Using Laser Diode Instabilities for Chip- Scale Stable Frequency References

Semiconductor lasers are known to undergo significant changes in their output characteristics when subjected to external optical perturbations such as near-resonant injection from an external source or optical feedback. Over a range of operating conditions, the perturbations can induce a periodic pulsating output where the pulsation frequency can be controlled by the bias point of the laser(s), and amplitude (and frequency offset) of the injection. The output optical spectrum can be adjusted to be dominated by two strong frequency components with a controllable offset. Adding a weak microwave modulation to the bias can lock the pulsation frequency to this reference. Such a spectrum is nearly ideal for the excitation of Coherent Population Trapping (CPT) resonances of gas-phase atomic media such as cesium (Cs) and rubidium. We describe the double locking of a laser diode to the CPT optical (852 nm) and microwave (9.2 GHz) resonances in Cs gas in a cell containing Cs and a buffer gas. The microwave power required for the modulation reference is a small fraction of the dc-bias power, unlike a directly modulated laser diode. The combination of all-optical excitation of the Cs gas and reduced microwave electronics specifications is very useful for the fabrication of ultrasmall frequency references. INTRODUCTION Interest in the fabrication of chip-scale atomic clocks (CSACs) has been spurred by recent work showing that all-optical excitation and probing of cesium (Cs) and rubidium (Rb) atomic vapors can be scaled down to very small sizes [1-3]. This work has made use of the novel nonlinear optical properties of the atomic medium that allow the creation of long-lived atomic coherences through Coherent Population Trapping (CPT) that alters the transmission properties of resonant light [4]. Because the atomic medium can be both excited and probed optically, the gas cell can be very small, sub-mm, and requires no direct microwave excitation, opening up the possibility of very small physics packages with low power budgets. The all-optical excitation requires light at two resonant optical frequencies with a very high mutual coherence. To date, this has been achieved principally by direct modulation of a semiconductor laser. The modulation causes sidebands to be generated about the carrier frequency. While the absolute *Current address: Army Research Lab., AMSRD-ARL-SE-EE, 2800 Powder Mill Road, Adelphi, MD 20783, USA. 35 Annual Precise Time and Time Interval (PTTI) Meeting 458 coherence of each of the laser frequency components is relatively large, with optical linewidths in 1-100 MHz range, the mutual coherence is determined by the linewidth of the microwave modulation source. Laboratory instruments that can generate highly coherent microwave signals are readily available. However, these units are bulky and consume excessive power for chip-scale implementation. Further, direct modulation requires that the modulation power be similar to, or larger than, the dc-bias power to the excitation laser [1]. It is well known that semiconductor lasers can be very sensitive to perturbation by near-resonant light due to strong nonlinear optical interactions within the semiconductor gain medium [5]. Incident light levels as low as 10 of the output level are sufficient to destabilize monochromatic laser output and induce a pulsating, multi-frequency output. Here, we wish to show that such pulsating output can be simultaneously locked to optical and microwave references, a double-locked laser diode (DLLD), with sufficient precision to be a useful excitation and probing source for CSACs that use CPT. NONLINEAR DYNAMICS IN SEMICONDUCTOR LASERS The semiconductor laser is an important physical system both because of its wide-ranging applications and because it is an excellent test system for investigations of the predictions of laser theory and nonlinear dynamics theory. It is a highly nonlinear system due to the nature of the coupling between the optical fields and the gain medium. For most applications, the laser is simply a source of coherent optical power and its nonlinear characteristics are suppressed. However, the nonlinear response of the system to an external perturbation, such as an injected optical field or feedback from a distant reflector, can lead to potentially useful changes in its output characteristics. Past experimental work on the semiconductor laser subject to external optical injection has established that a range of optical outputs can be produced. For a laser operating at a given bias current, external optical injection can induce stable locked output, multiwave mixing, oscillatory power output due to an undamping of the carrier-field resonance of the system, and chaotic dynamics depending on the amplitude and offset frequency of the external optical field [5]. It has been found that a relatively simple model describing the coupling between the external and circulating optical fields and the free carriers of the gain medium can reproduce the observed characteristics observed experimentally. Because the key dynamic parameters of the model can be determined experimentally, a quantitative comparison can be made between experimental data and model calculations. Recently, a full comparison of experimental observations and model calculations has been made where excellent agreement between experimental data and model calculations was observed [6]. Typically, the laser output power changes from cw, monochromatic output to a periodically modulated output for resonant injection levels on the order of 10, to chaotic output for power levels on the order of 10, and back to oscillating or pulsating output for injection levels on the order of 10. Because the pulsation frequency is easily controlled in this latter region and can be locked to a microwave reference, the nonlinear dynamics makes the laser an appropriate source without strong current modulation. However, no measurements have been made to show that excitation of the CPT resonance is possible with such a source. Figure 1 shows a mapping of the output dynamics of a semiconductor laser subject to external optical injection with transitions between different output characteristics identified using the model. The particular laser is a 1.55-micrometer Distributed Feedback (DFB) laser diode, but similar characteristics have been observed for conventional edge-emitting Fabry-Perot laser diodes and Vertical Cavity Surface Emitting Laser Diodes (VCSELs) [5]. The output characteristics are shown as a function of the amplitude and offset, with respect to the free-running characteristics, of the laser. The mapping is asymmetric with respect to the offset due to the fact that both the gain and the refractive index of the semiconductor medium are sensitive to the external injection. There is a region of stable injection locking of the slave 35 Annual Precise Time and Time Interval (PTTI) Meeting 459 laser to the injected signal, plus regions where the output power is oscillatory or erratic. Of particular interest to the CSAC application is the transition across a Hopf Bifurcation to a region where the laser output is dominated by two optical field components whose offset can be precisely controlled. The optical frequency of one of the two components is locked to the external injection, while the other strong component can be locked at a precise offset using a microwave current reference creating the doublelocked output [7]. In the CSAC application, the two frequency components are precisely locked to the optical and microwave resonance frequencies of the atomic medium. Figure 1. Transitions between regions of different operating characteristics in a single-mode DFB semiconductor laser subject to external optical injection. The injection field is proportional to the square root of the injected signal power, and the offset frequency of the injected optical beam is with respect to the free-running frequency of the slave laser. Diamonds mark the transition from unlocked to stable locked operation and squares from stable to pulsating output. Triangles mark transitions where the pulsation or unlocked power oscillation frequency is halved (period two) and circles a transition to period four oscillating output. The hashed regions mark regions where the output is chaotic. EXPERIMENTAL APPARATUS To demonstrate that the DLLD has sufficient stability to act as the pump and probe of the atomic medium for a CSAC, we constructed the experimental apparatus shown schematically in Figure 2. The -15 -10 -5 0 5 10 15 0 1 2 3 4 5 6 Injection Field (arb. Units) O ffs et F re qu en cy (G H z) 35 Annual Precise Time and Time Interval (PTTI) Meeting 460 semiconductor laser output is perturbed from steady-state free-running output by the injection of light from another laser. Both lasers used were commercially available VCSELs operating at 852 nm, resonant with the D2 absorption peak in Cs. Due to their small size, the optical frequency of VCSELs is very sensitive to current and temperature fluctuations, typically tens of GHz per mA of bias current and degrees C, respectively. Both lasers are under current and temperature control, with fluctuations below ± 1 μA and ± 0.01 C, respectively. The master laser is isolated from the output of the slave, so that it maintains stable, single-frequency output. The injection into the slave causes its output to oscillate in time at a frequency determined by the injection level and offset frequency of the master laser. It is adjusted to cause the slave laser to have an output dominated by two frequency components offset by the 9.2 GHz frequency of the Cs clock transition. The slave laser output is monitored by a fast photodiode connected to a microwave spectrum analyzer. Part of its output is split off and passed through a 1 mm thick cell containing Cs and 100 torr of argon buffer gas. The buffer gas limits the diffusion of the Cs vapor out of the beam and into contact with the cell walls without destroying the coherence set up by the optical excitation. A second, low-frequency photodiode monitors transmission through the cell. Figure 2. Schematic of the experimental apparatus. The attenuated output from an injection, or master, laser is used to perturb the output of a slave laser. After passing through beamsplitters, part of the slave laser output is transmitted through a shielded, temperature-controlled cell containing Cs and 100 torr of argon buffer gas to a photodiode. The other part is incident on a fast photodiode whose output is monitored by a microwave spectrum analyzer. The optical frequency of the master laser is locked to the Cs D2 resonance, while the induced pulsation frequency of the slave laser is locked to a weak, microwave-frequency current modulation generated by a microwave frequency synthesizer and an RF waveform generator, both locked to a stable frequency reference. The frequency of the synthesizer is modulated so that the laser pulsation can be locked to the CPT resonance by controlling the frequency of the waveform generator. Optical isolators are used to prevent back reflections. Master Laser Opt. Iso. & Atten. Slave Laser Fast PD MSA Cs w/ buffer gas