This review focuses on several recent research activities regarding precise and fast polarization-sensitive terahertz time-domain spectroscopy systems for imaging purposes, and explains three interesting application examples. Owing to modulation techniques that have recently been developed for the evaluation of the instantaneous terahertz electric-field (E-field) vector, fast and precise terahertz polarization imaging becomes feasible. This terahertz technology enables high-resolution surface topography, precise understanding of the spatial E-field vector distribution of the focused terahertz pulse, and examination of strain-induced birefringence in polymeric materials. These examples constitute a new application area of terahertz photonics with emphasis on both fundamental optics and industrial applications.

https://www.mdpi.com/2304-6732/5/4/58/pdf

Terahertz Polarization Imaging and Its Applications

The focusing properties of a series of polymeric zone-plate lenses are investigated around a target frequency of 1 THz. Their characterization is performed by means of terahertz (THz) time-domain spectroscopy, employing a modified knife-edge technique that compensates for asymmetries of the impinging THz beam shape of typical photoconductive antenna-based THz sources. The samples are fabricated by a three-axis milling technique on slabs of an ultralow-loss cyclo-olefin polymer. Three different zone plates are studied, a conventional binary zone plate, a conventional four-level zone plate, and a recently introduced double-sided zone plate consisting of the stack of two phase-reversal binary zone plates, which is simpler to fabricate and less sensitive to mechanical damage than multilevel zone plates. Experimental results, coupled with finite element simulations, demonstrate that the double-sided zone plate features a resolution increased by about 3λ with respect to the binary zone plate and comparable with that of the four-level zone plate. The double-sided zone plate has 40% lower focusing efficiency and approximately 7λ shorter depth of field compared to its four-level counterpart. Nevertheless, it outperforms conventional binary zone plates by 25% in power focusing efficiency and features a 10λ longer depth of field.

Terahertz focusing properties of polymeric zone plates characterized by a modified knife-edge technique

We have investigated the spatial distribution of the polarization state of a terahertz electromagnetic wave focused by an off-axis parabolic mirror (OPM) in the focal plane. We employed polarization-resolved terahertz time-domain spectroscopy and found that a steep spatial variation in the polarization state appears slightly distant from the focus when a linearly polarized terahertz wave is focused. The spatial variation includes an abrupt change in the polarization state (states change between circular and linear polarizations) within a wavelength. The observed phenomena are confirmed by numerical calculations and are shown to be intrinsic to the reflection from the OPM.

https://iopscience.iop.org/article/10.7567/APEX.9.052206/pdf

Spatial polarization variation in terahertz electromagnetic wave focused by off-axis parabolic mirror

We formulate and experimentally demonstrate a method to retrieve the undistorted temporal profile of an elliptically polarized terahertz pulse from the electric-field (E-field) vector waveform detected by electro-optic (EO) sampling. This method takes into account the distortion effects due to pulse width of the probe laser, absorption by the EO crystal, and frequency-dependent phase mismatch between the probe and terahertz pulses inside the EO crystal. Even with this distortion, the detected elliptically polarized terahertz vector waveform can be simply interpreted as that at the center of the EO crystal for detection. This interpretation enables us to retrieve the undistorted terahertz E-field vector waveform in front of the EO crystal by analyzing the detected EO signals in the frequency domain and then reconstructing those in the time domain. In order to verify our method, we experimentally demonstrate that the same elliptically polarized terahertz waveform can be retrieved even when we use different EO crystals for detection. Although the terahertz E-field vector waveforms measured by different EO crystals are significantly different due to the distortions, the retrieved waveforms show a good agreement without need for additional corrections.

Retrieving the undistorted terahertz time-domain electric-field vector from the electro-optic effect

A double-sided phase-reversal binary zone plate is numerically investigated and experimentally characterized at the frequency of 1 THz.The double-sided zone plate has a novel design based on a binary phase-reversal zone plate, in which the total zone thickness is split into two halves located at a distance optimized by means of numerical simulations.The samples are fabricated by a three-axis milling technique on slabs of an ultralow-loss cyclo-olefin polymer.The lenses’ characterization at the frequency of 1 THz is performed by means of a terahertz time-domain spectrometer, in terms of both focal length and spatial resolution.The focusing properties of the double-sided zone plate are compared with those of a conventional binary zone plate.The double-sided zone plate features $2.4\times $ smaller focal spot, $1.25\times $ higher focusing efficiency, and an approximately $10\lambda _{\mathbf {0}}$ longer depth of field than the conventional binary configuration.

High-Resolution Binary Zone Plate in Double-Sided Configuration for Terahertz Radiation Focusing

A linearly polarized electromagnetic wave is found to form divergent and rotation fields after focused by an off-axis parabolic mirror These distributions are generated within a subwavelength scale around the focus and at times when the electric field at the focus vanishes We theoretically and experimentally show that not only the direction but also the structure of the distributions varies with the incident polarization In addition, the distributions move in one direction with a phase velocity faster than the speed of light

Intrinsic formation of electromagnetic divergence and rotation by parabolic focusing

We present an experimental setup to dramatically reduce a measurement time for obtaining spatial distributions of terahertz electric-field (E-field) vectors. The method utilizes the electro-optic sampling, and we use a charge-coupled device to detect a spatial distribution of the probe beam polarization rotation by the E-field-induced Pockels effect in a ⟨110⟩-oriented ZnTe crystal. A quick rotation of the ZnTe crystal allows analyzing the terahertz E-field direction at each image position, and the terahertz E-field vector mapping at a fixed position of an optical delay line is achieved within 21 ms. Video-rate mapping of terahertz E-field vectors is likely to be useful for achieving real-time sensing of terahertz vector beams, vector vortices, and surface topography. The method is also useful for a fast polarization analysis of terahertz beams.

Video-rate terahertz electric-field vector imaging

This paper provides a detailed theoretical analysis of the unexpected transient divergent and rotational distributions of the focused electric field vector reported in Shibata et al (2015 Phys. Rev. A 92 053806). We reveal the physical origin of these distributions. More quantitatively, we derive the semi-analytic expressions and clarify how these distributions depend on the mirror size, offset angle, and the intensity distribution of the incident parallel light. We compare the formulas with numerical calculations and evaluate the area where linearity holds. If the wavelength and the mirror size are sufficiently shorter than the focal length, the radius of the linear area becomes longer than the wavelength. These formulas and evaluations are useful for studies, which require high spatio-temporal resolution.

https://iopscience.iop.org/article/10.1088/2040-8986/aa5a17/pdf

Mayuko Takai

Papers

Intrinsic formation of electromagnetic divergence and rotation by parabolic focusing

Spatial polarization variation in terahertz electromagnetic wave focused by off-axis parabolic mirror

Video-rate terahertz electric-field vector imaging

Detailed study of transient anomalous electric field vector focused by parabolic mirror