Spatial Sampling of Terahertz Fields with Sub-wavelength Accuracy via Probe Beam Encoding

TL;DR

This paper presents a simple, non-invasive method for spatially sampling terahertz fields with sub-wavelength accuracy using probe beam encoding and a single-pixel camera, eliminating the need for specialized THz devices.

Contribution

The authors introduce a novel approach that encodes an NIR probe beam to sample THz fields with high resolution without specialized THz modulation devices.

Findings

Achieved 128×128 field measurement with 62 μm resolution

Demonstrated sub-wavelength spatial resolution more than 15 times smaller than THz wavelength

Method is suitable for biomedical sensing and industrial inspection

Abstract

Recently, computational sampling methods have been implemented to spatially characterize terahertz (THz) fields. Previous methods usually rely on either specialized THz devices such as THz spatial light modulators, or complicated systems requiring assistance from photon-excited free-carriers with high-speed synchronization among multiple optical beams. Here, by spatially encoding an 800 nm near-infrared (NIR) probe beam through the use of an optical SLM, we demonstrate a simple sampling approach that can probe THz fields with a single-pixel camera. This design does not require any dedicated THz devices, semiconductors or nanofilms to modulate THz fields. Through the use of computational algorithms, we successfully measure 128$\times$128 field distributions with a 62 $\mu m$ transverse spatial resolution, more than 15 times smaller than the central wavelength of the THz signal (940 $\mu m$). Benefitting from the non-invasive nature of THz radiation and sub-wavelength resolution of our system, this simple approach can be used in applications such as biomedical sensing, inspection of flaws. in industrial products, and so on.

Full text

Spatial Sampling of Terahertz Fields with Sub-wavelength Accuracy via Probe Beam Encoding

Jiapeng Zhao

The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA

  

Yiwen E

The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA

  

Kaia Williams

The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA

  

Xi-Cheng Zhang

xi-cheng.zhang@rochester.edu

The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA

  

Robert W. Boyd

boydrw@mac.com

The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA

Department of Physics, University of Ottawa, Ottawa, K1N 6N5, Canada

Recently, computational sampling methods have been implemented to spatially characterize terahertz (THz) fields. Previous methods usually rely on either specialized THz devices such as THz spatial light modulators chan2009spatial ; watts2014terahertz , or complicated systems requiring assistance from photon-excited free-carriers with high-speed synchronization among multiple optical beams ulbricht2011carrier ; shrekenhamer2013terahertz ; stantchev2016noninvasive . Here, by spatially encoding an 800 nm near-infrared (NIR) probe beam through the use of an optical SLM, we demonstrate a simple sampling approach that can probe THz fields with a single-pixel camera. This design does not require any dedicated THz devices, semiconductors or nanofilms to modulate THz fields. Through the use of computational algorithms, we successfully measure 128$\times$128 field distributions with a 62 $\mu m$ transverse spatial resolution, more than 15 times smaller than the central wavelength of the THz signal (940 $\mu m$). Benefitting from the non-invasive nature of THz radiation and sub-wavelength resolution of our system, this simple approach can be used in applications such as biomedical sensing, inspection of flaws. in industrial products, and so on pickwell2006biomedical ; karpowicz2005compact .

I Introduction

The unique properties of terahertz (THz) radiation, such as the high transmittance in nonpolar material and the nonionizing photon energies, enable numerous novel possibilities in both fundamental research and industrial applications zhang2010introduction ; lee2009principles ; karpowicz2005compact ; wang2004metal ; pickwell2006biomedical ; kawase2003non ; eisele2014ultrafast . Consequently, the knowledge of the spatial profile of THz fields becomes very important. However, due to the lack of efficient and economical THz cameras escorcia2016uncooled ; grossman2010passive , characterizing the structures of THz fields usually relies on raster scanning either the detector or the sample, resulting in a low signal-to-noise ratio (SNR) and slow speed when the number of pixels increases. Recently, novel beam profiling approaches that involve computational sampling methods have emerged watts2014terahertz ; chan2009spatial ; ulbricht2011carrier ; shrekenhamer2013terahertz . Computational sampling methods, combining the computational algorithms with optical imaging techniques, can improve the sampling speed and image quality, particularly for weak illumination. These computational methods usually do not require conventional cumbersome techniques such as multi-element THz detection arrays and raster-scanning, but reconstruct the fields by computational algorithms with a single-pixel camera. Nevertheless, much of previous work has been based on spatially manipulating the THz beam directly with either dedicated THz spatial light modulators (SLMs) chan2009spatial ; watts2014terahertz , or modulating the THz spatial transmittance in semiconductors or nanofilms via photon-excited free carriers ulbricht2011carrier ; shrekenhamer2013terahertz ; stantchev2016noninvasive ; chen2019terahertz . Compared to optical SLMs, their THz counterparts usually have a low temporal modulation rate and a large pixel size, which is mainly limited by the relatively long THz wavelengths and leads to a relatively low spatial modulation accuracy and resolution chan2009spatial ; watts2014terahertz . Therefore, THz SLMs are not ideal devices for sampling applications that requires sub-wavelength features. Although approaches that use spatial transmission modulation via photon-excited free carriers can provide precise spatial modulations up to few microns, these methods require significant laser powers in order to excite free-carriers, as well as high-speed synchronization among multiple optical beams stantchev2016noninvasive . Thus, it is important to develop a simpler THz spatial sampling approach capable with up to a micron-level accuracy for practical application scenarios.

The electro-optic (EO) effect is one of the most widely used THz techniques for coherent detection wu1995free . When a THz field interacts with an EO crystal (usually ZnTe or GaP), it introduces a birefringence, which modifies the polarization of a co-propagating 800 nm NIR probe beam. This rotation in polarization is measured to determine the time-dependent THz electric field. Therefore, only THz fields that spatiotemporally overlap with the NIR probe beam result in a measurable polarization shift. From a sampling point of view, when we encode the NIR beam with desired patterns and carefully align these patterns with THz fields, those fields of interest can be selectively measured. Since we only spatially modulate the NIR probe beam, this indirect measurement is not only much easier than manipulating the THz fields directly, but also non-demolished to THz spatial information as well. This non-demolition nature may enable the possibility of THz quantum measurements in the future. Furthermore, considering that all the spatial manipulation comes from comparatively economical and well-developed optical SLMs, achieving fast temporal modulation rates and sampling accuracies at few microns is also feasible edgar2015simultaneous . Therefore, real-time sensing through the use of our probe-beam-encoding technique should be achievable in the future.

In this paper, we sample the spatial distribution of THz fields by encoding an 800 nm NIR probe beam through the use of a NIR SLM that provides a fast sampling rate up to the kilohertz (kHz) level, and a sampling accuracy up to few microns. As a demonstration, we impress a series of masks onto a NIR probe beam, and pass a THz beam through an object that is opaque to the NIR probe. Through the EO effect, the spatial information of the THz beam is transferred to the NIR probe whose total power is then measured. After repeating this procedure for each spatial mask, the THz field distribution carrying near-field information is successfully retrieved with 128$\times$128 sample points through the use of Hadamard Matrix (HM) algorithm harwit2012hadamard . The spatial resolution is estimated to be 62 $\mu m$, which is 15 times smaller than the THz central wavelength (940 $\mu m$ at 0.32 THz). By adopting the compressed sensing (CS) algorithm, we can recover high fidelity fields (near 90$\%$ fidelity) with a 20$\%$ sampling ratio. This simple technique provides up to few micron sampling accuracy and a sub-wavelength resolution while inheriting most advantages of THz sensing, such as broadband spectrum information and non-invasive detection to biomedical samples.

II Experimental configuration and resolution estimation

A THz pulse, generated through optical rectification from a ZnTe crystal as shown in the schematic Fig. 1(a) and (b), passes through a covered object and is detected through electro-optic sampling by another ZnTe crystal xie2006terahertz . A sequence of spatial masks are loaded on the SLM to encode the NIR probe pulse. Then this spatially encoded 800 nm probe beam first illuminates the detection ZnTe crystal in the counter-propagation direction of the THz pulse as shown in Fig. 1(b). On reflection from the left surface of the detection ZnTe crystal, the probe beam co-propagates with the THz pulse, and its polarization is modulated by this spatiotemporally coincident THz field in the detection ZnTe crystal. This change in the polarization is measured to retrieve the time-dependent THz signal. The object, a positive US Air Force (AF) target made with chromium, is wrapped in a 70-$\mu m$ thick piece of paper, and placed immediately before the detection crystal. Therefore, THz pulse only travels about 70 $\mu m$ before interacting with the detection crystal, and the near-field information is maintained kowarz1995homogeneous . The original time domain THz pulse and corresponding spectrum are shown in Fig. 1(b) and (c), respectively. As shown in the flowchart in Fig. 1(d), after retrieving the time-dependent THz signal and recording the corresponding patterns, the THz field information can be reconstructed with computational algorithms.

We first use the HM algorithm to probe the THz field, and successfully recover the field distribution with 128$\times$128 sample points. As shown in Fig. 2(a), we selectively sample the central elements of the AF chart to estimate the resolution limit. The recovered intensity is shown in Fig. 2(b), and has a square sampling pixel with 32 $\mu m$ width. In Fig. 2(c), we show the contrast of each element in group 2, and element 3-1 (the first set of elements in group 3) and 3-2 as a function of strip separation d in the X direction. We find that the element with d = 55 $\mu m$ (element 3-2) has a average contrast of 18.10$\%$, while the element with d = 62 $\mu m$ (element 3-1) has a 32.28$\%$ average contrast. Since from Rayleigh criterion, two points are barely resolved with a contrast equal to 20$\%$ (red dashed line in Fig. 2(c)), the resolution of our system is found to be 62 $\mu m$. Considering the central THz wavelength ($\lambda_{c}$) is 940 $\mu m$, we have achieved a resolution of about $\lambda_{c}/15$. It should be noted that the features in the X direction are better resolved than those in the Y direction due to the horizontal polarization of the THz beam stantchev2016noninvasive . A better resolution in the Y direction can be expected when the THz field is vertically polarized. Since the strip separations in elements 3-1 and 3-2 are 62 $\mu m$ and 55 $\mu m$ but the sampling pixel is 32 $\mu m$, we can see strong pixelization effects in the experimental data. The pixelization makes the reconstructed image blurred, and further limits the resolution of our scheme. Through the simulations shown in the Supplementary Material, we find that the resolution of our configuration (with a 32 $\mu m$ pixel size) is less than 35 $\mu m$. Another interesting observation from the simulation shows that a longer central wavelength can provide a better spatial resolution. This counter-intuitive conclusion comes from the nature of near-field imaging. As analyzed in Ref. kowarz1995homogeneous , for the diffraction field of a sub-wavelength object in the near-field region, a small ratio of $z/\lambda$ can maintain more features, where $z$ is the propagation distance. Therefore, the factors that limit the spatial resolution include the pixel size, the thickness of the detection crystal, the central wavelength of the THz pulse and the separation between the detection crystal and object. Thus, we can further improve the resolution to few microns through illuminating a longer wavelength THz pulse on a thinner crystal, as well as encoding the probe beam with a smaller pixel size and moving the sample closer to the detection crystal mitrofanov2006tetrahertz .

Note that, our scheme can probe any portion of the THz field without changing optics. This is because that we can change the location of the NIR probe on the THz field through the change of the location of the encoding masks on the SLM using Matlab. For instance, the results that we show above use the central part of the SLM for encoding, which yields a reconstructed field of the central part of THz field.

III Results with different computational algorithms

In the traditional THz beam profiling, raster scanning is the prevalent single-pixel sampling technique due to the lack of economical high performance cameras. The limitations in speed and contrast become apparent when the total number of sampling points increases. With a finer sampling and an increased number of pixels, the SNR on each pixel is reduced due to the reduction in the signal level on each pixel. As a result, one needs to significantly increase the integration time in order to average out the noise. Furthermore, finer sampling also requires very precise mechanical controls. To overcome these limitations, computational techniques that project multi-pixel spatial masks including random patterns and HM are introduced, which remove the requirement of mechanical scanning and result in an accurate sampling control. Because multiple pixels are sampled in each measurement, the limitations due to the detector noise are mitigated. Moreover, different algorithms can provide various benefits in image quality and reconstruction speed. For example, when the source noise is negligible, the HM algorithm that minimizes the mean squared error gives the best SNR harwit2012hadamard , and CS can reconstruct the field with sub-Nyquist sampling rates for a fast measurement (see Supplementary Material) li2011compressive .

The experimental comparison of different strategies is shown in Fig.3. The object is a positive 'UR'  mask (Fig. 3(a)) with a 300 $\mu m$ line width ($\lambda_{c}/3.13$). In comparing the recovered normalized field distributions obtained from raster scanning (Fig. 3(b)), random binary masks (Fig. 3(d)), HM (Fig. 3(c)) and CS (Fig. 3(e) and (f)), we see that all the computational algorithms have a better SNR than raster scanning for the same acquisition time. This is because for the pixel size of 64 $\mu m$, which is much smaller than the wavelength, the signal of the THz field on each single pixel is less than the detector noise. Therefore, the results measured by raster scanning only gives the detector noise but not reveal any spatial information about the THz field. Comparing the results from all computational algorithms, HM provides the best contrast, while the image reconstructed from random masks is the noisiest, which matches the expectation. By sub-sampling the field with a $20\%$ sampling ratio, the CS yields a field distribution with 89.6$\%$ fidelity. Fidelity is defined as the correlation coefficients between the recovered THz field and the original object. With a 50$\%$ sampling ratio, we can achieve $96.9\%$ fidelity, which is mainly limited by the background noise. One can further improve the fidelity by adding more image processing algorithms in the restoration stage, which is beyond the scope of this paper. Therefore, high fidelity field distributions are accessible with less than half of the original total measurement time by combining CS algorithms with more data processing algorithms. A faster acquisition time is mainly limited by the low switching speed of the SLM (60 Hz), and will be further limited by the repetition rate of our laser (1 kHz) if a high-speed (kHz-level) digital micromirror devices (DMDs) is used as the new SLM. Since a THz field with a uniform spatial distribution is the only requirement for field reconstruction with high quality, spintronic THz emitters pumped by a high repetition rate oscillator laser can be employed for ultrafast sampling seifert2016efficient , which can possibly leads to real-time beam profiling edgar2015simultaneous .

IV Discussion and Conclusion

We have demonstrated that our near-field spatial sampling technique through the use of a spatially encoded probe can have a better sampling accuracy, resolution, and contrast in comparison to raster-scanning methods. These advantages are facilitated by computational algorithms that offer a general advantage over all THz imaging methods based on raster scanning watts2014terahertz . Not only the amplitude distribution , but the phase and spectral distributions can also be extracted by recording the time-dependent THz waveforms chan2008single ; stantchev2018subwavelength . In relation to the EO imaging jiang19992d , we do not measure the THz spatial profile directly, but recover the field distribution through the use of computational algorithms. This non-demolished measurement gives rise to a better performance in both resolution and contrast without requiring high power lasers, especially when the detection crystal is thick (see Supplementary Material) mittleman2018twenty . Additionally, indirectly sampling the THz field can also circumvent the requirements of using high-energy lasers, which is a common requirement of most THz sub-wavelength imaging techniques. Furthermore, compared to the imaging techniques using photon-excited free carries, the probe beam encoding also waives the reliance on complicated high-speed synchronization among three arms, which makes the system more reliable stantchev2016noninvasive ; zhao2014terahertz . Therefore, due to the concise and robust configuration, it is possible to integrate our method into a plug-and-play system with high performance but low cost THz spintronic emitters, leading to numerous possible applications.

In summary, we demonstrate a simple method to spatially sample THz fields with up to kHz level sampling rates and a sampling accuracy of few microns. With this approach, we demonstrate a THz near-field sampling system using a single-pixel THz detector. The THz field after an object is successfully measured with 62 $\mu m$ ($\lambda_{c}/15$) resolution. By adopting the CS algorithm, we can recover high fidelity field distributions (near 90$\%$ fidelity) by sub-sampling the THz beam, providing a way to achieve fast beam profiling. Our approach can retrieve the spatial information of THz field without distorting it. Such a tool can be used in lossless beam profiling, biomedical sensing, flaw detection and security inspection.

Acknowledgement

The project is funded by Army Research Office (ARO) (W911NF-17-1-0428). We acknowledge the helpful discussions with Saumya Choudary, Yiyu Zhou and Qi Jin. Jiapeng Zhao thanks Brian McIntyre and James Mitchell for fabricating the samples. Robert.W.Boyd acknowledges support from Canada Research Chairs Program and National Science and Engineering Research Council of Canada.

Methods

An 800 nm Ti-sapphire amplifier laser (Coherent Legend Elite Duo with seed laser Coherent Vitara S) with 1 kHz repetition rate is used. The pulse duration is measured to be 100 fs by an autocorrelator. The collimated beam is split by a 90/10 beam splitter (BS1) at the front of the setup. After the delay line, the pump beam illuminates a $10\times 10\times 1$ mm ZnTe crystal to generate the THz pulse using optical rectification xie2006terahertz . A 10-mm-diameter iris is used before the generation crystal to select the center part of the beam, which gives a relatively uniform intensity distribution of the pump beam. The power used to generate THz is about 1.27 $\text{W/}\text{cm}^{2}$ corresponding to 1 mJ pulse energy. The generated THz beam illuminates the 'unknown'  object which is wrapped in a 70 $\mu m$ thick paper sheet after going through a silicon wafer that blocks the residual 800 nm pump beam. The paper is opaque to 800 nm and visible light. The NIR probe beam goes through a 15-mm-diameter iris, and is imaged onto the SLM screen (Hamamatsu LCOS-SLM X10468-02). The imaging system consists of one 25-cm focal-length lens and one 20-cm focal-length lens (not shown in the figure). Therefore, the beam diameter on the SLM is 12 mm, which is larger than the THz beam diameter. The SLM spatially encodes phase-only patterns onto the probe arm, and we then use a common-path interferometer to transfer these phase-only patterns to intensity patterns. The common-path interferometer consists of two polarizers (P1 and P2) and the HWP1. P1 is located before the SLM to make sure polarization is horizontal. The half-wave plate 1 (HWP1) then rotates the polarization to $45^{\circ}$. P2 is also set to $45^{\circ}$ and located after the SLM. Another HWP2 is used after P2 to rotate the polarization back to the horizontal direction. In the experiment, we observe that when we switch the patterns on the SLM, the polarization state of the beam has also slightly changed, which leads to a noise on the balanced detector. Therefore, two Glan-Taylor polarizers (GCL-0702) (P3) are used to increase the extinction ration in the horizontal direction so that all the vertical polarization get rejected after P3. A 25-cm focal-length lens (L1) and a 20-cm focal-length lens (L2) form an imaging system to image the SLM plane onto the left surface of the detection ZnTe crystal. On reflection from a 50/50 beam splitter (BS), the probe beam carrying spatial patterns goes to the detection ZnTe. The translation stage is well aligned to make sure that the probe pattern spatially overlaps with the THz field of interest, and temporally overlaps with the peak position of the THz pulse. The intensity in the probe beam is about 0.1 $\text{mW/}\text{cm}^{2}$ corresponding to 16.8 nJ pulse energy.

The unknown object to identify the resolution limit is a positive US Air Force target which matches MIL-S-150A standard (Thorlabs R3L3S1P). The target is made from 120-nm-thick chrome deposited onto a 1.5-mm-thick clear soda lime glass substrate. The surface with the test strips faces the detection crystal so that the THz field carrying the object information travels only 70 $\mu m$ before interacting with the detection ZnTe crystal, whose dimensions are $10\times 10\times 0.1$ mm.

To get a fair comparison, the acquisition times of all reconstructed fields in the Fig. 3 are set to be same. The details of how we probe the field using different algorithms can be found in the Supplement Material. Here we need to emphasis that the brighter center part of the recovered fields is caused by the non-uniform spatial distribution of the THz field which has a strong beam center.

The 'UR'  sample is positively fabricated with 100 nm thick chromium on a 170 $\mu m$ thick coverslip via physical vapor deposition (PVD). The sample is wrapped in the paper with characters facing the detection ZnTe which gives about 70 $\mu m$ separation between sample and the detection crystal. All the experiments are done in room temperature so that this technique should fit in most applicable scenarios directly.