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We present difference-frequency stabilization of free-running distributed-feedback (DFB) diode lasers, maintaining a stable phase-lock to a local oscillator (LO) signal. The technique has been applied to coherent hybrid THz imaging which employs a high-power electronic radiation source emitting at 0.62 THz and electro-optic detectors. The THz radiation of the narrow-band emitter is mixed with the difference frequency of the DFB diode laser pair. The resulting intermediate frequency is phase-locked to the LO signal from a radio-frequency generator using a fast laser-current control loop. The stabilization scheme can be adapted readily to a wide range of applications which require stabilized laser beat-notes.
©2010 Optical Society of America
1. Introduction
Stable, and possibly tunable, laser synchronization techniques are often required in optics communications [1, 2], millimeter- and submillimeter-wave photonics [3, 4, 5, 6, 7], etc. In many cases, the radiation frequency of two or more lasers must be fixed, e.g., if specific atomic transitions have to be addressed [9]. Then, the stabilization efforts must begin at the level of each individual laser. In recent years, progress in (sub-)millimeter-wave technology has brought an increased interest in continuous-wave laser systems delivering only a stable difference frequency and not individual stable laser lines, which lowers the stabilization effort needed significantly. A well-established technique for laser difference frequency stabilization is the use of an optical phase-locked loop (OPLL) [9, 10]. Those systems require narrow-linewidth lasers, short loop propagation delays and wideband loop filters for proper operation. The upper limit of the stabilized difference frequency is usually given by the detector bandwidth.
In this paper, we introduce a robust and cost-effective solution for laser difference-frequency locking from MHz to THz frequencies, which is based on a heterodyne OPLL scheme. In our system, we take advantage of a very fast proportional-integral-derivative (PID) controller to lock the tunable beat-signal of a distributed-feedback (DFB) diode laser pair to a stable radio-frequency (RF) LO signal. Hereby the PID controller alters the driver current of one of the lasers while the other one remains free-running. In order to achieve stable difference frequencies in the THz range, we additionally use a highly stable continuous-wave (CW) THz emitter combined with a ZnTe crystal for electro-optic (EO) down-conversion [11].
The thermally stabilized DFB laser diodes feature a grating structure in the laser-active region restricting the emission spectrum to a single longitudinal mode. The lasers’ center wavelength is selected by temperature tuning and can be fine-tuned by adjusting the laser current. Consequently, the laser diodes have to be operated in a mode-hop-free sector to provide proper functionality of the laser stabilization scheme. DFB diode lasers provide mode-hop-free tuning ranges above 1 THz [12]. Besides the easier handling, due to the absence of optomechanical components, this is advantageous over external-cavity diode lasers, whose mode-hop-free tuning range typically ranges from several 10 to 100 GHz [13, 14].
On the other hand, the spectral width of DFB lasers is usually larger than that of external-cavity systems. Spatial hole-burning effects within the laser-active medium rapidly change the local charge carrier density and therefore the local refractive index which leads to a broadening of the linewidth to hundreds of kHz on a microsecond time scale [15]. In addition, residual temperature drifts and current noise induce slow laser frequency fluctuations from several MHz to a few ten MHz on time scales of milliseconds to seconds, respectively.
2. Experimental approach
We use a polarization-maintaining 2×2 fiber array to combine the radiation of the DFB diode laser pair (Fig. 1). One of the fiber outputs is directed to the laser control loop, while the other one is guided to the experiment. A photodetector with a bandwidth of 100 MHz receives the fiber-guided laser beat signal to serve the fast laser control electronics, which is provided with a stable LO signal at 10 MHz from a RF generator. The high-bandwidth output of the control device adjusts the current of one of the lasers. Thereby, we control the fast and slow fluctuations of this laser such that its frequency follows the freely fluctuating frequency of the second laser diode, offset by the frequency of the LO.
For this scheme to work properly, linewidths of the free-running lasers below 1 MHz and small loop propagation delays of at most several 10 ns are necessary. These two factors determine the overall performance of the OPLL [10]. In order to fulfill the requirements, short wiring, fast electronic components and a high control bandwidth are used. We employ two DFB diode lasers from TOPTICA Photonics, Model DL DFB, with integrated 60-dB optical isolators. Each laser provides around 100mW of maximum output power. Due to fiber coupling losses, roughly 50 % of the laser power is available after the fiber array. The lasers operate at wavelengths from 852.0 nm to 854.8 nm, and 854.3 nm to 857.1 nm, respectively. In both cases, the wavelength is selected by temperature tuning (~ 25 GHz per Kelvin), while the fast fine-tuning of the controlled laser is done via the laser current (~ 1 GHz per mA). A delayed self-heterodyne linewidth measurement [16] with a free-running laser indicates a linewidth of ~ 500 kHz on a 5-μs time scale. Before the laser synchronization electronics is activated, the lasers are temperature-tuned until the beat frequency corresponds approximately to the frequency of the RF generator. The received laser beat signal of the diode laser pair is fed into the laser control unit (“Fast Analog Linewidth Control”, FALC 110, TOPTICA Photonics), which is complemented by an additional frequency mixer. When the controller is activated, the photo-detected laser beat signal is mixed with the LO signal and the resulting product serves as error signal for the control electronics. The controller’s output drives the fast field-effect-transistor circuit of one of the lasers, which provides a fast control means of the laser current.
In our setup, the control loop is set to null the error signal, thus any phase/frequency fluctuations between the laser beat signal and the LO signal are compensated. Consequently, the laser difference frequency is phase-locked to the signal of the RF generator.
The FALC 110 module is designed for high-speed operations and exceeds the flexibility of a conventional adjustable PID controller by allowing for an individual selection of multiple corner frequencies. The device has a response time of less than 15 ns and reaches a -3-dB bandwidth of 100 MHz.
Figure 2 shows the transfer function of the controller for the settings selected for optimized performance. The gain is maximized at low frequencies (up to several kHz) where most of the phase noise occurs as a result of electric-circuit and mechanical resonances as well as thermal effects (for the resonance features, see also Fig. 3(b)). This comes at the price of a steep gain roll-off at tens of kHz. With the help of the derivative element of the controller, one generates, however, a second, weaker gain maximum at about ten MHz, thus stabilizing the control loop well into the MHz range. All settings have to be chosen such that the phase lag / phase lead of the gain remains at all frequncies below 180° in order to avoid positive feedback. At the chosen settings, the maximal phase lag is 130° (at 6 kHz) and the maximum phase lead 50° (at 2 MHz).
3. Synchronization characteristics
Figure 3(a) compares the spectra of the laser beat frequency acquired without and with stabilization. In the free-running case, the beat signal drifts over several MHz on a ms time scale generating the broad signal band shown in the plot. On a time scale longer than the measurement time, the whole band drifts over tens of MHz. The drift is stopped upon locking and is replaced by a narrow beat signal band. The inset of Fig. 3(a) depicts a high-resolution measurement. The linewidth of the stabilized beat signal is found to be limited by the 10-Hz resolution bandwidth of the spectrum analyzer. Such a narrow line is evidence that the beat signal is phase-locked to the oscillator. The periodical side peaks seem to be harmonics of the typical 50-Hz noise of the environment. Coming back to the main panel of Fig. 3(a), one finds that the signal-to-noise (SNR) ratio is ~ 40 dB. The noise peaks at 10 MHz ± 3 MHz can be explained by the limited frequency modulation (FM) characteristics of the DFB laser diodes.
Fig. 3. a) Comparison of the laser beat signal with and without stabilization to a LO frequency of 10 MHz (RBW: 10 kHz, no averaging), Inset: High-resolution measurement in the region 10 MHz ± 0.5 kHz for the locked case (RBW: 10 Hz, no averaging); b) Phase-noise diagram of the phase-locked laser beat signal; The measurements were taken at TOPTICA Photonics AG in Munich.
We obtain a phase noise spectrum which is essentially flat over the stabilization range (Fig. 3(b). Mechanical vibrations and electronic circuit resonances are the likely cause of the noise signature in the frequency regime between 100 Hz and 10 kHz. The graph shows a roll-off above the band edge of the control loop at 3 MHz, due to the falling noise level of the beat signal.
In the following, we demonstrate the locking of a diode laser pair to a 620-GHz electronic emitter, and application of the coupled system for THz imaging.
4. Adaption of the radio-frequency laser synchronization scheme to the THz regime
The synchronization scheme presented above has been adapted to our recently demonstrated hybrid continuous-wave THz imaging system [17, 18, 19]. The hybrid concept is a heterodyne technique, which combines CW THz radiation of a highly stable narrow-band micro-electronic emitter with modulated laser radiation for EO sampling [11]. It can be performed with either femtosecond or two-color CW lasers. Only the first case is published until now, the second is the subject of the present publication. In the case of the femtosecond source, a Ti:sapphire laser was used for the read-out of the THz-field-induced birefringence of the EO ZnTe crystal. Hereby, the THz radiation is stroboscopically sampled at the pulse repetition rate of the laser for down conversion of the THz frequency into the RF range. Therefore, this technique enables THz detection with conventional photo-detectors and allows phase-sensitive measurements by applying a reference receiver. The hybrid system provides parallel read-out capabilities [20, 21] and consequently holds the potential for real-time imaging.
While the pulsed-laser approach, due to the high stability of both the laser’s repetition rate and the micro-electronic THz oscillator, doesn’t require any active synchronization [17], these hybrid systems rely on comparatively expensive and bulky Ti:Sapphire laser systems in stable lab environments. To overcome these drawbacks, the pulsed-laser is replaced by the DFB diode laser pair with the synchronization scheme described above.
For this approach, the lasers are operating at maximum output power and are tuned to a difference frequency close to the frequency of the THz radiation. Thereby, the EO read-out of the incident THz radiation with the two-color laser beam results in an intermediate-frequency (IF) signal equal to the difference frequency between laser-beat and THz signal. However, it is necessary to stabilize the beat-note because of the strong frequency fluctuations of the DFB lasers. An illustration of the hybrid THz imaging setup which is an extension of the one displayed in Fig. 1 is depicted in Fig. 4.
Fig. 4. Setup of the continuous-wave hybrid THz imaging system. The beat-note of the radiation of the two DFB lasers is phase-locked to the radiation of a 620-GHz emitter.
The implemented quartz-stabilized narrow-band emitter is a commercial product of Radiometer Physics GmbH [22] and consists of a synthesizer-driven W-band source followed by a power amplifier and a 6-× frequency multiplier. It provides 1.1 mW at 0.62 THz. In our setup, it serves both a reference and an imaging branch, each employing an EO detector unit readout by the fiber-guided two-color laser light. Each detector block (represented in Fig. 4 by the boxes marked as “Ref. det.” and “Sig. det.”) contains a 2-mm-thick 〈110〉-oriented ZnTe crystal, a quarter-wave plate, a polarizing beam-splitter and a differential photo-detector pair with a bandwidth of 100 MHz. In the detector blocks, the laser light travels in free space; the THz radiation is superimposed with the optical beam via a dichroic indium-tin-oxide reflector [23].
As in the first synchronization approach, a RF generator provides a 10-MHz LO signal for the modified FALC laser controller, which is connected to the reference detector unit. When the lasers are tuned to a beat frequency close to the THz signal, the received EO signal can be captured by the laser control electronics and is thereby phase-locked to the THz oscillator with a frequency offset given by the RF signal.
Fig. 5. a) Frequency spectrum of the phase-locked IF signal (RBW: 9 kHz, limited by the measurement device); b) Oscillogram of the IF signal; The measurements were taken at the University of Frankfurt.
Figure 5(a) illustrates the frequency spectrum of the synchronized IF signal. The central 10-MHz resonance has a linewidth of 9 kHz. This value corresponds to the limited resolution bandwidth of the spectrum analyzer, which was used for this measurement. The real linewidth of the locked signal is hence smaller than this value. Corresponding to the narrow linewidth, the repeated time traces shown in the oscillogram of Fig. 5(b) are phase stable except for some sub-oscillation-period jitter. The jitter’s build-up over two or three oscillation periods (0.2 – 0.3μm) is indicative for its origin which is found in the MHz-bandwidth noise pedestal, on which the phase-locked narrow-band line of Fig. 5(a) is sitting.
While a portion of the collimated THz beam is delivered to the reference arm, the other part is focused onto the object to be imaged. The reflected radiation is guided to the detector of the imaging branch. The resulting IF signal is fed to the signal input of a lock-in amplifier, whose reference signal is provided by the LO. Both amplitude and relative phase of the THz radiation returning from the object under test are resolved.
Fig. 6. Measured intensity (b) and phase (c) images of a European 50-cent coin (a), and topographic image (d) numerically derived thereof. Overall measuring time: 15 min.
Figure 6 shows x-y single-pixel raster-scan images of a European 50-cent coin moved in the focal plane of the THz beam. The intensity image of Fig. 6(b), obtained during a single scan with a lock-in time constant of 100 ms per pixel, exhibits a dynamic range of 40 dB. The corresponding phase map in Fig. 6(c) shows phase jumps which indicate that the coin was slightly tilted. A phase unwrap algorithm and a tilt correction are applied to generate the surface topographic image of the coin presented in Fig. 6(d).
5. Conclusion and outlook
In conclusion, we have demonstrated phase-locking of the beat signal of two DFB diode lasers to two types of electronic oscillators, a RF source and a THz emitter. The DFB lasers are not frequency-stabilized individually. By only locking the beat-note with the help of a heterodyne OPLL, the stabilization scheme promises the realization of cost-effective and compact measurement systems. The concept can be adjusted to be applicable for narrow-band THz spectroscopy or the synchronization of radio-antenna arrays (e.g. in the ALMA project [24]). Due to the parallel read-out capability of coherent electro-optic detection, fast hybrid THz imaging is possible. The concept even holds promise for real-time imaging. The performance of multi-pixel electro-optic detection is fundamentally limited by the laser shot-noise. Therefore, more laser power is desirable for parallel read-out in order to enhance the image frame-rate while maintaining a reasonable dynamic range. For this purpose, the DFB laser pair can be equipped with a tapered laser amplifier to reach power levels of several hundred mW, while maintaining the spectral properties of the seed lasers [8].
Acknowledgements
We are grateful for support by Torsten Löffler (SynView GmbH) and Radiometer Physics GmbH. This work has been funded by the LYNKEUS project (FKZ 16SV2304) of the Federal Ministry of Education and Research Germany (BMBF).
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