Thermal lensing effects on lateral leakage in GaN-based vertical-cavity surface-emitting laser cavities.

Lateral leakage of light has been identified as a detrimental loss source in many suggested and experimentally realized GaN-based VCSELs. In the present work we include thermal effects to realistically account for the substantial Joule heating in these devices. In contrast to what could be expected from the previous results, the induced thermal lensing does not make antiguided cavities more positively guided, so that they approach the unguided regime with extremely high lateral leakage. Rather, thermal lensing strongly suppresses lateral leakage for both antiguided and guided cavities. This is explained in terms of lowered launch of power from the central part of the cavity and/or lower total internal reflection in the peripheral part; the former effect is active in all cavities whereas the latter only contributes to the very strongly reduced leakage in weakly antiguided cavities. Thermal lensing suppresses lateral leakage both for the fundamental and the first higher order mode, but a strong modal discrimination is still achieved for the antiguided cavities. Thus, strongly antiguided cavities could be used to achieve single-mode devices, but at the cost of slightly higher threshold gain and stronger temperature dependent performance characteristics.

Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides: erratum.

We correct the value for the nonlinear Kerr effect of the silicon-rich nitride waveguide presented in [Opt. Express23, 25828 (20152015)].

Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides.

In this paper we introduce a low-stress silicon enriched nitride platform that has potential for nonlinear and highly integrated optics. The manufacturing process of this platform is CMOS compatible and the increased silicon content allows tensile stress reduction and crack free layer growth of 700 nm. Additional benefits of the silicon enriched nitride is a measured nonlinear Kerr coefficient n(2) of 1.4·10(-18) m(2)/W (5 times higher than stoichiometric silicon nitride) and a refractive index of 2.1 at 1550 nm that enables high optical field confinement allowing high intensity nonlinear optics and light guidance even with small bending radii. We analyze the waveguide loss (∼1 dB/cm) in a spectrally resolved fashion and include scattering loss simulations based on waveguide surface roughness measurements. Detailed simulations show the possibility for fine dispersion and nonlinear engineering. In nonlinear experiments we present continuous-wave wavelength conversion and demonstrate that the material does not show nonlinear absorption effects. Finally, we demonstrate microfabrication of resonators with high Q-factors (∼10(5)).

Analysis of structurally sensitive loss in GaN-based VCSEL cavities and its effect on modal discrimination.

Lateral loss causes optical energy to leave the laser cavity in the transverse, lateral, direction, and is sometimes neglected to simplify the numerical simulations. However, in contrast to outcoupling and absorption losses, we show that the lateral loss can change drastically with only nanometer-sized changes of the cavity structure, from being virtually zero to becoming the major source of cavity loss, since the cavity becomes antiguiding. This can be explained as the opening of a channel of efficient resonant lateral leakage of optical power at a certain oblique propagation angle. A number of different realizations of current apertures and top mirror designs in GaN-based VCSEL cavities, which have been suggested for realization of microcavity lasers emitting in the blue wavelength range, are simulated. Many of these are shown to lead to unintentional antiguiding, which can more than double the threshold gain for lasing. Notably, for strong enough antiguiding the resonant lateral leakage decreases so that the threshold gain values might again be tolerable. This regime has been suggested for robust single-mode operation since earlier predictions, building on analogies with slab waveguides, hinted at a very strong suppression of higher order modes. However, our simulations indicate that for the VCSEL cavities the derived formulas grossly overestimate the modal discrimination.

Calibration of spatial light modulators suffering from spatially varying phase response.

We present a method for converting the desired phase values of a hologram to the correct pixel addressing values of a spatial light modulator (SLM), taking into account detailed spatial variations in the phase response of the SLM. In addition to thickness variations in the liquid crystal layer of the SLM, we also show that these variations in phase response can be caused by a non-uniform electric drive scheme in the SLM or by local heating caused by the incident laser beam. We demonstrate that the use of a global look-up table (LUT), even in combination with a spatially varying scale factor, generally does not yield sufficiently accurate conversion for applications requiring highly controllable output fields, such as holographic optical trapping (HOT). We therefore propose a method where the pixel addressing values are given by a three-dimensional polynomial, with two of the variables being the (x, y)-positions of the pixels, and the third their desired phase values. The coefficients of the polynomial are determined by measuring the phase response in 8 × 8 sub-sections of the SLM surface; the degree of the polynomial is optimized so that the polynomial expression nearly replicates the measurement in the measurement points, while still showing a good interpolation behavior in between. The polynomial evaluation increases the total computation time for hologram generation by only a few percent. Compared to conventional phase conversion methods, for an SLM with varying phase response, we found that the proposed method increases the control of the trap intensities in HOT, and efficiently prevents the appearance of strong unwanted 0th order diffraction that commonly occurs in SLM systems.

Direct measurement of the spectral reflectance of OP-SDL gain elements under optical pumping.

We report on a direct measurement method for acquiring highly precise reflectance spectra of gain elements for semiconductor disk lasers under optical pumping. The gain element acts as an active mirror, and the active mirror reflectance (AMR) was measured with a weak and tunable probe beam coincident on the gain element with a high-power pump beam. In particular, we measured the spectral AMR of a gain element designed to have a broad and flat AMR spectrum by being anti-resonant at the center wavelength and employing a parametrically optimized anti-reflection structure. We were able to confirm that this sophisticated gain element performs according to design, with an almost constant AMR of ∼103% over a wavelength range of nearly 35 nm, very well matching the simulated behavior. Such gain characteristics are useful for optically pumped semiconductor disk lasers (OP-SDLs) designed for broadband tuning and short-pulse generation through mode-locking. The measurement technique was also applied to a conventional resonant periodic gain element designed for fixed wavelength OP-SDL operation; its AMR spectrum is markedly different with a narrow peak, again in good agreement with the simulations.

Full characterization of a high-power semiconductor disk laser beam with simultaneous capture of optimally sized focus and farfield.

We report on a beam characterization method that is based on the simultaneous measurement of the focus field and the farfield, thus avoiding problems with beam fluctuations during the measurement. By using reflections from both sides of a planoconvex lens, the method implements two branches of an optical system working simultaneously. Also, by letting the planoconvex lens be antireflection treated, and by allowing for both of the reflected fields to fill large and approximately equal areas on a camera detector array, the method significantly lowers the intensity onto the detector array, thus minimizing the need for additional disturbing attenuation filters to avoid camera saturation. In the numerical retrieval of the phase distribution, based on the measured intensity distributions of the focus and farfield, iterative propagation between the two branches is performed. The phase retrieval uses the two-step algorithm for the numerical field propagation conveniently providing an arbitrary choice of sampling distance in each plane.

Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change.

We present a method for reducing intensity fluctuations that typically occur when a spatial light modulator is updated between consecutive computer generated holograms. The method is applicable to most iterative hologram generating algorithms and minimizes the average phase difference between consecutive holograms. Applications with high stability requirements, such as optical force measurement with holographic optical tweezers, should benefit from this improvement.

Optical label-free nanoplasmonic biosensing using a vertical-cavity surface-emitting laser and charge-coupled device.

We present a compact platform for biochemosensing based on the combination of a vertical-cavity surface-emitting laser (VCSEL) light source, microelectromechanical systems (MEMS)-based microoptics, a specially designed nanoplasmonic sensing chip, and charge-coupled device (CCD) detector. The platform does not require any spectral analyzer for signal evaluation, showing good promise for facile integration, neither does it use any microscope setup for the signal collection or imaging. The analytical capabilities of the developed biochemosensing platform are demonstrated by evaluation of the protein-substrate (biotinylated bovine serum albumin-gold) and the protein-protein (biotin-NeutrAvidin) binding kinetics, which is further compared to detection based on conventional optical extinction spectroscopy. The instrument is able to detect low femtomoles of adsorbed proteins with the limit of detection comparable to the state-of-the-art research and commercial optical label-free biochemosensors.

Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm.

Algorithms based on the fast Fourier transform (FFT) for the design of spot-generating computer generated holograms (CGHs) typically only make use of a few sample positions in the propagated field. We have developed a new design method that much better utilizes the information-carrying capacity of the sampled propagated field. In this way design tasks which are difficult to accomplish with conventional FFT-based design methods, such as spot positioning at non-sample positions and/or spot positioning in 3D, are solved as easily as any standard design task using a conventional method. The new design method is based on a projection optimization, similar to that in the commonly used Gerchberg-Saxton algorithm, and the vastly improved design freedom comes at virtually no extra computational cost compared to the conventional design. Several different design tasks were demonstrated experimentally with a liquid crystal spatial light modulator, showing highly accurate creation of the desired field distributions.

Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model.

Intra-cavity diffraction in VCSELs is a loss mechanism that potentially can cause a significant decrease in efficiency and a rise in the threshold current, particularly in cavities with small lateral features with a high index contrast. One such VCSEL type is the 2.3 microm GaSb-based buried tunnel junction (BTJ) VCSEL studied in this work, where the BTJ induced topology of the top layers gives rise to excess loss through diffraction. Diffraction loss is difficult to measure, and also the numerical estimation must be done with care because of the non-axial propagation of the diffracted fields. We present a simulation method with spatially varying dimensionality, such that the field is three-dimensional (3D) in the entire cavity, whereas the material structure of the cavity is modelled in 3D near the BTJ and the layers with a varying topology, but elsewhere is assumed to be 1D like in a regular DBR structure. We find that the diffraction loss displays a non-monotonic behaviour as a function of the BTJ diameter, but as expected it rapidly increases below a certain diameter of the BTJ and may even become the dominant cause of loss in some device designs. We also show that the diffraction loss can be much reduced if the layers above the BTJ can be deposited such that the surface profile becomes smoother with increasing distance from the BTJ.

Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator.

The limited number of pixels and their quantized phase modulation values limit the positioning accuracy when a phase-only one dimensional spatial light modulator (SLM) is used for beam steering. Applying the straightforward recipe for finding the optimal setting of the SLM pixels, based on individually optimizing the field contribution from each pixel to the field in the steering position, the inaccuracy can be a significant fraction of the diffraction limited spot size. This is especially true in the vicinity of certain steering angles where precise positioning is particularly difficult. However, by including in the optimization of the SLM setting an extra degree of freedom, we show that the steering accuracy can be drastically improved by a factor proportional to the number of pixels in the SLM. The extra degree of freedom is a global phase offset of all the SLM pixels which takes on a different value for each steering angle. Beam steering experiments were performed with the SLM being set both according to the conventional and the new recipe, and the results were in very good agreement with the theoretical predictions.

The use of a deuterated calibrator for in vivo recovery estimations in microdialysis studies.

One of the crucial issues in quantitative microdialysis is the reliability of recovery estimates to correctly estimate unbound drug tissue concentrations. If a deuterated calibrator is used for retrodialysis, the calibrator has the same properties as the study drug. However, recovery of the calibrator may be affected by the presence of the drug in the tissues. The aim of this study was to investigate the recovery of deuterated morphine with time in the absence and presence of morphine in rat tissues. Microdialysis probes were placed in the brain and blood of eight rats. Ringer's solution containing D3-morphine was perfused throughout the study and recovery was estimated. After a stabilization period of 3 h, an exponential infusion of morphine was administered over 4 h. The presence of morphine did not affect the recovery of D3-morphine from brain or blood. The average recovery values (SD) were 0.145 (0.039) and 0.131 (0.048) during the stabilization and infusion periods, respectively, for the brain probe and 0.792 (0.055) and 0.790 (0.084), respectively, for the blood probe. The recovery of deuterated morphine was stable over time in the brain and in blood, and was not affected by the presence of pharmacologically concentrations of morphine.

Performance of diffractive optical elements for homogenizing partially coherent light.

The effectiveness of different types of diffractive optical element (DOE) for homogenizing partially coherent beams is analyzed, both analytically and numerically. The effectiveness is described by the homogenizing parameter, defined as the inverse of the normalized variance of the dose distribution. For an important class of DOEs designed with common discrete-Fourier-transform methods, it is found that the homogenizing parameter is only of the order of the number of coherence cells in the illuminating beam. However, for a different type of DOE that produces distinct beams under coherent illumination, the homogenizing parameter can be an order of magnitude higher. The inherent dehomogenizing effect caused by the limited temporal duration of the beam, a phenomenon sometimes referred to as dynamic speckle, is also considered.

Numerical algorithm for the retrieval of spatial coherence properties of partially coherent beams from transverse intensity measurements.

A novel algorithm for the retrieval of the spatial mutual coherence function of the optical field of a light beam in the quasimonochromatic approximation is presented. The algorithm only requires that the intensity distribution is known in a finite number of transverse planes along the beam. The retrieval algorithm is based on the observation that a partially coherent field can be represented as an ensemble of coherent fields. Each field in the ensemble is propagated with coherent methods between neighboring planes, and the ensemble is then subjected to amplitude restrictions, much in the same way as in conventional phase recovery algorithms for coherent fields. The proposed algorithm is evaluated both for one- and two-dimensional fields using numerical simulations.

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators.

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.

Three-level phase modulator based on orthoconic antiferroelectric liquid crystals.

Surface-stabilized orthoconic antiferroelectric liquid crystals (OAFLCs) have a director tilt of theta = 45 degrees and are, with no field applied, negatively uniaxial with the optic axis perpendicular to the cell substrates. We demonstrate that OAFLCs can be utilized to achieve lossless phase modulation with three almost equidistant phase levels. This turns out to be true also for polymer-stabilized OAFLCs, where the polymer network increases the switching speed of the device without affecting the phase modulation appreciably.

Diffraction-based determination of the phase modulation for general spatial light modulators.

We describe a characterization method based on diffraction for obtaining the phase response of spatial light modulators (SLMs), which in general exhibit both amplitude and phase modulation. Compared with the conventional interferometer-based approach, the method is characterized by a simple setup that enables in situ measurements, allows for substantial mechanical vibration, and permits the use of a light source with a fairly low temporal coherence. The phase determination is possible even for a SLM with a full amplitude modulation depth, i.e., even if there are nulls in the amplitude transmission characteristic of the SLM. The method successfully determines phase modulation values in the full 2pi rad range with high accuracy. The experimental work includes comparisons with interferometer measurements as well as a SLM characterization with a light-emitting diode (LED).

Analog low-loss full-range phase modulation by utilizing a V-shaped switched ferroelectric liquid-crystal cell in reflective mode.

We have studied the analog (V-shaped switching) mode in ferroelectric liquid crystals in reflective mode for analog phase modulation applications. We have found that several combinations of cell thicknesses and input polarization states exist for which near-lossless analog phase modulation with a range of approximately 2pi rad is obtained, and we demonstrate one such combination experimentally. Despite a slight deviation from the ideal conditions, e.g., the tilt angle was 38 degrees instead of the desired 45 degrees , virtually pure 1.6pi rad phase modulation was obtained; the measured values agree very well with our numerical simulations of the real device.

Near-lossless continuous phase modulation using the analog switching mode (V-shaped switching) in ferroelectric liquid crystals.

The analog switching mode in ferroelectric liquid crystals, sometimes referred to as 'V-shaped switching,' has, thanks to its submillisecond switching capability, attracted much interest for future fast electro-optic displays where it is to be used for amplitude modulation. We have studied this mode for analog phase-only modulation. As V-shaped switching is based on a conical motion of the index ellipsoid this presents a challenging problem since both the orientation of the slow and fast axes, as well as the amount of birefringence varies in the switching process. We show theoretically, partly by means of Poincaré sphere analysis, that it is in fact possible to obtain near-lossless analog phase modulation between zero and pi radians in an ideal V-shaped switching cell through careful tuning of the polarization state of the input light. Furthermore, we were able to demonstrate this experimentally in a fabricated cell. Although this cell deviated slightly from the ideal conditions, e.g., the tilt cone half-angle was 38 degrees instead of the desired 45 degrees , we still obtained a continuous phase modulation between zero and 0.78pi rad with less than 2% modulation of the amplitude; the measured values agree very well with our numerical simulations of the real device.