Signals measured with Chirped Laser Dispersion Spectroscopy (CLaDS) setup implemented with an intensity modulator are analyzed. We investigate the signal amplitude dependence on the modulator bias voltage and the signal generator output power. Potential strategies for signal retrieval are discussed. We demonstrate that choosing a bias voltage, an RF generator output power and a demodulation frequency is critical for CLaDS and strongly affects its performance.
© 2015 Optical Society of America
Chirped laser dispersion spectroscopy (CLaDS) is a gas sensing technique introduced in 2010 by Wysocki and Weidman . In contrast to methods typically used for sensitive and selective trace-gas detection (such as direct laser absorption spectroscopy , wavelength modulation spectroscopy , photoacoustic spectroscopy , cavity ring-down spectroscopy  or integrated cavity output spectroscopy ) which target absorption fingerprints of selected molecules, in CLaDS analyte concentration is retrieved through measurement of optical dispersion. In CLaDS optical waves separated in frequency by Ω propagate through the gas sample and are focused onto square-law photodetector where they produce a heterodyne beatnote. Phase of this beatnote is affected by the molecular dispersion which is proportional to the target molecule concentration. When these optical waves are frequency chirped across the molecular transition signal encoded in phase domain can be conveniently detected as frequency modulation of the carrier Ω (which is additionally enhanced by the factor proportional to the chirp rate) . The biggest advantage of CLaDS is its exceptional immunity to amplitude noise and transmission fluctuations. Because spectroscopic information is encoded in frequency of the beatnote (not in amplitude) signal in CLaDS does not require any power normalization (known from WMS ) even when significant optical/electrical power fluctuations are present [7, 8]. This makes CLaDS particularly suitable for open-path remote or standoff sensing [9, 10]. Moreover, while the molecular dispersion affects the frequency of the beatnote, the molecular absorption modifies its amplitude. Therefore, the absorption spectrum can also be retrieved with CLaDS (independently from the dispersion spectrum) using AM demodulation of the beatnote signal.
In the initial stage of its development CLaDS was implemented with an acousto-optical modulator (AOM) as a frequency shifter. By combining light directly form the distributed feed-back (DFB) semiconductor laser with the wave shifted by ΩAOM a dual-color beam was created. In this arrangement spectroscopic CLaDS signal is retrieved after FM-demodulation of the beatnote at ΩAOM. The drawback of this initial setup is the available frequency shift: usually it is in the range between 50 and 200 MHz, far below the typical linewidth of the molecular transitions in mid- or near-infrared at atmospheric pressure (few GHz). Small frequency spacing results in the reduced signal amplitude as described in . This drawback was mitigated in the CLaDS setup implemented with high-speed intensity modulator. Those can be used in near-infrared to produce an optical spectrum consisting of a carrier and two sidebands, with the sideband separation up to several GHz [11, 12]. This approach is simple in implementation and allows obtaining frequency spacing Ω comparable to the linewidth of the measured transition. Unfortunately, because signal is retrieved from two beatnotes (carrier and sideband + Ω, carrier and sideband -Ω) CLaDS amplitude is reduced by half. This signal reduction was experimentally demonstrated in  and theoretically explained in . Full signal amplitude and flexibility in choosing frequency spacing Ω can be obtained when dual parallel Mach-Zehnder modulators (DPMZMs) are used . Those can produce optical spectrum consisting of a carrier and a single side-band, thus only one RF beatnote is being generated and none of the signal is lost. However, given the cost of DPMZM and its complexity (requires three bias voltages to be adjusted) this configuration does not seem to be suitable for field applications, where stability and robustness are critical. In this respect layout with high speed intensity modulator producing three waves (carrier and two sidebands) seems to be the most reasonable compromise.
In the previous papers describing CLaDS implemented with high speed intensity modulator there was no information on how RF power driving the modulator was chosen and if the modulator bias voltage was controlled in any way. Here we demonstrate experimentally that these two parameters are critical for CLaDS operation since they can affect both the signal amplitude and, potentially, its long-term stability. The impact of the modulator bias and the RF power applied to the modulator on the dispersion signal amplitude is analyzed. We also demonstrate a more advanced numerical model of CLaDS. A very good agreement between this model and the experimental results is obtained.
2. Experimental setup and numerical model
2.1. Experimental setup
Figure 1 shows a schematic diagram of the experimental setup used in this work. A light from the DFB laser diode operating around 1552 nm was sent through a high-speed zero-chirp X-cut Mach-Zehnder intensity modulator (JDS Uniphase, model 10023707, RF port Vπ = 6V), a gas sample (fiber coupled hydrogen cyanide cell, 10 Torr) and focused onto the fast biased photodiode (Thorlabs DET08CL). Laser diode was thermally tuned to target a hydrogen cyanide (HCN) transition at 1551.31 nm. A modulator was driven at the frequency Ω = 2 GHz with a signal generator (Agilent E8257D, maximum RF power of 25 dBm). RF beatnote created at the output of the photodiode was demodulated using an RF spectrum analyzer (Rohde&Schwarz FSVR). Frequency demodulation (FM demodulation) and amplitude demodulation (AM demodulation) were used to retrieve CLaDS dispersion and absorption spectra, respectively.
2.2. Numerical model
In CLaDS spectroscopic signals are encoded into the RF beatnote amplitude (absorption spectrum) and frequency (dispersion spectrum). In  Wysocki and Weidman described CLaDS signal generation assuming that only one RF beatnote is created (between carrier and frequency shifted wave). In the following papers signal generation from the intensity modulated light wave was described [12, 13]. In this case it was assumed that the optical field consists of a carrier and two sidebands, and CLaDS signal is encoded into the pair of beatnotes. Unfortunately, this simple model that takes into account three waves is valid only when the intensity modulator is driven with relatively weak RF signal and the device is operated in its quasi-linear range (at the quadrature point for which bias voltage = Vquad). Otherwise higher order sidebands also contribute to the CLaDS signal generation and affect CLaDS amplitude.
In this paper we study CLaDS amplitude at different conditions (modulator bias voltage and RF power driving the modulator) and more advanced numerical model is needed to correctly recreate measured signals. A model proposed in this work takes into account nonlinear transfer function of the Mach-Zehnder modulator (Fig. 2). In theory, the optical spectrum at the output of this modulator consists of a carrier and infinite number of optical sidebands separated from the carrier by M × Ω (M is integer). In [12, 13] only first-order sidebands were taken into account for the signal analysis (M = + 1 and −1). A model used here includes E-fields of a carrier (E0) and eight sidebands (EM, M = ± 1, ± 2, ± 3, and ± 4). Amplitudes and phases of those nine waves are not chosen arbitrary but they are calculated for a given bias voltage and RF power of the signal driving the modulator. (Note: presented model was limited to four pair of sidebands based on our experimental observations: in practice higher order sidebands can be ignored during the simulations as they do not appear at the output of the modulator even for the strongest available driving signals.)
The target molecular line in our experiment was the HCN transition at 1551.31 nm. It was modeled (absorption and dispersion) using Voigt profile and HCN parameters provided in  (Doppler broadening of 450 MHz and pressure broadening of approximately 81 MHz/Torr). Based on the  (Eq. (2-4) the CLaDS dispersion and absorption signals were calculated as and , respectively, where
3. CLaDS signals under different experimental conditions
3.1 Detection at 1 × Ω
Signal demodulation at Ω is the most straightforward detection scheme for CLaDS implemented with intensity modulator driven at Ω . Figure 3 shows a set of CLaDS spectra (both dispersion and absorption) recorded for different bias voltages and for two different RF powers applied to the modulator (10 and 25 dBm; relatively low and high, respectively). Excellent agreement between experimental data and numerical model is obtained (for absorption spectra baseline was removed after fitting with a 3rd order polynomial function). In this 1 × Ω approach the two dominant beatnotes are present: between a carrier and a sideband at + Ω and between a carrier and a sideband at –Ω. For low RF powers nonlinearities of the modulator are not visible and other beatnotes (even if present) do not contribute significantly to the CLaDS signal. However, when RF power is increased beatnotes created between a sideband at + Ω and a sideband at + 2 × Ω and between a sideband at –Ω and a sideband at –2 × Ω become visible. Because of the phase relations between these waves their contribution eventually results in the increased CLaDS amplitude.
Figure 4 shows the measured CLaDS signal amplitude vs. bias voltage for two RF powers (10 and 25 dBm) recorded for different bias voltages and for unchanged experimental conditions. Gray area indicates bias voltages away from the quadrature positions for which the beatnote power at 1 × Ω significantly drops (modulator is operated at the maximum or minimum of its transmission curve). Small beatnote level makes these bias voltages practically unusable for 1 × Ω CLaDS measurements as they result in unstable and unreliable operation (signal amplitude strongly fluctuates). On the other hand, when modulator is driven anywhere around its quadrature point (Vbias = Vquad ± ~1.8V, where Vquad is the bias voltage at the quadrature position, indicated in Fig. 4 with arrows) CLaDS signal is almost immune to changes of the bias voltage. On the other hand, signal amplitude dependence on the RF power applied to the modulator is observed: as the electrical RF power is increased measured CLaDS amplitude grows. The origin of this effect is clearly visible in Fig. 3(f)-3(j): by increasing modulation depth sidebands at ± 2 × Ω become stronger (this is also schematically shown in Fig. 4); as they beat with the sidebands at ± 1 × Ω, they contribute to the total signal amplitude and enhance it. For the maximum power of the available signal generator ( + 25dBm) we obtained the increase of the signal amplitude by more than a half.
Obviously, enhancing the CLaDS signal through increasing the amplitude of the ± 2 × Ω sidebands is limited. Because the modulator transfer function is periodic, at sufficiently large RF powers it would generate higher order sidebands instead of ± 2 × Ω, thus no further increase in CLaDS signal will be obtained. In practice, however, when using typical, commercially available Mach-Zehnder modulators these conditions won’t even be achieved. For those devices RF power of 25 dBm is already a substantial value and applying stronger signal will damage the modulator instead of enhancing the CLaDS signal amplitude.
3.2 Detection at 2 × Ω
The concept of the CLaDS signal demodulation at 2 × Ω was previously mentioned in . This approach is conceptually more complex comparing to the demodulation at 1 × Ω since more optical waves are involved in the creation of CLaDS signal. In Fig. 5 a set of spectra retrieved through the beatnote demodulation at 2 × Ω is presented, recorded for different bias voltages and two different RF powers applied to the modulator. Again, very good agreement between model and measured data is obtained.
Particularly interesting is the dependence of the 2 × Ω CLaDS amplitude on the bias voltage, shown in Fig. 6 for two different powers of the signal applied to the modulator (10 and 25 dBm). Similar to Fig. 4 gray areas indicate bias voltages practically unusable for 2 × Ω detection. For those values of Vbias the dispersion signal amplitude is very unstable and is not suitable for precise measurements: 1) low beatnote level results in higher demodulation noise, and 2) due to strong dependence of the signal on the bias voltage even the smallest change of the modulator operating conditions leads to a very large change in the signal shape and amplitude. The resulting available bias voltage range for the 2 × Ω demodulation is small, approximately ± 0.8V around maximum or minimum points of the modulator transmission curve. Interestingly, signal behavior at these two positions is significantly different. When bias voltage around maximum transmission point is chosen (in the presented case between −3.5V and −2V, and between 6V and 8V) the optical field consists of three main components: carrier and two sidebands at ± 2 × Ω. As a result the obtained CLaDS amplitude is around 3.2 kHz, very close to the amplitude after demodulation at 1 × Ω in the low-power approach (Fig. 4(a), magenta color). The main differences between these cases are the sidebands separation (compare spectra in Fig. 5(a) and 5(e) with those in Fig. 3) and the signal dependence on the RF power applied to the modulator (when demodulating at 2 × Ω CLaDS signal amplitude does not change with the RF power; this is because even for the highest available RF power sidebands at 4 × Ω are very weak and do not contribute to the signal creation). On the other hand, when modulator is biased at the minimum transmission point (in the presented case between 1V and 3V) the optical field consists of two main waves: sideband at -Ω and sideband at + Ω. When they reach photodiode only one beatnote is created, thus there is no reduction of the signal amplitude . Additionally, when higher RF power is applied to the modulator sidebands at ± 3 × Ω appear in the optical spectrum and they can further enhance the signal amplitude (compare spectra in Fig. 5(c)-5(d) and 5(h)-5(i)).
4. Summary and conclusions
In this paper we have shown results of the experimental studies on the signal strengths and shapes in CLaDS implemented with an electro-optical intensity modulator. This optical layout for CLaDS was demonstrated previously as simplified version of the initial setup (based on acousto-optical modulator). It is suitable especially for near-IR applications (1.5-2 um) where high speed intensity modulators are available. In previous papers on CLaDS with an intensity modulator it was assumed that the optical spectrum after the modulator consists of a carrier surrounded by two sidebands. The two beatnotes were created which led to the reduced signal amplitude (half of what could be achieved with AOM-based approach).
Here we experimentally investigated how the signal amplitude in the intensity modulator-based CLaDS depends on the modulator parameters, when driven at the frequency Ω. We have found that when FM demodulation at 1 × Ω is used to retrieve CLaDS signal:
- -modulator should be operated around its quadrature points (Vbias≈Vquad) where the dependence of the CLaDS signal amplitude on the bias voltage is very small; this is very convenient when standard, commercially available modulator is used (usually Vquad≈0V),
- -biasing the modulator at the maximum or minimum of its transmission curve is not suitable for 1 × Ω CLaDS demodulation; at those positions RF beatnote at 1 × Ω is weak which results in high demodulation noise and signal amplitude is prone to large fluctuations,
- -signal amplitude can be enhanced by applying higher RF power to the modulator. Higher RF power produces additional sidebands in the optical spectrum after the modulator. Those sidebands generate other beatnotes which constructively contribute to the CLaDS signal and enhance its amplitude. For the modulator used in our study changing the power of the driving signal from 10 to 25 dBm led to >50% increase of the CLaDS signal amplitude.
We also analyzed CLaDS signal retrieval through FM demodulation of the beatnote at 2 × Ω. In this case we have found that:
- -demodulation at 2 × Ω is only feasible when modulator is biased at the maximum or minimum of its transmission point (a quadrature position should be avoided as explained in section 3.2),
- -a shown in Fig. 6, when the modulator is biased at the maximum of its transmission it produces similar signal amplitude as in 1 × Ω demodulation approach but with no visible dependence on the power applied to the modulator,
- -when modulator is biased at the minimum of its transmission significant increase in the signal amplitude can be obtained, even above level achievable with the AOM-based CLaDS; this is thanks to the multiple beatnotes contributing constructively to the signal amplitude.
Based on the presented results three strategies for the intensity modulator-based CLaDS can be proposed. First is the FM-demodulation at 1 × Ω and with low power applied to the modulator. In this case any drifts of the bias voltage or the signal generator output power will have very small impact on the CLaDS signal amplitude. Second strategy would be applying more power to the modulator and still demodulating at 1 × Ω. This approach has two advantages: not only CLaDS signal amplitude is enhanced but also stronger RF beatnote is recorded (this can further increase signal to noise ratio by lowering noise associated with FM demodulation ). Unfortunately, it also makes signal amplitude much more sensitive to drifts of the RF generator output power which can eventually affect system long-term stability. In the third strategy CLaDS signal is retrieved through the beatnote demodulation at 2 × Ω. In this approach large signal amplitude is obtained (even larger than in the AOM-based setup) without compromising the noise level (when modulator is driven with strong RF signal and properly biased, beatnote at 2 × Ω is strong and FM-demodulation noise is comparable to the 1 × Ω scenario). However, this approach also requires both bias voltage and RF generator output power to be very stable. Any drifts (especially changes in the modulator bias) will immediately affect the long-term stability of the spectroscopic instrument (re-calibration will be necessary). Unfortunately, those drifts are typical for LiNbO3 modulators [17–19]. Regardless of which implementation of CLaDS is chosen, for applications where high accuracy is required, one has to make sure that the modulator bias as well as the RF power applied to the modulator are chosen properly and are stable (additional bias stabilization circuit would be helpful).
Presented work was supported by the Homing Plus award 2012-6/8, funded by the Foundation for Polish Science and co-financed by the European Regional Development Fund.
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