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A simple thickness measurement method based on the coherent homodyne CW THz system was demonstrated; it does not require precise control of the frequencies of the beat source, and only accurate scanning of the optical delay line is needed. Three beat frequencies are sufficient for measuring the thickness of a sample without considering the modulo 2π ambiguity. A novel compact 1.55 μm λ/4 phase-shifted dual-mode laser (DML) was developed as an optical beat source for the CW THz system. The thickness of a sample was accurately estimated from the measurements using the proposed method. Our results clearly show the possibility of a compact, simple, and cost-effective CW THz system for practical applications.
©2012 Optical Society of America
1. Introduction
Terahertz (THz) technology has shown potential in a wide variety of applications such as spectroscopy, imaging, and sensing because of its unique properties [1–3]. Continuous wave (CW) THz systems based on photomixing have recently received considerable attention as an important candidate for industrialization because of their lower cost, smaller size, and higher frequency resolution compared to pulsed THz systems [4, 5]. For practical THz applications, a low-cost, compact CW THz photomixing system is preferred [6]. The optical beat source is the main component affecting the system’s size and cost. A typical beat source consists of two distributed feedback laser diodes (DFB LDs) or two external cavity laser diodes [7]. These two independent lasers need to match in polarization and spatial overlap and stabilize each frequency. A remarkable simplification can be achieved by using a monolithically integrated semiconductor laser emitting two wavelengths simultaneously [8]. The detuned dual-mode laser (DML) diode was reported as a compact optical beat source. However, it still has technological problems due to the compound cavity modes, although it exhibits superior characteristics such as a wide tuning range, high side-mode suppression ratio (SMSR), low relative intensity noise, and narrow linewidth [9]. Here, a λ/4 phase-shifted grating is added to the 1.55 μm detuned DML to suppress the compound cavity modes and increase the tuning range and output power without mode hopping.
A THz CW photomixing system has been used in THz spectroscopy. It can measure both the amplitude and phase of the THz CW and determine both the real and imaginary parts of the complex dielectric property [10, 11]. At the same time, it can measure the thickness of a sample by scanning difference frequencies for a fixed delay line or scanning the delay line for some fixed frequencies [12–16]. In both cases, the difference frequencies should be controlled exactly to determine the thickness of a sample, which means that the optical beat source should be precisely controlled. Consequently, a THz CW system used in real applications for thickness measurement needs an additional feedback block to control and monitor the beat source, which increases the cost and size.
In this paper, a simple thickness measurement method based on the coherent homodyne CW THz system is proposed. The proposed method does not require precise control of the beat frequencies, and it can measure the thickness of a sample without considering the modulo 2π ambiguity. A novel 1.55 μm λ/4 phase-shifted DML was developed as a compact, fast optical beat source for a CW THz spectroscopy system. The CW THz spectroscopy system based on the DML clearly resolved the absorption features of an α-lactose sample. Further, the thickness of a sample was accurately estimated from the measurements using the proposed method.
2. The 1.55 μm λ/4 phase-shifted dual-mode laser
The monolithically integrated DML based on DFB LDs has many advantages, such as its compactness, stable dual-mode operation, high SMSR, narrow linewidth, and the possibility of continuous tuning without mode hopping. However, the compound cavity mode in the detuned DML limits the operating current range, and its output power is not sufficient for use as the optical beating source. Although the compound cavity mode of the DML can be suppressed by the reverse biased phase section between two DFB LDs, the photon density inside each loss-coupled DFB LD is very high near the phase section, which can easily activate the compound cavity mode at a high operating current. The λ/4 phase-shifted DFB LD is adopted in order to change the photon density peak inside each DFB LD from the edges to the center. Photon density profiles having an intense peak near the phase-shifted region, which is placed at the center of the phase-shifted DFB LD, effectively suppress the compound cavity modes under a high operating current [17]. Therefore, the λ/4 phase-shifted gratings in DML extend the operating current window while maintaining the dual-mode operation; the output power of the phase-shifted DML increased three times compared to that of the detuned DML. Figure 1 shows a schematic diagram of the 1.55 μm λ/4 phase-shifted DML. It consists of two λ/4 phase-shifted DFB LDs and one phase section. The gratings of the two DFB LDs are fabricated by electron beam lithography, and their operating wavelengths are set to 1550 nm and 1555 nm, respectively. The cavity length of each DFB LD is 400 μm, and the length of the phase section is 50 μm. Micro-heaters are integrated on top of each DFB LD to independently tune their wavelengths.
The lasing modes of the λ/4 phase-shifted DML depend on the bias of the phase section. The phase-shifted DML can operate in dual mode from a reverse bias of −0.9 V, and the output power decreases as the reverse bias increases owing to the increased absorption in the phase section [17]. As the reverse bias in the phase section of the DML increases, the dual-mode operation becomes more stable at the expense of the output power. A reverse bias of −1.1 V is the optimum point for maximizing the output power of the DML while maintaining dual-mode operation without mode hopping. Figure 2(a) shows the mode tuning spectra of the λ/4 phase-shifted DML under a reverse bias of −1.1 V. The mode tuning spectra were obtained by adjusting only the micro-heater currents while maintaining all other conditions. The operating wavelength of the shorter of the two DML outputs increases as the temperature of the micro-heater near the DML output port increases, and the wavelength of the longer one also increases as the temperature of the other micro-heater increases. Consequently, the optical beat frequency was decreased from 0.76 THz to 0.27 THz by heating the micro-heater near the DML output port and increased from 0.76 THz to 1.28 THz by heating the other micro-heater. As shown in the inset of Fig. 2(a), the SMSR was more than 50 dB over the almost whole tuning range. And the strong four-wave mixing (FWM) signals indicate efficient mode beating and low phase noise [18]. The output powers were decreased from 9.8 mW to 7.7 mW and from 9.8 mW to 9.2 mW by controlling the micro-heaters near and far from the DML output port, respectively. The output powers can be kept constant by increasing the injection current. Figure 2(b) shows the tuning speed of the phase-shifted DML with the schematic diagram of the tuning speed measurement setup. The speed was estimated by measuring the thermal transients of the output wavelengths. Two narrow band-pass filters (BPFs) were used to distinguish two states of the optical outputs having different wavelengths from one of the DFB-LDs in the DML, which varied according to the function generator output for heating the micro-heater. The outputs of the two BPFs were coupled to a high-speed photodiode through a 2 × 1 optical combiner. The tuning speed for the wavelength of 3 nm was less than 10 ms, including both the heating and cooling times for maximum heater power. Thus, the total time required to sweep about 1 THz of bandwidth, which corresponds to the wavelength tuning of 8 nm at 1.55 μm, is less than 30 ms. This speed is clearly faster than that of a commercial system which controls the operating temperature of entire LD chip and submount by using thermo-electric cooler (TEC) inside LD package. The tuning speed of the λ/4 phase-shifted DML is fast enough to realize a compact, fast-sweeping CW THz system operating at 1.55 μm.
Fig. 2 Characteristics of the phase-shifted DML (a) mode tuning spectra, Inset shows the spectra showing the SMSR and FWM; (b) tuning speed of the λ/4 phase-shifted DML with the schematic diagram of the tuning speed measurement setup.
3. Coherent homodyne continuous-wave terahertz system
A coherent homodyne CW THz system setup is shown in Fig. 3 . The system consists of the λ/4 phase-shifted DML and an all-fiber path for the laser beams in order to increase the flexibility and compactness. The optical beat signal emitted from the DML package was amplified by an erbium-doped fiber amplifier (EDFA). The amplified spontaneous emission generated by the EDFA was filtered out by an optical BPF. The output signal from the BPF was coupled to a fiber-optic 50:50 splitter and divided into two integrated photomixer/antennas. They play the roles of THz transmitter and receiver, respectively, in the coherent homodyne CW THz system.
A photoconductive 1.2 μm In0.53Ga0.47As layer was grown on semi-insulating InP using a molecular beam epitaxy system at a temperature of 220°C for the photomixer/antenna. Be was doped with a concentration of 1.5e18 cm−3 to compensate for a background of n-type impurities. After growth, the layer was annealed in situ at a temperature of 550°C in ambient AsH3. The photocarrier lifetime of the low-temperature-grown (LTG) InGaAs was measured by transient absorption measurements. The measured photocarrier lifetime was 1.7 ps. For THz emission and detection, a log-spiral antenna and an interdigitated photomixer were fabricated on the LTG InGaAs using stepper lithography. To reduce the photomixer’s dark current, a mesa structure was adopted for the LTG InGaAs, and its surface was passivated using a SiNx layer, except over a central active area of 10 × 10 μm2. A log-spiral broadband antenna was designed and fabricated because its impedance, radiation pattern, and polarization characteristics are nearly constant in a broad range of frequencies [17]. The shape of an interdigitated capacitor was used for the photomixer to increase the optical-to-electrical conversion efficiency. A 0.2 μm SiNx antireflection coating layer was deposited on the photomixer to increase its responsivity. The fabricated photomixer was inserted into a compact fiber-pigtailed photomixer module having a heat-spreadable aluminum nitride submount and a hyper-hemispherical Si lens. The module has a small volume of less than 0.7 cc and is connected to a single-mode fiber [19].
The THz signal was measured by controlling only the two micro-heaters to sweep the beat frequency of the λ/4 phase-shifted DML from 273 GHz to 1280 GHz. The bias for the photomixers was modulated at a frequency of 7.03 kHz and a maximum voltage of 3 V. The lock-in time constant was set to 300 ms. Each photomixer was excited by an optical power of 40 mW. The noise photocurrent was measured by blocking the THz beam; its RMS value was 3.5 pA. Figure 4 shows the THz signal of the coherent homodyne CW THz system based on the λ/4 phase-shifted DML. The THz signal decreased from 1.04 nA to 75 pA as the beat frequency was varied from 273 GHz to 1280 GHz.
The absorption spectrum of α-lactose was measured using the coherent homodyne CW THz system based on the λ/4 phase-shifted DML. An α-lactose pellet was prepared from a 10% α-lactose and 90% polyethylene (PE) mixture. A 100% PE pellet was prepared as a reference. The weights of the two pellets were identical. The α-lactose and PE pellets were placed and measured at the central position between the two photomixers. The measured spectrum was compared with that measured by a fiber-coupled terahertz time-domain spectroscopy (THz-TDS), as shown in Fig. 5 . The absorption peak of the α-lactose measured in the homodyne CW THz system agreed well with the data obtained by our THz-TDS [19]. The strongest absorption appeared at 532 GHz in both cases. These results are comparable to the experimental results in previous reports [10, 12].
Fig. 5 Absorption coefficients of α-lactose pellet measured in (a) CW THz system and (b) PW THz system.
4. Thickness measurements by using coherent homodyne CW THz system
4.1 Theory and data analysis
The detected photocurrent in the coherent homodyne CW THz system is proportional to the THz electric field ETHz, and its phase depends on the phase difference between the THz CW and the laser beat signals for the transmitter and receiver, which can be written as:
The phase offset φ is frequency-independent. The path length difference ΔL can be changed by scanning the THz CW path (LTHz) or optical path for the THz transmitter (LTx) or receiver (LRx), as shown in Fig. 3. The period of the photocurrent oscillation is anti-proportional to ΔL in the frequency domain [16]. Especially when ΔL is zero, the normalized THz photocurrents are constant in the entire frequency band. Furthermore, the length of the THz path depends on the refractive index and thickness of a sample. Thus, the thickness of a sample having a known refractive index can be calculated exactly by determining the optical path length that maintains a constant normalized THz photocurrent in the frequency band. This optical path length can be found by simply scanning the optical delay line inserted in the optical path. In our system, the optical path length for the receiver is controlled by scanning a precise optical fiber delay line located between the laser source and the THz receiver while the optical path length for the transmitter is fixed, as shown in Fig. 3. The optical path lengths for the receiver that yield constant THz photocurrents in the measured beat frequency band are:where LRx_ref0 and LRx_sam0 are the optical path lengths for the reference and the sample, respectively, when the THz photocurrents are constant in the measured frequency band. For the reference data, the THz photocurrents could be measured through air without any sample in the frequency band. The refractive index of a sample is the same as its group refractive index if the measured frequency band is narrow enough for the sample not to be dispersive. Therefore, the relationship between the THz path lengths for the reference and the sample iswhere d and n are the sample’s thickness and refractive index, respectively. The thickness of a sample can be calculated by using Eqs. (2) and (3). In this thickness measurement method, there is no modulo 2π ambiguity, which can be a problem in methods that use exact frequency scanning at fixed optical path lengths [12, 13]. Moreover, this method does not require precise control of the beat frequency; only accurate scanning of a simple optical delay line is needed.4.2 Experimental results
To verify the feasibility of the proposed method, the PE pellet prepared as a reference in the α-lactose absorption measurement was measured using the coherent homodyne THz CW system based on the λ/4 phase-shifted DML. Figure 6 shows the normalized THz photocurrents measured without and with the PE pellet according to the variation in the optical delay in the frequency range from 448 GHz to 610 GHz in steps of about 4 GHz. The lock-in time constant was set to 100 ms to obtain every time trace for a thickness measurement. The total number of measured frequencies was 37. The step in the delay line was 0.05 ps, which determines the resolution of the thickness measurement and measuring time.
Fig. 6 Normalized THz photocurrent measured (a) without and (b) with the PE pellet according to the variation in the optical delay in the frequency range from 448 GHz to 610 Hz in steps of about 4 GHz.
The equi-phase positions of the delay line for the reference and the PE sample, at which the normalized THz photocurrents are constant in the measured frequency band, are located between 101.75 ps and 102.75 ps and between 106.65 ps and 107.55 ps, respectively. The equi-phase positions can be easily obtained by summing all the time traces measured at all 37 frequencies, as shown in Fig. 7 . The displacement of the maximum peak after THz CW penetration through the PE sample represents the phase delay of the THz CW through the PE sample because the phase offset φ is frequency-independent. The delay time of the THz CW caused by the PE sample was between 4.8 ps and 4.9 ps. The refractive index of the PE measured using our THz-TDS was 1.46. Therefore, the deduced thickness of the PE sample was between 3.13 mm and 3.19 mm. The measurement deviation was caused by the intensity fluctuation of the measured THz signal due to the variation of the optical polarization and phase during the propagation through the single-mode fiber. The measurement by the THz CW system agreed well with that obtained using a standard mechanical micrometer within the error range of the micrometer.
The equi-phase positions of the delay line can also be found by adding only three time traces measured at three frequencies. The three time traces were used to find the equi-phase positions exactly, even though two time traces could find the equi-phase positions in principle. Figures 8(a) and 8(b) show the summations of the three time traces measured at three frequencies without and with the PE sample, respectively, for various frequency spans from 20 GHz to 160 GHz. The central frequency was 523 GHz. The difference between the values of the maximum and second peaks decreased as the frequency span decreased from 160 GHz to 20 GHz. The difference between the adjacent frequencies determines the measurable maximum thickness of a sample. These results show that only three beat frequencies are sufficient for measuring the thickness of a sample, and they do not need to be exactly controlled. The summation of the three time traces which are not normalized can be directly obtained in a three-frequency-THz system [15].
Fig. 8 Summations of the three time traces measured at three frequencies (a) without and (b) with PE sample for various frequency spans.
Similar experiments were performed with five Teflon disks having different thicknesses to confirm the accuracy and feasibility of the proposed thickness measurement method. The thicknesses of the samples were 1.01 mm, 2.13 mm, 3.06 mm, 4.12 mm, and 5.19 mm, as measured using a mechanical micrometer within the error range. The 1.01 mm thick Teflon disk was considered as the reference instead of air to remove the measurement error due to sample mispositioning. Figure 9 shows the summations of time traces measured with the five Teflon disks; the time traces were measured at 60 frequencies to increase the difference between the maximum and second peaks. For a strict comparison, commercial tunable LDs were used as the beat source. The inset shows the optical delay position of the maximum peak according to the thickness of the Teflon disk. The delay time of the maximum peak shifts linearly from 103.05 ps to 109.05 ps as the thickness of the Teflon disk varies from 1.01 mm to 5.19 mm. From the measured results, the thicknesses of all four Teflon disks were accurately estimated within the error range of the micrometer.
Fig. 9 Summations of the time traces measured at 60 frequencies with five Teflon disks. Inset shows the optical delay position of the maximum peak according to the thickness of the Teflon disk.
5. Conclusion
We proposed a simple thickness measurement method based on the coherent homodyne CW THz system. This method does not require precise control of the beat frequency, and only accurate scanning of the optical delay line is needed. Moreover, three beat frequencies are sufficient for measuring the thickness of a sample without considering the modulo 2π ambiguity. A novel 1.55 μm λ/4 phase-shifted DML was developed as the optical beat source for a compact CW THz system. This device showed a continuous beat frequency tuning from 0.27 THz to 1.28 THz while maintaining stable dual-mode operation without mode hopping; the output power increased three times compared to that of the detuned DML. The absorption peak of an α-lactose sample was clearly resolved using the CW THz system. Also, the thickness of a sample was accurately estimated from the measurements using the proposed method. Our results show the feasibility of a compact, simple CW THz system based on the 1.55 μm λ/4 phase-shifted DML. Further, the proposed measurement method can be applied to a cost-effective thickness measurement terahertz system with simple tunable semiconductor lasers such as the phase-shifted DML.
Acknowledgment
This work was supported by the Joint Research Projects of ISTK and the Public welfare & Safety research program through the National Research Foundation of Korea (NRF), by the Ministry of Education, Science and Technology- grant #2012-0006565 and also Nano⋅Material Technology Development Program through the NRF of Korea- grant # 2012M3A7B4035095.
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