High-speed broadband frequency sweep of continuous-wave terahertz radiation

Dae-Su Yee; Ji Sang Yahng; Choon-Su Park; Hwi Don Lee; Chang-Seok Kim

doi:10.1364/OE.23.014806

1. Introduction

Time delay scanning is required to measure time-domain terahertz (THz) waveforms in THz spectroscopy and tomography using pulsed radiation [1]. In addition to a conventional mechanical delay line combined with lock-in detection, fast delay scanning methods were demonstrated using signal averaging, such as asynchronous optical sampling, electronically controlled optical sampling, optical sampling by laser cavity tuning, and specifically designed mechanical delay tools [2–6]. The fast delay scanning methods were used for high-speed THz spectroscopy or tomography applicable to real-time detection of explosives, fast nondestructive testing (NDT) of composites, etc [6,7].

On the other hand, a frequency sweep is required to measure frequency-domain THz signals in THz spectroscopy, tomography, and radar imaging using continuous-wave (CW) radiation [8–13]. While the frequency modulated CW (FMCW) THz method employing electronic components can have a high modulation rate of several kHz, the frequency modulation range is usually less than 100 GHz [10,12,13]. The FMCW THz method was exploited for THz radar imaging applicable to stand-off detection of concealed objects [12] and THz tomography applicable to NDT of composites [13]. The THz photomixing method can have a wide frequency sweep range of more than 1 THz but commonly requires a relatively long frequency sweep time due to slow laser frequency tuning [14,15]. The THz photomixing method was used in the coherent homodyne detection scheme for THz spectroscopy and thickness measurement [9,11,16–20].

In this paper, we present an experimental implementation of unprecedented THz frequency sweeping with a kHz sweep rate and a THz sweep range using THz photomixing where an optical beat source is comprised of a wavelength-swept laser (WSL) and a distributed feedback laser diode (DFB-LD) [21,22]. During the frequency sweep, frequency-domain THz interferograms are measured using the coherent homodyne detection method that specifically employs signal averaging instead of lock-in detection for noise reduction. The potential of this method for fast thickness measurement and THz tomography is demonstrated via measurement of a Si wafer.

2. Experimental setup

Figure 1(a) shows a schematic diagram of our experimental setup. To achieve the high-speed broadband THz frequency sweep, we use a beat-frequency-swept optical beat source with a kHz sweep rate in THz photomixing. The optical beat source consists of a DFB-LD and a WSL based on a semiconductor optical amplifier and a fiber Fabry-Perot tunable filter (FFP-TF) [23], of which the output power spectra are displayed in Fig. 1(b). The DFB-LD is operated at a fixed wavelength of 1545 nm, and the output wavelength of the WSL is swept from 1544 to 1558 nm at a kHz sweep rate by modulating the FFP-TF with triangular waveforms. Frequency-domain THz signals are measured in the frequency range up to 1.5 THz, where the large part of the output wavelength range of the WSL is used as indicated by the colored region in Fig. 1(b). The optical output of the WSL is amplified by a polarization-maintaining (PM) optical fiber amplifier and then combined with that of the DFB-LD by a 3 dB PM fiber coupler. One of the two output arms of the coupler is connected to a fiber-coupled THz CW transmitter module (TOPTICA Photonics) including a Si lens and a transmitter chip, an InGaAs-based photodiode with a bow-tie antenna [24]. The other is connected to a fiber-coupled THz CW receiver module (TOPTICA Photonics) through a variable optical delay line. The receiver module includes a Si lens and a receiver chip that is an InGaAs-based photomixer with a bow-tie antenna [24]. All the optical components are connected using PM fibers without the need to control the optical polarization.

Fig. 1 (a) Schematic diagram of our experimental setup for the high-speed broadband frequency sweep of CW THz radiation. WSL: wavelength-swept laser, OFA: polarization-maintaining optical fiber amplifier, DFB-LD: distributed feedback laser diode, PM fiber: polarization-maintaining fiber, THz-Tx: THz CW transmitter, WG: waveform generator, VODL: variable optical delay line, THz-Rx: THz CW receiver, DPG: digital delay/pulse generator, Amp: current preamplifier. (b) Output power spectra of the DFB-LD (blue line) and the WSL (black line).

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When the THz CW transmitter biased by a waveform generator is irradiated by the optical beat source, CW THz radiation is emitted from the transmitter and is guided into the receiver by two off-axis parabolic mirrors. A photocurrent is generated from the receiver that is biased by the electric field of the CW THz radiation and irradiated by the optical beat source. The photocurrent is amplified using a current preamplifier with a bandwidth of 220 kHz and a gain of 1 × 10⁷ V/A. A wavelength trigger signal is created at a wavelength of 1545 nm by filtering a portion of the optical output of the WSL with a fiber Bragg grating [25]. A digital delay/pulse generator triggered by the wavelength trigger signal produces a TTL signal at the same frequency as the sweep rate [7,26]. Frequency-domain data traces are consecutively acquired at the sweep rate from the preamplifier by a digitizer triggered by the TTL signal. At the same time, the TTL signal triggers the waveform generator to provide the transmitter with a bias voltage modulated at half the sweep rate. Noise traces are acquired with the bias off and THz data traces carrying noise are acquired with the bias on. The signal-to-noise ratio (SNR) of the THz data can be enhanced by subtracting the noise traces from the THz data traces carrying noise and averaging the resultant THz data traces. Using a Fabry-Perot interferometer with a free spectral range of 10 GHz, we measured the time variation of the optical frequency of the WSL and thus that of the THz frequency [27]. Hence, THz data traces can be obtained with respect to the THz frequency by converting the time to the THz frequency using the time variation of the THz frequency [4].

3. Experimental results

The time delay between the two paths leading to the receiver from the coupler can be varied by the variable optical delay line. Figure 2(a) shows THz data traces measured at different time delays, which were obtained by averaging 5,000 traces acquired in 10 s with the sweep rate set to 1 kHz. Here, we set the sampling rate of the digitizer to 3 MS/s. The THz data traces result from optoelectronic interference between the electric field of CW THz radiation and photocarriers in the receiver. The period of the interference pattern in the frequency-domain THz interferograms is equal to the reciprocal of the time delay [11]. In other words, the fast Fourier transform (FFT) of the frequency-domain THz interferograms results in peaks in the time-delay domain, as shown in Fig. 2(b). The frequency range of 0.5 – 1.5 THz was used for the FFT, yielding the sharp peaks. Including the lower frequency region for the FFT broadened the peaks, which may mainly be caused by the dispersion of the antennas of the transmitter and receiver [28]. The full width at half maximum (FWHM) of the peaks is about 1.37 ps, resulting from the wide frequency range. The FFT results of such frequency-domain THz interferograms can be used as axial-scan data in reflection-mode THz tomography utilizing time-of-flight information. In that case, the axial resolution would be approximately 0.21 mm, corresponding to the FWHM. The time delay (τ_e) at the maximum FFT amplitude is plotted versus the set time delay (τ_s) in Fig. 2(c). Figure 2(c) also shows that τ_e - τ_s tends to increase with the set time delay. This may be attributed to errors in the time-to-frequency conversion including inaccuracy of the free spectral range of the Fabry-Perot interferometer and the thermal shift of the sweep range of the WSL. The overall increase of about 0.2 ps in τ_e - τ_s amounts to 0.25% of the time delay range of 10 – 90 ps.

Fig. 2 (a) Normalized frequency-domain THz interferograms measured at different time delays with a sweep rate of 1 kHz. They are vertically shifted for clarity. (b) Normalized FFT amplitudes of THz interferograms measured at various time delays. (c) τ_e and τ_e - τ_s are plotted versus τ_s.

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Since using signal averaging instead of lock-in detection for noise reduction, we investigated noise reduction while increasing the number of averaged THz interferogram traces, i.e. the measurement time at a sweep rate of 1 kHz. The SNR of a THz interferogram is plotted against the measurement time in Fig. 3(a). The SNR was evaluated as the ratio of the maximum absolute value of a THz interferogram measured with a time delay of 19 ps to the standard deviation of a noise data obtained without the THz wave. The SNR increases with the measurement time and the line indicates the fit of the result to $Y = α \cdot X^{β}$ . The noise level is close to the shot noise limit because $β$ is 0.499 [4,29]. Figure 3(b) depicts the absolute values of extrema in the THz interferogram along with the absolute values of noise data obtained by averaging 5, 500, and 50,000 noise data traces acquired in 0.01, 1, and 100 s, respectively. The noise level decreases by a factor of 1/10 with the increase in the measurement time by a factor of 100. The THz signal is above the noise level in the measured frequency range even for a measurement time of 0.01 s.

Fig. 3 (a) SNR of a THz interferogram versus the number of averaged traces, i.e. the measurement time at a sweep rate of 1 kHz. The red line indicates the fit of the result to $Y = α \cdot X^{β}$ . (b) The absolute values of extrema in the THz interferogram and the absolute values of noise data obtained by averaging 5 (red line), 500 (green line), and 50,000 (blue line) noise data traces acquired in 0.01, 1, and 100 s, respectively.

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The THz interferograms in Fig. 2(a) and the FFT amplitudes of THz interferograms in Fig. 2(b) were normalized using their respective maximum absolute values. Actually, the maximum absolute value and the maximum FFT amplitude of a THz interferogram decrease with the increasing time delay. In Fig. 4(a), the blue dots show that the maximum FFT amplitude decreases with the increasing time delay at a sweep rate of 1 kHz. This is due to two factors: the coherence time of the WSL and the detection bandwidth determined by the preamplifier. The DFB-LD has a coherence time of several tens of ns corresponding to a spectral linewidth of several MHz. In Fig. 4(a), the black dots indicate the maximum FFT amplitudes of WSL interferograms measured at different time delays with a sweep rate of 1 kHz using the Mach-Zehnder interferometer illustrated in the inset. The coherence time of the WSL is estimated as 49 ps when the maximum FFT amplitude falls to 50%, corresponding to the coherence length of 14.7 mm. The coherence time of the WSL also corresponds to the instantaneous linewidth of 9.0 GHz under the assumption of Gaussian line shape. The optical beat source has the same coherence time as the WSL since the DFB-LD has relatively quite a long coherence time. Because the THz wave is generated using the optical beat source, the THz wave and the optical beat source are mutually coherent and thus the THz wave also has the same coherence time as the WSL [30,31]. The photocurrent output from the receiver is linearly proportional to the time integral of the product of the power of the optical beat source and the electric field of the time-delayed THz wave. Thus, the maximum FFT amplitude of the THz interferogram at a time delay is a measure of the coherence between the optical beat source and the THz wave at the time delay. Also, the maximum FFT amplitude of the WSL interferogram at a time delay is a measure of the coherence between the same optical electric fields of the WSL at the time delay. Therefore, the maximum FFT amplitude of the THz interferogram should decrease with the increasing time delay in the same way as that of the WSL interferogram.

Fig. 4 (a) Maximum FFT amplitudes of THz (blue dots) and WSL (black dots) interferograms measured at different time delays with a sweep rate of 1 kHz. WSL interferograms were measured using the Mach-Zehnder interferometer illustrated in the inset. PD: photodetector. (b) Maximum FFT amplitudes of THz interferograms measured at different time delays with various sweep rates.

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However, the maximum FFT amplitude of the THz interferogram decreases more rapidly with the increasing time delay than that of the WSL interferogram, as shown in Fig. 4(a). The detection frequency is linearly proportional to the time delay by $f = (d f_{T H z} / d t) τ$ , where $f$ and $τ$ are the detection frequency and the time delay, respectively, and $d f_{T H z} / d t$ is the sweep speed of the THz frequency that is 3.65 × 10³ THz/s on average at a sweep rate of 1 kHz. Thus, the time delay can be linearly converted into the detection frequency in Fig. 4(a). The difference between the maximum FFT amplitudes of the THz and WSL interferograms is ascribed to the gain spectrum of the preamplifier since the gain of the preamplifier decreases with the increasing detection frequency. The difference can be reduced with a broader detection bandwidth. However, a preamplifier with a broader bandwidth generally has a higher equivalent input noise current. Thus, the use of a preamplifier with a broader bandwidth would decrease the SNR of the THz interferogram, thereby increasing the measurement time required to reach a desired SNR [4].

Figure 4(b) shows the maximum FFT amplitudes of THz interferograms measured at different time delays with various sweep rates. In the measurements, we changed the sampling rate of the digitizer according to the sweep rate. When the sweep rate increases, the maximum FFT amplitude drops more sharply with the increasing time delay. The time delay when the maximum FFT amplitude falls to 50% decreases from 58 to 31 ps when the sweep rate increases from 0.2 to 1.8 kHz. With the increasing sweep rate, the sweep speed of the THz frequency increases and the coherence time of the WSL decreases. Thus, both the detection bandwidth and the coherence time of the WSL cause the maximum FFT amplitude to drop more sharply with the increasing time delay when the sweep rate increases. Hence, a higher sweep rate will reduce an axial-scan range while shortening an axial-scan time in THz tomography.

This method for the high-speed broadband THz frequency sweep is not suitable for precise THz spectroscopy because of the decrement in the amplitude with the increasing time delay. In return, we demonstrate its potential for fast thickness measurement and THz tomography. Figure 5(a) displays the normalized FFT amplitudes of THz interferograms measured with and without an undoped Si wafer in the THz path with the time delay set to 14 ps. The time delay difference between the main peaks in the reference and sample data is given by

Δ τ_{1} = \frac{(n_{g} - 1) d}{c}

where

n_{g}

and

d

are the group refractive index and thickness of the Si wafer, respectively, and

c

is the speed of light in vacuum. Also, the time delay difference between the peaks due to multiple reflections in the sample data is given by

Δ τ_{2} = \frac{2 n_{g} d}{c} .

Thus, the thickness and the group refractive index are expressed as

d = \frac{c}{2} (Δ τ_{2} - 2 Δ τ_{1}) and n_{g} = \frac{Δ τ_{2}}{Δ τ_{2} - 2 Δ τ_{1}},

respectively. Using Eq. (3), the thickness and group refractive index of the Si wafer are estimated as 0.512 mm and 3.401 from the reference and sample data in Fig. 5(a), respectively. The estimated thickness deviates by 0.4% from the thickness value of 0.510 mm mechanically measured using a micrometer with an accuracy of 0.5 μm. The deviation of the estimated thickness may mainly stem from errors in

Δ τ_{1}

and

Δ τ_{2}

due to the time-to-frequency conversion. The group refractive index is related to the phase refractive index by

n_{g} = n + f_{T H z} (d n / d f_{T H z})

where

n

is the phase refractive index. Since it is shown in Ref. [32] that the phase refractive index of Si is approximately 3.418 and varies by less than 5 × 10⁻⁵ over the frequency range of 0.5 – 1.5 THz, the difference between the group and phase refractive indices can be estimated to be less than 1 × 10⁻⁴ in the frequency range. Thus, the estimated group refractive index deviates by 0.5% from the literature value of 3.418 [32,33].

Fig. 5 (a) Normalized FFT amplitudes of THz interferograms measured with (blue line) and without (red line) a Si wafer in the THz path with the time delay set to 14 ps. (b) Result of deconvolution of the sample data with the reference data in (a).

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In addition, the high-speed broadband THz frequency sweep will be usable for fast axial scanning in THz tomography. The sample data in Fig. 5(a) imitates an axial-scan data in reflection-mode THz tomography, which clearly indicates the first and second round-trip peaks. Deconvolution of the sample data with the reference data can be used to obtain a better axial-scan data as shown in Fig. 5(b), where the low-amplitude noise broadening the peaks is significantly reduced.

4. Conclusion

We have presented a method for a high-speed broadband frequency sweep of CW THz radiation and its measurement. The use of a WSL along with a DFB-LD as a wavelength-fixed laser in THz photomixing enabled the THz frequency sweep with a kHz sweep rate and a THz sweep range. Frequency-domain THz interferograms could be conveniently measured using the coherent homodyne detection employing signal averaging. Thanks to recent developments in a THz CW transmitter and receiver operating in the 1.55 μm wavelength region, this method was successfully implemented exploiting well-developed telecommunication technologies. Further improvement in the SNR and spectral bandwidth of the combination of the THz CW transmitter and receiver will allow for faster measurement and a broader frequency sweep range. Potential applications of this method include high-speed THz tomography and fast thickness measurement. Due to the wide frequency sweep range and the coherence time of the WSL, this method will provide a higher axial resolution but a narrower axial-scan range for THz tomography, as compared to the FMCW THz method. The use of a WSL with a longer coherence time will increase an available time delay range, thereby extending an axial-scan range in THz tomography [34].

Acknowledgment

This work was supported in part by the National Research Foundation of Korea – Grant funded by the Korean Government (NRF-2012-M2A2A9-2012035659) and in part by the Ministry of Science, ICT and Future Planning through the project KRISS-15011034. We thank Prof. Min Yong Jeon and Dr. Kyung Hyun Park for helpful discussion and Dr. Kyong Hwan Jin and Prof. Jong Chul Ye for technical support at the early stage of this work.

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High-speed broadband frequency sweep of continuous-wave terahertz radiation

Abstract

1. Introduction

2. Experimental setup

3. Experimental results

4. Conclusion

Acknowledgment

References and links

Cited By

Figures (5)

Equations (3)

Optics Express