Optical frequency comb generation

Abstract

A ring cavity laser (10) based on a semiconductor gain medium providing a lasing transition between quantised energy bands. The laser's ring cavity (12) possesses a plurality of modes, at least one of which having a frequency around which sufficient gain can be generated to cause lasing action. An electrical driver circuit applies an injection current to the semiconductor gain medium to cause population inversion and lasing action. A modulator (18) provides phase modulation within the cavity optical path at a modulation frequency near- resonant with an integer multiple or fraction of one of the mode frequencies. The phase modulation causes the laser to output a stable optical frequency comb which is established by random quantum walk in a photonic lattice created by said mode and its neighbouring resonator modes. A random quantum walk arises when these modes are coupled by the phase modulation.

Description

[0001] TITLE OF THE INVENTION

[0002] OPTICAL FREQUENCY COMB GENERATION

[0003] BACKGROUND OF THE INVENTION

[0004] The invention relates to optical frequency comb generation.

[0005] Since at least the late 1990s, optical frequency combs (OFCs) have gained significant attention for applications in metrology, precise distance measurements, spectroscopy, and telecommunications. OFCs are characterised by a spectral structure of equidistant lines in frequency space.

[0006] A review article on OFCs is found in the following:

[0007] • Fortier, T., Baumann, E. 20 years of developments in optical frequency comb technology and applications. Commun Phys 2, 153 (2019). https: / / doi.Org / 10.1038 / s42005-019-0249-y [Ref. 1]

[0008] Another review article on OFCs, more specifically technologies available for fabricating integrated OFC sources, is found in:

[0009] • Chang, L., Liu, S. & Bowers, J.E. Integrated optical frequency comb technologies. Nat. Photon. 16, 95-108 (2022). https: / / doi.org / 10.1038 / s41566-021-0Q945-1 [Ref. 2]

[0010] A still further review article on OFCs, in particular for lasers with fast recovery times, is found in:#

[0011] • Piccardo M and Capasso F Laser Frequency Combs with Fast Gain Recovery: Physics and Applications. Laser and Photonics Reviews Volume 16, Issue 2 https: / / doi.Org / 10.1002 / lpor.202100403 [Ref. 3].#

[0012] OFCs are of relevance in the fields of telecommunication for increasing the number of channels in wavelength division multiplexing (WDM). Traditionally a WDM transmitter for optical telecommunication has a bank of independent lasers whose outputs are combined by suitable couplers. However, since the lasers are independent of each other, their output wavelengths will drift independently, resulting in relatively large guard bands being needed between adjacent wavelength channels to ensure there is no crosstalk. An OFC WDM source avoids the need for wide guard bands, since all channels drift collectively, so more of the available bandwidth can be used. This topic has been explored in recent years and high data transmission rates have been achieved using optically pumped microcomb ring resonators producing a Kerr frequency comb.

[0013] • Jorgensen, A. A., Kong, D., Henriksen, M.R. et al. Petabit-per-second data transmission using a chip-scale microcomb ring resonator source. Nat. Photon. 16, 798-802 (2022). https: / / doi.Org / 10.1038 / s41566-022-01082-z [Ref. 4],

[0014] • Li, C. et al. Hybrid WDM-MDM transmitter with an integrated Si modulator array and a micro-resonator comb source. Opt. Express 29, 39847-39858 (2021) https: / / doi.org / 10.1364 / OE.444493 [Ref. 5],

[0015] However, Kerr frequency combs have the following limitations:

[0016] • Uneven spectral power distribution: There is a large variation in intensity between comb modes due to soliton mode locking being associated with a sech2-envelope (squared hyperbolic secant) and due to the finite power extinction ratio of the optical pump laser.

[0017] • Uneven temporal power distribution: Kerr combs and solitons are AM OFCs and thus exhibit a pulsed output. The high peak intensities make these combs more prone to non-linear effects in the fibres and detectors, which, in turn, can lead to crosstalk between WDM channels.

[0018] • Low power conversion efficiency / High power consumption: Microcomb rings are generated via strong optical pumping, necessitating an additional high-power pump laser. Through non-linear effects in the passive ring cavity, this monochromatic pump light is partially converted into a comb spectrum. Incomplete power conversion leads to inefficiencies in the energy consumption and additional heating.

[0019] • Device footprint: Kerr comb generation relies on a continuous wave pump laser to activate the Kerr nonlinearity in the nonlinear gain medium. The need for a separate optical pump laser increases the device footprint and complicates the device integration.

[0020] • Spectral efficiency / high comb spacing: Due to limitations in the fabrication of microcomb resonators, the free spectral range (FSR) is limited to a maximum of several hundred GHz.

[0021] It would therefore be desirable to provide an improved OFC source that could avoid or at least mitigate one or more of the above limitations of Kerr frequency combs. SUMMARY OF THE INVENTION

[0022] According to a first aspect of the invention, there is provided a laser for outputting laser light, the laser comprising: a semiconductor gain medium element comprising a plurality of semiconductor materials configured to provide a lasing transition between first and second quantised energy bands; a ring cavity formed from an optical path forming a loop having propagating and counter-propagating directions for passage of an optical field, wherein the ring cavity has a net gain spectrum and possesses a plurality of cavity modes separated by a mode spacing, wherein there is sufficient net gain at the frequency of at least one of the cavity modes to provide for single mode lasing; an output coupling portion or element of the ring cavity for coupling out a portion of laser light; an electrical driver circuit arranged to apply an injection current to the semiconductor gain medium to cause population inversion between the first and second quantised energy bands and said single mode lasing; and a phase modulator operable to provide phase modulation in the optical path at a modulation frequency near-resonant with an integer multiple or fraction of the mode spacing to cause coherent side-mode generation by quantum walk around the cavity mode responsible for said single mode lasing resulting in output of a stable optical frequency comb of finite bandwidth.

[0023] OFC generation by quantum walk is distinguishable from conventional OFC generation through several characteristic differences compared to other OFC-generating lasers. A QW OFC has a bandwidth value which varies proportionally to the square root of amplitude of the RF modulation. A QW OFC has different dynamics in that the phase-modulation induced sidemode generation causes a ballistic expansion of the comb bandwidth followed by stabilisation of the comb at a finite bandwidth which can be predicted from the laser design (e.g., net gain, dispersion) and the laser’s operating conditions (e.g. as set by temperature, drive current and phase modulation). A QW OFC exhibits a smooth continuous variation of its bandwidth with tuning of the injection frequency (after stabilization).

[0024] The OFCs according to the invention are generated by random quantum walk in a photonic lattice. A synthetic lattice is created by the modes of the resonators. A quantum walk arises when these modes are coupled by the periodic phase modulation applied at a frequency matched to the mode separation. The modes that survive in the long term are selected by the fast gain recovery. Random walk is a general mathematical concept describing a walker taking random steps in a discretised space. The spread of a classical random walker is characterised standard deviation after N steps. The random walk has a quantum counterpart, the quantum random walk (referred to as the quantum walk) which occurs when the particle performing the random walk has a wave nature. Since the particle also behaves as a wave, it interferes with itself. In this quantum walk, the standard deviation of the position scales linearly with the number of steps, enabling a so-called ballistic spread or expansion. Photonic lattices are capable of generating quantum walks, since coherent light mimics the interference of quantum particles.

[0025] It is possible to realise lasers for QW OFC generation according to the invention which provide one or more of the following desirable characteristics which may be of more or less relevance depending on the particular application, e.g., telecommunications, spectroscopy, sensing:

[0026] • Steady spectral power distribution: The OFC can output a near Bessel-shaped, very flattopped spectra, meaning an even intensity distribution across the bandwidth.

[0027] • Lower non-linear effects: The OFC comb is an FM comb and as such displays a near constant output power over time, i.e. , there is a steady temporal power distribution. Consequently, four wave mixing is lower, since the QW laser has a lower peak power for a given average power compared with a laser that relies on pump pulses to generate a nonlinearity. Moreover, spatial hole burning does not occur because of the unidirectional nature of the emission in the ring. For telecommunications applications this is a significant advantage, since non-linear effects cause undesirable crosstalk between channels and are also a source of noise.

[0028] • Power efficiency: Semiconductor diode lasers have famously impressive wall plug efficiencies, so the use of a semiconductor diode as the basis for OFC generation is much more power efficient than for a prior art optically pumped microcomb ring resonator producing a Kerr frequency comb. Moreover, heating effects are relatively low, so heat dissipation measures are simpler and / or higher repetition rates are possible.

[0029] • Smaller device footprint: The absence of a separate optical pump laser facilitates module miniaturisation and photonic integration.

[0030] • Spectral efficiency / tuneable comb spacing: The FSR is a design parameter, where higher FSR values can be achieved by reducing the optical path length of the ring cavity. Another design measure for achieving higher FSR values is to base lasing on a higher order harmonic of the cavity resonance frequency spacing instead of the fundamental of the cavity mode spacing being used for lasing. A higher harmonic of a cavity mode spacing can be selected for lasing through choice of a suitable multiple of the phase modulation frequency compared to the fundamental.

[0031] • Large bandwidth and tuneable bandwidth: The bandwidth of the OFC that is generated is set by the bandwidth of the cavity which in turn depends on dispersion, gain curvature, gain saturation and RF modulation. Bandwidth can thus be increased by varying one or more of these parameters, for example by decreasing dispersion through incorporation of a dispersion compensation within the cavity. Moreover, since RF modulation is an electrical parameter under operational control, the bandwidth may be set or varied within a certain range over which the QW OFC regime persists. More precisely, the bandwidth is proportional to the square root of the RF modulation amplitude.

[0032] • Stability and low noise: The QW OFC has been shown by our experiments to exhibit excellent noise characteristics and to be stable over long periods, with prototype lasers already demonstrating stable operation at a fixed working point over several days. Indeed, since the quantum walk laser, in the absence of modulation, operates in a single mode in a stable manner, the noise of the comb will be determined primarily by the noise of the RF electrical injection.

[0033] • Wide wavelength range: Lasers according to the invention can be fabricated to cover the wide range of wavelengths accessible by semiconductor diode lasers. With the lasing transition being an interband transition, lasing wavelengths in the near-UV to near-IR can be accessed based on lll-V quantum well semiconductor heterostructures. With the lasing transition being an intersubband transition, lasing wavelengths in the near-IR to far-IR can be accessed by quantum cascade lasers (QCLs) based on lll-V quantum well semiconductor heterostructures.

[0034] There are different options for realising the phase modulator.

[0035] In one option, the phase modulator is a part of the electrical driver circuit which is configured to generate an AC current at the modulation frequency and apply it to the semiconductor gain medium.

[0036] In another option, the phase modulator is an electro-optical modulator operable to modulate the optical field at the modulation frequency. The electro-optical modulator and the semiconductor gain medium element could be integrated in a semiconductor chip.

[0037] Alternatively, the electro-optical modulator could be a discrete component separate from the semiconductor gain medium element.

[0038] The laser may be based around either an interband or intraband semiconductor transition as the lasing transition. Namely, in some embodiments an interband design is adopted in which the first and second quantised energy bands are within a conduction band and a valence band localised to one of the semiconductor materials. On the other hand, in other embodiments an intraband design is adopted in which the first and second quantised energy bands are first and second subbands within a conduction band or valence band localised to one of the semiconductor materials, which may also be referred to as an intersubband design.

[0039] In some embodiments, the ring cavity is formed as a planar waveguide integrally within the semiconductor gain medium element. The planar waveguide may be configured to suppress back scattering of light at the mode frequency from the propagating direction to the counterpropagating direction. Alternatively, in such embodiments based on an integrated, single-chip structure, an optical isolator could be integrated in the chip or some other type of element that causes loss to be increased or decreased in one propagation direction differently to the other propagation direction.

[0040] In some embodiments, the output coupling portion or element is formed by a length portion of the planar waveguide that is configured to have increased loss, thereby coupling out a proportion of the laser light from the ring cavity. In other embodiments, the output coupling portion or element is formed by a further planar waveguide formed integrally with the semiconductor gain medium element and having a length portion extending tangentially to a neighbouring portion of the ring cavity planar waveguide so as to be evanescently coupled thereto. In certain embodiments where heterogeneous integration of the interband laser to on chip passive waveguides is desired, the output coupling portion or element is formed by lateral adiabatic couplers.

[0041] In certain embodiments, the optical path forming the loop around the ring cavity comprises free- space portions and the semiconductor gain medium element is arranged as a discrete component within the ring cavity. An optical element may additionally be arranged in the cavity to provide different propagation loss values in the propagating and counter-propagating directions around the loop. With a free-space cavity design, the output coupling portion or element can be formed by a mirror or beamsplitter element with a partially reflective surface or interface.

[0042] In some embodiments, the modulation frequency of the phase modulator is one times the mode spacing, i.e., the integer multiple is unity. In other embodiments, an integer multiple of two or more times the mode spacing is used. In still further embodiments, the modulation frequency of the phase modulator is an integer fraction of the mode spacing such as one half, one third etc.

[0043] A controller may be additionally provided. The controller may be configured to vary the phase modulation in at least one of amplitude and frequency. In certain embodiments, an artificial noise source may be provided. The artificial noise source generates artificial noise that is used for shaping the spectral form of the QW OFC output by the laser. The artificial noise source may be integrated with the electrical driver circuit or the phase modulator to add artificial noise to the phase modulation or the injection current respectively. Moreover, the artificial noise source may be under control of the controller to vary the bandwidth and / or power of the artificial noise.

[0044] In summary, we have developed lasers based on a semiconductor diode gain medium that are capable of emitting a FM OFC based on a quantum walk. These lasers have in many respects better properties than known optically pumped microcomb ring resonators that produce OFCs by the Kerr effect.

[0045] A further aspect of the invention relates to a WDM transmission system incorporating one or more lasers according to the invention. A further aspect of the invention relates to a transmitter of a WDM transmission system incorporating one or more lasers according to the invention, where the WDM channels are generated by the laser. A further aspect of the invention relates to a receiver of a WDM transmission system incorporating one or more lasers according to the invention, where the WDM channels are generated by the laser, where the laser generates a multitude of local oscillator tones to decode the received signal.

[0046] A further aspect of the invention relates to a photonic convolution accelerator incorporating a laser according to the invention.

[0047] A further aspect of the invention relates to a non-dispersive infrared (NDIR) gas sensor with a gas cell and a laser according to the invention.

[0048] A further aspect of the invention relates to an NDIR gas sensor for ambient gas sensing that incorporates a laser according to the invention.

[0049] A further aspect of the invention relates to a photoacoustic gas sensor incorporating a laser according to the invention.

[0050] BRIEF DESCRIPTION OF THE DRAWINGS

[0051] This invention will now be further described, by way of example only, with reference to the accompanying drawings.

[0052] Fig. 1 is a schematic graph to illustrate the principles of the dynamics of QW OFC generation according to the invention which shows the efficiency of the coupling by modulation M between the dispersed modes, with frequencies spaced by 1 of the cold cavity, where gain, g, is also playing a role.

[0053] Fig. 2 and Fig. 3 are corresponding plots in frequency space and time space respectively to show the eigenmodes of the modulated ring laser, referred to as the supermodes of order ISM. More precisely, Fig. 2 shows the calculated intensity of the supermodes of the modulated ring cold cavity as a function of frequency in units of mode number and Fig. 3 shows the calculated intensity of the supermodes of the modulated ring cold cavity as a function of cavity time.

[0054] Fig. 4 shows two simulations that compare the behaviour of a fast gain laser embodying the invention with the behaviour of an otherwise equivalent laser with slow gain as a comparative example. They plot the spectrum in units of cavity mode number vs. time.

[0055] Fig. 5 is a schematic plan view of a laser according to a first embodiment of the invention.

[0056] Fig. 6 is a schematic circuit diagram of a laser module incorporating a laser according to a first embodiment of the invention.

[0057] Fig. 7A and Fig. 7B are respectively simulated and experimental plots of spectrum vs. wavenumber in units of cmA-1 vs. as a function of the RF modulation frequency in GHz for a range of modulation frequencies around resonance with the lasing cavity mode frequency for a laser according to a first embodiment of the invention. Fig. 70 are theoretical and experimental plots of lasing mode intensity, I, in arbitrary units (normalised) vs. wavenumber in units of cmA- 1 showing behaviour at different modulation frequencies. Fig. 7D are simulated and experimental plots of instantaneous wavelength in units of cmA-1 vs time in picoseconds with the four panels - Panel 1 to Panel 4 - showing behaviour at the four different modulation frequencies shown by the vertical dashed lines in Fig. 7B. Column I (experimental) shows the experimental results. Column II (numerical) shows simulated data. Column III (analytical) shows theoretical data from an analytically derived expression.

[0058] Fig. 8 shows an experimental set up for shifted-wave interference Fourier-transform spectroscopy (SWIFTS) which was used to measure the coherence and spectral phase of the laser output. Fig. 9 shows corresponding theoretical results and experimental results plotting intensity, I, in arbitrary units vs. wavelength in units of cmA-1 , which show the establishment of the OFC by quantum walk and its stabilisation after approximately 250 ns from time zero which is the time of activation of phase modulation.

[0059] Fig. 10 is a plot of experimental results showing output spectra in units of wavenumber cmA-1 in a first prototype laser according to the first embodiment at a number of different values of injected modulated power (modulation amplitude) up to 33.8 dBm for resonant and near- resonant phase modulation, the plots being of the QW OFC after stabilisation.

[0060] Fig. 10A corresponds to Fig. 10 for a second prototype laser according to the first embodiment with near-resonant phase modulation.

[0061] Fig. 11 is a plot of the OFC bandwidth vs the square root of the injected modulation power in the first and second prototype lasers of Fig. 10 and Fig. 10A respectively. Circles and crosses show results for the first and second prototype devices respectively. The dashed lines are fitted curves. The dotted lines indicate the uncertainty of that fit.

[0062] Fig. 12 is a schematic drawing of a laser according to a second embodiment of the invention, which is based on a semiconductor optical amplifier serving as the gain medium element and arranged in an external ring cavity.

[0063] Fig. 13 is a graph plotting output power in dBm vs frequency in THz for a prototype laser according to the second embodiment while lasing in the QW OFC regime.

[0064] Fig. 14 is a schematic drawing of an example WDM transmission system incorporating lasers according to an embodiment of the invention, where the WDM channels are generated by the QW OFC.

[0065] Fig. 15 is a schematic drawing of an example photonic convolution accelerator incorporating a laser according to an embodiment of the invention.

[0066] Fig. 16 shows an example NDIR gas sensor with a gas cell and a laser module according to an embodiment of the invention.

[0067] Fig. 17 shows an example NDIR gas sensor for ambient gas sensing that incorporates a laser module according to an embodiment of the invention.

[0068] Fig. 18 shows an example photoacoustic gas sensor incorporating a laser module according to an embodiment of the invention. DETAILED DESCRIPTION

[0069] In this document, reference to specific numerical values, for example as range end points, are to be taken as exact values and are not to be rounded whether that be by significant figures, number of decimal places or otherwise.

[0070] DEFINITIONS

[0071] Quantum cascade laser (QCL): A QCL is based on cascading intraband transitions between subbands of quantum wells in a Type I superlattice structure. Intraband refers to the fact that the transitions are taking place within a single energy band of the semiconductor, typically the conduction band. Since these intraband transitions take place between different subbands of a quantum well, they are sometimes also referred to as intersubband transitions. QCLs having been demonstrated with emission wavelengths from 2.6 pm up to 250 pm. A QCL may be of the ring type, which is the type of particular interest for QCL embodiments of the present invention. Ring cavity and linear cavity QCLs are well-known OFC sources.

[0072] Ring cavity laser: A ring cavity laser is one with a resonator in the form of a loop (as opposed to a linear cavity laser formed as a Fabry-Perot resonator).

[0073] Unidirectional ring cavity laser: A unidirectional ring cavity laser is one that under at least some operating conditions lases only or predominantly in one of the two propagation directions around the ring. One way to provide for unidirectional lasing in a ring cavity is to engineer the cavity to have different losses in the two propagation directions, wherein the difference need only be very small. A straightforward way of achieving this is in an external ring cavity is to insert an optical isolator. Another way to provide for unidirectional lasing is through a difference in net gain between the two propagation directions that may arise in a ring cavity after symmetry breaking. Asymmetric net gain can be achieved in an integrated ring planar waveguide provided that the waveguide has low back scattering so that power transfer between the two propagation directions is low resulting in lasing in one propagation direction becoming dominant over the other propagation direction shortly after laser threshold is attained.

[0074] External-Cavity Diode Laser: An external-cavity diode laser is a laser with a semiconductor gain medium element which is not fully integrated with the ring cavity but rather has the ring cavity formed at least in part by one or more optical components that are not part of the semiconductor chip, such as an external output coupler mirror. In an external-cavity laser, the semiconductor chip appears structurally in the cavity as a piece of semiconductor gain medium through which light propagates, typically through a planar waveguide formed in the semiconductor chip, the planar waveguide incorporating an active region layer of the semiconductor diode which forms the gain medium. In an external cavity design, the ring cavity need not be in the shape of a geometrical ring and, for example, may have beams that cross in free space as they travel between cavity mirrors, such as a figure-of-eight shape. With an external-cavity diode laser, an optical isolator can be added to the ring cavity to provide a large difference in propagation loss in opposing directions, which ensures that only unidirectional lasing operation is possible.

[0075] Laser Diode: A laser diode is a semiconductor laser formed in a single semiconductor chip which lases via current injection to cause population inversion at the p-n junction or more usually p-i-n junction formed by semiconductor heterostructure.

[0076] Ring waveguide: In an integrated ring-cavity semiconductor laser, the ring is formed by a planar waveguide having a shape such as: circular, ellipsoid, oval, running-track shaped or egg-shaped (in particular in the shape of a Hugelschaffer egg).

[0077] Optical frequency comb (OFC): a form of laser output consisting of a series of discrete, equally spaced frequencies, referred to as teeth, lines, or modes. OFCs can be classified by their temporal behaviour into amplitude modulated (AM) OFCs, with periodic intensity outputs as often associated with ultrafast optical pulses, and frequency modulated (FM) OFCs, which exhibit temporally varying instantaneous frequencies while maintaining near constant optical intensities.

[0078] Free spectral range (FSR): the spacing in optical frequency between two neighbouring comb teeth sometimes referred to as beatnote frequency, frep.

[0079] Intermodal beat time: Intermodal beat time, Trep, is the inverse of the FSR, frep.

[0080] DESCRIPTION OF FIGURES

[0081] Fig. 1 is a schematic graph to illustrate the principles of the dynamics of QW OFC generation according to the invention which shows the efficiency of the coupling by modulation M between the dispersed modes, with frequencies spaced by 1 of the cold cavity, where gain, g, is also playing a role. Single mode lasing is established (M = 0) at the maximum of the cavity net gain spectrum, where the net gain spectrum is shown schematically by the arched curve. Namely, applying a sufficiently large (DC) injection current through the semiconductor diode overcomes cavity losses and brings the ring cavity above its lasing threshold so that single mode lasing occurs at the cavity mode frequency with the highest net gain. The cavity mode spacing may also be thought of as the roundtrip frequency as defined by the inverse of the roundtrip time of light propagating around the ring cavity. When a phase modulation is additionally applied to the optical field at a modulation frequency matched near resonantly to the lasing cavity mode spacing, the single lasing mode performs a spectral quantum walk and expands ballistically in discrete frequency steps of a size that is determined by the coupling strength, C, which is in turn proportional to the modulation strength, M, these equal steps being illustrated schematically in Fig. 1. The near-resonant phase modulation causes coherent side-mode generation by quantum walk around the single mode laser mode and a continuous increase in the comb's bandwidth occurs. After some time, the cavity’s intrinsic bandwidth limitations are reached and the OFC spectrum stabilises at a bandwidth which can be predicted from the cavity properties of net gain curve, dispersion in the semiconductor gain medium and other factors.

[0082] The OFC is thus generated by a quantum walk and is hence referred to in this document as a QW OFC. The QW OFC is characterised by a relatively flat spectral envelope and near constant intensity between the comb ‘teeth’. This is in contrast with broadband OFCs generated by pulsed mode-locked lasers or by nonlinear generation in microresonators, which stabilise into a peaked spectrum that is typical of a pulsed state. Additionally, in the proposed laser design exploiting a quantum walk to generate the OFC, the bandwidth of the frequency comb is continuously tuneable by varying the amplitude of the phase modulation (e.g. through varying the modulation amplitude of an AC component of the injection current).

[0083] We consider a synthetic lattice comprised of the resonator modes of an active ring cavity. To enable linear coupling among lattice sites in the synthetic space and observe the continuoustime quantum walk, a ring cavity geometry is needed. This is not possible in a linear cavity (Fabry-Perot), since spatial hole burning would prevent the quantum walk from occurring. The underlying mechanism of the random quantum walk can only occur if the gain medium has a sufficiently fast gain recovery time, 7 , in relation to its intermodal beat time, Trep, which is the inverse of the OFCs FSR, i.e., on the ratio: ^ / T^p. The capability of the laser to operate in the QW OFC regime can therefore be expressed by the ratio ^ / T^p exceeding a certain threshold, for example at least unity. The fast gain recovery time, i.e., high value of the ratio T / Trepstabilises the QW OFC spectrum at a certain bandwidth, which is determined by the following factors: dispersion, gain curvature, gain saturation and RF modulation. Since phase modulation is an easily controllable operational parameter, the bandwidth of the frequency comb (and also the beatnote frequency) is controllable. Without fast gain, dissipative mechanisms would make the laser operate in a narrow Gaussian regime as opposed to the high bandwidth achievable with fast gain.

[0084] The QW OFC is characterised by a flat-topped comb spectrum (approximating to a Bessel function shape) with the comb teeth have near equal intensity across the comb. The number of teeth in the frequency comb may be several thousand. These mutually coherent comb lines can be used for telecommunications as WDM channels. For infrared sensors, the comb lines can be used for observing distinct absorption wavelengths of gas molecules of interest. In a dual-comb spectrometer, two combs can be provided to generating radio frequencies through beating between the two combs.

[0085] We now discuss and compare generation of a QW OFC based on either an intersubband lasing transition in a QCL or an interband lasing transition in a more conventional semiconductor diode structure.

[0086] In the case of a QCL, the gain recovery times are of the order of hundreds of femtoseconds which is fast enough for the QCL to stabilize on a broad spectrum. The fast gain recovery times of QCLs are understood to follow from the intraband nature of the carrier relaxation in a QCL.

[0087] In the case of interband semiconductor lasers, the gain recovery times for the interband transition between the conduction and valence bands are understood in the literature to be several orders of magnitude slower. For example, gain recovery times, 7 , are quoted to be around 1 ns for InGaAs in the literature; see Figure 1C of Ref. 3 - Piccardo and Capasso 2021 , which of the order of 1000 times slower than for a QCL. The normally quoted gain recovery time for conventional semiconductor diode lasers is however taken from the interband carrier relaxation time, i.e. , the time taken for an electron-hole pair to recombine. The present inventors have exploited the realisation that this slow gain relaxation time is not an inherent property of the interband transition. Rather, if the semiconductor diode is subject to sufficiently strong current injection, interband stimulated emission is characterised instead by the intersubband relaxation time, i.e. the fast relaxation time conventionally associated with QCL operation.

[0088] In other words, QW OFC generation is possible not only semiconductor lasers such as QCLs where the lasing transition is an intersubband transition but also in semiconductor lasers where the lasing transition is an interband transition provided that special conditions are fulfilled in the design and operation of the interband semiconductor laser to ensure the gain relaxation time follows from fast intersubband relaxation time and not the slow interband relaxation time. These special conditions include DC current injection far above threshold, the presence of near-resonant phase modulation and unidirectional lasing around a ring cavity. A fast gain recovery time in the ring cavity can also be achieved by increasing the quality factor, Q, of the cavity, since a higher Q-factor provides greater optical field build up in the ring cavity. A higher Q-factor is achieved by reducing cavity losses, i.e., increasing photon lifetime, which in an external ring cavity can be achieved by reducing optical losses of the different optical components that make up the cavity. In summary, the gain recovery of intersubband (i.e. intraband) lasers is qualitatively different from their interband counterparts. In intersubband lasers, the gain recovery is a result of fast intersubband carrier capture and relaxation, whereas in interband lasers it is a result of a slower interband processes. Nevertheless, the fast gain recovery times associated with intersubband lasers can also be induced in interband lasers by increasing the optical field circulating in the cavity and / or increasing the magnitude of the phase modulation.

[0089] Phase modulation introduces coupling giving rise to continuous-time quantum walk dynamics in the ring cavity. For a fixed coupling C, corresponding to a certain value of the current component lAc, the broadest achievable lasing state is limited by the dispersion in the system, which causes mode resonances to move apart, resulting in less efficient coupling.

[0090] Qualitatively, dispersion induces an effective potential well in frequency space, while the width of the band created by modulation limits the maximum achievable "kinetic energy" and, consequently, the system's bandwidth. Through this argument, for instance, quadratic dispersion will constrain the highest accessible mode to

[0091] M nmax2D where M = 2C represents the modulation strength and D signifies dispersion. This system can be analogously mapped to a quantum harmonic oscillator, which can only occupy a finite number of possible modes.

[0092] Unidirectional lasing in an integrated structure in which the ring cavity is formed by a closed- loop planar waveguide is provided by symmetry breaking and the consequent asymmetric net gain which causes lasing in one of the propagation directions to dominate over the other. This behaviour is possible by taking measures to reduce backscattering which would otherwise couple the clockwise and counterclockwise propagating light fields strongly enough to prevent symmetry breaking, since the self-gain saturation is smaller than the cross-gain saturation that arises from the counterpropagating mode. If backscattering is too large, lasing will tend to occur in both propagation directions, and the laser will not be capable of generating a QW OFC according to the invention. The design and fabrication measures that we adopted to reduce backscattering in our integrated structures are as follows, and this may not represent an exhaustive list. Firstly, the ring cavity is designed to avoid step changes of curvature, which would generate mode-mismatch losses. Secondly, during fabrication, a wet-etch process is used for forming the waveguide, since this tends to produce smoother sidewalls. Thirdly, anti- reflective coatings are deposited on the waveguide sidewalls which are semiconductor-air interfaces, to reduce the amount of waveguided light with wavelengths within the bandwidth of the laser that is reflected back into the waveguide. In ring cavities where backscattering and hence coupling between clockwise and counterclockwise propagating modes is sufficiently low, spontaneous symmetry breaking occurs just above threshold, enabling the laser to operate in a unidirectional single-mode state from just above threshold. When a phase modulation component of the optical field is included, and provided that the gain recovery time is sufficiently short, the laser changes from single mode operation to frequency comb generation. Here it will be understood that the phase modulation frequency must be matched to, i.e. , be near resonant with, a cavity resonance frequency. Most straightforwardly this will be the fundamental mode. However, it may alternatively be some higher integer multiple thereof for harmonic mode lasing, e.g., one of 2, 3, 4, 5, 6, 7,8, 9 and 10 times the fundamental resonance frequency. Moreover, lasing at the fundamental mode may also be generated by a phase modulation frequency that is an integer fraction of the (fundamental) resonance frequency, e.g., one half, one third, one quarter, one fifth, one sixth, one seventh, one eight, one ninth or one tenth.

[0093] Fig. 2 and Fig. 3 are corresponding plots in frequency space and time space respectively to show how varying the gain recovery time varies the number of supermodes, ISM, that exist in the QW OFC and how varying the gain recovery time also varies the bandwidth of the QW OFC. The plots are of the number of QW OFC supermodes, ISM, VS. the cavity mode number, m. The number of OFC supermodes, ISM, is the number that will be generated at a given value of the gain recovery time. A family of curves is shown in order of decreasing / increasing order of the supermode. Notably, eigenmodes that are temporally broad also display a spread-out distribution in time, and vice versa In analogy to the quantum harmonic oscillator, the zeroth order supermode corresponds to a Gaussian pulse in the discretised frequency (bottom trace of Fig. 2 and Fig. 3).

[0094] Fig. 4 shows two simulations that compare the behaviour of a fast gain laser embodying the invention with the behaviour of an otherwise equivalent laser with slow gain as a comparative example. The fast gain laser behaviour is shown in the left panel and the slow gain laser behaviour in the right panel. A family of curves is shown for each example at different times, t’, after the start of phase modulation at zero time. Time evolves from zero for the bottom traces long enough to show stabilisation of the laser output in both the inventive and comparative example. The time, t', is in units of the maximum mode number divided by twice the coupling strength, C. The output light spectral intensity of the lasers shown in the curves is normalised and in arbitrary units. The light frequency is plotted in units of cavity mode number, m. The simulation of the inventive example laser (left panel) shows that after application of the phase modulation at time zero, quantum walk ballistic expansion occurs and then the QW OFC stabilizes at a certain bandwidth (top three curves of left panel are after stabilization). The dynamics of the fast gain laser (left panel) are characterised by an initial ballistic expansion upon the onset of nearest-neighbour coupling, C, followed by a stabilisation of the OFC spectrum due to dispersion and dissipative effects. The simulation of the comparative example laser (right panel) shows that after application of the phase modulation at time zero, an initial ballistic expansion starts collapsing until the laser output stabilizes with an output of a single narrow Gaussian profile (right panel, top trace). The frequency-dependent gain and dispersion leads to a contraction into the narrow Gaussian supermode.

[0095] First Embodiment

[0096] Fig. 5 is a schematic plan view of a laser 10 according to a first embodiment of the invention. The ring cavity 12 of laser 10 is shaped in the form of an egg, to have a single high curvature point 20, to produce emission from a single point in one of the two directions 22 or 24. The length of the device is 2a and its width is 2b. The device is modulated only in part of the circumference 18.

[0097] Fig. 6 is a schematic circuit diagram of a laser module 100 incorporating a laser 10 according to the first embodiment of the invention. The laser module 100 includes a driver circuit 30 and a controller 32. In Fig. 6, the laser 10 is shown electrically as a diode. The laser 10 may be an intraband semiconductor laser such as a QCL or an interband semiconductor laser. In the first embodiment, the ring cavity and the semiconductor gain medium are integrated on a single semiconductor chip 14 by a planar waveguide 12 that has a ring shape, such as the illustrated egg shape. The laser 10 has separate contacts 16, 18 for delivering DC and AC current components to the semiconductor laser. These are shown connected to the anode side but may be either on the anode side or cathode side depending on whether the laser is driven via a current source or a current sink ('push' or 'pull'). This is a design decision. The driver circuit 30 will be appropriately designed. Equivalently, a single anode contact could be used for delivering both DC and AC current components to the semiconductor laser via a single wire connection, the DC and AC current components being combined or jointly generated in the driver circuit 30.

[0098] The anode contacts 16, 18 may be formed by metallization on top of the planar waveguide, which may be formed as a ridge waveguide. The cathode contact 19 can be formed by blanket metallization of the substrate, i.e., on the underside of the chip, or on the top surface, e.g., by etching down to allow a conductive connection to a lower cladding layer. Current injection into the laser 10 is controlled by the driver circuit 30 which is connected across the anode and cathode electrodes 16, 18, 19 by a pair of anode lines 34, 36 and a common cathode line 38. The anode and cathode electrodes are metal or metallic and form an ohmic connection with the semiconductor material to which they are interfaced. A conductive path is thus formed between the common cathode 19 and the driver circuit 30 and separate conductive paths 34, 36 between the DC and AC anodes 16, 18 and the driver circuit 30. The driver circuit 30 act as a current source that receives respective voltage signals VDc and VAC from the controller 32 as input and output correspondingly modulated currents lDc and lACto drive the laser 10. The DC biasing current lDc serves to switch the laser 'on' and 'off' and the AC modulated current lACacts as a phase modulation to generate and adjust the OFC.

[0099] Laser light is coupled out of the ring cavity by engineering a length portion of the planar waveguide to have increased light loss at the lasing frequency. This can be done by producing that length portion with greater bending losses at its outer radial sidewall. For example, this can be achieved through the outcoupling portion having a smaller radius of curvature, which is the case when the ring cavity is shaped with the geometry of a Hugelschaffer egg as illustrated. In doing so, the higher curvature at the tip of the egg creates an out-coupling point as schematically illustrated in Fig. 5. For clockwise lasing, the output beam is shown with reference numeral 22. For counterclockwise lasing, the output beam is shown with reference numeral 24. Only one of these output beams will exist for unidirectional lasing, which is established in this integrated design by asymmetric net gain, as described elsewhere in this document.

[0100] Another way to provide output coupling would be to reducing the refractive index difference on the outer sidewall of the waveguide over a certain length portion to give that portion higher losses.

[0101] A further way to provide output coupling would be to provide another waveguide extending tangentially to a portion of the ring waveguide so as to allow evanescent coupling of laser light into this other waveguide.

[0102] Coupling of the resonator modes in the ring is achieved through near-resonant RF current modulation of the semiconductor chip via electrode 18. This effect is enabled by the active region itself, as gain modulation is translated into phase modulation through a non-vanishing linewidth enhancement factor.

[0103] In a variation of the design, it is noted that the phase modulation need not be provided by an AC component of the injection current. Instead, phase modulation could be induced in a length portion of the ring by electric field induced modulation of the refractive index in the active region. Separate electrodes could be provided for this purpose to generate an electric field (without current flow) at the desired modulation frequency across a length portion of the ring waveguide.

[0104] First Embodiment: Example Prototypes

[0105] Three example ring cavity QCL devices according to a first embodiment of the invention were fabricated from the same wafer. This wafer was grown with a semiconductor multi-quantum well stack. More specifically, a strain-balanced multi-quantum well structure with InGaAs wells and InAIAs barriers was grown on an InP substrate. The alloy compositions in the multiquantum well layer sequence were InQ 595GaQ 4Q5As and In036Al064As. For one period of the QCL active region, starting with the injection barrier, the layer sequence was as follows with the thicknesses specified in Angstrom:

[0106] The sheet carrier density was 1.04E11 cmA-2.

[0107] These QCLs lase in the mid-infrared spectral region at around 8 pm.

[0108] Each QCL was fabricated using the inverted buried-heterostructure process according to

[0109] • Beck M, Hofstetter D, Aellen T, Faist J, Oesterle U, llegems M, Gini E, Melchior H. Continuous wave operation of a mid-infrared semiconductor laser at room temperature.

[0110] Science. 2002 Jan 11;295(5553):301-5 https: / / www.science.Org / doi / 10.1126 / science.1066408 [Ref. 6] from the active region specified above. The width of the wet-etched active waveguides was between 6 pm and 10 pm. The chip was mounted epitaxial side up to allow access to a gold top contact for precise current injection. The wires for the DC component of the injection current were spread over the whole top contact to achieve homogeneous electrical pumping, while the wires for the RF component of the injection current were positioned in close proximity to each other over a relatively small length portion 18 of the ring cavity distal the tip of the egg. The highest emission from the ring cavity occurred at the tip of the egg, as schematically illustrated, as expected owing to its tighter radius of curvature leading to higher bending losses.

[0111] The different prototype devices differed in the geometric parameters defining the Hugelschaffer egg shape which is characterised by the parameters a, b, d. A Hugelschaffer egg shape is defined by a first circle with centre O and radius b and a second circle with a centre offset from the first circle by a distance d and having a radius a. Details of the three prototype devices are as follows:

[0112] First Embodiment: characterising the spectral output

[0113] Fig. 7A and Fig. 7B are respectively simulated (theory) and experimental plots of spectrum vs. wavenumber in units of cmA-1 vs. as a function of the RF modulation frequency in GHz for a range of modulation frequencies around resonance with the lasing cavity mode frequency for a laser according to a first embodiment of the invention.

[0114] Fig. 70 are theoretical and experimental plots of lasing mode intensity, I, in arbitrary units (normalised) vs. wavenumber in units of cmA-1 showing behaviour at different modulation frequencies.

[0115] Fig. 7D are simulated and experimental plots of instantaneous wavelength in units of cmA-1 vs time in picoseconds with the four panels - Panel 1 to Panel 4 - showing behaviour at the four different modulation frequencies shown by the vertical dashed lines in Fig. 7B. Column I (experimental) shows the experimental results. Column II (numerical) shows simulated data. Column III (analytical) shows theoretical data from an analytically derived expression. Figs. 7A to 7D consider four different working points labelled 1 to 4. Working point 2 is on resonance (phase modulation frequency equals lasing cavity mode frequency). Working point 1 is far away from resonance. Working point 3 is near resonance. Working point 4 is further away from resonance than working point 3 but still near resonance in the sense that QW OFC generation is still supported. As the modulation frequency is detuned from resonance, the QW OFC bandwidth narrows continuously.

[0116] Fig. 8 shows the SWIFTS experimental set up used to obtain the experimental steady-state spectra shown in Figs. 7B to 7D. The main component of the optical set-up is an interferometer designed in a folded Mach-Zehnder configuration that minimizes back- reflections into the laser. The RF-modulated injection current was provided by a microwave signal generator (Model SMF100A from Rohde & Schwarz). The laser light output from the QCL was collimated into a beam with suitable collimation optics and directed into the input port of the interferometer. At the interferometer's output, a fast (bandwidth » 20 GHz) quantum well infrared photodetector (non-commercial, customized) is used, from which the DC and RF traces can be read simultaneously. A reference laser at a wavelength of 1550.48 nm is used to acquire the optical path delay from the moving mirror of the interferometer. The spectrally resolved RF signal of the fast detector is down-mixed to » 20 MHz to fall in the bandwidth of the Lock-In amplifier (Model HF2LI from Zurich Instruments) from which are obtained the quadrature components. To avoid crosstalk between the reference signal used for demodulation and the RF from the quantum well infrared photodetector, two circulators were used to improve isolation between the two RF paths. The reference laser, the DC trace, and the quadrature components are synchronously acquired and resampled afterwards.

[0117] Absent near-resonant phase modulation, the device operates as a single-mode laser lasing at 1280 cmA-1 at the investigated working point at a DC injection current of 1.456 A and at temperature of -16°C. When the RF modulation current component was added, the QW OFC gradually and reliably broadens to a bandwidth of 70 cmA-1.

[0118] For resonant modulation (working point 2), the spectral envelope showcases lobes on both sides and a nearly flat centre, as expected for a quantum walk stabilizing on a highly excited state. For this resonant injection, a participation ratio, given by where Imis the intensity of the m-th optical mode, of 74.3 is computed for the 132 involved lattice sides, indicating a highly delocalised, i.e. flat, spectrum. As the modulation frequency detunes away from resonance, the spectra narrow continuously and displays an imbalance (working points 3,4), which rectifies far from resonance (working point 1). The theoretical data shown in Fig. 7A, Fig. 7C and Fig. 7D are obtained from modelling based on the model disclosed in

[0119] • David Burghoff, "Unraveling the origin of frequency modulated combs using active cavity mean-field theory," Optica 7, 1781-1787 (2020) https: / / doi.org / 10.1364 / 0 PTICA.408917 [Ref. 7]

[0120] • Nikola Opacak and Benedikt Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity”, Phys. Rev. Lett.

[0121] 123, 243902 (2019) https: / / doi.Org / 10.1103 / PhysRevLett.123.243902 [Ref. 8] while neglecting spatial hole burning, since there is no counterpropagating wave in our case. In this model, the phase of the optical field follows the modulation with depth M and detuning AQ from the cavity resonance. Through this model, assuming instantaneous gain for QCLs and thus a constant intensity, we calculated the steady state of the electric field in the corotating frame of reference. By adjusting only a small set of parameters, we accurately reproduced the experimental spectra shown in Fig. 7A, Fig. 7C and Fig. 7D. The bandwidth of the comb under resonant modulation reaches the previously discussed fundamental limit of the synthetic lattice. The FSR of the devices was around 1 GHz.

[0122] Upon closer examination of the phases predicted by our model, we observe the existence of two distinct lasing regimes, which depend on the detuning AQ of the injected frequency from the cavity resonance. In the case of highly off-resonant phase modulation, the comb state exhibits Bessel-like spectra and sinusoidal instantaneous frequency with the periodicity of the injected signal, akin to the characteristics previously observed in pure FM lasers as described in:

[0123] • S. Harris and O. McDuff, "Theory of FM laser oscillation," in IEEE Journal of Quantum Electronics, vol. 1, no. 6, pp. 245-262, September 1965 https: / / doi.Org / 10.1109 / JQE.1965.1072231 [Ref. 9]

[0124] However, within a range of near-resonant phase modulation, we observed another FM QW OFC regime characterised by a discontinuous cosine phase at only half the modulation frequency (Fig. 7D). The phase adheres to the following analytically derived relation (labelled 'ana' in Fig. 7D), assuming a constant intensity: where K represents the cavity wavenumber, and N1and N2denote the amplitudes of phase modulation, which directly rely on the modulation depth M and dispersion (3. The steady-state SWIFTS measurements confirmed coherence over the entire bandwidth of the QW OFCs as well as the ability to continuously and predictable tune the OFCs both in bandwidth and FSR.

[0125] First Embodiment: Quantum Walk Dynamics

[0126] To investigate the quantum walk dynamics from its onset until it stabilises or locks into a steady-state spectra, we conducted measurements and simulations which explore the underlying transient processes.

[0127] Fig. 9 shows corresponding theoretical results and experimental results (in the format of Fig. 4B) plotting intensity, I, in arbitrary units vs. wavelength in units of cmA-1. The time evolution shows the establishment of the OFC by quantum walk - the ballistic expansion - and its subsequent stabilisation at a finite bandwidth after approximately 250 ns from time zero which is the time of activation of phase modulation.

[0128] The theoretical modelling and experimental results are for a prototype laser according to the first embodiment. The modelling results are from simulations based on the Maxwell-Bloch master equation and reproduce the ballistic expansion and subsequent locking to a spectrally broad supermode. The time-resolved experimental measurements are in close agreement with the modelled theoretical data. To track the dynamical comb broadening under RF modulation, we employed boxcar averaging in conjunction with an FTIR at 10 ns temporal resolution. The experimental spectra exhibit a ballistic expansion to a maximum bandwidth of 70 cmA-1 after a quantum walk time of approximately 250 ns. After that the spectral state remained stable for the duration of the investigated time periods.

[0129] Building upon these experimental findings, we now discuss the underlying theoretical model, using the Maxwell-Bloch framework to unravel the dynamics of the quantum walk responsible for the observed spectral broadening during RF modulation. As mentioned earlier, the free- running laser solely occupies the resonator mode with the highest gain, but when resonant injection is introduced, mixing of the optical photons and modulation quanta Q leads to nearest-neighbour gain in the photonic lattice. Through discrete hopping between resonator modes, the photons perform a continuous-time quantum walk, resulting in a ballistic broadening of the spectrum, whose bandwidth increases linearly with the number of quantum walk steps. Once the spectrum reaches the frequency boundary dictated by the dispersion and modulation parameters, it stabilises into a broad supermode both spectrally and temporally, maintaining this state for subsequent time intervals. The only clear difference between the experiment and our model is the much slower experimental decay of the central mode at 1287 cmA-1 in the measured spectra. The otherwise remarkable agreement between our simulated and experimental spectra provides compelling evidence for the rapid expansion and stable locking of the QW OFC.

[0130] First Embodiment: Tuneability and stability

[0131] Fig. 10, Fig. 10A and Fig. 11 show experimental data and theoretical modelling results for example prototype lasers according to the first embodiment while operating in the QW OFC generation regime. Fig. 10 is a plot of experimental results showing output spectra in units of wavenumber cmA-1 in a first prototype laser according to the first embodiment at a number of different values of injected modulated power (modulation amplitude) up to 33.8 dBm, the plots being of the QW OFC after stabilisation. Fig. 10A corresponds to Fig. 10 for a second prototype laser according to the first embodiment. The second prototype device (Fig. 10A, Fig. 11, fitted curve for cross data points) showed bandwidths of up to 100 cmA-1 but could not be driven at resonance. Fig. 11 is a plot of the route of injected modulation power vs. OFC bandwidth in the first and second prototype lasers of Fig. 10 and Fig. 10A respectively. Circles and crosses show results for the first and second prototype devices respectively. The dashed lines are fitted curves. For the first prototype device, the progressive broadening of the spectra with increasing injection power (Fig. 10) follows the predicted M (and V?) dependence up until saturation at around 31.5 dBm (Fig. 11 , fitted curve for circle data points). For the second prototype device, the progressive broadening of the spectra with increasing injection power (Fig. 10A) follows the predicted M (and V?) dependence up until saturation at around 10 dBm (Fig. 11 , fitted curve for cross data points).

[0132] Solving the Maxwell-Bloch equations at resonance, we can determine the state on which the quantum walk stabilises, leading to a bandwidth dependence of . This power dependence of the bandwidth offers a quadratic improvement over the MA1 / 4 relation typically seen in active mode-locking of lasers. Since the modulation depth M is proportional to the square root of the injected power, a parameter that we experimentally control through injection current and voltage, we anticipate observing a PA1 / 4 dependence of the bandwidth.

[0133] Confirming this expectation, a power sweep at resonance validated the predicted scaling behaviour, with saturation occurring around 66 cmA-1 at 31.5 dBm for the investigated device (Fig. 10). We attribute the deviations from the expected behaviour at high power to nonlinearities in the modulation dynamics of the QCL active region, as well as higher-order dispersion. The simple relationship between modulation power and optical bandwidth allows the power per comb line to be controlled flexibly and with very short time delays, since the average laser power remains approximately constant. The inset of Fig. 10 shows results for another one of the prototype devices, which exhibited an even broader bandwidth that reached 100 cmA-1; however, it could not be driven to full resonance. The most likely reason is a larger amount of third-order dispersion resulting from the wider waveguide. Under resonant phase modulation by RF injection current modulation, the comb demonstrates the same level of stability as the free-running single-mode laser, providing evidence that the modulating the injection current does not introduce additional noise contributions. In particular, the measured amplitude noise power spectral density is unchanged by modulation.

[0134] Performance is shot noise limited above approximately 100 kHz and exhibits the distinct 1 / f dependence for lower frequencies. These remarkable characteristics attest to the exceptional stability of the QW OFC. With the stable RF current modulation being faithfully transferred to the optical spectrum, the quantum walk comb presents a highly promising platform for the generation of broadband, tuneable, and stable OFCs.

[0135] While the above discussion of tuneability and stability of the QW OFC is made in the context of the first embodiment, i.e. , the QCL embodiment based on intersubband lasing transition, the same comments apply to embodiments based on an interband lasing transition, specifically the second embodiment.

[0136] Alongside controlling the injection frequency and power, the QW OFC offers an additional capability of shaping its spectral output through the introduction of artificial phase noise. This can be achieved, for instance, by employing a Gaussian noise source and applying phase modulation to the radio-frequency injector before it is supplied to the laser gain medium. This results in temporally varying additional frequency components alongside the resonant injection frequency, which can influence the emitted optical spectra of the QW OFC in various ways, depending on the bandwidth and relative power of these phase noise contributions. Firstly, with negligible or sufficiently low phase noise excursion, the near-Bessel spectra of the unperturbed resonantly modulated QW OFC are observed. Secondly, with larger phase noise excursions, the spectrum becomes delocalised, exhibiting an increased participation ratio as its spectral intensity distribution flattens and broadens slightly. Thirdly, with even higher phase noise excursion, the QW OFC emits an optical spectrum with a Gaussian envelope and reduced participation ratio compared to the aforementioned cases. Lastly, with very high phase noise excursion, the spectrum decays exponentially on both sides of the original singlemode emission, resembling distributions known from localisation phenomena.

[0137] Second Embodiment

[0138] Fig. 12 is a schematic drawing of a laser 10 according to a second embodiment of the invention, which is based on an interband semiconductor optical amplifier (SOA) 50 serving as the gain medium arranged in an external ring cavity. The laser 10 of the second embodiment is thus an external-cavity diode laser in which the gain medium element is provided by a SOA. The SOA is a semiconductor chip with a planar waveguide extending between end facets of the chip. Light is coupled into one end facet, travels through the planar waveguide and is coupled out of the other end facet, with the light being subject to optical amplification in the waveguide by electrical current injection across the semiconductor diode.

[0139] The ring cavity is formed by cavity mirrors 42 and 44 and a reflective internal surface of a beamsplitter 20, which serves as a cavity mirror with less than 100% reflectivity (e.g. 90%), and thereby constitutes the output coupler. An optical isolator 40 is arranged in the optical path of the cavity to provide greatly different propagation loss values in the clockwise and counterclockwise propagation directions and thus ensure that only unidirectional lasing is possible. In the illustration, the optical isolator only permits clockwise propagation by way of example. It will be understood that the placement of the optical isolator 40 and SOA 50 within the cavity is arbitrary so long as they lie in the optical path. Moreover, it will also be understood that other optical elements could be used instead of an optical isolator to provide the desired difference between propagation losses in the two directions. In an integrated version of the second embodiment. One option would be to incorporate an active S-bend structure with opposite chirality in the respective ring resonators where parity-time (PT) symmetry can be spontaneously broken, which could lead to unidirectional lasing. Another option would be to couple a ring / race track laser to a multi-mode interferometer (MMI) section terminated into two reflectors with relatively strong reflection on one side and a weaker reflection on the other side leading to unidirectional lasing.

[0140] The SOA 50 is connected to a suitable laser driver circuit 30 (not shown) for generating the DC and AC drive current components and a controller 32 (not shown) for providing suitable control signals to the drive circuit 30, which will typically be voltage signals. In this embodiment, the semiconductor chip has a single drive electrode 46, e.g., on its anode, which receives a drive current on a single connection line 45 carrying summed AC (referred to as RF) and DC current components. The AC and DC current components are separately generated by the driver circuit 30 (not shown) and supplied to a combiner circuit 48 via respective DC and AC connection lines 34 and 36.

[0141] The magnitude of the current injection applied to the SOA is significantly above the threshold current for lasing in order to provide the fast gain associated with the intersubband relaxation time. Specifically, in certain embodiments based on an interband lasing transition in a semiconductor gain medium, the magnitude of the injection current is at least one of: 2, 3, 4 or 5 times that of the threshold current.

[0142] It will be understood that the number of cavity mirrors (including the output coupler) used to form the ring cavity can be chosen as desired and also that the ring cavity need not be in a loop form but may involve crossings, e.g., in a figure-of-eight configuration.

[0143] With an external ring cavity, there is also the option of providing the phase modulation away from the semiconductor chip. For example, phase modulation could be provided by an electro- optic modulator (EOM) arranged in the cavity. The SOA would then only be biased with the DC current.

[0144] It is further noted that the approach mentioned in connection with the first embodiment could also be used in external ring cavity designs, namely on-chip refractive index modulation of a length portion of the waveguide by applied electric field. The planar waveguide would then have an SOA gain section with DC current injection in series with a phase modulation section with its own independent electrodes to generate a variable electric field to modulate the refractive index along a length portion of the waveguide.

[0145] Second Embodiment: Example Prototype

[0146] The SOA 50 is a C-band booster optical amplifier chip which is a traveling wave, high saturation (18 dBm at -3 dB), polarization maintaining optical amplifier with a centre wavelength of 1550 nm. The SOA 50 incorporates a straight waveguide with a length of 1.5 mm. The active region is formed by a strain-engineered InP / lnGaAsP multi-quantum well heterostructure. Respective aspheric lenses (not shown) are arranged in the optical path to couple the light into the SOA 50 and to collimate the light output from the SOA 50. The beamsplitter 20 is a non-polarizing cube beam splitter. At the optimum operation point of the cavity, the beam splitter has 90% reflectivity and 5% transmissivity with an additional 5% of estimated losses. The cavity mirrors 42, 44 are broadband dielectric mirrors. The optical isolator 40 is a fixed band isolator consisting of two Faraday rotators in series. At the single mode optimum operation point of the laser cavity, the isolator has an 84% transmission and 50 dB isolation. This level of isolation is sufficient to allow lasing in only one direction.

[0147] Lasing occurs when the net gain equals zero in the laser, i.e. , modal gain equals modal loss. The main loss mechanism in this external ring cavity can be attributed to the coupling of light circulating in the cavity to the waveguide end facets of the SOA chip. A lasing threshold of 59 mA is observed. The SOA is operated at several times above its lasing threshold current, with the multiple being at least 3 in our experiments. This leads to more than 15 dBm optical power circulating in the cavity.

[0148] To achieve an actively mode-locked laser operating in the OFC generation, an RF modulation is added, which is done here by adding the RF modulation to the SOA drive current so the drive current has an AC component added to its DC bias current.

[0149] When the RF modulation is swept in frequency around the cavity’s resonance frequency (its fundamental) over a range of about ±250 KHz, it is observed that the laser lases in two different OFC generation regimes depending on the offset between the RF modulation frequency and the cavity resonance frequency. There is a conventional OFC regime at large offset which switches to a QW OFC regime at small offset. These two comb generating regimes are distinct in the way the optical bandwidth is related to the RF modulation depth. In the conventional OFC regime, the bandwidth is linearly proportional to the phase modulation amplitude (here the AC current modulation amplitude) while in the QW OFC regime there is a square root dependency between the two. In other words, the QW OFC generation regime is uniquely identifiable, and distinguishable from the conventional OFC regime, by its square root dependency between bandwidth and phase modulation strength.

[0150] Fig. 13 is a graph plotting output power in dBm vs frequency in THz for a prototype laser according to the second embodiment while outputting a QW OFC. The OFC has a bandwidth of 1.072 THz and an RF injection input of 15 dBm. The lasing frequency bandwidth lies between approximately 188.6-189.8 THz corresponding to a wavelength range of 1580.67 nm to 1590.61 nm. The frequency comb shown in this figure has a relatively flat-top bandwidth resulting in an even intensity distribution across its bandwidth.

[0151] Concluding Remarks

[0152] In conclusion, ballistic expansion, and stabilization of the spectrum in a synthetic photonic lattice has been observed experimentally in real time in both QCLs, where an intersubband transition is the lasing transition, and an external ring cavity laser based on a semiconductor gain medium, where an interband transition is the lasing transition. This effect is induced by resonant phase modulation and is due to a nonlinear continuous-time quantum walk. In particular, the fast gain saturation that constrains the output to a near-constant intensity leads the quantum walk to the spectrally broadest state allowed by dispersion. The quantum walk comb exhibits high predictability, tunability, and stability. In this way, we address an issue raised many years ago: active mode-locked devices with slow gain recovery operate on the fundamental narrowest Gaussian mode with limited comb bandwidth, all other modes being unstable. Leveraging the insights gained from our work, deliberate design strategies for wide- bandwidth comb sources could open applications in fields such as spectroscopy and telecommunications, both for infrared wavelength ranges accessible by QCLs but also shorter wavelengths accessible by interband semiconductor transitions. Furthermore, this approach holds promise for the application of quantum walk algorithms in systems featuring designated nonlinear interactions among qubits and can be generalised to higher dimensional lattices in either real space with coupled resonators or synthetic space using additional modulation frequencies.

[0153] WDM / DWDM System Application Example

[0154] A promising approach to meet future data transmission requirements is to employ optical interconnects based on silicon photonics integrated circuits. These systems rely on wavelength division multiplexing (WDM) or dense wavelength division multiplexing (DWDM) to provide a high degree of parallelism. Optical frequency combs can be generated with hundreds of “teeth” and hence provide hundreds of optical carrier channels of a highly precise and equally spaced channel wavelengths. As such, OFCs are natural candidates for WDM or DWDM systems.

[0155] Fig. 14 is a schematic drawing of an example WDM transmission system comprising a WDM transmitter (Tx) 70 and a coherent receiver (Rx) 80 interconnected via an optical fibre telecommunications line (fibre link) 65. Both the transmitter 70 and the receiver 80 incorporates a laser 10 according to an embodiment of the invention to generate a QW OFC where each ‘tooth’ corresponds to a WDM channel in the WDM transmission system. The transmitter’s OFC laser 10 output is first amplified by an optical amplifier 72 and sent via a waveguide to the input of a WDM modulator 74. Here data are encoded on each line in the WDM modulator 74 which comprises a WDM demultiplexer (DEMUX) 75 paired with a corresponding WDM multiplexer (MUX) 78, the demultiplexer 75 and multiplexer 78 being interconnected via an array of dual-polarization l / Q modulators 76 as well as two unmodulated outer channels 77 which serve to synchronize the local oscillator (LO) comb frequencies to the frequencies of the OFC laser comb generated by the laser 10. The signal output from the multiplexer 78 is then boosted by an optical amplifier 79 prior to transmission from the transmitter 70 at the transmitter output 71. The transmitter output 71 is coupled into and transmitted over the optical fibre telecommunications line (fibre link) 65 to the coherent receiver 80. The coherent receiver 80 receives the transmitted signal at a receiver input 81. The input signal is passed through an optical preamplifier 82 and received by a WDM demodulator 83. The WDM demodulator 83 uses a multitude of LO tones derived from an OFC generating laser 10 according to the invention. The data carrying optical signal and the OFC output by the receiver’s laser 10 are first demultiplexed via respective WDM demultiplexers 84 which are connected back-to-back via an array of coherent detectors 85 which pick out the data carried on each WDM channel.

[0156] Convolution Neural Network System Application Example

[0157] Convolutional neural networks (CNN) are a powerful category of artificial neural networks. They are inspired by biological visual cortex systems and can abstract representations of input data in their raw form and then predict their properties. CNNs can, for example, process multidimensional data for image classification and object recognition tasks. By harnessing the unique properties of light, photonic vector convolution accelerators represent an innovative approach to accelerating CNN computations. Photonic principles are used to perform matrix multiplications and convolutions. Neural network parameters are encoded into optical signals. Using optical interference or modulation techniques allows convolution operations to be executed in parallel across a large number of channels. The speed of light coupled with a high level of parallelism enables photonic accelerators to offer ultra-high-speed computations with lower latency compared to their electronic counterparts.

[0158] Fig. 15 is a schematic drawing of an example photonic convolution accelerator incorporating a laser according to an embodiment of the invention.

[0159] The OFC output from the laser 10 is shaped via an optical spectrum shaper 93 using the weights in a kernel vector W 92. The system can perform simultaneous image convolution depending on the number of weights in the kernel vector. The later depends on the number of lines in the OFC. Each kernel occupies a certain number of wavelengths. For example, if 160 lines are available in the OFC, then it is possible to incorporate ten kernels with 4 x 4 = 16 weights each. The output of the spectral shaper 93 enters an electro-optical modulator (EOM) 94. An electrical input waveform X 95 is multi-cast onto the shaped comb lines via the electro- optical modulator 94 generating replicas weighted by a weighting factor W. To achieve both time and wavelength interleaving, the optical waveform exiting the EOM 4 is transmitted through a dispersive optical fibre delay line 96. An optical demultiplexer 97 is connected to the end of the fibre delay line 96. The function of the optical demultiplexer 97 is to separate the different subbands corresponding to the number of kernels used, i.e. , ten in above example. These subbands are then detected and converted into electronic signal via high-speed photodetectors 96 where the subband signals are summed. This results in each time slot yielding a convolution output Y 99 between X and W for a given convolution window [Ref 10],

[0160] Gas Sensor System Application Examples

[0161] One application area of interest for lasers embodying the invention is for incorporation into a gas sensor of the type based on detecting absorption of light by an absorption line of a species of gas molecule to be sensed. For molecular gases that are of commercial interest for sensing, several relevant absorption lines lie in the wavelength range 2-12 pm, for example. Two example types of such gas sensors are the non-dispersive infrared sensor (NDIR) and the photoacoustic sensor.

[0162] Fig. 16 shows an example NDIR gas sensor 52 comprising a gas cell 64, a laser module 100 according to an embodiment of the invention and a photodetector 54 as well as the optional components for an Internet of Things (loT) device of a battery 60 for powering the gas sensor 52 and a wireless transceiver 62 operable to transmit the detector signal and / or the concentration of gas molecules to a remote receiver. One example commercial product is the CA-8210 transceiver chip from Cascoda Limited. Other known loT sensor components may also be included for known functions, such as for energy harvesting to directly power the electronic components and / or recharge the battery 60. The photodetector 54 is shown schematically arranged to receive light that has been transmitted through the gas cell 64. Alternatively, the photodetector 54 may be arranged to receive light that has been back- scattered or scattered at some other angle from the gas molecules in the gas cell 64. The photodetector 54 may be a simple photodiode, such as a p-i-n diode, that is configured to output an electrical signal having a magnitude proportional or otherwise indicative of the flux of photons received. The measurement signal output by the photodetector 54 has a magnitude indicative of the concentration of the gas molecules within the gas cell 64. In an N DIR sensor, absorption will cause a reduction in the detector signal, since fewer photons will reach the photodetector.

[0163] Fig. 17 shows an example NDIR gas sensor 52 for ambient gas sensing comprising a laser module 100 according to an embodiment of the invention, a photodetector 54 as well as the optional components for an loT device of a battery 60 and a wireless transceiver 62. The detector 54 is arrranged to measure absorption of photons from the laser beam by molecules of the gas to be sensed when the laser beam has passed through a sample space potentially containing the gas to be sensed. The schematic illustration is of oblique angle scattering for ease of representation but in reality will most commonly either be by back-scattering (e.g. LiDAR) or by transmission. For example, a ceiling mounted gas sensor for use in a building may operate in transmission with the laser beam passing through a volume of ambient air (which may be within the gas sensor housing) that constitutes the sample space and the detector receiving a portion of the laser beam after it has passed through the sample space.

[0164] Fig. 18 shows an example photoacoustic gas sensor 52 incorporating a laser module 100 according to an embodiment of the invention and a gas cell 64, in which is arranged an acoustic detector 54, i.e. a microphone 54, as well as the optional components for an loT device of a battery 60 and a wireless transceiver 62. In a photoacoustic sensor, absorption will cause an increase in the detector signal, since more sound will be generated. The molecular species of interest will of course in most cases be mixed with other gas species, e.g. if the measurement is taking place in air.

[0165] It will be clear to one skilled in the art that many improvements and modifications can be made to the foregoing exemplary embodiment without departing from the scope of the present disclosure.

[0166] Further details of the invention may be found in:

[0167] • Heckelmann, Ina & Bertrand, Mathieu & Dikopoltsev, Alexander & Beck, Mattias & Scalari, Giacomo & Faist, Jerome. (2023). Quantum walk comb in a fast gain laser. Science. 382. 434-438. DOI: 10.1126 / science.adj3858

[0168] [Ref. 11] published on 27 October 2023 which is incorporated by reference in its entirety. REFERENCE NUMERALS

[0169] 10 laser

[0170] 12 ring waveguide

[0171] 14 semiconductor chip

[0172] 16 drive electrode, DC, for biasing (anode side)

[0173] 18 drive electrode, AC, for RF modulation (anode side)

[0174] 19 drive electrode (cathode side)

[0175] 20 output coupler (#1 = waveguide bend; #2 = beam splitter)

[0176] 22 laser output, CW

[0177] 24 laser output, CCW

[0178] 30 laser driver circuit

[0179] 32 controller

[0180] 34 DC drive electrode connection line (anode side)

[0181] 36 AC drive electrode connection line (anode side)

[0182] 38 drive connection line (cathode side)

[0183] 40 optical isolator

[0184] 42 cavity mirror

[0185] 44 cavity mirror

[0186] 45 common connection line to common drive electrode

[0187] 46 common drive electrode for AC + DC (anode side)

[0188] 48 combiner circuit for AC and DC drive current components

[0189] 50 semiconductor optical amplifier (SOA) chip

[0190] 52 gas sensor

[0191] 54 detector, e.g. microphone or photodetector (e.g. p-i-n diode)

[0192] 56 detector signal conversion logic

[0193] 58 detector signal interpolation algorithm for determining gas concentration

[0194] 60 battery

[0195] 62 wireless transmitter or transceiver

[0196] 64 gas cell

[0197] 65 optical fibre telecommunications line (fibre link)

[0198] 70 transmitter, Tx

[0199] 71 transmitter output

[0200] 72 transmitter optical amplifier

[0201] 74 transmitter WDM modulator

[0202] 75 transmitter WDM demultiplexer (DEMUX)

[0203] 76 transmitter dual-polarization l / Q modulator array channels

[0204] 77 transmitter outermost modulator array channels 78 transmitter WDM multiplexer (MUX)

[0205] 79 transmitter optical amplifier

[0206] 80 coherent receiver, Rx

[0207] 81 receiver input

[0208] 82 receiver optical preamplifier

[0209] 83 receiver WDM demodulator

[0210] 84 receiver WDM demultiplexers

[0211] 85 receiver coherent detector array

[0212] 90 photonic convolution accelerator

[0213] 92 weighting factor W

[0214] 93 optical spectrum shaper

[0215] 94 electro-optical modulator (EOM) 94

[0216] 95 electrical input waveform X

[0217] 96 dispersive optical fibre delay line

[0218] 97 optical demultiplexer

[0219] 98 high-speed photodetectors

[0220] 99 convolution Y between X and W

[0221] 100 laser module

[0222] REFERENCES

[0223] 1. Fortier, T., Baumann, E. 20 years of developments in optical frequency comb technology and applications. Commun Phys 2, 153 (2019). https: / / doi.org / 10.1038 / s42005-Q19- 0249-y.

[0224] 2. Chang, L., Liu, S. & Bowers, J.E. Integrated optical frequency comb technologies. Nat. Photon. 16, 95-108 (2022). https: / / doi.Org / 10.1038 / s41566-021 -00945- 1.

[0225] 3. Piccardo M and Capasso F Laser Frequency Combs with Fast Gain Recovery: Physics and Applications. Laser and Photonics Reviews Volume 16, Issue 2 https: / / doi.Org / 10.1002 / lpor.202100403. #

[0226] 4. Jorgensen, A. A., Kong, D., Henriksen, M.R. et al. Petabit-per-second data transmission using a chip-scale microcomb ring resonator source. Nat. Photon. 16, 798-802 (2022). https: / / doi.Org / 10.1038 / S41566-022-01082-z.

[0227] 5. Li, C. et al. Hybrid WDM-MDM transmitter with an integrated Si modulator array and a micro-resonator comb source. Opt. Express 29, 39847-39858 (2021) https: / / doi.Org / 10.1364 / OE.444493.

[0228] 6. Beck M, Hofstetter D, Aellen T, Faist J, Oesterle U, llegems M, Gini E, Melchior H. Continuous wave operation of a mid-infrared semiconductor laser at room temperature. Science. 2002 Jan 11 ;295(5553):301-5 https: / / www.science.Org / doi / 10.1126 / science.1066408

[0229] 7. David Burghoff, "Unraveling the origin of frequency modulated combs using active cavity mean-field theory," Optica 7, 1781-1787 (2020) https: / / doi.Org / 10.1364 / OPTICA.408917

[0230] 8. Nikola Opacak and Benedikt Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity”, Phys. Rev. Lett. 123, 243902 (2019) https: / / d0i.0rg / l 0.1103 / PhysRevLett.123.243902

[0231] 9. S. Harris and O. McDuff, "Theory of FM laser oscillation," in IEEE Journal of Quantum Electronics, vol. 1 , no. 6, pp. 245-262, September 1965 https: / / doi.org / 10.1109 / JQE.1965.1072231

[0232] 10. Xu, X., Tan, M., Corcoran, B. et al. "11 TOPS photonic convolutional accelerator for optical neural networks” Nature 589, 44-51, January 2021

[0233] 11. Heckelmann, Ina & Bertrand, Mathieu & Dikopoltsev, Alexander & Beck, Mattias & Scalari, Giacomo & Faist, Jerome. (2023). Quantum walk comb in a fast gain laser. Science. 382. 434-438. DOI: 10.1126 / science.adj3858

Claims

CLAIMS1. A laser for outputting laser light, the laser comprising: a semiconductor gain medium element comprising a plurality of semiconductor materials configured to provide a lasing transition between first and second quantised energy bands; a ring cavity formed from an optical path forming a loop having propagating and counter-propagating directions for passage of an optical field, wherein the ring cavity has a net gain spectrum and possesses a plurality of cavity modes separated by a mode spacing, wherein there is sufficient net gain at the frequency of at least one of the cavity modes to provide for single mode lasing; an output coupling portion or element of the ring cavity for coupling out a portion of laser light; an electrical driver circuit arranged to apply an injection current to the semiconductor gain medium to cause population inversion between the first and second quantised energy bands and said single mode lasing; and a phase modulator operable to provide phase modulation in the optical path at a modulation frequency near-resonant with an integer multiple or fraction of the mode spacing to cause coherent side-mode generation by quantum walk around the cavity mode responsible for said single mode lasing resulting in output of a stable optical frequency comb of finite bandwidth.

2. The laser of claim 1 , wherein the phase modulator is a part of the electrical driver circuit which is configured to generate an AC current at the modulation frequency and apply it to the semiconductor gain medium.

3. The laser of claim 1 , wherein the phase modulator is an electro-optical modulator operable to modulate the optical field at the modulation frequency.

4. The laser of claim 3, wherein the electro-optical modulator and the semiconductor gain medium element are integrated in a semiconductor chip.

5. The laser of claim 3, wherein the electro-optical modulator is a discrete component separate from the semiconductor gain medium element.

6. The laser of any one of claims 1 to 5, wherein the first and second quantised energy bands are within a conduction band and a valence band localised to one of the semiconductor materials.

7. The laser of any one of claims 1 to 5, wherein the first and second quantised energy bands are first and second subbands within a conduction band localised to one of the semiconductor materials.

8. The laser of any one of claims 1 to 7, wherein the ring cavity is formed as a planar waveguide integrally within the semiconductor gain medium element.

9. The laser of claim 8, wherein the planar waveguide is configured to suppress back scattering of light at the mode frequency from the propagating direction to the counterpropagating direction.

10. The laser of claim 8 or 9, wherein the output coupling portion or element is formed by a length portion of the planar waveguide that is configured to have increased loss, thereby coupling out a proportion of the laser light from the ring cavity.

11. The laser of claim 8 or 9, wherein the output coupling portion or element is formed by a further planar waveguide formed integrally with the semiconductor gain medium element and having a length portion extending tangentially to a neighbouring portion the ring cavity planar waveguide so as to be evanescently coupled thereto.

12. The laser of any one of claims 1 to 7, wherein the optical path forming the loop around the ring cavity comprises free-space portions and the semiconductor gain medium element is arranged as a discrete component within the ring cavity.

13. The laser of claim 12, further comprising an optical element arranged in the cavity to provide different propagation loss values in the propagating and counter-propagating directions around the loop.

14. The laser of claim 12 or 13, wherein the output coupling portion or element is formed by a mirror or beamsplitter element with a partially reflective surface or interface.

15. The laser of any one of claims 1 to 14, wherein said integer multiple or fraction is unity to cause lasing around the mode frequency.

16. The laser of any one of claims 1 to 14, wherein said integer multiple or fraction is at least two.

17. The laser of any one of the preceding claims, further comprising a controller configured to vary the phase modulation in at least one of amplitude and frequency.

18. The laser of any one of the preceding claims, further comprising an artificial noise source configured to generate artificial noise, the artificial noise source being included as partof the electrical driver circuit or the phase modulator and connected to add artificial noise to the phase modulation or the injection current respectively.

19. The laser of claim 18 when dependent on claim 17, wherein the controller is configured to vary at least one of bandwidth and power of the artificial noise.

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