More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission ($K$-factor) and the effective $α$-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.
The linewidth enhancement factor (LEF) has recently moved into the spotlight of research on frequency comb generation in semiconductor lasers. Here we present a novel modulation experiment, which enables the direct measurement of the spectrally resolved LEF in a laser frequency comb. By utilizing a phase-sensitive technique, we are able to extract the LEF for each comb mode. We first investigate and verify this universally applicable technique using Maxwell-Bloch simulations and then present the experimental demonstration on a quantum cascade laser frequency comb.
We demonstrate a hybrid integrated and widely tunable diode laser with an intrinsic linewidth as narrow as 40 Hz, achieved with a single roundtrip through a low-loss feedback circuit that extends the cavity length to 0.5 meter on a chip. Employing solely dielectrics for single-roundtrip, single-mode resolved feedback filtering enables linewidth narrowing with increasing laser power, without limitations through nonlinear loss. We achieve single-frequency oscillation with up to 23 mW fiber coupled output power, 70-nm wide spectral coverage in the 1.55 $μ$m wavelength range with 3 mW output, and …
Silicon nitride (Si3N4), as a complementary metal-oxide-semiconductor (CMOS) material, finds wide use in modern integrated circuit (IC) technology. The past decade has witnessed tremendous development of Si3N4 in photonic areas, with innovations in nonlinear photonics, optical sensing, etc. However, the lack of an integrated laser with high performance prohibits the large-scale integration of Si3N4 waveguides into complex photonic integrated circuits (PICs). Here, we demonstrate a novel III-V/Si/Si3N4 structure to enable efficient electrically pumped lasing in a Si3N4 based laser external cavi…
Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning optical communications, metrology and sensing provide unrivalled performance. To transfer these capabilities from the laboratory to the real world, a key missing ingredient is a mass-produced integrated laser with superior coherence. Here, we bridge conventional semiconductor lasers and coherent optical systems using CMOS-foundry-fabricated microresonators with record high $Q$ factor over 260 million and finesse over 42,000. Five orders-of-magnitude noise reduction in the pump laser is demonstrated, and for the firs…
Semiconductor mode-locked lasers can be used in a variety of applications ranging from multi-carrier sources for WDM communication systems to time base references for metrology. Their packaging in compact chip- or module-level systems remains however burdened by their strong sensitivity to back-reflections, quickly destroying the coherence of the mode-locking. Here, we investigate the stabilization of mode-locked lasers directly edge coupled to a silicon photonic integrated circuit, with the objective of moving isolators downstream to the output of the photonic circuit. A 2.77 kHz 3 dB RF line…
Hybrid integrated semiconductor laser sources offering extremely narrow spectral linewidth as well as compatibility for embedding into integrated photonic circuits are of high importance for a wide range of applications. We present an overview on our recently developed hybrid-integrated diode lasers with feedback from low-loss silicon nitride (Si3N4 in SiO2) circuits, to provide sub-100-Hz-level intrinsic linewidths, up to 120 nm spectral coverage around 1.55 um wavelength, and an output power above 100 mW. We show dual-wavelength operation, dual-gain operation, laser frequency comb generation…
Highly coherent optical sources are a key element in several fields of physics, in particular in time frequency metrology. Over the past decennia, there has been particular efforts in developing such sources to the expense of sophisticated laser systems and relatively smart electronics. We propose here a new general principle of a self-adaptive oscillator where the intricate operation of a 100-m-long active optical resonator and a standard semiconductor laser offers a very high spectral purity and can be tailored to any wavelength. Single frequency operation of this self-adaptive photonic osci…
This paper describes a calculation of the spontaneous emission limited linewidth of a semiconductor laser consisting of hybrid or heterogeneously integrated, silicon and III-V intracavity components. Central to the approach are a) description of the multi-element laser cavity in terms of composite laser/free-space eigenmodes, b) use of multimode laser theory to treat mode competition and multiwave mixing, and c) incorporation of quantum-optical contributions to account for spontaneous emission effects. Application of the model is illustrated for the case of linewidth narrowing in an InAs quant…
Planar metal-semiconductor Yagi-Uda type antennas for tunable narrow-linewidth quantum dot emitters
Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）；Indian Institute of Technology Delhi（德里印度理工学院）；Instituto de Física Gleb Wataghin, Universidade（格列布·瓦塔金物理研究所，大学）
To increase the spectral efficiency of coherent communication systems, lasers with ever-narrower linewidths are required as they enable higher-order modulation formats with lower bit-error rates. In particular, semiconductor lasers are a key component due to their compactness, low power consumption, and potential for mass production. In field-testing scenarios their output is coupled to a fiber, making them susceptible to external optical feedback (EOF). This has a detrimental effect on its stability, thus it is traditionally countered by employing, for example, optical isolators and angled ou…
In this tutorial, the physical origins and mathematical analyses of laser linewidths are reviewed. The semi-classical model is based on an equation for the light-mode amplitude that includes random source terms, one term for each process that affects the amplitude (stimulated and spontaneous emission, stimulated absorption, and facet and material loss). Although the source terms are classical, their assigned strengths are consistent with the laws of quantum optics. Analysis of this equation shows that the laser linewidth is proportional to the sum of the (positive) source strengths for all gai…
We present an integrated hybrid semiconductor-dielectric (InP-Si$_3$N$_4$) waveguide laser that generates frequency combs at a wavelength around 1.5 $μ$m with a record-low intrinsic optical linewidth of 34 kHz. This is achieved by extending the cavity photon lifetime using a low-loss dielectric waveguide circuit. In our experimental demonstration, the on-chip, effective optical path length of the laser cavity is extended to 6 cm. The resulting linewidth narrowing shows the high potential of on-chip, highly coherent frequency combs with direct electrical pumping, based on hybrid and heterogeneo…
We show that the emission of broad area semiconductor amplifiers and lasers can be efficiently stabilized by introducing, two-dimensional periodic modulations simultaneously on both the refractive index and the pump (gain-loss) profiles, in the transverse and longitudinal directions. The interplay between such index and gain-loss modulations efficiently suppresses the pattern forming instabilities, leading to highly stable and bright narrow output beams from such sources. We also determine the stabilization performance of the device as a function of pump current and linewidth enhancement facto…
We present an integrated semiconductor-dielectric hybrid dual-frequency laser operating in the 1.5 $μ$m wavelength range for microwave and terahertz (THz) generation. Generating a microwave beat frequency near 11 GHz, we observe a record-narrow intrinsic linewidth as low as about 2 kHz. This is realized by hybrid integration of a single diode amplifier based on indium phosphide (InP) with a long, low-loss silicon nitride (Si$_3$N$_4$) feedback circuit to extend the cavity photon lifetime, resulting in a cavity optical roundtrip length of about 30 cm on a chip. Simultaneous lasing at two freque…
We report on an optical frequency comb with 14nm (~1.8 THz) spectral bandwidth at -3 dB level that is generated using a passively mode-locked quantum-well (QW) laser in photonic integrated circuits (PICs) fabricated through an InP generic photonic integration technology platform. This 21.5-GHz colliding-pulse mode-locked laser cavity is defined by on-chip reflectors incorporating intracavity phase modulators followed by an extra-cavity SOA as booster amplifier. A 1.8-THz-wide optical comb spectrum is presented with ultrafast pulse that is 0.35-ps-wide. The radio frequency beat note has a 3-dB …
Recent advances in the processing of thin-film LNOI have enabled low-loss photonic integrated circuits, modulators with improved half-wave voltage, electro-optic frequency combs and novel on-chip electro-optic devices, with applications ranging from 5G telecommunication and microwave photonics to microwave-to-optical quantum interfaces. Lithium niobate integrated photonic circuits could equally be the basis of integrated narrow-linewidth frequency-agile lasers. Pioneering work on polished lithium niobate crystal resonators has led to the development of electrically tunable narrow-linewidth las…
Laser stabilization sits at the heart of many precision scientific experiments and applications, including quantum information science, metrology and atomic timekeeping. These systems narrow the laser linewidth and stabilize the carrier by use of Pound-Drever-Hall (PDH) locking to a table-scale, ultra-high quality factor (Q), vacuum spaced Fabry-Perot reference cavity. Integrating these cavities, to bring characteristics of PDH stabilization to the chip-scale, is critical to reduce their size, cost, and weight, and enable a wide range of portable and system-on-chip applications. We report a si…
In this paper, we analyze the dynamics and formation mechanisms of bound states (BSs) of light bullets in the output of a laser coupled to a distant saturable absorber. First we approximate the full three-dimensional set of Haus master equations by a reduced equation governing the dynamics of the transverse profile. This effective theory allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability of BSs. In addition, our analysis reveals a non-intuitive dependence of the stability region as a function of the linewidth enhancement fac…
The linewidth enhancement factor (LEF) describes the coupling between amplitude and phase fluctuations in a semiconductor laser, and has recently been shown to be a crucial component for frequency comb formation in addition to linewidth broadening. It necessarily arises from causality, as famously formulated by the Kramers-Kronig relation, in media with non-trivial dependence of the susceptibility on intensity variations. While thermal contributions are typically slow, and thus can often be excluded by suitably designing the dynamics of an experiment, the many quantum contributions are harder …
The stabilization and manipulation of laser frequency by means of an external cavity are nearly ubiquitously used in fundamental research and laser applications. While most of the laser light transmits through the cavity, in the presence of some back-scattered light from the cavity to the laser, the self-injection locking effect can take place, which locks the laser emission frequency to the cavity mode of similar frequency. The self-injection locking leads to dramatic reduction of laser linewidth and noise. Using this approach, a common semiconductor laser locked to an ultrahigh-$Q$ microreso…
We introduce modeling and simulation of the noise properties associated with types of modal oscillations induced by scaling the asymmetric gain suppression (AGS) in multimode semiconductor lasers. The study is based on numerical integration of a system of rate equations of 21-oscillating modes taking account of the self- and cross-modal gain suppression mechanisms. AGS is varied in terms of a pre-defined parameter, which is controlled by the linewidth enhancement factor and differential gain. Basing on intensive simulation of the mode dynamics, we present a mapping (AGS versus current) diagram…
Laser is one of the most important discoveries in the 20th century, and inorganic semiconductor lasers (ISCL) are most frequently used in many applications nowadays. Organic semiconductor lasers (OSCL) have many attractive features when they compared to ISCLs, such as flexibility, human friendliness, feasible and inexpensive production process, light weight, and multicolor emission. However, electrically driven OSCLs (el-OSCL) have not yet been realized, although they are possible in an optically driven mode. Here, we report that an el-OSCL can be realized in field-effect transistor (FET) stru…
A III-V compound semiconductor nanowire is an attractive material for a novel hybrid quantum interface that interconnects photons, electrons, and phonons through a wavelength-tunable quantum structure embedded in its free-standing structure. In such a nanomechanical element, however, a challenge is how to detect and manipulate a small number of phonons via its tiny mechanical motion. A solution would be to couple an optical cavity to a nanowire by introducing the ``cavity optomechanics'' framework, but the typical size difference between them becomes a barrier to achieving this. Here, we demon…
We study the linear optical absorption of bulk semiconductors in the presence of a homogeneous constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption coefficient is calculated from the time evolution of the interband polarization excited by an optical pulse. We apply the formalism to a numerical calculation for GaAs using a 14-band $\textbf{k} \cdot \textbf{p}$ model, which allows us to properly include interband coupling, and the exchange self-energy to account for the excitonic effects due to the electron-hol…
Demand for low-noise, continuous-wave, frequency-tunable lasers based on semiconductor integrated photonics has been advancing in support of numerous applications. In particular, an important goal is to achieve narrow spectral linewidth, commensurate with bulk-optic or fiber-optic laser platforms. Here, we report on laser-frequency-stabilization experiments with a heterogeneously integrated III/V-Si widely tunable laser and a high-finesse, thermal-noise-limited photonic resonator. This hybrid architecture offers a chip-scale optical-frequency reference with an integrated linewidth of 60 Hz and…
We present a traveling wave model for a semiconductor diode laser based on quantum wells. The gain model is carefully derived from first principles and implemented with as few phenomeno- logical constants as possible. The transverse energies of the quantum well confined electrons are discretized to automatically capture the effects of spectral and spatial hole burning, gain asym- metry, and the linewidth enhancement factor. We apply this model to semiconductor optical amplifiers and single-section phase-locked lasers. We are able to reproduce the experimental re- sults. The calculated frequenc…
