Large-area photoconductive switches as emitters of terahertz pulses with fully electrically controlled linear polarization

Kenneth Maussang; José Palomo; Juliette Mangeney; Sukhdeep S. Dhillon; Jérôme Tignon

doi:10.1364/OE.27.014784

1. Introduction

Technological advances in terahertz (THz) frequency spectroscopy have resulted in a wide variety of applications ranging from materials science [1–3] to sensing [4–6]. One outstanding property of THz waves is their ability to be transmitted through optically opaque materials [7,8]. THz radiation has high penetration depths in different materials such as ceramics, minerals, plastics, pharmaceuticals, and other natural products, which are otherwise opaque to visible light [9]. Beyond dispersion and absorption, the vector nature of light permits to obtain information on a physical system based on polarization measurements, known has ellipsometry. This powerful method permits access to a wide range of dielectric properties of materials and, in particular, is well-suited for thin films studies [10,11]. Polarimetric mesurements are also relevant when a system presents an optical anisotropy. It might be a natural anisotropy like birefringence, an induced anisotropy from external field (e.g. Kerr or Pockels effect) or a stress-induced birefringence. In the latter case, it has an important application in the optical range for stress monitoring in transparent materials known as photoelasticimetry [12]. For materials opaque to optical waves, photoelasticimetry at THz frequencies has attracted a strong interest and recent achievements have been reported [13–16]. Sensitive polarization measurements in the THz domain are also highly relevant for other applications such as cancer detection based on THz polarimetry imaging [17], anisotropic structures studies such as wood [8,18], coating thickness measurements [19] or even optically active or chiral substances.

With the emergence of ultrafast lasers, a popular technique for THz spectroscopy is THz time-domain spectroscopy (TDS). Whilst other spectroscopic methods are conducted directly in the frequency domain, THz-TDS provides direct access to the time-resolved THz electric field, using femtosecond laser pulses for the generation and detection of single cycle THz pulses. With high penetration depth in opaque materials, in combination with high signal-to-noise ratio (SNR) at ambient conditions and submillimeter spatial resolution, THz-TDS has become an important technique over the last two decades.

2. Photoconductive switches for THz emission and detection

Although a wide range of methods can be used to generate and detect such THz pulses, one of the most common uses photoconductive switches, which have the advantage of a large spectral bandwidth and a high signal-to-noise ratio. In a typical experimental arrangement, metallic electrodes are fabricated on the top of a semiconductor substrate (such as GaAs) via standard photolithography technics. Then, through interband excitation of the substrate using an ultrafast laser (e.g. a Ti:Sapphire laser with λ ~810 nm, 100 fs pulses), photocarriers are generated. When operated as an emitter, the photocarriers are accelerated by a static electric field applied between the electrodes, and the corresponding time-varying current generates an electromagnetic pulse in the THz frequency range. Importantly, the polarization of the emitted radiation is linear, fixed by the direction of the static electric field, and consequently directly results from the geometry of the electrodes on the substrate. When operated as a detector, the incident THz electrical field accelerates the photocarriers, which are then collected by the electrodes, generating a current detected that is proportional to the THz electric field component perpendicular to the electrodes direction. Once again, the geometry of the electrodes fixes the direction of the THz electrical field detected.

Polarization measurements based on THz-TDS experimental setup have been widely studied and reported in literature [20–30]. In these measurements, radiation is initially linearly polarized, passes through the sample of interest and finally the detector intrinsically measures only one direction of polarization, either based on photoconductive switches as mentioned before, or electro-optic detection based on Pockels effect in a non-linear crystal [31]. These experimental setups are mostly based on mechanical rotations like discrete rotations of the detection system [21], spinning detectors [25] or spinning polarizers [26] to polarization modulation with an electro-optic-modulator [30]. Those mechanical parts inherently limit the precision and/or the acquisition swiftness. Polarization control on a THz emitter based on optical rectification in 〈111〉 ZnTe crystal has been reported, and polarization analysis with the same type of crystal [32]. However, this method still requires to mechanically rotate an optical wave plate and does not permit fast modulation of THz polarization in the kHz frequency range. In order to achieve more reliable and sensitive measurements, electrical control of the electrical field polarization emitted or detected has been studied. A four contact geometry for the emitter has demonstrated the possibility to generate circularly polarized THz pulses [33], while an eight-contact photoconductive switch as emitter allows discrete rotation angles by steps of 45° of linearly polarized THz pulses [34]. Because this geometry allows only discrete rotational steps, it still requires the use of a pair of Wire-Grid Polarizers (WGP) for precision measurements. As a detector, a three-contact geometry in a photoconductive switch has demonstrated the ability to measure two orthogonal polarization components at the same time, without the need of rotation [35,36], while a four-contact geometry has been reported recently [37]. The multi-contacts geometries mentioned above are however not scalable for large active area and thus more powerful emission and/or more sensitive detection devices.

In this work, we propose an innovative design of a photoconductive switch that provides full control of the polarization emitted by electrical means only. Such emitter permits to produce THz pulses linearly polarized, with continuous control on the polarization to arbitrary directions, while multi-contact geometries emitters result in discrete incremental rotation of polarization. Moreover, the polarization might be modulated at frequencies up to several tens of kHz. This opens perspectives for using such emitters in a lock-in detection scheme for high precision birefringence measurements, resulting in an important improvement of sensitivity compared to standard THz polarimetric experimental setups. Besides, it opens the possibility to perform fast polarization measurements with acquisition time in the millisecond range, well suited for studies of out-of-equilibrium systems, and time-resolved THz polarimetry of fast and ultrafast phenomena. Finally, this design is scalable, based on an interdigitated geometry [38–40], providing large area emitters.

3. Intermixed photoconductive switches design

In the THz domain, it is possible to design photoconductive switches that possess dimensions smaller than the wavelength emitted (1THz = 300µm). Interdigitated photoconductive switches (iPC) consist in the combination of two digits of electrodes interlaced, deposed on a substrate. Each gap between digits can be polarized by applying the same voltage between the corresponding pair of electrodes (see Fig. 1(a)). In a standard iPC, the metallic electrodes structure (with anode and cathode) is realized on top of semiconductor substrate via standard photolithography. The photoconductive switch is excited with an ultrafast laser (λ~810nm), generating electromagnetic pulses in the THz range. The emitted pulse is linearly polarized, with a direction fixed by the electrodes’ digits, more precisely perpendicular to them (direction ${\vec{u}}_{x}$ on Fig. 1(a)). A second metallic layer is composed of metallic fingers covering gaps with a spatial period twice as large as the first, isolated from the first metallic layer by a 300 nm thick layer of SiO₂. This second layer insures that the pulses are emitted only from gaps with the same polarity direction to insure constructive superposition in the far field. The amplitude of the emitted field is directly proportional to the voltage applied on the electrodes. To summarize, the voltage applied to the electrodes fixes the amplitude of the emitted field while the geometry of the electrodes fixes the direction of the linear polarization emitted. The size of the active area of an iPC might be chosen almost arbitrarily, limited only by technical issues from the fabrication process. Instead of a single orientation of the interdigitated electrodes over a large active area, it is possible to assemble several small area iPCs emitters with different properties at a subwavelength scale but which act as single THz element in the far-field. Combining two type of emitters of orthogonal polarizations and independently adjustable amplitudes at subwavelength scale, the THz far field is equivalent to a single emitter of arbitrary linear polarization. This polarization is determined by the relative amplitude of each type of emitter. The principle of the design proposed is depicted in Fig. 1(b) [41]. It consists in an intermixed assembly of small iPC switches (so-called after small individual emitters) that emit orthogonal polarizations (in directions ${\vec{u}}_{H}$ and ${\vec{u}}_{V}$ , red and green electrodes respectively). The vertical component (resp. horizontal) might be controlled independently from the other one, through the application of a voltage V_V (resp. V_H). Each individual emitter has a characteristic spatial length smaller than the diffraction limit of the shortest wavelength of the broadband emitted pulse. Consequently, in the far field, the radiation emitted by individual small interdigitated switches overlap and the structuration of individual small iPCs is not distinguishable at the wavelength scale.

Fig. 1 (a) Cut view of an interdigitated photoconductive switch. Interdigitated gold electrodes on top of the GaAs layer consist of 4μm wide electrodes, equally spaced by a distance $Δ$ = 4μm. A second metallic layer is composed of metallic fingers covering gaps with a periodicity double that of the first, isolated from the first metallic layer by a 300nm thick layer of SiO₂. The femtosecond excitation pulse is focused on the front face of the photoconductive switch generating carriers in the GaAs layer (electrons in blue and holes in red). (b) Top view of the intermixed geometry principle (only the first metallic layer is represented). The pairs of digits share a common ground potential V_G, but can be polarized independently with two different electrical potentials V_H and V_V, resulting is respectively horizontal and vertical polarization. (c) Large area implementation investigated experimentally (only the first metallic layer is represented). The total area of the gold finger electrodes is 450μm × 450μm. (d) Orientation of the wire-grid polarizer $\vec{u}$ with respect to the interdigitated structure directions $({\vec{u}}_{H}, {\vec{u}}_{V})$ for the emitted field experimental characterization.

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For a given propagation direction, the electrical field can be decomposed as a superposition of two orthogonal polarizations

\vec{E} (\vec{r}, t) = E_{H} (\vec{r}, t) {\vec{u}}_{H} + E_{V} (\vec{r}, t) {\vec{u}}_{V},

where H (resp. V) refers to the so-called horizontal (resp. vertical) polarization, and

{\vec{u}}_{H} \cdot {\vec{u}}_{V} = 0.

Introducing the angle

θ

such that

θ = \tan^{- 1} (\frac{V_{V}}{V_{H}}) - \frac{π}{4},

and the electric field

E_{0} (\vec{r}, t)

such that

E_{0} (r, t) = α A (\vec{r}, t) \sqrt{V_{H}^{2} + V_{V}^{2}},

where

A (\vec{r}, t)

is the spatial profile in far-field and

α

the conversion factor from voltage applied to amplitude emitted, the emitted field can be rewritten as follows:

\vec{E} (\vec{r}, t) = (\cos (θ + \frac{π}{4}) {\vec{u}}_{H} + \sin (θ + \frac{π}{4}) {\vec{u}}_{V}) E_{0} (\vec{r}, t)

The angle $θ$ is defined such that $θ = 0$ when the electrical field $\vec{E}$ is aligned with the direction $\vec{u} = ({\vec{u}}_{H} + {\vec{u}}_{V}) / \sqrt{2}$ , justifying the $- π / 4$ factor in the definition of $θ$ . Then, $θ$ is the direction of polarization of the electrical field with respect to direction $\vec{u}$ (see Fig. 1(d)). The relative value between $V_{V}$ and $V_{H}$ permits to directly control the polarization direction $θ$ in a continuous way, by applying the appropriate voltages. It permits a full electrical control of the linear polarization emitted allowing fast modulation of its direction, up to tens of kHz for the design proposed. To be efficient, it requires that individual interdigitated switches are small enough so that in the far-field, the individual small emitter pattern is not distinguishable compared to the diffraction limit. The finite size of this pattern will result in polarization inhomogeneities over the emerging wavefront as discussed further in section 6. In order to provide a large area emitter but at the same time satisfy this subwavelength pattern condition, a so-called hereafter sickle geometry is proposed in Fig. 1(c). The point of this geometry consists in intermixing two directions of electrodes, with a large total area of emission but avoiding any crossing between lower metallization, for simpler clean-room process, similar to standard iPC switches.

4. Experimental characterization of the emission

The intermixed iPC switches studied consist in a sickle geometry with a 450µm wide active area, originating from a pattern with a smallest spatial length $Δ$ of 75µm (see Fig. 1(c)). Electrodes are made out of 4µm wide, 150nm thick gold wires on a semi-insulating GaAs substrate. A 300nm thick SiO₂ insulating layer is deposed prior to the second metallization gold layer which is 150nm thick to occult one gap over two as illustrated on Fig. 1(a). The gap between electrodes is 4µm wide. The intermixed iPC switches have been experimentally characterized with a standard THz-TDS system, schematically shown in Fig. 2(a). They were biased by the mean of two common-ground bipolar voltage generators, synchronized together, delivering independent voltage ranging from −5V up to + 5V, which corresponds to applied electric fields up to 12.5 kV/cm in amplitude. An ultrafast (100 fs pulses) Ti:Sapphire oscillator (80MHz repetition rate) centered at a wavelength of 810 nm was used to photoexcite carriers in the GaAs active layer (average excitation powers of ~130mW). The generated THz pulses were collected from the front surface of the GaAs active layer in a reflection geometry, with a parabolic mirror of 0.25 numerical aperture. Standard electro-optic sampling was used to measure the electric field of the THz pulses emitted, using a 200μm thick 〈110〉 ZnTe crystal placed on 2 mm thick host substrate and a balanced photodiode scheme [31]. A Wire-Grid Polarizer (WGP) placed before the ZnTe crystal insures that the field detected is properly polarized along the direction $\vec{u}$ at 45° from the interdigitated structure directions $({\vec{u}}_{H}, {\vec{u}}_{V})$ . Therefore, after the WGP, the field measured corresponds to a superposition of both components as follow

{\vec{E}}_{measured} (\vec{r}, t) = \frac{1}{\sqrt{2}} (E_{H} (\vec{r}, t) + E_{V} (\vec{r}, t)) \vec{u} .

Then, this configuration permits to fully measure

E_{H} (\vec{r}, t)

if the vertical component is set to 0, and

E_{V} (\vec{r}, t)

if the horizontal component is set to 0, without the need of any mechanical rotation of an element on the experimental setup. A mechanical delay line is used to sample the THz ultrafast pulse as a function of time. The THz-TDS setup is placed in a dry-air purge chamber (typically < 2% humidity) to reduce water absorption of THz radiation. In order to characterize experimentally the emission of the proposed design of the iPC intermixed switch, voltages are applied to electrodes so that the amplitude of the emitted field is kept constant but the polarization direction might be adjusted electrically. Consequently, V_H and V_V are computed for a given value

θ

of the polarization. Assuming a maximum amplitude of

5 V

on each type of electrode, the amplitude of the electrical field is fixed consequently. The transmission through the WGP will be maximum for

θ = 0 °

, satisfied for

V_{H} = V_{V} = 5 V / \sqrt{2} \approx 3.54 V

(corresponding to roughly 8.85 kV/cm static electrical field), when the emitted field is polarized along the direction

\vec{u}

.

Fig. 2 (a) Experimental setup for time-domain and spectral characterization of the emission. Two synchronized voltage generators polarize the electrodes of the photoconductive switches at values V_H and V_V. An ultrafast Ti:Sapphire oscillator was used to photoexcite carriers in the GaAs active layer. The generated THz pulses were collected from the front surface of the GaAs active layer in a reflection geometry, by the mean of parabolic mirror with numerical aperture of 0.25. Standard electro-optic sampling was used to detect the electric field of the THz pulses. A mechanical delay line is used to sample the THz ultrafast pulse as a function of time. The THz-TDS setup is placed in a dry-air purge chamber (typically < 2% humidity) to reduce water absorption of THz radiation. (b) Intensity measurements with a commercial pyrometer. THz beam is chopped mechanically at 10Hz for lock-in detection scheme. (c) Relative orientation of the emitter with respect to the WGP, which defines the angle $θ$ .

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Firstly, voltages are applied to electrodes so that the field is aligned with the direction $\vec{u}$ . In that configuration, the time trace $E_{measured} (t)$ of the emitted electrical field along $\vec{u}$ is shown in the inset of Fig. 3(a). From the time trace, a simple FFT calculation permits to get access to the amplitude spectrum (Fig. 3(a)). The spectrum measured is similar to the spectrum obtained with a standard interdigitated photoconductive switch of similar interdigitated gap but no polarization modulation ability [36]: the emitted spectrum has not therefore been affected by the multi-electrodes geometry.

Fig. 3 (a) Spectral density in amplitude of the emitted electrical field (log scale), with an applied bias field of 8.85 kV/cm on each electrodes. The photoconductive switch emitter is oriented such that the field component detected is the direction $\vec{u} = ({\vec{u}}_{H} + {\vec{u}}_{V}) / \sqrt{2}$ . Voltages $V_{H} = V_{V} = 5 V / \sqrt{2} \approx 3.54 V$ applied on electrodes are such that the THz radiation emitted is polarized along the direction $\vec{u}$ . Inset: time trace of the emitted field measured. (b) Normalized spectrum measured after a wire-grid polarizer in the direction $θ_{WGP} = 0 °$ , as a function of the expected angle of polarization $θ$ of the radiation emitted. The angle $θ$ defines the voltages that have to be applied on the electrodes (Eq. (2)).

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5. Experimental control of the polarized emission

In order to demonstrate the ability to control electronically the direction of the linear polarization emitted, we have performed intensity measurements of the field after the WGP with a commercial pyrometer (Fig. 2(b)). For lock-in detection scheme, the field is modulated with a mechanical chopper at 10Hz. In order to emit a pulse in the direction $θ$ , as defined in Fig. 2(c), one should apply the following voltages on the electrodes

V_{H} = V_{\max} \cos (θ + \frac{π}{4}); V_{V} = V_{\max} \sin (θ + \frac{π}{4}) .

When both electrodes H and V are active, the signal detected on the pyrometer has the following dependence with

θ

S_{H + V} = S_{m} (1 + \cos 2 θ),

with

S_{m}

the maximal amplitude detected. If one deactivates the H electrodes, the signal detected

S_{V}

measures only the projection of the V component of the field

S_{V} = S_{m} \frac{1 - \sin 2 θ}{2} .

Similarly, if one deactivates the V electrodes, the signal detected

S_{H}

measures only the projection of the H component of the field

S_{H} = S_{m} \frac{1 + \sin 2 θ}{2} .

The corresponding signals $S_{H}$ , $S_{V}$ and $S_{H + V}$ have been measured experimentally with the previous stickle geometry photoconductive switch, reported in Fig. 4. The uncertainty of this measurement is dominated by the fluctuations of the lock-in signal from the pyrometer, as a result of a mechanically chopped THz beam. Error bars in Fig. 4 represent an estimation of the uncertainty of the measurement (statistical uncertainty), due to pyrometer signal noise. $S_{H + V}$ has been fitted by the following function of $θ$

S_{H + V} (θ) = S_{m} (1 + \cos 2 θ) + ε,

where

S_{m}

and

ε

are the fit parameters. While

S_{m}

is the amplitude mentioned previously,

ε

is the offset of the pyrometer detector. The blue line of Fig. 4 corresponds to this fit. Then, expected curve

S_{H}

and

S_{V}

are calculated assuming the same offset

ε

with an amplitude

S_{m}

obtained both from the fit of

S_{H + V}

. Then, expected curves are plotted in red and green in Fig. 4 and are not a fit. It demonstrates unambiguously the vector addition of the electrical fields emitted from both pairs of interdigits in orthogonal directions. It is possible to estimate the Degree Of Polarization (DOP) of the emitted THz field, defined afterwards as follow

DOP = \frac{2 S_{m} - ε}{2 S_{m} + ε} = \frac{I_{∥} - I_{⊥}}{I_{∥} + I_{⊥}},

where

I_{∥}

is the intensity of the electrical field in the direction expected, and

I_{⊥}

the intensity of the electrical field in the direction orthogonal to the expected one. From the values of the offset

ε

and amplitude

S_{m}

obtained from the fit mentioned previously, the DOP can be calculated from Eq. (11). From this procedure it is estimated to be at least of 90%. This measured value is nevertheless dominated by the noise of the pyrometer used and indicates only a lower bound on the DOP of the emitter. Moreover, the pyrometer integrates the intensity over the whole spectrum emitted, while in a THz-TDS system, the spectral bandwidth is limited by the detector. The DOP value will depend on the spatial overlap between both polarizations in far field due to diffraction and, consequently, on the wavelength considered. Thus, the DOP has to be estimated within the spectral bandwidth of the detector to be relevant, which not achievable with a pyrometer detector.

Fig. 4 Demonstration of the vector addition of polarization with a pyrometer and a wire-grid polarizer. Pyrometer signal measured as a function of parameter $θ$ when both electrodes are activated (blue circles), when only the H electrodes are actives (green diamond) and when only the V electrodes are actives (red square). The blue solid line corresponds to a numerical fit with amplitude and offset as free parameters. Red and green lines are expected curves using previous fit parameters. Error bars represent an estimation of the statistical uncertainty of the measurement, due to pyrometer signal fluctuations.

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The principle of operation of the intermixed iPC switches proposed relies on the linear relationship between the amplitude of the emitted field and the amplitude of the electrical bias field applied between the electrodes. However, the applied bias field ranges from 0 up to few tens of kV/cm, above the threshold for side valley transfer in GaAs. Consequently, high frequency components of the emitted radiation are relatively enhanced for high bias field, invalidating the assumption of linearity. In the experiment performed, the extinction angle has been chosen in the situation where equivalent voltages are applied to the electrodes $(V_{H} = - V_{V})$ , so that for small rotations around the extinction $(θ = \pm 90 °)$ or around the maximal transmission $(θ = 0 °)$ , this effect remains small and has not been observed within uncertainties of measurement. This effect is rather small for frequencies around 1 THz, while from the spectral measurements of Fig. 3, one may estimate that 81% of the emitted power is concentrated in the 0.5 THz – 1.5 THz spectral bandwidth. This non-linearity is not a strong limitation of the intermixed iPC switches proposed when used for spectroscopy, if it is combined with a detector resolved in time and polarization (e.g. similar intermixed iPC switches but adapted for detection). Small spectral distortions during the rotation of polarization could be calibrated prior to measurement, as a reference measurement (standard procedure in spectroscopy).

The THz-TDS system combined with a WGP should provide a more sensitive measurement of the DOP. The spectrum measured in THz-TDS after the WGP (of fixed direction) as a function of $θ$ is represented in Fig. 3(b). No spectral distortion of extinction is visible at first sight. From these measurements, one may extract for each frequency f the spectral amplitude transmitted $S_{f} (θ)$ as a function of $θ$ . This quantity permits to estimate the degree of polarization for the spectral component at frequency f, hereafter called spectral DOP(f), defined as follow

DOP (f) = \frac{I_{∥} (f) - I_{⊥} (f)}{I_{∥} (f) + I_{⊥} (f)},

where

I_{∥} (f)

and

I_{⊥} (f)

are the spectral intensities respectively of the polarization not attenuated by WGP and the one perpendicular to it. Approximating

I_{∥} (f) \approx \max (| S_{f} (θ) |^{2})

and

I_{⊥} (f) \approx \min (| S_{f} (θ) |^{2})

, a lower bound of the spectral DOP(f) might be estimated, and is represented Fig. 5(a). Therefore, the spectral DOP(f) is greater than 96% over the 0.1THz – 4THz spectral bandwidth. Moreover, as mentioned previously, 81% of the emitted power is concentrated in the 0.5 THz – 1.5 THz spectral bandwidth, where the spectral DOP(f) is measured to be higher than 98%. Integrating the spectral DOP(f) pondered by the spectral power of the emitted spectrum, the global DOP of the emitter is estimated to be larger than 98% from those measurements. This value is consistent with the measurement performed with the pyrometer (90%), which was limited by the sensitivity of the detector. In order to investigate it further, a numerical investigation has been performed.

Fig. 5 (a) Experimental measurement of the spectral Degree Of Polarization (DOP(f)), for numerical aperture NA = 0.26 (used in experiment of Fig. 3(b)). (b) Numerical calculation of the spectral DOP(f) for the sickle geometry considered in Fig. 1(c), for different numerical apertures of the collection optics (NA = 0.5, 0.26 and 0.13). For clarity, the quantity 1-DOP(f) is plotted. The excitation beam waist is $w_{e} = 300 µ m$ while the probe waist is $w_{p} = 200 µ m$ . (c) Zoomed in for DOP(f) greater than 98%.

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6. Numerical investigation of the polarization distortion

In the far-field regime, each type of polarization has a spatial distribution related to the initial corresponding emitting area geometry. In the detection process, the initial emitter pattern is imaged on the electro-optic crystal, but affected by the finite aperture of the optical system and diffraction during the beam propagation. The emitter is designed such that two types of emitters are intermixed on a subwavelength scale, so the emitter acts as a punctual source to neglect the initial spatial differences between both polarizations. Consequently, in regard to the diffraction limit of the experimental setup, the size of each small individual iPC emitter will impact directly the maximum frequency on which both polarizations overlap properly in far-field. Any mismatch in spatial overlap of two orthogonal polarizations in far-field results in a spatial inhomogeneity of the local direction of polarization, so-called hereafter polarization distortion. Previous measurements however do not permit to analyze the spatial polarization distortion over the beam profile. Indeed, in the case of electro-optic measurement, while wave front distortion of THz pulses has been explored [42], to authors knowledge, no simple method exists to perform sensitive measurements of the polarization distortion over a THz pulse profile with a low field amplitude. Therefore, it has been investigated through numerical calculations of wave propagation of the THz radiation emitted from the geometry of Fig. 1(c).

The key physical effect that permits both polarizations to overlap properly in far-field is diffraction. Consequently, the optical system is modeled using the relevant parameter for diffraction: the numerical aperture. Each types of electrodes are considered as a spatial pattern which is imaged by an optical system, for a given frequency. The radiation emitted in far-field limit is calculated prior to the first optic in the reciprocal k-space. The propagation of the wave in the THz-TDS system is modeled by a wave-vector cut-off in k-space defined by the finite numerical aperture of the system. Afterwards, the inverse transformation back into to real space permits to obtain the electrical field in the focal plane of the detector, pondered by the probe beam spatial profile. The calculation assumes no additional aberrations and that the numerical aperture of the final focusing optic is the same than the collection optic (which is the case in the experimental setup). For a given frequency, amplitudes of each polarization are calculated at the focal plane of the last parabolic mirror where the THz beam is focused for electro-optic detection. Different numerical apertures of the experimental system have been considered (NA = 0.13, 0.26 and 0.5). To quantify the polarization distortion over the THz beam, one calculates the spectral Degree Of Polarization DOP(f). The spectral DOP(f) is given by the ratio of the intensity difference of the two polarizations components divided by the total intensity of the beam, integrated over the probe beam profile, at a given frequency f. The DOP defined in Eq. (11) corresponds to the average spectral DOP(f) over the detector bandwidth. In order to estimate the spectral DOP(f) of the intermixed iPC switch proposed, the less favorable case is considered, where H- and V-polarizations have the same amplitude. The emitted field is expected to be polarized in the direction $\vec{u} = ({\vec{u}}_{H} + {\vec{u}}_{V}) / \sqrt{2}$ . From the numerical calculation of the electrical field $\vec{E} (f; x, y)$ at a given frequency f, the expression of the spectral DOP(f) at this frequency is the following

DOP (f) = 2 \times \frac{{∭ | \vec{E} (f; x, y) \cdot \vec{u} |}^{2} \frac{e^{- \frac{x^{2} + y^{2}}{2 w_{p}^{2}}}}{\sqrt{2 π w_{p}^{2}}} d x d y}{{∭ | \vec{E} (f; x, y) |}^{2} \frac{e^{- \frac{x^{2} + y^{2}}{2 w_{p}^{2}}}}{\sqrt{2 π w_{p}^{2}}} d x d y} - 1,

where

(x, y)

are the coordinate of a point in the focal plane, and

w_{p}

is the waist of the laser probe beam of the THz-TDS considered.

This laser beam is assumed to be gaussian with a M² factor of 1, so that the laser intensity profile in the focal plane is the following

I (x, y) = I_{0} \frac{e^{- \frac{x^{2} + y^{2}}{2 w_{p}^{2}}}}{\sqrt{2 π w_{p}^{2}}},

where

I_{0}

is the total intensity of the probe laser. While previously

\vec{r}

denoted the position anywhere in space,

(x, y)

are only used to refer to the position in space where the detection of the THz field occurs in a THz-TDS systems, i.e. the focal plane of the last parabolic mirror (the fourth one in the case of Fig. 2(a), focusing onto the ZnTe electro-optic crystal).

The results of these calculations are represented in Fig. 5 (1-DOP(f) is plotted for clarity). For a numerical aperture of NA = 0.26, the sickle geometry has an expected spectral DOP(f) better than 99% up to 3 THz, and better than 98% in the 0-4THz spectral range which corresponds to the spectral response window of the 200µm thick ZnTe crystal used in the experiment. The spectral DOP(f) calculated is consistent with the measured one in Fig. 5(a) up to 3.5 THz. For higher frequencies, the signal-to-noise ratio (SNR) of the THz-TDS signal is lower than 7 (see Fig. 3(a)) so that the uncertainty of the measurement is larger than the discrepancy observed between calculations and the measured spectral DOP(f). THz-TDS measurements have an SNR better than 100 between 200 GHz and 2 THz, spectral domain in which the expected DOP(f) is higher than the measured one, so calculations are consistent with measurements (limited by imperfections of the setup). Consequently, numerical simulations can be used as a guideline for the development of more performant designs of intermixed iPC switches. Using a lower aperture, down to NA = 0.13, it is possible to reach spectral DOP(f) better than 99.9% in the 0-4THz spectral range. As a comparison, commercial free-standing WGP are proposed with spectral DOP(f) better than 99.9%. So the device proposed in this work offers equivalent spectral DOP(f) performances than commercial WGP but integrated on-chip with modulation ability up to tens of kHz. Besides, the spectral DOP(f) of a commercial free-standing WGP usually drops down at low frequencies while the device proposed has an increasing spectral DOP(f) at low frequencies, resulting in complementary THz components for broadband polarimetric measurements.

7. Conclusion and further prospects

In conclusion, we have demonstrated an innovative concept of device for the generation of linearly polarized terahertz pulses, with full electrical control over the direction of polarization. It consists in two intermixed orthogonal interdigitated photoconductive switches, and independently-controlled static electrical bias field. It provides powerful large area sources of linearly polarized THz pulses, electrically controlled in polarization. By adjusting the relative field amplitude between those two intermixed switches, the direction of the polarization can be adjusted electrically with a high degree of precision, and is inherently fast owing to its electronic nature, allowing polarization modulation up to tens of kHz. The sickle geometry proposed in this work has been investigated both experimentally and numerically regarding the DOP estimation. The spectral DOP(f) has been estimated experimentally to be better than 96%, with an average value of 98%, consistent with the expected value from numerical calculations within experimental imperfections. Such design is fully compatible with current clean-room process of iPC switch, without cross-connection issues. This opens the development of THz emitters combining polarization control with other functionalities already demonstrated for iPC switches such as high spectral resolution ability [39,40]. However, the spectral bandwidth is dependent on the size of the active area. Further work would consist in the development of a geometry that permits to decouple the size of each individual emitter and the total size of the active area. By the use of a technical solution for a fully scalable intermixed geometry, it would permit the development of powerful THz pulse emitters of large area, with a direction of polarization fully electrically controllable over a large spectral bandwidth. Further work would also consist in the full characterization of the emitted radiation, including the spatial dependence of the direction of polarization over the beam. Such a mapping of the local direction of polarization could be compared to the expected one obtained by numerical calculations.

Moreover, these intermixed photoconductive switches design might be used as detectors of THz pulses, resolved in polarization, assuming the use of an adapted active layer such as low-temperature-grown GaAs (LT-GaAs) [40]. It offers then a major improvement for THz polarimetry, since polarization control and measurement might be performed with large area devices and without the need of any mechanical degree of freedom on the experimental setup. It opens the field of precision measurements in THz polarimetry and lock-in detection scheme for small polarization change measurements resulting from an external constraint, but also sensitivity and acquisition rate improvements for time-resolved studies of fast and ultrafast phenomena. Such precision THz polarimetry could impact the field of material sciences studies such as polymers or anisotropic materials like wood [8]. Besides birefringence measurements of anisotropic materials, it also opens the field of improved spectroscopy of dielectric properties of materials in reflectivity. In the case of THz spectroscopy in reflection, the acquisition of a reference spectrum to retrieve precise value of dielectric constant is an issue for precision measurements. With a precise control over the polarization, reflectivity measurements for different polarizations permit to retrieve the dielectric constant of the material from Fresnel’s coefficient without the need for a reference [43].

Funding

European Union’s Horizon 2020 research and innovation programme, No 737017 FET-Open MIRBOSE.

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Large-area photoconductive switches as emitters of terahertz pulses with fully electrically controlled linear polarization

Abstract

1. Introduction

2. Photoconductive switches for THz emission and detection

3. Intermixed photoconductive switches design

4. Experimental characterization of the emission

5. Experimental control of the polarized emission

6. Numerical investigation of the polarization distortion

7. Conclusion and further prospects

Funding

References

Cited By

Figures (5)

Equations (14)

Optics Express