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We experimentally demonstrate thermo-optic locking of a semiconductor laser to an integrated toroidal optical microcavity. The lock is maintained for time periods exceeding twelve hours, without requiring any electronic control systems. Fast control is achieved by optical feedback induced by scattering centers within the microcavity, with thermal locking due to optical heating maintaining constructive interference between the cavity and the laser. Furthermore, the optical feedback acts to narrow the laser linewidth, with ultra high quality microtoroid resonances offering the potential for ultralow linewidth on-chip lasers.
©2009 Optical Society of America
1. Introduction
Toroidal microcavities (microtoroids) are of interest for a wide range of fundamental studies and applications, including cavity quantum electrodynamics [1] cavity optomechanics [2] compact optical elements for telecommunications [3] and high-sensitivity chemical/biological sensors [4]. Such interests arise from both the ultra-high quality factors Q (108) [5] achievable in whispering gallery mode (WGM) resonances, and the lithographic fabrication which leads to natural scalability and straightforward integration into microchip architectures.
Separately, there is a growing need for semiconductor lasers with high spectral purity for high-precision interferometry, high-resolution spectroscopy and metrology. Typically, unstabilized laser diodes have a broad linewidth of around 1-10 MHz due to the low Q of the laser cavity. The use of wavelength-selective optical feedback is a common technique for linewidth narrowing and wavelength tuning [6]; with the feedback achieved by a number of methods including the use of a diffraction grating [6], or resonant reflection from an external optical cavity [7–9]. Since external cavities are highly wavelength selective, they offer the advantages of improved laser line narrowing and long term frequency stability [10]. However, active control of the path length between the laser and the cavity is required to ensure constructive feedback, which to date has been achieved electronically.
In this Letter we demonstrate a new application of microtoroids as a wavelength-selective optical feedback element for semiconductor lasers by taking advantage of the back-scattered light from the microtoroid. This backscattered light is the result of surface imperfections and the long photon lifetimes in microtoroids which cause strong modal coupling between counter propagating modes [11]. Here we show that feedback both reduces the laser linewidth and improves the frequency stability over both very short and very long time intervals. Furthermore we utilize the thermal bistability present in silica microtoroids [12] to achieve thermo-optic locking between the laser and cavity for periods surpassing 12 hours, eliminating the requirement of electronic servo control. Although electronic servo control is a mature and sophisticated technology, the capacity to lock lasers without relying on such systems provides significant benefits, including for example reduced power consumption, higher control bandwidth, a simple and cost effective architecture, and removal of the requirement of spectral sidebands common to electronic locking.
2. Theory
Figure 1 shows a schematic of the thermo-optic locking configuration studied in this article. A laser diode generates an optical beam with electric field Ein(t). This field propagates a distance L through a material of refractive index n before being evanescently coupled to a WGM cavity, with input coupling rate of γin, and loss rate of γl due to imperfections such as surface scattering and material absorption. Degenerate counter-propagating WGMs are coherently coupled via optical back-scattering from scattering centers within the cavity, with the coupling rate characterized by the parameter g [13]. This coupling returns a fraction of the incident field to the laser diode which acts as an optical seed. In the frequency domain, the reflected field has the form [14]
and the field transmitted past the WGM cavity iswhere λ is the laser diode wavelength, γ = γl + γin is the total decay rate of the cavity, and ω and Δ are, respectively, the optical frequency detuning and WGM resonance frequency detuning from the free-running frequency of the laser Ω0. It can be shown from these equations that when the laser and cavity frequencies are matched () and the input coupling rate is chosen to satisfy, the transmitted field is fully extinguished and the reflected field amplitude is maximized [15]. This is termed the critical coupling point.The well known sensitivity of laser diodes to optical feedback is a result of the very flat free-running gain spectrum, the short cavity with low finesse, and the fact that when light is returned to the cavity the laser acts as a photodetector generating more carriers across the junction and affecting the net laser gain [6]. Given the flatness of the free-running gain spectrum, the interference between the emitted field Ein and the feedback field Efb provides the dominant source of gain modulation. The laser emission grows fastest at the frequency of maximum gain, quenching emission at other frequencies. Hence, the laser frequency is pulled to maximize the total electric field amplitude at the laser diode, . Including the phase shift due to propagation back from the cavity to the laser diode, the feedback field is
where is the free-spectral-range (FSR) of the weak-cavity formed in the path between the laser diode and the WGM cavity, and as is the experimentally relevant case the free-running laser wavelength λ0 = 2πc/Ω0 has been chosen to ensure constructive interference with the field emitted by the laser diode Ein(t) in the on-resonance case (). The locked laser frequency is given by where is the optical frequency detuning ω which maximizes. can be calculated analytically, however due to its complexity the analytical solution will be omitted here. The key result is that the feedback acts to pull the laser frequency towards the WGM resonance frequency as shown in Fig. 4 .
Fig. 4 Measurement and model of thermo-optic locking process for a toroid with γl/2π = 61 MHz. γin/2π = 31 MHz, g/2π = 8 MHz, and nL = 1.8 m. (a) Measurement showing the back reflected power immediately after obtaining lock. (b-d) Model of the thermally shifted microtoroid spectral response with the laser locking frequency indicated by the vertical line, corresponding to the three labeled points in the experimental data. The thermal detuning of the resonator was Δ/2π = 0, 20, and 40 MHz respectively for b), c), and d).
3. Experiment description
Figure 2 illustrates our experimental setup. To facilitate optical seeding, this work used a laser diode (ML925B45F, λ0 = 1553 nm, 5 mW maximum optical power) without an antireflection coating on the output facet. The frequency of the laser diode was tuned by varying the current and temperature, while the power and polarization of the laser diode output was controlled with an attenuator, and quarter- and half-wave plates, respectively. A reference laser was used to characterize the locking and to locate a suitable WGM resonance. The reference laser was an external cavity stabilized single mode semiconductor laser (New Focus Velocity® 6328), with a specified resolution bandwidth (RBW) of 300 kHz over a 50 ms integration time. This laser had a built in isolator and polarization controller, was temperature stabilized at a level of ± 1 mK, and was able to scan the large FSR (~11 nm) of the microtoroid without mode hopping.
Fig. 2 (Color online) Schematic of the experimental setup. Solid and dashed red lines respectively show optical paths in fiber and in free space. “A” indicates the point where switching between the reference laser and the laser diode is performed.
The output from either the laser diode (for optical feedback) or the reference laser (to characterize cavity resonances) was coupled into the tapered fiber through a fiber coupler at point “A” in Fig. 2. To avoid parasitic backscattering from the taper, we used a high efficiency (95%) adiabatic tapered optical fiber to couple the evanescent fields of the taper and the microtoroid. The microtoroid was positioned on a piezoelectric actuator which provided precise control of the coupling distance, and hence the coupling strength; and the optical path length between laser diode and microtoroid was nL = 1.8 m. The transmitted (forward-propagating) and feedback (backward-propagating) fields were detected with New Focus 125-MHz photoreceivers. The feedback field was split with a 50/50 fiber coupler so that the feedback into the laser diode could be monitored.
The spectral characteristics of the laser diode were determined by spectral analysis of the beat signal generated by interfering the laser diode and reference laser beams. The resulting spectrum is the convolution of the laser diode and reference laser lineshapes. As a consequence the measurement resolution is limited by the linewidth of the reference laser, which in our case was 300 kHz. The beat signal was measured on a 1 GHz bandwidth detector and monitored either on a spectrum analyzer (Agilent N9320A) to determine the laser lineshape, or a frequency counter (Stanford Research Systems SR620) to determine its Allan variance.
The microtoroids used in this study were manufactured with the same fabrication process as described in [5], with each chip consisting of forty microtoroids. Figure 3(a) shows the transmitted and feedback signals from the microtoroid for a typical resonance at 1560.4 nm in the critical coupling regime. In comparison, Fig. 3(b) shows the same WGM resonance in the under-coupled regime, where the tapered fiber has been pulled far from the cavity. Here, we see that the resonance splits into a doublet due to the coupling between the two counter propagating WGMs [11,16]. This mode splitting is a prerequisite for optical locking, indicating that the backscattering rate is larger than the loss rate of the system, and hence that significant backscattered power can be achieved. The observed behavior shows good agreement with the model of Eqs. (1) and (2), as shown by the fits in the figure; and provides a microtoroid intrinsic quality factor of Q = Ω/γin = 3.1 × 106.
Fig. 3 (Color online) Spectral response of the forward and backward propagating fields in the microtoroid in the critically coupled (a) and under-coupled (b) regimes. Top curve: forwards propagating field. Bottom curve: backwards propagating field. Solid lines: theoretical model of the transmission T = |ET/Ein|2 and reflection R = |ER/Ein|2 with g/2π = 33 MHz, Δ = 0, and γl/2π = 15 MHz; and input coupling rates of γin/2π = 36 and 5.4 MHz, respectively, for the critically coupled and under-coupled regimes.
4. Thermo-optic locking
As discussed in Section 2, optical feedback locks the laser diode frequency close to the WGM resonance, providing fast frequency corrections to the laser and significantly narrowing its linewidth. However optical locking alone does not resolve the problem of long term stability. The path length between the laser and the feedback element fluctuates over time scales longer than a millisecond due to environmental factors such as mechanical vibrations, thermal effects and air turbulence. This alters the phase of the feedback into the laser diode. If the interference between the feedback and the field in the laser diode becomes destructive, the laser will lose lock.
To achieve long term stability we use the thermal response of the microtoroid to preserve the constructive feedback required to keep the laser on WGM resonance. This thermal response has been used previously to lock a microtoroid onto a laser isolated from optical feedback [17]. In this case, optical heating due to light within the cavity causes thermal expansion and a corresponding shift in the microtoroid resonance frequency. In silica microtoroids the dominant effect is due to the temperature dependent refractive index of the material which results in a negative frequency shift with increasing temperature. Locking is achieved in a region where the laser frequency is detuned above that of the cavity. In this region, heating due to optical excitation of a cold cavity pushes the WGM resonance further from the laser frequency, and hence reduces the intracavity power and decreases the heating effect. At sufficient detuning, the rate of heat loss to the environment balances the optical heating and a stable equilibrium is established.
In our case the situation is more complex, with competition between the thermal and optical feedback based locking processes. As described in Section 2, the optical feedback locking optimizes the laser frequency with respect to the microtoroid resonance to maximize the constructive interference between the feedback and intracavity laser fields; whilst the thermal locking optimizes the microtoroid resonance frequency with respect to the laser frequency to balance optical heating and thermal heat loss. Since the optical locking occurs over fast timescales compared to the microtoriod thermal decay time, we can model this process assuming that the optical feedback locking dominates and the laser frequency is always such that the constructive interference between feedback and intracavity laser fields is maximized.
To understand the combined locking system, consider the case where the current and temperature of the laser diode are adjusted such that the free running laser frequency is matched to the WGM resonance (). This ensures constructive interference at the cold cavity resonance. Upon turn-on, the laser will immediately oscillate at this frequency, with the feedback power maximized. However, optical heating then drags the microtoroid resonance frequency lower, both decreasing the feedback power and degrading the constructive interference at the WGM resonance frequency. The laser frequency is consequently also pulled lower, but no longer aligns exactly with the microtoroid resonance since improved constructive interference can now be achieved off resonance. The result over time is a net negative shift in the laser frequency, and an exponential decay of both the microtoroid intracavity power and the feedback power; until, as with thermal locking alone, the optical heating and thermal heat loss exactly balance and a stable equilibrium is established. Figure 4(a) shows experimental measurements of the exponential decay of the feedback power into equilibrium, giving a thermal time constant of about ~40 µs. Figure 4(b-d) present models of the thermal pulling process which are well matched to the experimental observations.
5. Results
The power of the forwards and backwards propagating fields as the tapered optical fiber is brought towards the toroid is shown in Fig. 5 , with the free running laser frequency set to near the toroid resonance. One observes discrete power steps, as the laser diode locks to different toroid modes, with the backwards propagating light jumping from zero power initially to a maximum of 18 µW. At this point the taper position was held fixed, with the laser maintaining thermo-optic lock for periods upwards of 12 hours and both forwards and backwards propagating powers maintained stably, with fluctuations due only to only to variation of the tapered optical fiber position. Figure 5(c) shows the power reflected from the partial reflector with 10% reflectivity shown in Fig. 2. The linewidth of this beam is narrowed in the same way as those interacting with the toroid, however its intensity is insensitive to taper position fluctuations and therefore provides a highly intensity stable output. This output was used to characterize the linewidth of the stabilized laser through a beat frequency measurement with the reference laser.
Fig. 5 (Color online) Typical trace of the laser acquiring lock. (a) Forward- propagating power. (b) Backward-propagating power. (c) Laser diode power tapped off from partial reflector.
Figure 6(a) shows the beat signal between the free running laser and the reference laser, while Fig. 6(b) shows the beat signal of the laser when it is thermo-optically locked. The beat linewidth for the free running laser was observed to be in the range of 1.4-10 MHz full width half maximum (FWHM), depending on the laser diode temperature and current. On the other hand, the locked laser has an observed beat linewidth of 300 kHz (FWHM) limited by the linewidth of our reference laser. By comparison with other WGM/optical feedback locking experiments, it is reasonable to expect the actual locked laser linewidth to be significantly lower [2,18]. The locked laser was observed to transition between single and multimode behavior as the laser diode current was varied. Clear signatures of multimode operation were provided both by instability in the power tapped off the partial reflector, and the presence of multiple spectral peaks spaced by the FSR of the weak cavity formed between laser diode and microtoroid ωFSR/2π = 83 MHz. Single mode operation was achieved over the full 12 hours locking period through careful selection of the laser diode current.
Fig. 6 (Color online) Comparison of beat signals for thermo-optically locked and free running lasers. (a) Beat signal for unlocked laser (100 kHz RBW; 30 kHz video bandwidth). (b) Beat signal for locked laser (300 kHz RBW; 30 kHz video bandwidth). Solid lines: Lorentzian fit. (c) Root Allan variance of unlocked (solid blue line) and locked (dashed red line) laser beat signals (300 kHz RBW, 30 kHz video bandwidth).
Allan variance measurements of the beat signal allowed a frequency stability comparison to be made between the locked and free running lasers. In an ideal analysis, the reference laser used for such measurements should have at least an order of magnitude superior frequency stability. Since the absolute frequency stability of our reference laser was not accurately known, the results presented here for both locked and unlocked lasers provide only an upper bound on the Allan variance. Absolute quantification of the Allan variance is therefore not possible. However, it is still possible to compare the relative stability of the locked and unlocked lasers. Since, both Allan variance measurements would be identical if the instability of the reference laser was dominant; any differences in the measured Allan variances must be attributed to differences in frequency stability between the locked and unlocked lasers.
Figure 6(c) shows the Allan variance for the free running and locked laser diode over a 12 hour period. It is clear that over time scales less than about 5 seconds the stability of the locked laser, with the narrow linewidth, surpasses that of the free running laser. Over relatively long times, greater than thirty minutes, the locked laser also outperforms the monotonic frequency drift of the unlocked laser. Between these time scales the free running laser outperforms the thermo-optically locked laser diode. The degradation in the thermo-optically locked lasers performance is due to fluctuations in the path length between laser diode and the microtoroid. As the path length fluctuates, the lock adjusts the laser frequency to maintain constructive feedback. One can envisage overcoming this issue with a system of the type proposed by [18] where the microtoroid-laser diode distance is on the order of several millimeters. Indeed the whole laser waveguide and toroid system could be fabricated on the same thermally stabilized chip. This should dramatically reduce the Allan variance of the locked laser across the whole frequency spectrum.
Thermo-optic locking and line narrowing was demonstrated for several microtoroids on the same silicon chip with locked wavelengths spanning a 5 nm range, as shown in Fig. 7 . This on-chip architecture comprising of an array of microtoroids provides scope for integration of multiple stable laser sources at a range of output wavelengths; with the ability to thermally tune the cavity resonance [19] and control the free-spectral-range lithographically, enabling tuning and locking of the wavelength in such a conceived system.
Fig. 7 (Color online) (a) Schematic of single chip with multiple integrated microtoroids; with each cavity enabling low linewidth thermo-optically locked lasers at different wavelengths. (b) Wavelength spectrum from two different microtoroids with far separated cavity resonance wavelengths. (c) Typical beat spectra for each laser (300 kHz RBW).
Conclusion
In conclusion, we have demonstrated a new type of wavelength-selective thermo-optic feedback element based on microtoroid cavities. We demonstrate stable locking over twelve hours with a reduction in linewidth from 1.4 MHz to 300 kHz, limited by measurement resolution. The locking is achieved without any electronic locking techniques, and has immediate applications in areas which require intra-cavity enhancement of optical fields such as nonlinear optics based experiments and optical cavity based biological or chemical sensors. Such a device could enable low cost very low linewidth lasers and, in future, an on-chip array of high stability, low cost frequency references.
Acknowledgements
We thank Joachim Knittel for useful discussions. This research was supported by the Australian Research Council Discovery Project DP0987146 and the New Zealand Foundation for Research Science and Technology under the NERF contracts UOOX0703 and C08X0702.
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