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Abstract
Compared to other parts of the electromagnetic spectrum, the terahertz frequency range lacks efficient polarization manipulation techniques, which is impeding the proliferation of terahertz technology. In this work, we demonstrate a tunable and broadband linear-to-circular polarization converter based on an InSb plate containing a free-carrier magnetoplasma. In a wide spectral region (∼ 0.45 THz), the magnetoplasma selectively absorbs one circularly polarized mode due to electron cyclotron resonance and also reflects it at the edges of the absorption band. Both effects are nonreciprocal and contribute to form a near-zero transmission band with a high isolation of –36 dB, resulting in the output of a near-perfect circularly polarized terahertz wave for an incident linearly polarized beam. The near-zero transmission band is tunable with magnetic field to cover a wide frequency range from 0.3 to 4.8 THz.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves, ranging from 0.1 THz to 10 THz, fall in the spectral region between microwaves and optical waves. THz technology is currently employed in various commercial applications, such as biomedical imaging, sensing, spectroscopy, and beyond-5 G wireless communications. However, for THz technology to be scalable and be able to compete with other technologies, numerous challenges must still be addressed. One of the challenges is a lack of devices for efficiently manipulating the polarization of THz waves. A quarter-wave plate (QWP) is a device that gives a phase delay of 90° between two mutually perpendicular components of an electromagnetic wave, thus converting linearly polarized light into circularly polarized light (CPL). Traditional QWPs are fabricated using anisotropic transmission properties of crystals [1], liquid crystals [2], total internal reflection on a prism interface [3], and reflections at different planes [4] to achieve the required phase delay. THz CPL can also be generated by manipulating/tailoring the incident laser pulses [5,6] or laser-induced gas plasmas [7,8]. The ability of biological or metallic chiral metamaterials to selectively reflect broadband CPL has also been utilized to fabricate QWPs [9–15], greatly enriching the library of optical devices. However, the QWPs fabricated using these techniques/materials in the THz frequency region have degraded isolation and/or limited operating bandwidth, compared with commercial QWPs in the optical region.
In this work, we demonstrate that a crystal of n-type InSb in a magnetic field at low temperatures possesses a broadband (∼ 0.45 THz) zero-transmission region for CPL. When a linearly polarized THz beam is normally incident on the sample along the magnetic field direction, the left circularly polarized (LCP) component is completely blocked in the zero-transmission region while the right circularly polarized (RCP) component propagates essentially with no attenuation except the surface reflection loss. The two components are interchangeable by reversing the magnetic field direction. In addition, the zero-transmission region is tunable with magnetic field to cover a wide spectral range from 0.3 to 4.8 THz. Thus, the sample can be used as a QWP to generate near-perfect (∼100%) CPL in a wide THz range.
2. Results
2.1 Terahertz time-domain magnetospectroscopy
The sample studied was a large (∼ 0.8 × 20 × 30 mm3) crystal of Te-doped n-InSb with an electron density of 2.3 × 1014 cm-3 and a 2 K mobility of 7.7 × 104 cm2 V-1s-1. At a temperature (T) of 40 K, the Fermi energy EF = 0.9 meV (or 0.21 THz), the plasma frequency ωp = 2πfp = 2π × 0.3 THz, and the scattering rate ν = 0.03 THz [16]. We used a time-domain THz magneto-spectroscopy setup [17,18] equipped with a commercial THz QWP and wire-grid polarizers to characterize the sample (see Appendix A). Figure 1 shows experimental and calculated transmittance contour maps and spectra for LCP and RCP modes at magnetic fields (B) of 0, 0.3, 0.6, and 0.9 T at T = 40 K. At B = 0 T, a sharp plasma edge exists at 0.3 THz for both the LCP and RCP modes. For the LCP mode (which is the cyclotron resonance active, or CRA, mode), with increasing B, the plasma edge moves towards higher frequencies, and a wide near-zero transmission region appears, whose center also moves towards higher frequencies with increasing B. However, for the RCP mode (which is the cyclotron resonance inactive, or CRI, mode), the plasma edge moves towards lower frequencies with increasing B and eventually becomes unobservable when it becomes lower than the low-frequency limit of our setup (∼ 0.15 THz). At B > 0.3 T, the transmittance spectrum for the RCP mode is a horizontal line without any spectral features, as shown in Fig. 1(f) and 1(h).
Fig. 1. THz transmittance contour maps and spectra of n-InSb for left and right circularly polarized THz light at various magnetic fields. a-h, Experimental and theoretical THz transmittance contour maps (a, c, e, g) and spectra (b, d, f, h) for n-InSb at magnetic fields of 0, 0.3, 0.6, and 0.9 T at 40 K for LCP (a-d) and RCP (e-h) modes. A wide near-zero-transmission region in the spectra is present only for LCP and is tunable with changing B field. The white dotted line in (c) shows the cyclotron resonance frequency fc = ωc/2π.
These results indicate that a linearly polarized incident THz beam with a frequency inside the zero-transmission band, propagating along the direction of the applied B field, is fully converted into CPL, i.e., the RCP mode. Note that the roles of the two modes are interchanged when the direction of the B field is flipped. Namely, if a linearly polarized THz beam with a frequency inside the zero-transmission band propagates in the negative B direction, it will be fully converted into the LCP mode. Furthermore, the transmission of a circularly polarized THz beam would be nonreciprocal. A RCP THz beam will transmit through (be blocked by) the InSb plate if it propagates in the positive (negative) B direction. Therefore, the InSb plate inB also works as a broadband isolator for circularly polarized THz light [19–22]. These concepts are schematically depicted in Fig. 2(a).
Fig. 2. Schematic diagram of the functionalities and the dielectric constant of an n-InSb plate in a magnetic field in the THz range. a, n-InSb works as a THz linear-to-circular polarization converter and an isolator for CPL. b, characteristic lines of real dielectric constants ${\varepsilon ^{\prime}_ \pm }$ equal to 0, 1, and ∞ (similarly to Figure 9 from Ref. [23]). The shadowed area bounded by the 0 and ∞ lines represents the region of negative ${\varepsilon ^{\prime}_ \pm }$, where no wave propagation can occur (reflectivity ≈ 1). The ${\varepsilon ^{\prime}_ \pm }$ = ∞ line represents cyclotron resonance for the LCP mode or ω = 0 for the RCP mode. fc = ωc/2π is the cyclotron frequency, and fp = ωp /2π is the plasma frequency.
We calculated transmittance spectra using classical transmission analysis of a THz pulse through a thick sample slab (see Appendix A). The obtained transmittance spectra are in good agreement with the experimental spectra, as shown in Fig. 1. The calculated isolation of the RCP mode, which is defined as Iso = 10·lg(TLCP/TRCP), where TRCP and TLCP are the transmittances of the RCP mode and LCP mode at fc, is as high as –449 dB at 0.9 T. The isolation value obtained from the experimental results is about –36 dB, limited only by the signal-to-noise ratio of the THz experimental setup. The insertion loss (IL) for the RCP mode can be defined as IL (dB) = -10lg(TRCP). The IL at fc for this device is about 3.9 dB.
2.2 Theory
When a magnetic field is applied to an n-InSb sample along the light propagation direction (that is, in the Faraday geometry), a linearly polarized THz wave propagates in the sample as a superposition of the two transverse normal modes of the magnetoplasma: the LCP mode, also called the ‘extraordinary’ or CRA mode, and the RCP mode, also called the ‘ordinary’ or CRI mode. The “dielectric constants” (squares of refractive indices) for the LCP (+) and RCP (−) modes are given by [23]
Figure 2(b) shows the lines of ${\varepsilon ^{\prime}_ \pm }$ equal to 0, 1, and ∞. The shadowed area bounded by the 0 and ∞ lines represents the region of negative ${\varepsilon ^{\prime}_ \pm }$, where LCP mode is almost totally reflected (reflectivity ≈ 1). The line of ${\varepsilon ^{\prime}_ \pm }$ = 1 (the real part of the refractive index = 1) represents reflectivity = 0, while the ${\varepsilon ^{\prime}_ \pm }$ = ∞ line represents cyclotron resonance for the LCP mode or ω = 0 for the RCP mode. The ${\varepsilon ^{\prime}_ \pm }$ = 0 line represents the plasma edge, which splits into the two magnetoplasmon frequencies with increasing B, given by
As B increases, the frequency ${\omega _\textrm{ + }}$ asymptotically approaches the electron cyclotron frequency ${\omega _\textrm{c}}$, whereas ${\omega _ - }$ monotonically decreases and asymptotically approaches zero as $B \to \infty $. The total-reflection region (shadowed area) becomes narrower for both the LCP and RCP modes with increasing B. The two modes are interchangeable by flipping the direction of the B field, as indicated by Eqs. (1) and (2). The nonreciprocal behavior of CPL in the zero-transmission band in Fig. 1 comes from the gyrotropic dielectric tensor, which results in the plasma-edge splitting of the InSb magnetoplasma [23]. In this work, we concentrate on the zero-transmission region in the LCP mode, while the zero-transmission region in the RCP mode would work for microwave and millimeter waves.
Figures 3 shows that the real and imaginary parts of the dielectric constants ${\varepsilon _ \pm }$ for both the LCP and RCP modes in the InSb sample at T = 40 K and B = 0.5 T. In Figure 3, Im(ε+) shows a resonance peak at 1 THz and Re(ε+) shows a Lorentz dispersion shape due to cyclotron resonance. The lower shadow area represents the high reflectivity region where Re(ε+) is negative. The top shadow area also represents a high reflectivity region where Re(ε+) is large. Re(ε−) and Im(ε−) do not show any spectral feature at the frequency of cyclotron resonance. Therefore, under cyclotron resonance conditions, the LCP mode is strongly attenuated due to resonance absorption whereas the RCP mode propagates without any attenuation except for the interface reflection loss. In addition, the high reflectivity on both sides of the resonance frequency further attenuates the LCP mode. Both absorption and reflection contribute to the near-zero transmittance. Which one is more important depends on sample and experiment parameters such as scattering rate, sample thickness, temperature, magnetic field, etc. The absorption is exponentially dependent on the thickness, while reflection loss is a fixed value for a particular sample. For our sample at 40 K and 0.5 T, the reflection contributes more than 60 % of the total loss, and the absorption contributes the rest of the loss in the zero-transmission region.
Fig. 3. The real and imaginary parts of the dielectric constants for the CRA and CRI modes in an n-InSb crystal at T = 40 K and B = 0.5 T.
By tuning the B field, near-perfect circularly polarized THz light with a tunable broad bandwidth is realized. The bandwidth of the zero-transmission region is about 0.45 THz for this sample, which is proportional to the electron scattering rate ν, as indicated in Eq. (1). The tunable frequency range of the zero-transmission region is from ƒp (∼ 0.3 THz) to the Reststrahlen absorption band starting at 160 cm-1 (∼ 4.8 THz) [24]. By using other lightly doped semiconductors that have different Reststrahlen absorption bands, one would be able to generate CPL covering the whole THz frequency band (0.3 − 10 THz). In addition, with increasing sample thickness, the bandwidth (zero-transmission region) for the LCP mode also increases, while the influence for the RCP mode is almost negligible.
2.3 Demonstration of a near-perfect circularly polarized THz beam
To further illustrate the one-way nonreciprocal propagation of circularly polarized THz light, we placed a THz narrow bandpass filter [25] before the sample (see Appendix A), in order to obtain a circularly polarized THz wave after the sample. The filter has a central frequency (∼ 1 THz) right in the middle of the zero-transmission region of the InSb sample at B = ±0.5 T. We reconstructed the time evolution of the transmitted CPL field vector by measuring both the x and y components of the transmitted electric field. The red curve in Fig. 4(a) shows the RCP THz electric field E(t) at B = + 0.5 T; each point on the trace represents the tip of the THz electric field vector. The amplitude E(t) decays gradually as it rotates in the form of a clockwise helix looking from the positive z-direction. The black curve is the projection of E(t) onto the Ex− t plane, that is, the measured electric field Ex(t), while the green curve is the projection of E(t) onto the Ey− t plane, that is, the measured electric field Ey(t). The orange curve is the projection of E (t) onto the Ex− Ey plane.
Fig. 4. Electric fields of right and left circularly polarized THz radiation in three-dimensional space, their Ex(t) and Ey(t) components, and calculated ellipticities. a, The time evolution of the electric-field vector E(t), and its two orthogonal components Ex(t) and Ey(t), measured by time-domain THz magnetospectroscopy at B = +0.5 T. b, The time evolution of the electric-field vector E(t), and its two orthogonal components Ex(t) and Ey(t), measured by time-domain THz spectroscopy at B = −0.5 T. c, The time-domain waveforms of Ey(t) at B = +0.5 T and −0.5 T, respectively, showing an exact π phase shift. d, Calculated and experimental ellipticities using Eq. (4).
At B = −0.5 T, the transmitted THz wave is LCP. Traces in Fig. 4(b) can be understood in the same way as in Fig. 4(a). We plotted Ey(t) for both B = + 0.5 T and B = − 0.5 T in Fig. 4(c). The two traces are mirror-symmetric with respect to the horizontal line y = 0, and have an exact π phase shift, indicating the facile conversion of right/left CPL by switching the B field direction. The inset shows the frequency-domain spectra of the time-domain waveforms. In order to quantify the purity of the CPL, we calculated the ellipticity $\eta (\omega )$ using the following formulas [26,27]
3. Discussion
In our previous work [27], we have shown that InSb has a giant tunable Faraday effect and could be used as broadband terahertz polarization optics. There the entire broadband THz spectrum was used to characterize the ellipiticity and Faraday rotation, therefore the transmitted THz signal is mostly elliptically polarized. In addition, the nonreciprocity and its use as a THz isolator was not discussed there. In this work, we concentrated on the zero-transmission region using which a near-perfect, tunable and broadband CPL could be generated. These excellent characteristics have not been simultaneously fulfilled/demonstrated before in the THz region according to our knowledge. InSb and its combination with artificial microstructures as magneto-optical polarization devices have also been measured at lower magnetic fields (< 0.15 T) by other groups in Ref. [28–30]. We have to admit that the underlying magneto-optical physics in InSb is not new, which has been extensively discussed in literatures [17,23,27–30]. This work focuses on the propagation properties in the zero-transmission region of an InSb slab and demonstrates its excellent performance as a quarter wave-plate as well as a circular-polarization-dependent isolator.
Material scientists are seeking elusive lossless metals [31], that is, materials with a purely real and negative dielectric constant ($\varepsilon ^{\prime\prime}$ ≈ 0 and $\varepsilon ^{\prime}$ < 0), which would be ideal candidates to replace metals in plasmonic and metamaterial devices. Doped InSb represents a unique low-density metal in the frequency range below 100 GHz, which has a low loss due to low carrier density and a negative dielectric constant for the RCP mode as shown in Figures 2(b) and 3. Unfortunately, no experimental data to support this claim, because the spectral range is limited by the THz detection scheme. In addition, a chiral plasma medium consisting of chiral objects embedded in a magnetized plasma has been proposed to enable a negative refractive index (both ε and ∓ are negative) in a broad frequency range [32].
It is well known that nonreciprocal devices for microwaves are made using antiferromagnetic resonance in ferrites [33]. However, great difficulties exist in using ferrites for millimeter and submillimeter (or THz) waves, such as the necessity for a strong B field and an increase in the forward loss. These difficulties can be overcome by using magnetoplasmas in doped semiconductors. To achieve efficient operation of semiconductor nonreciprocal devices based on a magnetoplasma, it is necessary to satisfy the condition ${\omega _c}\tau \gg 1$, where $\tau$ = 1/ν is the momentum relaxation time. For n-InSb, the condition can be easily satisfied with a small magnetic field [16]. In addition, our device can work at liquid nitrogen temperature and using permanent magnets to fulfil the above conditions below 2.5 THz [17].
4. Conclusion
In this work, we demonstrated a versatile THz polarization modulator based on an n-InSb plate, which can work as a tunable quarter waveplate for creating a near-perfectly circularly polarized THz beam as well as a circular-polarization-dependent isolator in a wide THz spectral range by changing and reversing the applied magnetic field. InSb is a promising material for fabricating a THz photoelastic modulator for vibrational circular dichroism spectroscopy. The directional and tunable manipulation of light transmission by application of a magnetic field creates unparalleled technological possibilities.
Appendix A: Materials and methods
A.1. THz time-domain magnetospectroscopy
The time-domain THz magneto-spectroscopy system consisted of a Ti: Sapphire femtosecond amplifier (Astrella, Coherent, Inc.) with a wavelength of 800 nm and a pulse width of 35 fs and a pair of 〈110〉 ZnTe crystals to generate and detect coherent radiation from 0.1 to 2.5 THz through surface rectification and electro-optic sampling, respectively. We used a magneto-optical cryostat (SpectromagPT, Oxford Instruments, Inc.) to generate magnetic fields up to 7 T and vary the sample temperature from 1.6 to 300 K. We used a standard lock-in scheme for time-domain signal detection. In order to eliminate the influence of water vapor absorption on the spectrum, the THz system was fully sealed and filled with dry nitrogen.
For transmittance measurements shown in Figure 1, we have employed a commercial QWP in which the phase retardation of the two orthogonal THz electric fields is manipulated through internal reflections in a multi-stacked prism [3]. It has an ellipticity larger than 0.8 and a bandwidth from 0.2 - 2.5 THz. The QWP is mounted in-between a wire-grid polarizer and the sample to ensure a circularly polarized THz light incident on the sample. The extinction ratio of the wire-grid polarizers is 10−3 in power. We have measured the waveforms of the transmitted THz wave through the sample and an empty hole (reference signal). Then we Fourier-transformed the time-domain waveforms into the frequency domain and normalized the power spectra to obtain transmittance spectra.
The electro-optic-sampling-based ZnTe detector is polarization-sensitive. The approach permits precise and direct measurement of the magnitude and direction of the electric field vector as a function of time. For the electric field measurements in Figure 3, we have used two wire-grid polarizers and a band-pass filter in the time-domain THz magneto-spectroscopy system. The first WGP was place before the sample to make incident THz wave linearly polarized along x axis. THz wave goes through the band-pass filter and the sample and then becomes circularly polarized. The x-component of the THz electric field (Ex(t)) was measured by setting the second WGP parallel to the first GWP and the [001] direction of the ZnTe crystal parallel to the probe beam polarization. To measure the y-component of the THz electric field (Ey(t)), the second WGP was placed in cross-Nicole geometry before the ZnTe crystal, whose [001] axis was perpendicular to the polarization of the probe beam, that is, rotating both the second WGP and the ZnTe crystal 90°. We assume that the two geometries of the electro-optic sampling described above had the same sensitivity to the x- and y-components of the THz electric field, enabling quantitative comparison between the two.
A.2. Theoretical model
For theoretical calculation of the transmittance in Figure 1, the bulk n-InSb sample is treated as a plane-parallel slab. The transmittance of a THz CPL can be calculated by ${T_ \pm }(\omega )= {\tilde{T}_ \pm }(\omega ){\tilde{T}_ \pm }{(\omega )^ \ast }$, where ${\tilde{T}_ \pm }(\omega )$ is the complex transmission coefficient of the right (+) / left (−) circularly polarized THz electric field, given by
Funding
Fujian Province Key Laboratory of Terahertz Functional Devices and Intelligent Sensing (FPKLTFDIS202304); Natural Science Foundation of Fujian Province (2023J01055, 2023J05096); National Natural Science Foundation of China (62105068); Education and Scientific Research Foundation for Young Teachers in Fujian Province (JAT220032); Engineering Research Center for CAD/CAM of Fujian Universities (K202203); Engineering Research Center of Smart Distribution Grid Equipment (KFRC202203).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data supporting the findings in this study are available within the article and from the corresponding author upon reasonable request.
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