On-axis Intensity Research Articles

Arbitrary shaping of on-axis amplitude of femtosecond Bessel beams with a single phase-only spatial light modulator.

Arbitrary shaping of the on-axis intensity of Bessel beams requires spatial modulation of both amplitude and phase. We develop a non-iterative direct space beam shaping method to generate Bessel beams with high energy throughput from direct space with a single phase-only spatial light modulator. For this purpose, we generalize the approach of Bolduc et al. to non-uniform input beams. We point out the physical limitations imposed on the on-axis intensity profile for unidirectional beams. Analytical, numerical and experimental results are provided.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

Analysis of electromagnetic focusing properties of multi-annular nanostructured metasurfaces

To explore the electromagnetic focusing properties of multi-annular nanostructured metasurfaces, the material property, dispersion property, and error-tolerance property have been studied through a combination of the vectorial angular spectrum theory and the three-dimensional finite-difference time-domain (FDTD) method. An obvious focal shift has been observed and the thickness for the Ag, Al, and Au films is suggested to be within the range of 50–100nm for the illumination wavelength of 640nm. The light dispersion effect of the metasurface is remarkable and the focal length decreases with the increase of the wavelength; however, the on-axis intensity distributions retain a similar, shifted shape when the wavelength deviation is less than 10nm. The fabrication error has a strong impact on the on-axis intensity distribution; when it occurs for the middle annulus, a more severe impact will be induced. The above findings provide theoretical guidance for applying multi-annular metasurfaces in the fields of super-resolution focusing, micro-nano fabrication, and nanoscopic imaging.

Evolution of Anomalous Hollow Gaussian Beams in Strongly Nonlocal Nonlinear Media Under the Off-Waist Incident Conditions

We investigate the evolution of anomalous hollow Gaussian beams in strongly nonlocal nonlinear media under the off-waist incident condition. We obtain analytic expressions of the beam propagation, the on-axis intensity, and the beam width and curvature. We perform some numerical simulations to illustrate the propagation properties of anomalous hollow Gaussian beams. The results show that, under the off-waist incident condition, the beam evolution is always periodic, whatever the input power is, being different from that under the on-waist incident condition. We discuss the influences of the input power and the departure distance on the propagation properties and present the physical reasons.

Third-order nonlinear optical investigations of the 1,1′-methylenedipyridinium tetrachloridocuprate(II) using Z-scan technique

We report here the third order nonlinear optical properties of the 1,1′-methylenedipyridinium tetrachloridocuprate(II) in chloroform (CHCl3) solution using Z-scan technique. Measurements were performed with a CW Diode laser at 635nm wavelength and 26mW power. The nonlinear optical absorption coefficient (β) and nonlinear refraction (n2) were of the order 4.46×10−4cm/W and 3.74×10−8cm2/W, respectively. The operating mechanism is reverse saturable absorption (RSA) as the excited-state absorption cross-section was found higher than ground state absorption cross-section. The magnitude of nonlinear absorption coefficient (β) was found decreasing with on-axis input intensity (I0). Our results suggest that this material is considered as a promising candidate for future optical devices applications.

Z-scan measurements of single walled carbon nanotube doped acetylenedicarboxylic acid polymer under CW laser

Z-scan measurements of single walled carbon nanotube (SWCNT) doped with acetylenedicarboxylic acid (ADC) polymer are performed using a CW diode laser at 635nm wavelength with 17mW power. The nonlinear absorption coefficient (β), nonlinear refractive index (n2), the real and imaginary parts of the third-order nonlinear optical susceptibility (Re χ3), (Im χ3) of the investigated samples are calculated. It was found that the β values decrease with increase in on-axis input intensity I0. Also, these values are found to be proportional with sample concentrations. The excited-state absorption cross sections were calculated to be at σex=5.08×10−14cm2 for the (SWCNT) and at 15.1×10−14cm2 for the ADC polymer. It was found that the σex is larger than ground-state absorption cross sections, indicating that the reverse saturable absorption mechanism (RSA) is the dominating mechanism for the observed absorption nonlinearities.

On-axis intensity of hollow beams in nonlinear media with a high nonlocality

In this paper, we focus on the on-axis intensity evolutions of hollow beams in nonlinear media with a high nonlocality. It is found that, the evolutions of on-axis intensity with different beam powers are always periodic during propagation, whereas, depending on different beam powers, the evolution curves of on-axis intensity in each period may exhibit themselves as three different types, namely, a concave, a platform, or a convex shape. The critical power, the extreme values of on-axis intensity and their corresponding positions are all given analytically.

Study of downstream light intensity modulation induced by mitigated damage pits of fused silica using numerical simulation and experimental measurements

For high-power UV laser facilities, one of the key problems limiting the maximum light influence and safe routine operation is that the UV laser induces damage to fused silica optics. The most effective mitigation protocol of the damaged optics is the CO2 laser processing that leads to make locally melt or evaporate the damage. While the mitigated damage sites possess particular morphology, which may modulate the passing laser beam and induce the downstream intensification that will ruin the neighbor optics. In this work, the morphology features of the mitigated damage pits of fused silica optics are systematically investigated. According to the measured morphology features, a 3D grid model of mitigated pit is built, and the downstream light intensity distribution of the mitigated pit model under incident 351 nm laser is studied by scalar diffraction theory and fast fourier transform (FFT) methods. Results indicate that there are two kinds of downstream intensification: off-axis and on-axis intensifications. In the former intensification, the maximum intensity is located near the output surface of the optics and comes mainly from the depth of the mitigated pit; it increases with the depth. In the alter intensification, the maximum intensity is located far from the output surface of the optics and is mainly dependent on the height of the rim structure at the fringe of the mitigated damage pit; so it increase with increasing height. In addition, it is found that the location of the maximum off-axis or on-axis intensity can approach the output surface of the optics with increasing maximum intensity. For comparison, experimental measurements of downstream intensification induced by the mitigated pits are carried out, and the experimental results are almost consistent with the numerical simulation, implying the validity of the numerical simulation of the mitigated pit model. Results of this research indicate that the downstream intensification of mitigated pits can be suppressed by controlling the morphology features of mitigated pits. this is significant for the development and improvement of the mitigated techniques of damage optics.

An analytical model for top-hat long transient mode-mismatched thermal lens spectroscopy

It has been shown that a top-hat excitation beam gives rise to a more sensitive signal for the thermal lens spectroscopy (TLS). Recently, a numerical model has been presented for a top- hat excitation beam in a dual-beam mod-mismatched TLS [Opt. Lett. 33(13), 1464-1466 (2008)]. In this work, we present a full analytical version of this model. Our model was based on a new solution of time-dependent heat equation for a finite radius cylindrical sample exposed to a top-hat excitation laser beam. The Fresnel diffraction integration method was then used to calculate on-axis probe-beam intensity variations due to thermal lensing by taking the aberrant nature of the thermal lens into account. The model was confirmed with experimental data of LSCAS-2 with an excellent agreement.

Determination of an optical vortex topological charge using an astigmatic transform

It It is shown both theoretically and experimentally that if a cylindrical lens is placed into a laser beam, having an optical vortex with integer topological charge n and on-axis intensity null, then at the double focal distance behind the lens, the n-fold degenerate intensity null is split into n isolated intensity nulls. These intensity nulls lie on a straight line in the transverse plane at an angle of + 45 or – 45 degrees to the axis of the cylindrical lens, depending on the vortex helicity direction (i.e. sign of the topological charge). Experiments show that such a method can be used to determine higher-order topological charges up to n = 100.

Optical nonlinearity investigation of the tetracarbonyl(2,2′-bipyridyl)molybdenum(0) using Z-scan technique

Abstract The third order nonlinear optical properties of the Tetracarbonyl(2,2′-bipyridyl)molybdenum(0) in CHCl 3 solution have been studied using Z-scan technique. Measurements were performed with a CW Diode laser at 635 nm wavelength and 15 mW power. The nonlinear optical absorption coefficient ( β ) and nonlinear refraction ( n 2 ) were found at 2.86 × 10 −3 cm/W and 4.28 × 10 −7 cm 2 /W respectively. The nonlinear absorption coefficient β values decrease with increase in on-axis input intensity I 0 . The reverse saturable absorption (RSA) mechanism was responsible for the optical limiting effect. The results suggest that this material is considered as a promising candidate for future optical devices applications.

Rigorous electromagnetic test of super-oscillatory lens.

Thus far, the vector field of light probed by a nanostructured super-oscillatory lens (SOL) has mostly been studied by approximate theoretical means. Here the first rigorous electromagnetic (EM) test has been presented through an established electromagnetic model solved by the three-dimensional (3D) finite-difference time-domain (FDTD) method. It is found through comparisons that scalar/vectorial theories currently used for designing the metal-film-coated SOL can effectively predict the on-axis intensity behind a SOL simulated by FDTD for both linearly and circularly polarized beams; however, they cannot reflect the true 3D EM vector field distribution particularly for the linearly polarized beam and imprecise results for the total electric energy density have appeared in certain transverse planes, e.g. a relative error as high as 26% is produced for the size of the main focus behind a SOL of 14 μm large in diameter. Besides, it is found that current theories cannot be used for designing the glass-etched phase-type SOL.

Self-imaging, self-healing beams generated by photorefractive volume holography

Self-imaging beams consisting of three-dimensional intensity voids are generated via photorefractive volume holography. Reconstruction of a volume hologram recorded at 594 nm is performed with a Bessel readout beam. The holographic output is similar in appearance to a Bessel beam, with the central spot oscillating between maximum and zero intensity over a propagation distance of 10 to 55 cm. The oscillation period for the on-axis intensity is 30 cm. The reconstruction is capable of self-healing, with a fully recovered central core after the beam propagates 40 cm. Dual-wavelength reconstruction at 632.8 nm produces an output beam with similar self-imaging and self-healing properties. A theoretical framework based on the interference of a plane wave and a Bessel beam simultaneously reconstructed from a volume hologram is able to describe our experimental results.

Intensity distribution and spectral degree of coherence for array beams in non-Kolmogorov atmospheric turbulence

The propagation expressions of the intensity distribution and the spectral degree of coherence for radial array Gaussian Schell-model beams in non-Kolmogorov atmospheric turbulence have been derived. There exists a maximum of the on-axis intensity for radial array beams on propagation. The optimal propagation distance where the maximum appears has been analyzed in detail. The influence of the generalized structure constant and the initial spatial coherence parameter for the correlated superposition beam is different from the uncorrelated one. In particular, the on-axis intensity maximum exhibits a minimum when the generalized exponent α = 3.1. The spectral degree of coherence for the correlated superposition beam is larger than the uncorrelated one, and the difference between the two superposition styles becomes larger when the spatial coherence parameter becomes larger and the turbulence becomes weaker. Moreover, when α = 3.1 the spectral degree of coherence exhibits a minimum.

Pressure effects on the femtosecond laser filamentation

We investigate the pressure effects on the propagation of the laser pulse with wavelength of 800nm by numerical simulations. We consider the effects on the on-axis intensity, the beam radius and the energy of the filament, as well as the on-axis density of plasma. Numerical results show that when the pressures increase, the length, radius and energy of the light filament become shorter, narrower and lower, respectively. Moreover, we find that the length and the radius of filament are approximately inversely proportional to the pressure and the square root of pressure, respectively, and the pulse with shorter duration is easier to be affected by the pressure. We also obtain the conclusion that the plasma is not necessary to generate the filament in gases in various pressures, as stated by Béjot et al. [1] for the case of standard atmosphere pressure.

Complex degree of coherence and power moments of cylindrical sinc Gaussian beam

Complex degree of coherence and power moment aspects of cylindrical sinc Gaussian beam are investigated. To do this, we have used the random phase screen approach. It is seen that on the source plane, cylindrical sinc Gaussian beam has zero on-axis intensity and the sidelobes resemble the sinc or the Gaussian profile depending on the relative magnitudes of width parameter and the source size. Upon propagation in turbulent atmosphere, the initially flat complex degree of coherence becomes curved as the beam propagates, it then partially follows the intensity profile, and eventually turns into a delta function. Power moments are evaluated up to the fifth degree and over two different aperture sizes. In the aperture size of pointlike scintillations, the behaviors of power moments are similar to those of intensity moments. In aperture averaging conditions however, the differences between the variations of moments with respect to the propagation distance and degree of the moments become much less.

Analytic Expressions for the Interaction of Modified Hollow Gaussian Beams in Highly Nonlocal Nonlinear Media

We obtain two equivalent analytic expressions describing the propagation of two interacting modified hollow Gaussian beams in highly nonlocal nonlinear media. We carry out some numerical simulations to illustrate their interaction properties, such as the transverse intensity distributions and the on-axis intensity evolutions. We find that the evolutions of two interacting modified hollow Gaussian beams in highly nonlocal nonlinear media are periodical. The two beams always attract each other for the in-phase case and even for the out-of-phase case. The difference is that a prominent intensity peak appears at the center of the interacting region for the in-phase case, while it is zero for the out-of-phase case.

Intensity Fluctuations of Laser Array Beams in Non-Kolmogorov Turbulence

On-axis intensity fluctuations of laser array beams are evaluated when they are used in a weakly turbulent non-Kolmogorov atmosphere. Our formulation of the scintillation index is based on the Rytov method, which in the limiting case, correctly reduces to the known Gaussian beam scintillation index in weak Kolmogorov turbulence. When the radius of the ring (on which the array beamlets are placed), number of beamlets forming the laser array, source size of the beamlets, propagation distance or the wavelength is fixed, a decrease in the power law exponent of the non-Kolmogorov spectrum is found to decrease the scintillation index. Examining for any realization of the non-Kolmogorov spectrum, it is observed that an increase in the ring radius, number of beamlets, wavelength, and decrease in the source size of the beamlet, propagation distance reduces the intensity fluctuations.

Dynamics of Passively Phased Ring Oscillator Fiber Laser Arrays

In this paper, we study fiber laser arrays coupled in a spatially filtered ring oscillator geometry that produces a tiled-array output. In particular, we examine the passive phasing dynamics, the efficiency of coherent combination, and the dependence of the system’s behavior on nonlinearities in the fibers. For an array containing a small number of elements, we find that the fibers achieve a co-phased state within two round trips after a perturbation. Steady-state results agree with the previous work. We also find that the Kerr nonlinearity decreases the combining efficiency as determined from the on-axis intensity in the far-field output.

Geometrical on-axis access to high-finesse resonators by quasi-imaging: a theoretical description

We describe a novel method for providing geometrical on-axis access to an optical enhancement resonator through an on-axis aperture at one of its mirrors. A superposition of transverse modes in a stable degenerate resonator is used to form a field distribution which avoids the aperture and therefore exhibits small loss. Upon propagation in the resonator the modes acquire a different phase, and an on-axis intensity maximum is formed at a different position. We call this a quasi-imaging resonator, because it is related to imaging in the sense that a hole in the field distribution, exacted by the aperture, is reproduced after a resonator round trip.