Optimization of Laguerre-Gauss truncated series

Borghi, Riccardo; Gori, Francesca; Santarsiero, Massimo

doi:10.1016/0030-4018(96)00015-6

Cited by 22 publications

(27 citation statements)

References 8 publications

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“…This results in the expansion coefficients a f p and a b p being truncated without loss of accuracy as the magnitude of the coefficients decreases with the expansion. In addition, for a basis size corresponding to the beam waist size of the physical cavity, minimum truncation errors are incurred [20]. This formalism is consistent with the resonance condition requirement that the resonant field of the cavity does not change during a round trip, except for a complex constant; in this scenario it is applied to both the forward and backward traveling fields, which are related to one another through the boundary conditions at the mirrors, e.g.…”

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confidence: 71%

Observing mode propagation inside a laser cavity

et al. 2012

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The mode inside a laser cavity may be understood as the interference of two counter-propagating waves, referred to as the forward and backward waves, respectively. We outline a simple experimental procedure, which does not require any additional components, to study the forward and backward propagating waves everywhere inside a laser cavity. We verify the previous theoretical-only prediction that the two fields may differ substantially in their amplitude profile, even for stable resonator systems, a result that has implications for how laser resonators are conceptualized and how the disparate traveling waves interact with nonlinear intra-cavity elements, for example, passive Qswitches and gain media.The eigenmodes, i.e. the spatial (transverse) structure of a field that reproduces after a round trip, of an empty resonator made up of two spherical mirrors depend upon the resonator symmetry. For rectangular (circular) symmetry they are the well-known Hermite-Gaussian (Laguerre-Gaussian) modes HG nm (LG pl ) [1]. The particularities of these eigenmodes are: (i) only the lowest-order modes, HG 00 and LG 00 , are characterized by a smooth intensity profile, and are described by the Gaussian function; (ii) the higher-order modes are made up of circular rings (spots) of light for the LG pl (HG mn ) family; and (iii) the higher-order modes spread

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confidence: 71%

Observing mode propagation inside a laser cavity

et al. 2012

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“…Free-space di raction can be investigated by expansion into Hermite±Gaussian beam components [12,13]. Borghi et al [13] have shown that, when expanding an arbitrary function into a series of Hermite±Gaussians, there is an optimum width for the assumed Gaussian.…”

Section: Free-space DI Raction and Fractional Fourier Transformmentioning

confidence: 99%

“…Borghi et al [13] have shown that, when expanding an arbitrary function into a series of Hermite±Gaussians, there is an optimum width for the assumed Gaussian. The Hermite±Gaussian functions are special in the sense that they can be invariant under the fractional Fourier transform operation.…”

Section: Free-space DI Raction and Fractional Fourier Transformmentioning

confidence: 99%

Free-space diffraction and the fractional Fourier transform

Sheppard

1998

Journal of Modern Optics

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An explicit expression is derived for free-space propagation in terms of the fractional Fourier transform. The expression contains two arbitrary parameters, which can be, for example, an original phase curvature together with a scaling parameter or, alternatively, the order of fractional transformation. Appropriate choice of these parameters is discussed. This approach is then applied to the free-space propagation of Gaussian beams.

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“…The expansion of light fields in LG modes is a well known technique used mostly for monochromatic light [9], with the exception of a few works in which this is employed to analyze the dynamics of ultrashort pulses [10,11]. In [10], Liu et al determine the propagation of the ultrashort pulse Laguerre-Gaussian Beam.…”

Section: Introductionmentioning

confidence: 99%

Femtosecond spatial pulse shaping at the focal plane

Martínez-Matos¹,

Vaveliuk²,

Izquierdo³

et al. 2013

Opt. Express

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Abstract:Spatial shaping of ultrashort laser beams at the focal plane is theoretically analyzed. The description of the pulse is performed by its expansion in terms of Laguerre-Gaussian orthonormal modes. This procedure gives both a comprehensive interpretation of the propagation dynamics and the required signal to encode onto a spatial light modulator for spatial shaping, without using iterative algorithms. As an example, pulses with top-hat and annular spatial profiles are designed and their dynamics analyzed. The interference of top-hat pulses is also investigated finding potential applications in high precision pump-probe experiments (without using delay lines) and for the creation of subwavelength ablation patterns. In addition, a novel class of ultrashort pulses possessing non-stationary orbital angular momentum is also proposed. These exotic pulses provide additional degrees of freedom that open up new perspectives in fields such as laser-matter interaction and micro-machining.

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Optimization of Laguerre-Gauss truncated series

Cited by 22 publications

References 8 publications

Observing mode propagation inside a laser cavity

Observing mode propagation inside a laser cavity

Free-space diffraction and the fractional Fourier transform

Femtosecond spatial pulse shaping at the focal plane

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