4f Setup Research Articles

Terahertz digital holography: Two- and four-step phase shifting technique in two plane image recording

A two- and four-step phase shifting (PS) technique in terahertz (THz) digital holography is proposed. Relying on the Mach–Zehnder interferometer-based setup, it was demonstrated that the two-step and four-step PS in Fresnel holograms can assist in a five times greater background subtraction. It allows us to improve the quality of the obtained holographic images, in particular when objects introduce phase changes. It was shown that the recording of holograms of an object consisting of two separated planes can enable qualitative reconstruction of 3D images. Here, the planes were separated by 30 mm, thus defining the longitudinal (depth) resolution in this experiment. It is shown that the PS can serve in distinguishing transparent objects and, by a proper selection of phase variation within the 0–2π range, enable us to increase the quality of the reconstructed hologram. Finally, the advantages of the suggested holographic technique are illustrated by comparing the results with the data of weak absorbing objects obtained via point-to-point, plane-to-plane (4f setup), and dark-field THz imaging approaches. Experiments were performed at frequencies of 0.3 and 0.6 THz recording THz images using resonance antenna-coupled titanium microbolometers.

Upconversion dark-field imaging with extended field of view at video frame rate.

Dark-field imaging is a well-known optical method for obtaining edge-enhanced images of objects containing steep gradients in either amplitude or phase. Edge enhancement is commonly achieved by using a small physical obstruction in the center of the Fourier plane of a 4f imaging setup. By blocking the low spatial frequencies in the center of the Fourier plane, only the higher spatial frequencies from the object reach the image plane. In this work, simultaneous optical image processing (i.e., dark-field imaging) and sum-frequency generation are performed by placing a periodically poled lithium niobate crystal in the Fourier plane of a 4f setup and using a 1575 nm upconversion pump beam with a dark core. We demonstrate upconversion dark-field (UDF) imaging in which edge-enhanced images are obtained at the upconverted wavelength ($\sim{630}\;{\rm nm}$∼630nm) as a result of infrared object illumination ($\sim 1\;\unicode{x00B5}{\rm m}$∼1µm). Furthermore, we experimentally confirm that UDF imaging can be extended from collinear to noncollinear interactions between the signal and pump. The presented system allows for adjustment of the spatial cutoff frequency while maximizing the power conversion efficiency. Simultaneous collinear and noncollinear upconversion imaging of phase objects is demonstrated using broadband 1 µm illumination with a spectral bandwidth of 6 nm-resulting in a UDF imaging system with an enhanced field of view at video frame rates.

Polarization envelope helicity dependent photovoltage in GaAs/Al0.3Ga0.7As modulation-doped quantum well.

In this study, we demonstrate the switching of the direction of the photocurrent in an n-type GaAs/Al0.3Ga0.7As modulation-doped quantum well using a polarization pulse-shaping apparatus containing a 4f setup. The right- and left-polarization-twisting pulses with a polarization rotation frequency in the THz-regime are incident on a modulation-doped quantum well. The results show that the sign of the photovoltage is dependent on the direction of rotation of the polarization-twisting pulses, which can be explained by the circular photogalvanic effect combined with the production of a classical edge photocurrent from the acceleration of free electrons in the vicinity of the sample edge by the incident optical electric field. The wide range over which the polarization-rotation frequency may be tuned makes this method a powerful tool to investigate the response of an extensive variety of materials in the THz-regime.

1D Confocal Broad Area Semiconductor Lasers (Confocal BALs) for Fundamental Transverse Mode Selection (TMS#0)

Previously in this journal we have reported on fundamental transverse mode selection (TMS#0) of broad area semiconductor lasers (BALs) with integrated twice-retracted 4f set-up and film-waveguide lens as the Fourier-transform element. Now we choose and report on a simpler approach for BAL-TMS#0, i.e., the use of a stable confocal longitudinal BAL resonator of length L with a transverse constriction. The absolute value of the radius R of curvature of both mirror-facets convex in one dimension (1D) is R = L = 2f with focal length f. The round trip length 2L = 4f again makes up for a Fourier-optical 4f set-up and the constriction resulting in a resonator-internal beam waist stands for a Fourier-optical low-pass spatial frequency filter. Good TMS#0 is achieved, as long as the constriction is tight enough, but filamentation is not completely suppressed.

Modulating complex beams in amplitude and phase using fast tilt-micromirror arrays and phase masks.

The Letter proposes a system for the spatial modulation of light in amplitude and phase at kilohertz frame rates and high spatial resolution. The focus is fast spatial light modulators (SLMs) consisting of continuously tiltable micromirrors. We investigate the utilization of such SLMs in combination with a static phase mask in a 4f setup. The phase mask enables the complex beam modulation in a linear optical arrangement. Furthermore, adding so-called phase steps to the phase mask increases both the number of image pixels at constant SLM resolution and the optical efficiency. We illustrate our concept based on numerical simulations.

基于光强传输方程与SLM的快速相位恢复

The transport of intensity equation(TIE) offers an experimentally simple technique for computing phase information directly from several defocused images. In this work we developed the traditional TIE intensity acquisition system. In order to avoid the shifting of CCD, a quadratic phase pattern was displayed on the SLM to provide a lens effect for realizing different defocus distance by varying the focal length of the lens. Two kinds of phase imaging experimental configurations guided by two different theories were designed. In most instances, since a camera is used to capture images in which the phase modulation of lens cannot be ignored, the former intensity acquisition system was designed based on the single lens optical propagation system, and the relationship between the focal length and the image distance in the lens law was used to facilitate the varying of the defocus distance by changing the phase pattern displayed on the SLM. The latter was designed by locating a SLM in the Fourier domain of the 4f setup, according to the Fourier transform property of the lens and the Fresnel diffraction theory, the relationship between the defocus distance and the focal length of the quadratic phase pattern can be derived. The experimental results verify that the proposed phase retrieval methods are reasonable and correct.

Fundamental Transverse Mode Selection (TMS#0) of Broad Area Semiconductor Lasers with Integrated Twice-Retracted 4f Set-Up and Film-Waveguide Lens

Previously we focused on fundamental transverse mode selection (TMS#0) of broad area semiconductor lasers (BALs) with two-arm folded integrated resonators for Fourier-optical spatial frequency filtering. The resonator had a round-trip length of 4f, where f is the focal length of the Fourier-transform element (FTE), that is, a cylindrical mirror in-between the orthogonal resonator branches. This 4f set-up can be called “retracted once” due to the reflective filter after 2f; that is, the 2f path was used forwards and backwards. Now the branches are retracted once more resulting in a compact 1f long linear resonator (called “retracted twice”) with a round-trip length of 2f. One facet accommodates the filter, while the other houses the FTE, now incorporating a film-waveguide lens. The BAL facet with the filter represents both the Fourier-transform plane (after 2f, i.e., one round-trip) as well as the image plane (after 4f, two round-trips). Thus filtering is performed even after 4f, not just after 2f. Experimental results reveal good fundamental TMS for pump currents up to 20% above threshold and a one-dimensional beam quality parameter M1D2 = 1.47. The BALs are made from AlGaInAsSb, but the concept can equally well be employed for BALs of any material system.

Generation of intense femtosecond optical vortex pulses with blazed-phase grating in chirped-pulse amplification system of Ti:sapphire laser

We demonstrate the generation of an intense femtosecond optical vortex (OV) pulse by employing an OV converter set between two laser amplifiers in a chirped-pulse amplification (CPA) system of a Ti:sapphire laser. The OV converter is composed of a liquid-crystal spatial light modulator (LC-SLM) exhibiting a blazed-phase computer-generated hologram, a concave mirror, and a flat mirror in the 4f setup. Owing to the intrinsic nature of the 4f setup, the OV converter is free from chromatic and topological-charge dispersions, which are always induced in a spiral phase plate conventionally used to convert an intense Gaussian laser pulse to an OV pulse, while we can avoid damage to the LC-SLM by the irradiation of a low-energy pulse before the second amplifier. We have increased the throughput of the OV converter to 42% by systematically investigating the diffraction efficiency of the blazed-phase hologram on the LC-SLM, which relaxes the gain condition required for the second amplifier. The combination of the high-throughput OV converter and the two-stage amplification enables us to generate OV pulses with an energy of 1.63 mJ and a pulse duration of 60 fs at a wavelength of ~720 nm, at which the gain of the Ti:sapphire laser is only 60% of the peak gain around 800 nm.

Improved data pages for an interference-based cryptosystem

In this paper, we propose a novel input wave front modulation method to enhance the security level of a Mach-Zender interferometer-based Fourier encryption system. The input data is encoded in the two wave fronts propagated in the arms of the interferometer. Both arms contain a 4f setup, and two independent Fourier keys are used to encrypt these wave fronts. During decryption the encrypted wave fronts are propagated through the interferometer. In the case when correct Fourier keys are used for decryption, the reconstructed data page is shown by the interference pattern of the output. We propose a method to synthesize two phase modulated input images for this cryptosystem. The modulation method has a user defined phase parameter. We prove that the security level of the proposed cryptosystem can be significantly improved compared with previous solutions, by using an optimally chosen phase parameter.

Enhanced deterministic phase retrieval using a partially developed speckle field

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.

Two-photon fluorescence of Coumarin 30 excited by optimally shaped pulses

We optimized the two-photon fluorescence (TPF) of a Coumarin 30 dye by using a feedback-controlled femtosecond pulse shaping technique. For optimization we implemented an evolutionary algorithm with a liquid crystal phase-only pulse shaper in a folded 4f setup. The optimization procedure applied to the second harmonic generation, and TPF noticeably improved the output signals and demonstrated good convergence. In addition, signal ratios involving TPF and second harmonic generation (SHG) were successfully optimized. The correlation between TPF and SHG was studied, and it was found to decrease when the pulse shape was close to the optimum. These experimental results are of interest for potential applications of coherent control to complex molecular systems as well as in biomedical imaging.

Spatial phase dislocations in femtosecond laser pulses

We show that spatial phase dislocations associated with optical vortices can be embedded in femtosecond laser beams by computer-generated holograms, provided that they are built in a setup compensating for the introduced spatial dispersion of the broad spectrum. We present analytical results describing two possible arrangements: a dispersionless 4f setup and a double-pass grating compressor. Experimental results on the generation of optical vortices in the output beam of a 20 fs Ti:sapphire laser and the proof-of-principle measurements with a broadband-tunable cw Ti:sapphire laser confirm our theoretical predictions.

Vortices in femtosecond laser fields.

We experimentally generate optical vortices in the output beam of a 20-fs Ti:sapphire laser. Screw phase dislocations are imposed on the spectral components of the short pulses by aligning a computer-generated hologram in a dispersionless 4f setup.

Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping

The self-controlled compression of widely tunable pulses in the visible generated by a non-collinear-type optical parametric amplifier is accomplished by a pulse shaper based on a 4f setup with a pixeled mask in the Fourier plane which is controlled by an evolutionary algorithm in a feedback loop. Pulse durations below 16 fs are achieved by shaping the pulses such that their second-harmonic signal is maximized. The optimization process generally requires less than five minutes. It is shown that the algorithm eventually determines the shaper settings which produce the global optimum for the SH signal. Moreover, pulses having propagated through a disturbing medium which introduced additional group velocity dispersion have been recompressed to below 16 fs. An acceptable value for the phase difference between two adjacent pixels of the liquid crystal mask is experimentally found to be 1.6. The described setup provides a powerful tool for delivering ultrashort tunable pulses to any location within an experiment, as well as tailored sub-20-fs pulses for optimal control studies.

Fourier-optical selection of higher order transverse modes in broad area lasers

A partially and a highly antire ection coated broad area laser are operated in an external cavity Fourier-optical 4f set-up to experimentally investigate transverse mode selection. The external cavity consists of a lens and a spatial frequency filter. Running freely the lasers show non-stationary filamentation. Placing the spatial filter unit directly onto the optical axis gives cw fundamental mode operation and a transverse shift of the spatial filter in the plane of the active region allows for selective excitation of higher order modes.

Microoptical and integrated optical fs/ps pulse shapers

The generation of 875 fs nearly rect-shaped pulses from 96 fs sech 2 shaped Ti:sapphire laser pulses by means of a microoptical pulse shaper is presented conceptually and experimentally. Pulse shaping is performed by time frequency filtering of the input spectrum within a Fourier optical 4f setup with entrance and exit grating. The setup uses an optimized reflective filter concept with 40 nm filter bandwidth giving improved pulse shape at acceptable temporal pulse extension. Moreover, an integrated optical concept with inherent dispersion compensation for shaping ps pulses is proposed which employs an integrated film waveguide based telescopic system with curved waveguide mirrors for improved filtering of a limited spectral bandwidth.