HT@810 nm, HR@1067 nm) and a flat output coupler (HR@1067 nm), the cavity dimensions was d1 = 13 mm, d = 1 mm and d2 = 13 mm.
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    16860
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    The laser beam profiles were captured by means of a CCD-camera. Thermal lens was considered as a thin one, as the absorption length in the Nd:KGdW at 810 nm for light polarization is shorter than 300 μm
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    [8]
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    . Results At low pumping levels the Nd:KGdW laser is characterized by circular output mode profile. However, when the pump power is increased, the output mode profile becomes elliptic (figure 6).
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  12. Start
    17883
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    The beam expands in the direction of A axis and compresses in the direction of B axis. It should be noted that the orientation of these axes (principal meridional planes) corresponds to principal frame of thermal expansion tensor for KGdW crystal
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    [9]
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    . Indeed, A axis coincides with the X'1 axis and the B one – with the X'3 axis. In the measurement plane (Nm-Ng plane), the X'1 corresponds to the minimum thermal expansion coefficient, while X'3 axis – to the maximum thermal expansion coefficient.
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    19921
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    radius on the pump intensity in the principal meridional planes (points), calculated dependencies of the output beam radius on the thermal lens optical power (curves) for diode-pumped Nd:KGdW laser Thermal lens parameters determined in present paper agree well with previous results obtained for flashlamp-pumped Np-cut Nd:KGdW at the wavelengths of 633 and 1064 nm
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    [5]
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    : thermal lens was found to have different signs along principal meridional planes that corresponds to the X'1 and X'3 axes. In [7, 10], thermal lens in the Np-cut diode-pumped Nd:KGdW was found to have different signs at the light wavelengths of 1067 and 1351 nm, but the principal meridional planes were not determined.
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  14. Start
    20154
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    power (curves) for diode-pumped Nd:KGdW laser Thermal lens parameters determined in present paper agree well with previous results obtained for flashlamp-pumped Np-cut Nd:KGdW at the wavelengths of 633 and 1064 nm [5]: thermal lens was found to have different signs along principal meridional planes that corresponds to the X'1 and X'3 axes. In
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    [7, 10]
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    , thermal lens in the Np-cut diode-pumped Nd:KGdW was found to have different signs at the light wavelengths of 1067 and 1351 nm, but the principal meridional planes were not determined.
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  15. Start
    20374
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    In [7, 10], thermal lens in the Np-cut diode-pumped Nd:KGdW was found to have different signs at the light wavelengths of 1067 and 1351 nm, but the principal meridional planes were not determined. In
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    [6, 11]
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    , thermal lens in the flashlamp-pumped Np-Nd:KGdW was found to be negative (the study with respect to meridional planes was not performed). Conclusions An experimental setup was developed for measurements of thermal lensing in the anisotropic diode-pumped laser crystals.
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