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We propose a hybrid architecture for continuous wave terahertz spectroscopy employing a conventional two color photomixing system combined with a quasi time domain spectrometer, driven by a multimode laser diode. This approach fuses high spectral intensity with broadband frequency information and overcomes the ambiguity of standard continuous wave thickness measurements.
©2010 Optical Society of America
1. Introduction
The high potential of terahertz (THz) technology induced a dramatic increase in the research effort in recent years and a variety of different system architectures were proposed. Especially optoelectronic THz systems, where infrared laser radiation is converted into THz waves, have been successfully employed in a plethora of application scenarios, ranging from art conservation [1–3] over quality inspections [4–6] to biological and chemical related areas [7–9]. Besides that, the progress in THz system engineering enabled a wide range of scientific investigations, e.g. to deeper understand carrier dynamics [10,11], or cellular processes [12].
The most common THz spectrometers are THz time domain spectroscopy (TDS) systems based on down-conversion of ultrashort femtosecond laser pulses into broadband THz pulses. Optical probe pulses from the same laser source are employed for detection. To record the time domain waveform of the THz signal, an optical delay line is used to mechanically change the path length of the laser radiation that is incident onto the detector antenna in respect to the THz wave. Please see [13] for a comprehensive review. While this technique allows for a broadband sample characterization with a single shot measurement, its major drawbacks are the difficult handling and the high price for the femtosecond laser source.
In an alternative approach, laser diodes that emit continuous wave (cw) laser radiation are utilized to generate cw THz waves by difference frequency mixing. These so called photomixing systems have the neat advantage of being compact and fairly cheap compared to TDS systems and offering a high spectral resolution at the same time. The cw signal is usually generated by photomixing of dual color laser radiation in a photoconductive antenna (PCA) made of low-temperature-grown (LT) GaAs [14–16]. However, in contrast to a pulsed THz spectrometer these systems lack the ability to measure thickness and dielectric THz properties simultaneously. In the case of samples thicker than the THz wavelength a 2π phase ambiguity distorts the extracted thickness information [17].
Recently the authors introduced a broadband quasi time domain spectroscopy (QTDS) technique [18] based on inexpensive, multimode (MM) laser diodes. Here, the individual modes of the lasers are mixed in a PCA to generate multiple THz frequencies. Due to the equidistant mode spacing of typical MM laser diodes in the range of several GHz, most of the generated THz mixing products are degenerate in frequency and thus, the THz wave comprise a frequency comb like spectrum [18]. The resulting signals of QTDS spectrometers provide not only information over a wide range of frequencies with just a single shot measurement but exhibit also a pulse like waveform that allows for time domain signal processing like time of flight analysis [19,20]. However, the spectral resolution is limited by the mode spacing of the laser source.
In this paper we present the combination of the conventional, single frequency cw THz spectroscopy and the QTDS approach. Overlapping the beams of a freely tunable two color laser setup and a MM laser diode on the PCAs generates a hybrid THz signal, consisting of both, a tunable high intense spectral component (cw signal) and broadband pulses (QTDS signal). Thus, this combination merges the advantages of conventional cw systems like the high spectral brightness and an unbeatable frequency resolution with the broadband frequency information and the superior thickness determination ability of QTDS systems at low costs.
2. Theory
The theory behind photomixing THz systems is well studied [16]. In a standard photomixing spectrometer, driven by a two color laser system with a difference frequency Δf, the resulting THz signal ID is a function of the path length difference between emitter and detector path, ΔX, and exhibits a sinusoidal like shape:
where A(Δf) is the spectral system efficiency, P1 and P2 are the optical powers of the two laser modes and c0 is the speed of light.The case of mixing multiple laser modes has been thoroughly investigated as well [18]. For an equidistant mode-spacing of δf, the resulting THz signal can be described by:
Here, M denotes the amount of modes and P the total power of the laser radiation that is assumed to be uniformly spread over the multiple laser modes. Since the THz signal is not a function of the random phase relation between the individual laser modes, the signal exhibit a pulse like shape [18].It is interesting to learn that just those components of the THz wave induce a detectable photocurrent in the optically modulated detector antenna, which are generated by the same laser modes at the emitters position. This allows for combining two different laser sources to drive the THz spectrometer without crosstalk. Consequently, it is possible to overlap a tunable two colors laser system and a MM laser diode. Both will generate their characteristic signals, a narrow band sine on the one hand and broadband pulses on the other. If the two laser systems operate at different wavelengths, e.g. in the visible and the infrared regime, the corresponding laser modes are spaced by more than 100 THz. Thus, there will be no mixing between them that generates THz waves due to the low pass characteristics of the photoconductive antennas [18,21]. Alternatively, different polarization could be employed to suppress cross mixing. In either case, the signal will be the superimposition of the two basic waveforms and the detected photocurrent will take the form:
Figure 1 shows theoretical waveforms and the corresponding spectra for a hybrid system consisting of a two color laser system and a MM laser diode with a mode spacing of 25 GHz. For the simulations we have assumed a 100 µm dipole antenna that’s frequency characteristics can be described by a simple model:
where the first term describes the low pass characteristics with τ as the carrier lifetime in the range of 100 fs [22]. The second term regards for the characteristics of the dipole shape with f0 as resonance frequency.
Fig. 1 Simulated THz signals (a) and the corresponding spectra (b) of the proposed hybrid system approach. In the case of a two color laser system excitation, a pure sinusoidal signal is generated, inhibiting a high spectral brightness. The signal of the MM laser diode driven spectrometer consists of a pulse train with a THz frequency like spectrum. The hybrid system combines both characteristics.
The resulting waveforms consist of a sinusoidal component the frequency of which is determined by the adjustable difference frequency of the two color laser and a pulse train originating from the MM laser diode. Due to the antenna characteristics, the sinus amplitude decreases in respect to the pulses amplitude for higher frequencies. However the narrow line width of this component results in a high spectral brightness compared to the QTDS component as seen in the spectra. Consequently, the spectral signal to noise ratio of the cw component is superior to that of the QTDS component. In the case of a noisy background this allows for an accurate sample characterization at the cw frequency while the QTDS signal can be used to eliminate the 2π ambiguity.
3. Measurements and results
To physically implement the hybrid approach, several possible ways exist to unite the two optical beams. The most practical ones are either to use orthogonal polarizations or to merge the beams through a dichroic mirror at different wavelengths. The latter has the upside of generating no parasitic mixing products between the cw and the QTDS signal due to the high wavelength discrepancy without ensuring a perfect orthogonal polarization between the laser beams.
For the measurements we employed a tunable two color laser system operating around 852 nm. The system consists of two DFB lasers that can be tuned in the range of 3 nm. In the free running system, the linewidth of each laser mode is about 3 MHz with an accuracy of the adjusted difference frequency in the range of 1 GHz. Using an electronic frequency stabilization based on a quadrature interferometer (“iScan” [23]), the linewidth and thus the accuracy of the difference frequency can be optimized down to 1 MHz [23]. As multimode laser source we utilized a laser diode emitting at 658 nm that exhibits a mode spacing of 25 GHz.
The two laser beams from the two laser sources are superimposed using a dielectric dichroic mirror that is nearly transparent for one wavelength and highly reflective for the other. Afterwards, the combined laser radiation is divided by a beam splitter into two parts. One of them is directly guided and focused onto the emitter antenna. The other one is guided over a linear translation stage to the detector antenna. Both antennas consist of LT-GaAs and exhibit a 100 µm dipole shape. The system is illustrated in Fig. 2 .
Fig. 2 Schematic of the hybrid CW THz System. A two color laser system and a MM laser diode are superimposed in a dichroic mirror. The resulting laser beam is divided into two parts by a beam splitter (BS). One of the beams is focused onto an emitter PCA, the other one is guided over a delay stage and then focused onto a detector PCA.
Figure 3 shows the detected electrical field versus the time delay for three different difference frequencies (220 GHz to 350 GHz and up to 490 GHz) of the cw system. The QTDS MM laser diode was kept at a constant optical output power and temperature. Due to the PCA’s lower conversion efficiencies at higher frequencies the amplitude of the cw signal decreases as can be seen in the figure.
Fig. 3 Measured THz signals of the hybrid system for different difference frequency of the two color laser system ((a): waveforms, (b): spectra).
To illustrate the practical advantage of the hybrid cw approach, we employed the system to analyze two different samples. Placing a dielectric material into the THz beam path induces a phase shift and reduces the amplitude due to reflection and absorption losses. Even a thin silicon (Si) wafer results in a phase retardation larger than one period of the cw signal. For an even thicker sample (approx. 6 mm thick silica glass) the retardation is in the order of several cw periods (cf. Fig. 4 (a) ).
Fig. 4 (a). THz signal through a Si wafer and silica glass compared with the reference measurement. The difference frequency of the two color laser system was set to 500 GHz. (b): The spectral amplitude of the signals. (c): The phase shift between reference and sample measurements.
Thus, the phase information of the cw component alone does not allow for an accurate characterization of the sample due to the 2π ambiguity. Yet, if the time shift of the pulses in the hybrid signal is considered additionally, an absolute measurement of the phase and thus, the sample’s dielectric properties or thickness is possible.
Our combined time domain - frequency domain approach for the phase extraction is the following: First we determine the time delay of the QTDS pulses Δtp between the sample and the reference measurement. Then we obtain the phase difference Δφcw at the frequency fcw of the cw component with a Fourier transformation of the detected THz signal. Latter one is affected by the 2π ambiguity in the case of thicker samples. The corrected phase shift Δφcw,cor can then be calculated by:
where the operation RD denotes for round down to the nearest integer of the argument. Since Δφcw,cor is the absolute phase shift induced by the sample, the absolute sample thickness T can be identified knowing its index of refraction n at the frequency fcw:Considering the corresponding refractive indices of the materials, the thicknesses of the investigated samples were determined from the measurements using EqS. (5-6) to be 6.25 mm (glass) and 550 µm (Si) which agrees with the values obtained by micrometer screw measurements.An alternative to this procedure is to utilize the phase shift of the QTDS frequency components to determine the absolute value Δφcw,cor as illustrated in Fig. 4(c). A linear interpolation trough the discrete phase values of the QTDS signal and the intersection at (f = 0, Δφ = 0) allows for correcting the 2π ambiguity at the cw frequency component in the case of low dispersive samples. Here, the integer N is determined so that the value of Δφcw,cor = Δφcw - 2π N is closest to the linear interpolation trough the QTDS components.
4. Conclusion
We presented a hybrid system approach for cw THz spectrometers that is capable of enhancing the information accessible from a single measurement. Monitoring the time delay of the QTDS signal pulses allows for overcoming the 2π ambiguity of conventional photomixing systems and thus, an accurate sample characterization is possible. In addition, the extreme compactness and the low costs for the multimode laser diodes offer the potential to easily upgrade existing cw system designs.
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