Schawlow-Townes Linewidth Research Articles

InP high power monolithically integrated widely tunable laser and SOA array for hybrid integration.

We present a monolithic InP-based photonic integrated circuit (PIC) consisting of a widely tunable laser master oscillator feeding an array of integrated semiconductor optical amplifiers that are interferometrically combined on-chip in a single-mode waveguide. We demonstrate a stable and efficient on-chip coherent beam combination and obtain up to 240 mW average power from the monolithic PIC, with 30-50 kHz Schawlow-Townes linewidths and >180 mW average power across the extended C-band. We also explored hybrid integration of the InP-based laser and amplifier array PIC with a high quality factor silicon nitride microring resonator. We observe lasing based on gain from the interferometrically combined amplifier array in an external cavity formed via feedback from the silicon nitride microresonator chip; this configuration results in narrowing of the Schawlow-Townes linewidth to ∼3 kHz with 37.9 mW average power at the SiN output facet. This work demonstrates a new approach toward high power, narrow linewidth sources that can be integrated with on-chip single-mode waveguide platforms for potential applications in nonlinear integrated photonics.

Narrow linewidth characteristics of interband cascade lasers

Narrow-linewidth mid-infrared laser sources are highly demanding for high-resolution gas spectroscopy applications. Interband cascade lasers (ICLs) are power-efficient laser sources emitting in the mid-infrared range. This work unveils the low phase noise characteristics of distributed feedback ICLs driven by a battery source. We show that the measured spectral linewidth of ICLs is as narrow as 284 kHz (at a 1 ms observation time), which is smaller than those of common quantum cascade lasers. On the other hand, raising the pump current reduces the intrinsic linewidth down to 12 kHz. The linewidth broadening factor is in the range of 2.0–3.0, leading to a Schawlow–Townes linewidth as narrow as 1.6 kHz. This work suggests the high potential of developing battery-driven, high-resolution gas spectroscopy instruments using ICLs.

Higher-order QAM data transmission using a high-coherence hybrid Si/III-V semiconductor laser.

We experimentally demonstrate the use of a high-coherence hybrid silicon (Si)/III-V semiconductor laser as the light source for a transmitter generating 20 Gbaud 16- and 64- quadrature amplitude modulated (QAM) data signals over an 80 km single-mode fiber (SMF) link. The hybrid Si/III-V laser has a measured Schawlow-Townes linewidth of ${\sim}{10}\;{\rm kHz}$∼10kHz, which is achieved by storing modal optical energy in low-loss Si, rather than the relatively lossy III-V materials. We measure a received bit error rate (BER) of ${4.1} \times {{10}^{ - 3}}$4.1×10-3 when transmitting the 64-QAM data over an 80 km SMF using the hybrid Si/III-V laser. Furthermore, we measure a BER of $ {\lt} {1} \times {{10}^{ - 4}}$<1×10-4 with the Viterbi-Viterbi digital carrier phase recovery method when transmitting the 16-QAM data over an 80 km SMF using the hybrid Si/III-V laser. This performance is achieved at power penalties lower than those obtained with an exemplary distributed feedback laser and slightly higher than those with an exemplary narrow-linewidth external cavity laser.

Linewidth of the laser optical frequency comb with arbitrary temporal profile

For many applications, optical frequency combs (OFCs) require a high degree of temporal coherence (narrow linewidth). Commonly, OFCs are generated in nonlinear media from a monochromatic narrow linewidth laser source or from a mode-locked laser pulse, but in all the important mid-infrared (MIR) and terahertz (THz) regions of the spectrum, OFCs can be generated intrinsically by free-running quantum cascade lasers (QCLs) with high efficiency. These combs do not look like conventional OFCs as the phases of each mode are different, and in the temporal domain, OFCs are a seemingly random combination of amplitude- and phase-modulated signals rather than a short pulse. Despite this “pseudo-randomness,” the experimental evidence suggests that the linewidth of a QCL OFC is just as narrow as that of a QCL operating in a single mode. While universally acknowledged, this observation is seemingly not fully understood. In this work, we explicate this fact by deriving the expression for the Schawlow-Townes linewidth of QCL OFCs and offer a transparent physical interpretation based on the orthogonality of laser modes, indicating that despite their very different temporal profiles, MIR and THz QCL OFCs are just as good for most applications as any other OFCs.

Relative intensity noise in high-speed hybrid square-rectangular lasers

Relative intensity noise (RIN) and high-speed modulation characteristics are investigated for an AlGaInAs/InP hybrid square-rectangular laser (HSRL) with square side length, rectangular length, and width of 15,300, and 2 μm, respectively. Single-mode operation with side-mode suppression larger than 40 dB has been realized for the HSRL over wide variation of the injection currents. In addition, the HSRL exhibits a 3 dB modulation bandwidth of 15.5 GHz, and an RIN nearly approaches standard quantum shot-noise limit 2hv/P=−164 dB/Hz at high bias currents due to the strong mode selection of the square microcavity. With the increase of the DC bias current of the Fabry–Perot section, significantly enhanced modulation bandwidth and decreased RIN are observed. Furthermore, intrinsic parameters such as resonance frequency, damping factor, and modified Schawlow–Townes linewidth are extracted from the noise spectra.

Demonstration of a highly subluminal laser with suppression of cavity length sensitivity by nearly three orders of magnitude.

We have demonstrated a laser in which the frequency shift due to small cavity fluctuations is far less than what would be expected from a conventional laser. The factor of sensitivity suppression is inferred to be equal to the effective group index experienced by the laser, implying that this laser is subluminal. We have observed a suppression factor as high as 663. Such a laser is highly self-stabilized compared to a conventional laser, and is expected to have a far smaller Schawlow-Townes linewidth. As a result, this laser may have potentially significant applications in the fields of high-precision optical metrology and passive frequency stabilization.

Quantitative test of general theories of the intrinsic laser linewidth

We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (α factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.

Linewidth Measurement of Distributed-Feedback Semiconductor Lasers Operating Near 2.05 &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\mu \text{m}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;

The first unambiguous linewidth measurements are reported for fiber-pigtailed high-power distributed feedback (DFB) semiconductor lasers operating near 2.05 $\mu \text{m}$ wavelength range. The DFB lasers are packaged inside standard 14-pin butterfly package with polarization- maintaining output fiber and an integrated optical isolator. The Schawlow-Townes linewidth was measured using the coherent frequency-discriminator technique with a fiber Mach-Zehnder interferometer and the total linewidth was characterized using a heterodyne setup. Our measurements indicate less than 100 KHz Schawlow-Townes linewidth and a total linewidth of less than 200 KHz over 50 ms measurement time.

Thermalization and breakdown of thermalization in photon condensates

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot ``phase diagrams'' distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence ${g}^{(2)}$ and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.

Relative intensity noise and emission linewidth of polariton laser diodes

We study the relative intensity noise (RIN) per unit bandwidth in polariton laser diodes (LDs) for two pumping geometries, namely, the direct electrical and the intracavity ones as originally described in I. Iorsh et al. [Phys. Rev. B 86, 125308 (2012)], by using rate equations including Langevin noise sources that are adapted from equations employed to describe conventional semiconductor LDs. The obtained expressions for the RIN, which can be used for all inorganic semiconductor polariton LDs, are specifically applied to the case of III-nitride devices. It is highlighted that for frequencies larger than the relaxation resonance frequency the expected minimum RIN of polariton LDs---whatever the pumping geometry---is equal to the standard quantum limit ($\frac{2h\ensuremath{\nu}}{{P}_{0}}$). The general RIN line shape as a function of frequency and optical output power is discussed for the two geometries and simplified expressions for the RIN are given. Then a comprehensive account of the expected evolution of the linewidth of III-nitride polariton LDs upon increasing pumping strength is also given by considering the most advanced theories available to date. The modified Schawlow-Townes linewidth is estimated from the effective ground-state polariton lifetime at threshold, leading to a predicted linewidth as narrow as $\ensuremath{\sim}$15 MHz at room temperature for the two pumping geometries when using a consistent set of parameters for III-nitride polariton LDs.

Characterization of a high coherence, Brillouin microcavity laser on silicon

Recently, a high efficiency, narrow-linewidth, chip-based stimulated Brillouin laser (SBL) was demonstrated using an ultra-high-Q, silica-on-silicon resonator. In this work, this novel laser is more fully characterized. The Schawlow Townes linewidth formula for Brillouin laser operation is derived and compared to linewidth data, and the fitting is used to measure the mechanical thermal quanta contribution to the Brillouin laser linewidth. A study of laser mode pulling by the Brillouin optical gain spectrum is also presented, and high-order, cascaded operation of the SBL is demonstrated. Potential application of these devices to microwave sources and phase-coherent communication is discussed.

Quantum theory of frequency pulling in the cavity-QED microlaser

The spectrum of the cavity-QED microlaser/micromaser is expected to show distinctive features of the coherent light-matter interaction, which are obscured in the conventional Schawlow-Townes linewidth theory. However, the spectral studies has been limited to resonant atom-cavity interaction so far. Here we consider the dispersive interaction in the off-resonance case, from which we uncover a quantum frequency pulling effect in the microlaser/micromaser spectrum. We present a quantum theory of the spectrum which introduces the notion of a frequency-pulling distribution associated with the photon number. In contrast to the conventional laser, periodic variation of the mean frequency pulling is observed with increasing pump parameter and it is attributed to the strong atom-cavity coupling. The pulling distribution gives rise to a spectral broadening, which can be dominant over the non-dispersive broadening addressed in the previous works. We also developed a corresponding semiclassical theory and discuss how the introduction of the frequency shift fits in with the extended quantum theory.

Anomalous linewidth behavior in short-cavity single-frequency fiber lasers

An experimental investigation of the anomalous linewidth behavior in a distributed feedback fiber laser is presented. It is found that not only does the linewidth deviate from the Schawlow-Townes linewidth formula by increasing with pump and laser power, but it also varies significantly with the pumping configuration. These observations have potentially important implications for the design and operation of such fiber lasers.

The noise of ultrashort pulse mode-locked lasers beyond the slowly varying envelope approximation

The zero-point fluctuations in an L–C circuit of finite Q are revisited. The zero-point energy is shown to approach the value of only in the limit of an infinite Q. A Fabry–Perot resonator, on the other hand, has bounded zero-point energies of its modes that are equal to for each resonance. Based on the Fabry–Perot resonator with broadband noise, we analyse the noise of an ultrafast mode-locked laser when the slowly varying envelope approximation (SVEA) is not valid. This is achieved by reinterpreting the quantized form of the master equation of mode locking as an equation of motion for the electric field rather than for the creation operator of a photon. It is found that in this formulation quantum correlations exist that are not present in the SVEA. The correlations become evident in the spectrum of the zero-point fluctuations and therefore in the background noise of the laser. This behaviour can be detected by homodyne detection of the laser output. The linewidth of the frequency comb generated by the mode-locked laser is not affected by these correlations and is given by the Schawlow–Townes linewidth of an equivalent continuous wave taking the additional intracavity loss due to the mode locking process into account.

Relative intensity noise measurements of a widely tunable sampled-grating DBR laser

The intensity noise of a sampled-grating distributed Bragg reflector laser with 50-nm tuning range and 45-dB side-mode suppression ratio has been measured. The resonance frequency, damping factor, and modified Schawlow-Townes linewidth are extracted from the noise spectra. At high output power, the relative intensity noise (RIN) of the laser is below the photodiode shot noise limit, which is -160 dB/Hz. The laser has uniform shot noise limited RIN properties along the whole tuning range. The maximum resonance frequency is 5.4 GHz at a bias current of 120 mA and the K factor is 0.58 ns.

Scaling effects on vertical-cavity surface-emitting lasers static and dynamic behavior

We investigate the influence of oxide aperture size and number of top distributed Bragg reflector pairs on the performance of oxide confined vertical-cavity surface emitting lasers. Several counteracting mechanisms are shown to result in nonmonotonic behavior, which limits the performance of very small cavities. Static, dynamic, and noise behavior are considered. We examine static operation by means of steady-state measurements, whereas dynamic behavior and noise performance are described by the intrinsic relaxation oscillation frequency, damping coefficient, and Schawlow–Townes linewidth. These parameters are extracted from relative intensity noise measurements. Reducing the oxide aperture up to a given optimal diameter is shown to improve the device’s characteristics. We attribute the performance degradation below this value to increased diffraction losses, reduced confinement factor, and enhanced spontaneous emission. Similarly, increasing the number of Bragg reflector pairs first yields better overall performance as a consequence of reduced mirror losses. However, beyond an optimal value, significant reduction of the differential gain is observed that is attributed to gain compression and possibly thermal effects, degrading both the steady-state and high-frequency performance of the device.

Polarization-resolved linewidth-power product of a vertical-cavity semiconductor laser

We have studied the linewidth around threshold of the lasing and nonlasing polarization mode (x and y) in a TEM00 oxide-confined vertical-cavity semiconductor laser (VCSEL). We experimentally demonstrate: (i) that the nonlasing mode shows surprising behavior when the lasing mode passes through threshold, and (ii) that the polarization fluctuations in a VCSEL are limited by the same quantum noise that sets its finite Schawlow–Townes linewidth.

Loss rates of laser cavities

The loss rate of a laser cavity can differ from the loss rate of the same cavity mode in the absence of gain. It is shown that this difference arises from longitudinal inhomogeneities in the gain, the loss or the energy flow density. A similar ambiguity arises in the definition of the partial loss rate through the out-coupling mirror. This affects the calculation of the equivalent Schawlow–Townes linewidth of an unstable laser cavity from experimentally accessible quantities, and thereby the determination of the excess noise factor of the set-up.

Transverse excess noise factor in geometrically stable laser resonators

The excess noise factor due to the nonorthogonality of the transverse modes of a geometrically stable cavity subject to large diffraction losses is calculated. This calculation is based on an exact determination of the transverse field distribution of the cavity fundamental eigenmode. It is shown that when the modes become essentially determined by diffraction, the transverse modes are far from being orthogonal, leading to the appearance of a large excess noise factor that must multiply the standard Schawlow-Townes linewidth. Moreover, in the presence of two diffracting apertures, the excess noise factor is shown to exhibit a resonant behavior reminiscent of the one observed in unstable cavities. We estimate that, in the case of circular apertures, excess noise factors as large as 100 can be experimentally measured using a high-gain gas microlaser.

Experimental Observation of a Large Excess Quantum Noise Factor in the Linewidth of a Laser Oscillator Having Nonorthogonal Modes.

Several authors have predicted a substantial excess noise factor ${K}_{p}$ multiplying the quantum-limited Schawlow-Townes linewidth for laser oscillators having nonorthogonal spatial modes, such as unstable-resonator lasers. Experimental observations of this factor have to date, however, been limited in both number and detail. We report here a detailed experimental measurement of this factor in a diode-pumped hard-edged unstable-resonator Nd:YV${\mathrm{O}}_{4}$ laser. The measured excess noise factor ${K}_{p}\ensuremath{\simeq}330$ is in reasonable agreement with the theoretically predicted value.