Dynamic modeling of mode-locked pulses and frequency combs in strongly microwave-modulated semiconductor lasers

In this paper the characteristics of a SESAM mode- locked frequency comb with an intra-cavity electro-optic modulator are examined. To our knowledge this is the first time an intra-cavity EOM is used within a SESAM mode-locked erbium fiber frequency comb. Hereby the sensitivity of the combs offset and repetition frequency is determined as a function of pump power setpoints and EOM voltages considering the cavity's temperatures. In addition the impact of the pump laser's relative intensity noise on the offset frequency's linewidth is analyzed, where a standard FBG pump diode and a hybrid external cavity laser are used for comparison. To prove the comb's function as a stable and accurate interface between optical and HF standards, e.g. for atomic clocks, three different locking schemes for the comb's repetition rate are presented and analyzed using phase noise measurements as reference.

1. Introduction Frequency combs have been investigated in the laboratory over the course of the last 25 years in a wide range of implementations and applications including but not limited to precision metrology, optical atomic clocks, LIDAR, low-phase-noise RF generation, and precision spectroscopy [1]. While the Nobel prize winning technology of frequency combs have shown their usefulness in a variety of applications, there have been few demonstrations of this technology in real-world applications [2, 3]. Here we present a mode-locked oscillator that has been designed to be environmentally robust and low cost, while maintaining suitability for use in frequency comb applications. Vescent Photonics is designing and manufacturing fiber mode-locked oscillators and frequency combs for government customers whose application deployments include satellites and terrestrial moving platforms. These designs allow for repetition rate matching at the time of manufacture, which is an important consideration for integration of this technology into optical atomic clocks, dual comb spectroscopy, and low-phase-noise radio frequency generation. Vescent currently is manufacturing oscillators at 100 and 200 MHz repetition rates, and these designs could be modified to give repetition rates between 80 and 250 MHz. While performance and environmental robustness are necessary metrics for real-world applications of frequency combs, the cost of these devices can also be a barrier to wide-spread deployment. Vescent Photonics is diligently working on optimizing all three parameters (performance, environmental robustness, and cost) to bring a deployable mode-locked laser and frequency comb solution to market. 2. Mode-locked oscillator performance The compact mode-locked oscillators presented here have been designed to be low-cost, low-volume, highperformance, and environmentally robust for field-deployed applications. Figure 1a shows the mechanical enclosure for the fiber oscillator measuring 0.12 L (10.75 cm x 6.35 cm x 1.72 cm) in volume; it should be noted that pump diodes have not been included in this packaging due to thermal considerations. An enclosure for a frequency comb system (optic only) has also been designed with a volume of 0.62 L (19.05 cm x 11.30 cm x 2.86 cm). Two length actuators are included in this design; a fast PZT with >200 kHz bandwidth that allows 150 Hz of tuning on a 100 MHz repetition rate, and slow temperature control of the fiber with a ~10 s thermal time constant and >40 kHz of tuning on a 100 MHz repetition rate. The oscillator optical spectrum is included in Figure 1b. Average optical powers out of the oscillators are on the order of a few milliwatts, and pulses are close to transform limited (~250 fs). Erbium-doped fiber amplifiers and pulse compression stages are routinely added to the oscillator outputs to achieve average powers >200 mW and pulse durations <100 fs. While these parameters are useful for a wide range of mode-locked laser applications, it also allows the detection of the carrier envelope offset frequency ( , a fundamental comb parameter) in an f-2f interferometer with greater than 40 dB SNR in 300 kHz resolution bandwidth (Figure 1c). To show suitability of these fiber mode-locked oscillators in frequency comb applications, fractional Allan Deviations of the in-loop stabilized signals have been included in Figure 1d where the absolute frequency deviations have been divided by the distance between the frequency comb lock points. Typical optical clock performance has also been plotted, where the performance of the locks is more than suitable for this application. 3. Summary A compact, low-cost, environmentally robust mode-locked oscillator has been shown to be suitable for frequency comb experiments. Detection and stabilization of the fundamental comb parameters is suitable for optical atomic clocks, as well as a host of real-world frequency comb applications including dual comb spectroscopy, low phase noise RF generation, and optical metrology.

A new Floquet-based method is introduced which can be used widely in calculations on atoms and molecules in strong microwave or laser fields. Accurate calculations using this new method take several orders of magnitude less CPU time than with the standard Floquet approach and are less expensive in terms of computer memory than with the single Brillouin zone method. Illustrative results have been obtained for an experimentally examined threshold microwave spectrum of potassium; novel structure in this has been found and understood theoretically.

The research work carried out within the framework of this PhD has focused on the generation of Optical Frequency Combs (OFC) in semiconductor lasers using the gain-switching (GS) technique. The work has been mainly experimental, although simulations have been used to contribute to a better understanding of the internal physics of the OFCs generation process. Various types of lasers have been used, specially distributed feedback (DFB) lasers and discrete mode lasers (DML). An exhaustive experimental characterisation of the properties of the OFCs generated by GS in a full range of operating conditions has been performed. Two ranges of repetition frequencies have been explored: the GHz range with applications in optical communications, and the range of hundreds of MHz for application in spectroscopy. The effect of the optical injection (OI) on the properties of the OFCs has been investigated, and interesting results have been obtained, such as the improvement or deterioration of the quality of the spectra depending on the GS and OI conditions. The optimal operating conditions to generate high quality OFCs at the different frequencies considered have been found. In order to improve the understanding of the different physical processes involved in the generation of the OFCs generated by GS, a simulation tool based on the rate equation model for semiconductor lasers has been developed, with detailed treatment of the noise sources. For a correct simulation of the OFCs the values of a set of internal laser parameters is are required. They were obtained through an original procedure based on the measurement of the relative intensity noise (RIN) spectra. Using this procedure, the uncertainty in the simulated results has been reduced, since it allows to extract more parameters than other procedures due to an adequate analytical treatment of the RIN equations. The simulations have completely reproduced the temporal and spectral response of different lasers in a wide range of electrical and optical injection conditions. From the simulations, the predominant physical processes that contribute to the generation of OFCs, dynamic chirp at high repetition frequencies, and adiabatic chirp at low frequencies, have been identified. It has been shown that it is possible to improve the characteristics of low frequency OFCs by driving the laser with electric pulses, instead of using sinusoidal driving. High quality 100 MHz OFCs (up to 866 tones in 10 dB) with good carrier-to-noise (CNR) ratio have been generated. It has also been shown that step-recovery diodes (SRDs) can be used as a source of electrical pulses to generate OFCs, thus reducing the cost and size of the equipment involved, while maintaining the quality of the OFCs. The role of the “jitter” of the electrical source in the quality of the OFCs has been studied theoretically and experimentally. Finally, the OFCs generated by gain-switching and optical injection have been used to measure the absorption spectra of different elements, using three different architectures: heterodyne detection, and dual-comb spectroscopy and a new implementation of this technique. In this implementation the dual-comb is generated from a single GS laser by alternating the repetition frequency. Promising results for the application of these OFCs in gas spectroscopy have been obtained.

We show our progress towards integrated modelocked lasers producing short pulses with high peak power and low timing jitter for applications in frequency combs and optical frequency synthesizer.

We study optical frequency comb (OFC) generation using cascaded injection of semiconductor lasers in this work. The OFC generation system is operated in two cascaded optical injection stages. When a master laser optically injects into the first stage with proper injection power and frequency, period-one (P1) dynamics are invoked in an optically injected semiconductor laser of the first stage. Another semiconductor laser in the second stage is then optically injected by the P1 dynamics. With proper injection power adjusted in the second stage, the P1 dynamics are regenerated, and the semiconductor laser relaxation oscillations (ROs) become undamped so that subharmonic oscillations appear. Because a subharmonic oscillation frequency is half of an oscillation frequency of the P1 dynamics, extra optical frequency components appear in the middle of the adjacent optical frequency components of the P1 dynamics, thus signaling OFC generation. The OFC signals exhibit at least 15 comb lines, resulting in a bandwidth greater than 140 GHz. Microwave comb signals are obtained after photodetection, although the microwave linewidth is on the order of a few megahertz because of the semiconductor laser noise. Thus, we propose a cascaded injection-locking scheme to stabilize the P1 dynamics and OFC signals. We have demonstrated pure microwave generations with a linewidth of less than 3 Hz and low phase noise.

The improved frequency-stability and the very broad frequency-band of femtosecond mode-locked optical frequency comb (FOFC) have led to new applications in several precision metrology application areas such as high-precision optical frequency metrology, spectroscopy, and distance measurements. We have analyzed the temporal coherence function of the FOFC. As a result, it has been understood that the temporal coherence peaks exist during the time which is equal to the repetition interval in the traveling direction of the FOFC. In order to make the best use of the temporal coherence characteristic of an FOFC, we propose an FOFC-based multiplex Michelson interferometer that can use as a distant estimation. The present technique is expected to be useful for high-precision measurement of distances for not only science purposes but also industry requirements.

Flexible broadband optical frequency comb generation assisted by injection locking of semiconductor laser

Infrared laser-absorption sensing for combustion gases

The effective-field concept is used to derive a breakdown criterion for a model gas subjected to strong laser and microwave fields. This classical model includes diffusion, collisions, and the finite pulse length. The pressure dependence of this criterion is explored, and it is found that, under the proper conditions, it is possible to produce one or two narrow pressure regions in which breakdown will occur, or two broad breakdown regions separated by an extremely narrow nonbreakdown region. The criterion is extended to account for time-dependent field intensities and frequencies.

Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microresonators ("microcombs") has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: Combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spanning spectra but mode spacings beyond electronic detection limits. However, it has not yet been possible to achieve these two key requirements simultaneously, as will be critical for most microcomb applications. Here we present a route to overcome this problem by interleaving an electro-optic comb with the spectrum from a parametric microcomb. This allows, for the first time, direct control and stabilization of a microcomb spectrum with large mode spacing (>140 GHz) with no need for an additional mode-locked laser frequency comb. The attained residual 1-sec instability of the microcomb comb spacing is 10(-15), with a microwave reference limited absolute instability of 10(-12) at a 140 GHz mode spacing.

Mode spacing of an optical frequency comb of a harmonic mode-locked laser is studied by using an optical cavity. It turns out that mode spacing disagrees with pulse repetition rate for the harmonic mode-locked comb.

Optical frequency combs function as extremely broad bandwidth photonic synthesizers, capable of generating ultra-low noise signals from radio frequency to optical domains. We present synthesis results with both mode-locked laser and microresonator frequency combs.

High-capacity data transmission for intra- and inter-data center links is essential to handle the massive increase in data traffic. To address the insatiable demands, IEEE has been working on creating specifications for 800 GbE (IEEE 802.3df) and 1.6 TbE (802.3dj) using a multi-lane distribution method by aggregating 100 Gbps and beyond lanes. Optical frequency comb sources based on semiconductor mode-locked laser (MLL) are cost- and energy-efficient optical sources that can enable multi-lane transmission systems. Here, we demonstrate 14×100 Gbps PAM4 signals and 10×100 Gbps probabilistically shaped PAM8 signals over 10 km SMF with an O-band InAs/InGaAs quantum dot mode-locked laser (QD-MLL) consuming only ∼284 fJ/bit. We also successfully demonstrated 128 Gbps/λ OOK signal transmission with four lines from the QD-MLL spaced at 160 GHz, with a single booster amplifier for multichannel amplification. We show that the performance of the ≥1 Tbps and 512 Gbps WDM signals is within the standard FEC limits with preamplifier and booster semiconductor optical amplifiers, respectively.

Fiber-optic thermometry is advantageous for applications in electrically-hostile environments, such as in high DC electric or magnetic field, or in strong RF or microwave fields. The dielectric nature of the optical fiber is also important in safety applications, such as in measurements in an explosive environment or when monitoring patients.