Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators

Laguerre-Gauss beams versus Bessel beams showdown: peer comparison

We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.

Transverse-mode selective laser operation by unicursal fast-scanning pumping

We demonstrate that higher order transverse-mode beams can be selectively operated by creating their suitable gain distributions in a laser gain medium. By adjusting the scanning angles and the phase difference between two resonant scanning mirrors used for the manipulation of pump beam patterns, a wide variety of gain distributions such as linear, elliptical, and circular patterns were generated. As a result, single transverse-mode operations of many higher order transverse modes of Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian beams were realized. The switching of these modes was readily and quickly accomplished without further mechanical alignment and any optical elements.

Correction of depth-induced spherical aberration for deep observation using two-photon excitation fluorescence microscopy with spatial light modulator

We demonstrate fluorescence imaging with high fluorescence intensity and depth resolution in which depth-induced spherical aberration (SA) caused by refractive-index mismatch between the medium and biological sample is corrected. To reduce the impact of SA, we incorporate a spatial light modulator into a two-photon excitation fluorescence microscope. Consequently, when fluorescent beads in epoxy resin were observed with this method of SA correction, the fluorescence signal of the observed images was ∼27 times higher and extension in the direction of the optical axes was ∼6.5 times shorter at a depth of ∼890 μm. Thus, the proposed method increases the depth observable at high resolution. Further, our results show that the method improved the fluorescence intensity of images of the fluorescent beads and the structure of a biological sample.

Free space optical communication using beam parameters with translational and transverse rotational invariance

Two natural requirements on a measurable quantity possessed by a paraxially propagating light-field to be suitable for free space optical communication are invariance under free space propagation and invariance under transverse plane rotation. While the former invariance ensures that the measurable quantity is robust while signalling through free space, the latter invariance ensures that a detector measuring the quantity can be oriented at any angle in the transverse plane, and a measurement by the detector yields the same value for the quantity irrespective of the transverse angle, thus avoiding alignment issues. The variance matrix of a paraxially propagating light-field is analyzed from the perspective of the aforementioned invariances. That the "charge" of a paraxial light-field, which is contained in the variance matrix, and which has been previously well studied for its suitability toward free space optical communication, possesses these two invariance properties, emerges naturally in the analysis. Seven functionally independent quantities other than charge, which are derived from the variance matrix, and which share these invariances, are presented and studied for their suitability toward signalling through turbulent atmosphere using the low-order Hermite-Gaussian modes. It is found that the spot size of a Gaussian light-field can be effectively used as a switch, to communicate through short distances in a turbulent atmosphere.

High-order optical vortex position detection using a Shack-Hartmann wavefront sensor

Optical vortex (OV) beams have null-intensity singular points, and the intensities in the region surrounding the singular point are quite low. This low intensity region influences the position detection accuracy of phase singular point, especially for high-order OV beam. In this paper, we propose a new method for solving this problem, called the phase-slope-combining correlation matching method. A Shack-Hartmann wavefront sensor (SH-WFS) is used to measure phase slope vectors at lenslet positions of the SH-WFS. Several phase slope vectors are combined into one to reduce the influence of low-intensity regions around the singular point, and the combined phase slope vectors are used to determine the OV position with the aid of correlation matching with a pre-calculated database. Experimental results showed that the proposed method works with high accuracy, even when detecting an OV beam with a topological charge larger than six. The estimated precision was about 0.15 in units of lenslet size when detecting an OV beam with a topological charge of up to 20.

Stable and flexible multiple spot pattern generation using LCOS spatial light modulator

The LCOS spatial light modulator (LCOS-SLM) can generate desired multiple spot patterns (MSPs) via the application of suitable computer-generated-holograms (CGHs), but the MSP intensity distribution varies because ambient temperature affects the phase modulation characteristic and causes wavefront distortion. To generate high-optical-quality MSPs we use our hardware-compensated (with a Peltier system to even out phase modulation) and software-corrected (via multiplication of the CGH by temperature correction coefficients) LCOS-SLMs. Experimental results with a 14 × 14 MSP generation show that the hardware-compensated LCOS-SLM provides stable MSPs between 9 to 32 °C. The software-corrected LCOS-SLM provides uniform spots over twice the temperature range obtained with conventional SLM method. We confirm that our methods are highly efficient for use in two-photon excitation microscopy application such as multifocal mulitphoton microscopy.

Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates

Spiral phase plates for the generation of Laguerre-Gaussian (LG) beam with non-null radial index were designed and fabricated by electron beam lithography on polymethylmethacrylate over glass substrates. The optical response of these phase optical elements was theoretically considered and experimentally measured, and the purity of the experimental beams was investigated in terms of LG modes contributions. The far-field intensity pattern was compared with theoretical models and numerical simulations, whereas interferometric analyses confirmed the expected phase features of the generated beams. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order LG beams.

An intracavity, frequency-doubled self-Raman vortex laser

We demonstrate intracavity frequency doubling of the self-Raman field generated within a diode end-pumped, solid state Nd:GdVO(4) vortex laser. A maximum output power of 727 mW is generated at 586 nm with an overall diode-to-yellow conversion efficiency of 4%. Conservation of orbital angular momentum is observed under intracavity frequency doubling, with the topological charge of the yellow beam being twice that of the Stokes beam.

An adaptive approach for uniform scanning in multifocal multiphoton microscopy with a spatial light modulator

We propose high-quality generation of uniform multiple fluorescence spots (MFS) with a spatial light modulator (SLM) and demonstrate uniform laser scanning in multifocal multiphoton microscopy (MMM). The MFS excitation method iteratively updates a computer-generated hologram (CGH) using correction coefficients to improve the fluorescence intensity distribution in a dye solution whose consistency is uniform. This simple correction method can be applied for calibration of the MMM before observation of living tissue. We experimentally demonstrate an improvement of the uniformity of a 10 × 10 grid of MFS by using a dye solution. After the calibration, we performed laser scanning with two-photon excitation to observe fluorescent polystyrene beads, as well as the gastric gland of a guinea pig specimen.

Observation and analysis of single and multiple high-order Laguerre-Gaussian beams generated from a hemi-cylindrical cavity with general astigmatism

We experimentally verified that anisotropic Hermite-Gaussian modes can be generated from a hemi-cylindrical laser cavity and can be transformed into high-order Laguerre-Gaussian modes using an extra-cavity cylindrical lens. We further combined the Huygens integral and the ABCD law to clearly demonstrate the transformation along the propagation direction. By controlling the pump offset and the pump size in hemi-cylindrical cavities, we experimentally observed the unique laser patterns that displayed the optical waves related to the coherent superposition of Laguerre-Gaussian modes.

Formation of optical vortices through superposition of two Gaussian beams

We observe phase singularities in the superposed field of two Gaussian beams. It is seen that the formation of these singularities depends on the tilt between two Gaussian beams and the separation of their beam axes. By reversing the angle or the position of the beams, one can change the sign of the vortex. We have shown the formation of single as well as multiple vortices by changing the tilt angle and the position of two Gaussian beams. The experimental results are verified with theoretical analysis. We also observe that such a vortex structure can be formed through superposition of two backreflected Gaussian beams from any optical element with two flat surfaces, as illustrated through a beam splitter and a neutral density filter. This technique is very useful for generation of vortices with high-power lasers where one cannot use a spatial light modulator.

The generation of higher-order Laguerre-Gauss optical beams for high-precision interferometry

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light.

We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

Generation of high-purity higher-order Laguerre-Gauss beams at high laser power

We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical-type LG33 mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.

Direct generation of a first-Stokes vortex laser beam from a self-Raman laser

We demonstrate the direct generation of a first-order LG(01) Laguerre Gaussian (vortex) mode operating at the first-Stokes wavelength of a diode end-pumped, Nd:GdVO(4) self-Raman laser. To the best of our knowledge, this is the first report of intracavity stimulated Raman scattering (SRS) being used as a method for frequency conversion of a vortex laser beam and it is effective in enabling the frequency-converted (Stokes) beam to have the same LG(01) mode as the fundamental beam.

Helico-conical optical beams self-heal

An optical beam is said to be self-healing when, distorted by an obstacle, the beam corrects itself upon propagation. In this Letter we show, through experiments supported by numerical simulations, that Helico-conical optical beams self-heal. We observe the strong resilience of these beams with different types of obstructions, and relate this to the characteristics of their transverse energy flow.

Position measurement of non-integer OAM beams with structurally invariant propagation

We present a design to generate structurally propagation invariant light beams carrying non-integer orbital angular momentum (OAM) using Hermite-Laguerre-Gaussian (HLG) modes. Different from previous techniques, the symmetry axes of our beams are fixed when varying the OAM; this simplifies the calibration technique for beam positional measurement using a quadrant detector. We have also demonstrated analytically and experimentally that both the OAM value and the HLG mode orientation play an important role in the quadrant detector response. The assumption that a quadrant detector is most sensitive at the beam center does not always hold for anisotropic beam profiles, such as HLG beams.

Rotation of nanowires with radially higher-order Laguerre-Gaussian beams produced by computer-generated holograms

In this paper, the influence of radially higher index p of Laguerre-Gaussian (LG) beams on the rotation of nanowires is studied. Radially higher-order LG beams are produced by computer-generated holograms, which are displayed on a spatial light modulator. A series of experiments on manipulating ZnO nanowires was performed on our holographic optical tweezers platform. The experiments demonstrated that radially higher-order LG beams could effectively rotate nanowires along the innermost bright ring of themselves. Compared with radially low-order LG beams, they have larger torques exerted on nanowires and can make nanowires rotate more quickly.

High-quality generation of a multispot pattern using a spatial light modulator with adaptive feedback

We propose and demonstrate high-quality generation of a uniform multispot pattern (MSP) by using a spatial light modulator with adaptive feedback. The method iteratively updates a computer generated hologram (CGH) using correction coefficients to improve the intensity distribution of the generated MSP in the optical system. Thanks to a simple method of determining the correction coefficients, the computational cost for optimizing the CGH is low, while maintaining high uniformity of the generated MSP. We demonstrate the generation of a 28×28 square-aligned MSP with high uniformity. Additionally, the proposed method could generate an MSP with a gradually varying intensity profile, as well as a uniform MSP consisting of more than 1000 spots arranged in an arbitrary pattern.

Radial mode dependence of optical beam shifts

It is known that orbital angular momentum (OAM) couples the Goos-Hänchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(ℓ,p) beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not.

Fraunhofer diffraction of light with orbital angular momentum by a slit

We study the Fraunhofer diffraction problem while taking into account the orbital angular momentum of light. In this case, the phase singularity of the light beam is incident on the slit in two different cases: in one, it is incident slightly above the slit, and in the other it is centered on the slit. We observed that the symmetry and the fringe formation in the interference pattern strongly depend on the amount of orbital angular momentum and the slit position in relation to the beam.

Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.

Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors

We report on the first experimental demonstration of higher-order Laguerre-Gauss (LG(p)(ℓ)) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LG(p)(ℓ) modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG(0)(0) Gaussian beam into an LG(3)(3) mode with a purity of 98%. The ratio between the power of the LG(0)(0) mode of our laser and the power of the LG(3)(3) transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG(0)(0), we inferred that the conversion efficiency specific to the LG(3)(3) mode was 49%. We illuminated a Michelson interferometer with the LG(3)(3) beam and achieved a visibility of 97%.

Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes

We investigate optical singularities in coaxial superpositions of two Laguerre-Gaussian (LG) modes with a common beam waist from the viewpoints of a general formulation of phase structure, experimental generation of various superposition beams, and evaluation of the generated beams' fidelity. By applying a holographic phase-amplitude modulation scheme using a phase-modulation-type spatial light modulator, output fidelity beyond 0.960 was observed under several typical conditions. Additionally, an elliptic-type folded singularity, which provides a different class of phase structures from familiar helical singularities, was predicted and observed in a superposition involving two LG modes of both radially and azimuthally higher orders.

Extreme spin-orbit coupling in crystal-traveling paraxial beams

The dynamics of the spin-orbit coupling in elegant and standard Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG) beams propagating through a uniaxial crystal are analyzed. We consider the structure of the electric fields of the paraxial beams and show that the extreme values of the spin and orbital angular momenta are inherent in the elegant HG and LG of high orders. The spin-orbit coupling in the BG beam of the lowest order can result in nearly 100% energy transport from a vortex-free beam to the vortex-bearing beam at a relatively small crystal length. The extreme spin-orbit coupling does not manifest itself in standard HG and LG beams.

Partially coherent standard and elegant Laguerre-Gaussian beams of all orders

Partially coherent standard and elegant Laguerre-Gaussian (LG) beams of all orders are introduced as a natural extension of coherent standard and elegant LG beams to the stochastic domain. By expanding the LG modes into a finite sum of Hermite-Gaussian modes, the analytical formulae are obtained for the cross-spectral densities of partially coherent standard and elegant LG beams in the source plane and after passing through paraxial ABCD optical system, based on the generalized Collins integral formula. A comparative study of the propagation properties of the partially coherent standard and elegant LG beams in free space is carried out via a set of numerical examples. Our results indicate that the intensity and spreading properties of partially coherent standard and elegant LG beams are closely related to their initial coherence states, and are very different from the corresponding results for the coherent standard and elegant LG beams. In particular, an elegant LG beam spreads slower than a standard LG beam, while this advantage disappears when their initial coherences are very small. Our results may find applications in connection with laser beam shaping, singular optics and astrophysical measurements of angular momentum of radiation.

Mode purities of Laguerre-Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators

We investigate output mode purities of Laguerre-Gaussian (LG) beams generated from four typical simultaneous amplitude and phase modulation methods with phase-only spatial light modulators (SLMs). Numerical simulations supposing the practical SLM, i.e., stepwise phase modulation with a pixelated device, predict an output mode purity of beyond 0.969 for the LG beams of less than radially and azimuthally fifth order. Experimental results of generating LG beams are also shown to demonstrate the effects of the simultaneous phase and amplitude modulation.