Coupled laser array

Abstract

A laser system is provided. The laser system comprises a plurality of lasers, and is configured such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers with a non-zero phase delay. Methods of operating such laser systems are also provided.

Description

Coupled Laser ArrayField of the Invention

[0001] The present invention relates to laser systems, specifically to nanolaser arrays, and methods of operating such systems.Background

[0002] Lasers are a pervasive technology underpinning a broad range of techniques from security screening for airports, to LIDAR for self-driving cars.

[0003] Lasers typically provide multiple laser cavity modes, meaning that such lasers operate on multiple spatial and / or spectral modes. This is referred to as ‘multimode operation’. Multimode operation decreases spatial and temporal coherence of a laser’s output, leading to intensity fluctuations and reducing the collimation or focussing power.

[0004] Nanoscale lasers miniaturise lasers by trapping and enhancing light in sub-micron scale structures. If the size of the nanolaser structure is comparable with the light wavelength, the operation can be restricted to a single laser mode. However, the small size can in turn limit such lasers to low power operation.

[0005] It is known in the art to operate a group of similar lasers, and in particular nanolasers, as a laser array. Doing so will enhance the overall emission brightness (i.e. output power) as compared to a single laser. However, the lasers in the array will either operate independently, which can destroy the coherence of the output of the laser array, or else near-field coupling between the lasers in the array sets in. In the latter case, multiple laser modes will be supported by the array of lasers, once coupled together, and so operation of an array of near-field coupled nanolasers can give rise to multimode operation, which in turn decreases spatial and temporal coherence.

[0006] Multimode operation of such nanolaser arrays prevents the creation of high-power single mode laser sources that can be integrated on chips.

[0007] There have been attempts to suppress additional modes in nanolaser arrays. These include providing periodic nanostructures to create photonic crystals and topological lasers, or suppressing multimode operation using symmetry, interference between bright and dark modes, or using geometrical perturbations. However, these methods are complex and require high nanofabrication accuracy, hindering practical applications.

[0008] It is an object of the present invention to provide a laser array, in particular a nanolaser array, with improved output emission characteristics in terms of brightness and coherence. It is a further object of the present invention to provide a nanolaser array which can provide single mode operation with reduced manufacturing constraints compared to the prior art.Summary of the Invention

[0009] In a first aspect of the invention, a laser system is provided. The laser system comprises a plurality of lasers and is configured such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers with a non-zero phase delay.

[0010] It has been found that coupling lasers in a laser array to one another with a non-zero phase delay (i.e. with phase delayed coupling) causes the collective modes in the array to differ in gain, which has the effect of supressing multimode operation and in turn leads to the laser array operating with a single high-gain mode. This in turn allows for high power single mode operation of the laser array.

[0011] In some embodiments, the lasers of the plurality of lasers are arranged as a periodic array. In other embodiments, the plurality of lasers are arranged as an aperiodic array.

[0012] In some embodiments, the lasers are arranged such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers through free space coupling. Such an arrangement can allow for relatively simple manufacture, because the lasers can be coupled directly to each other, without the need to couple to an intervening waveguide structure (for example). In such embodiments, the phase delay in the coupling is principally controlled by the propagation distance (in free space) between the lasers.

[0013] In some embodiments, the laser system further comprises a waveguide structure, wherein each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers through the waveguide structure. Such a configuration advantageously allows for the coupling radiation to be constrained to the waveguide, minimising loss. Moreover, the properties of the waveguide structure (its spatial configuration and its material properties) can be used to control the amount of phase delay imparted to the coupling radiation exchanged between lasers of the laser array.

[0014] In some embodiments, the waveguide structure comprises a plurality of waveguides, each waveguide coupling one of the plurality of lasers to only one other laser of the plurality of lasers.

[0015] In some embodiments, the waveguide structure comprises a linear waveguide which is configured to couple each of the plurality of lasers to at least one other laser of the plurality of lasers. The linear waveguide may be folded within a two-dimensional plane.

[0016] In some embodiments, the waveguide structure comprises an array of linear waveguides, wherein each linear waveguide of the array of linear waveguides is configured to couple two or more of the plurality of lasers together. The array of linear waveguides may comprise a first set of waveguides which extend in a first horizontal direction, and a second set of waveguides which extend in a second horizontal direction. The first and second horizontal directions may be orthogonal to each other.

[0017] In some embodiments, the waveguide structure comprises a planar waveguide which is configured to couple each of the plurality of lasers to at least one other laser of the plurality of lasers.

[0018] In some embodiments, the waveguide structure is horizontally displaced from the plurality of lasers. In other embodiments, the waveguide structure is horizontally aligned with the plurality of lasers and is vertically displaced from the plurality of lasers.

[0019] In some embodiments, the laser system further comprises a planar substrate extending in a horizontal direction, wherein the plurality of lasers are disposed on the substrate.

[0020] In some embodiments which comprise a planar substrate, the lasers may be arranged such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers via the surface of the substrate. In such embodiments, the phase delay in the coupling is principally controlled by the propagation distance (across the substrate surface) between the lasers.

[0021] In embodiments having both a planar substrate and a waveguide structure, the waveguide structure may also be disposed on the substrate.

[0022] Each laser of the plurality of lasers may be one of a disk laser; a microring laser; a laser with a pillar structure; a vertical cavity surface-emitting laser (VCSEL); and a photonic crystal surface-emitting laser.

[0023] In some embodiments, the plurality of lasers is a plurality of nanolasers. Each laser may have at least one dimension of less than 10 pm, or each laser may have at least one dimension of less than 1 pm.

[0024] In some embodiments, the laser system further comprises a pumping means configured to provide pump energy to the plurality of lasers.

[0025] In some embodiments, the pumping means is an electrical pumping means.

[0026] In other embodiments, the pumping means is an optical pumping means. The optical pumping means may be configured to provide non-uniform optical pumping across the plurality of lasers where not all lasers receive the same optical pump power. The optical pumping means may comprise one of a digital micromirror device; and a spatial light modulator.

[0027] Advantageously, this results in different lasers across the plurality of lasers having different gain from each other. This in turn allows for an additional degree of mode selection.

[0028] In some embodiments, the plurality of lasers comprises at least five lasers. The plurality of lasers may comprise at least ten lasers.

[0029] The laser system may be configured such that, in operation, the non-zero phase delay suppresses multimode operation of the laser system so as to enable single mode emission from the laser system.

[0030] The laser system may be configured to provide single mode emission, wherein the array is configured such that the non-zero phase delay is sufficiently high that, for at least one mode other than the single laser mode, that other mode is unstable above its lasing threshold. Preferably, the array is configured such that the non-zero phase delay is sufficiently high that, for a plurality of modes other than the single laser mode, each of the other modes is unstable above its lasing threshold. The array may be configured such that the other mode, or each other mode of the plurality of other modes, is unstable at all pump powers above its lasing threshold.

[0031] Advantageously, because the non-zero phase delay causes other modes to be unstable at powers above their threshold, the threshold for the onset of multimode operation of the laser system increases drastically, allowing much higher power of single-mode lasing emission from the system.

[0032] In some embodiments, the non-zero phase delay modulo 2TT is greater than 0.

[0033] In a second aspect of the invention, a method of generating laser radiation is provided. The method comprises providing a plurality of lasers; coupling each laser to at least one other laser of the plurality of lasers with a non-zero phase delay; and operating all of the plurality of lasers to generate the laser radiation.

[0034] In some embodiments, coupling each laser to at least one other laser of the plurality of lasers with a non-zero phase delay is to suppress multimode operation of the laser system. Operating all of the plurality of lasers may comprise providing the laser radiation with a single mode.

[0035] The method of generating laser radiation may be performed using any of the laser systems disclosed herein.List of Figures

[0036] Figure 1 is a diagrammatic representation of the difference between real coupling and complex coupling.

[0037] Figure 2 illustrates results from theoretical modelling of single-mode lasing via complex coupling.

[0038] Figure 3 illustrates results from theoretical modelling of complex coupling in a sphere dimer.

[0039] Figure 4 illustrates results from theoretical modelling of the laser output from a large array, illustrating that increased coupling phase gives rise to single mode operation.

[0040] Figure 5 illustrates an arrangement for lasers in a laser array which allows for free space coupling and / or coupling via the substrate interface.

[0041] Figure 6 illustrates a waveguide coupling arrangement for lasers in a laser array.

[0042] Figure 7 illustrates a further waveguide coupling arrangement for lasers in a laser array.

[0043] Figure 8 illustrates a top-down view of a laser array arranged for free-space coupling.

[0044] Figure 9a illustrates a top-down view of a laser array with a planar waveguide coupling structure. Figures 9b and 9c show side-on views of different planar waveguide coupling structures.

[0045] Figure 10 illustrates a top-down view of a laser array with a linear waveguide array.

[0046] Figure 11 illustrates a top-down view of a laser array with a folded linear waveguide.

[0047] Figure 12 illustrates a top-down view of a laser array with a nearest-neighbour waveguide coupling structure.

[0048] Figure 13 illustrates a top-down view of a laser array with a folded nearest-neighbour waveguide coupling structure.

[0049] Figure 14 illustrates a top-down view of a laser array with an offset folded linear waveguide.

[0050] Figure 15 illustrates a top-down view of an aperiodic laser array with a pair-wise coupling waveguide structure.

[0051] Figure 16 is a top-down electron microscope image of a nanolaser array.

[0052] Figure 17 is a graph showing the optical spectrum recorded from operation of the nanolaser array shown in figure 16.Single-mode emission by phase-delayed coupling between laser systems

[0053] Embodiments of the present invention exploit phase-delayed coupling between lasers of a laser array to achieve single mode operation of the laser array. ‘Phase-delayed’ coupling is, by definition, the exchange of light between lasers, where the light exchanged carries a nonzero phase.

[0054] Without wishing to be bound by any particular theory, it has been found that providing a nanolaser array structure in which phase-delayed coupling is provided between lasers of the array, multimode operation can be suppressed and single mode operation provided.Complex Coupling: Single-Mode Lasing from a Phase-Delayed Dimer

[0055] The principle of complex coupling between lasers will now be explained with reference to Figure 1, which diagrammatically illustrates coupling in a system of two freguency- detuned coupled resonators. The resonators operate on freguencies coi and co2, respectively, K denotes the coupling coefficient between the two resonators and <|) is the phase delay in the coupling.

[0056] In coupled mode theory (CMT), coupling is typically considered as real to account for evanescent interaction between nearby lasers, and this results in the modes of the system splitting in frequency. This is illustrated in Figure 1a, where <|) = 0. Under real coupling, the modes repel in real frequency [Re(co)] when the lasers are pumped equally. The threshold pump required for each mode to initiate lasing, [lm(co)], is very similar to that for the individual lasers, and is principally determined by the passive cavity losses for each laser.

[0057] Conversely, as illustrated in Figure 1 b, where there is complex coupling between adjacent lasers (i.e. the phase delay in the coupling, <|) > 0) a difference in lm(co) develops such that the coupled modes have not only different (real) frequencies but also different losses (imaginary frequencies). Complex coupling arises from phase delay, obtainable through light propagation distances of the order of the wavelength, and can be implemented for example using a waveguide near the individual lasers.

[0058] Figure 2 illustrates results from modelling complex coupling between two frequency detuned lasers.

[0059] Figure 2a shows the linear gain for two frequency detuned lasers (difference in frequency, co2- wi = 0.2) with equal gain (yi = y2= 2.5) interacting through coupling with no phase delay (<|) = 0). The y-axis corresponds to increasing pump power to laser 2 (P2) and the x- axis corresponds to increasing pump power on laser 1 (Pi). Shading indicates the linear gain above threshold. When the two coupled lasers are pumped unequally, the lasing threshold of each mode depends on both excitations, i.e. on both Pi and on P2. This is illustrated by the solid curve which indicates the threshold of one of the laser modes, in this case mode 1 , and has dependence on both Pi and P2.

[0060] Fig 2b demonstrates the effect of increasing phase delay (<])) in the coupling between the two lasers on the threshold curve for both mode 1 and mode 2. At <|) = 0, the threshold curves cross symmetrically such that for equal pump power (Pi = P2), indicated by the grey dotted line, lasing threshold is reached simultaneously for both laser modes. On increasing <|), the threshold curves become asymmetric and separate from each other, one mode reaches its threshold just before the other, enabling a limited range of single-mode operation. For a specific value of the coupling phase, here <j> = 0.1 , the eigenvectors of the two modes coalesce at an exceptional point (EP). For <j> > 0.1 , the thresholds separate from each other with one curve becoming convex and the other becoming concave. Beyond this, one mode consistently reaches its threshold before the other, leading to a large range of single-mode operation.

[0061] However, above threshold, linear CMT provides an incomplete picture with unphysical exponential growth of mode amplitudes with time. In real lasers, mode amplitudes are constrained by gain saturation. This results in a nonlinearity which leads to the emergence of more coupled modes, referred to herein as nonlinear coupled modes. These modes can be identified through nonlinear coupled mode theory (nonlinear CMT). Jacobian stability analysis can be used to assess the stability these modes to identify the modes observable in experiments. The results of such an analysis are set out in Figures 2c and 2d.

[0062] The stability of the modes was confirmed using time-domain simulations of the underlying coupled differential equations, starting from zero amplitude and adding random noise. As shown in Figure 2c, it was observed that the system state (light track) converges to one of the stable modes (Figure 2c, roundels) and never to any unstable mode (circles). This confirms that the modes assigned stable are the ones which would be experimentally observed.

[0063] Nonlinear CMT predicts an extended range of single-mode operation enabled by complex coupling compared to linear CMT, as can be demonstrated by the results shown in Figure 2d, showing the results from a theoretical model of the output of two lasers subject to nonlinear coupling, within increasing coupling phase <|). As the coupling phase <|) increases, the lasing threshold decreases, and the second mode requires a higher pump intensity to attain stability than the linear onset (Figure 2d). That is, even above the threshold of the second mode, the second mode remains unstable for a range of pump intensities. At high values of <|), the second mode is unstable at all pump values above its threshold, resulting in a single stable lasing mode at all powers above threshold. This observation is attributed to the significant separation between the threshold curves. Even with gain saturation, any mode arising from the higher threshold curve will retain enough gain for a mode from the lower curve to emerge and dominate it.

[0064] These results indicate that introducing a high phase delay can thus effectively suppress multimode behaviour in laser dimers, allowing for the sustained operation of a single stable lasing mode.Phase-Delayed Coupling in a Sphere Dimer

[0065] Nanolasers can be fabricated with a variety of structures, including cylindrical, hexagonal or spherical. It will be appreciated that, for a given nanolaser, the resonant modes of the nanolaser can be predicted from its structure. The description above is based on a treatment of each laser as point-like. To validate the above analysis beyond an idealised systemof point-like lasers, Figure 3 illustrates the results from modelling the coupling between the lowest-order vector spherical harmonic modes in a dimer of identical spheres. Mie theory can be used to compute the coupled modes of a dimer of spheres in vacuum.

[0066] Phase-delayed coupling can be achieved in coupled sphere nanolasers by adding a physical distance between them. <|) increases with the separation between the spheres, but at the expense of reducing the magnitude of the coupling strength K as the fraction of the scattered light reaching the other sphere reduces.

[0067] Figure 3a shows the result of simulating two coupled nanolaser spheres of radius r separated by distance d. The inner track illustrates the mode of a single sphere. The outer tracks indicate the modes of the coupled spheres, showing that there has been splitting into two modes. This confirms that when two unpumped spheres are coupled, the coupled modes (outer tracks) have distinct values of real frequency and gain (imaginary part), indicating a complex effective coupling constant. As the pump is increased in both spheres equally, the gains of the modes increase, until eventually one mode reaches lasing threshold on intersecting the real axis before the other.

[0068] Thus single mode operation is provided, validating that the observations from CMT set out above apply to realistic nanolaser structures.

[0069] Figure 3b shows threshold curves of the dimer which vary in separation as the distance is between the two spheres is varied, making one mode have more gain than the other. In particular, Figure 3b shows the threshold curve (lm[kr] = 0) plotted for two intra-sphere distances d / r = 4.5 (solid line) and d / r = 3.5 (dotted line), where d is the ratios between the distance and sphere radius. For d / r = 4.5 the threshold curves of the two modes intersect, resembling the prediction from CMT under real coupling. However, for d / r = 3.5, a noticeable gap emerges between the two threshold curves. This observation indicates that one mode requires significantly less pump power to reach the lasing threshold compared to the other, aligning with the prediction from CMT under highly complex coupling.

[0070] Figure 3c shows the coupled modes of the system with increasing distance between the spheres. Increasing the distance between the spheres changes both the amplitude and the phase of coupling, resulting in the coupled modes moving ‘spirally’ around the single sphere mode. The continuous variation in the complex phase of the coupling makes the coupled modes encircle the single mode and separates them in gain. Furthermore, the magnitude of the coupling decreases as the spheres move apart, bringing the coupled mode frequencies closerto the single mode frequency. These results illustrate that manipulating the distance between the spheres in the dimer can effectively tune the phase of the coupling, in turn enabling optimisation of the lasing threshold to achieve single-mode operation of the coupled system.Single-Mode Lasing in Large Arrays of Nano-Lasers

[0071] Single-mode operation due to phase-delayed coupling can be generalised to larger arrays of lasers. To demonstrate this, up to ten coupled lasers in a linear array are modelled using stochastic differential equations, with nearest neighbour interactions. The results of this model are shown in Figure 4. Phase-delayed coupling reduces the lasing threshold (lower solid line). It has also been found that this effect increases when more and more lasers are coupled.

[0072] The pump range permitting single-mode operation in the array also increases with the phase of coupling. This is due to a combination of the same two factors explained above in relation to the dimer system: Increasing the coupling phase delay <|) not only increases the linear gain difference between different modes but also makes the low-gain modes unstable even above their respective newly increased thresholds, and thus unattainable at low power. As some modes lose stability entirely with non-zero values of complex phase, the threshold for the onset of multimode operation increases drastically, allowing much higher power of single-mode lasing emission from the system.

[0073] Unlike the dimer systems explained above, the stochastic evolution of the 10-particle system shows non-eigen multifrequency solutions, but these are also suppressed with complex coupling.

[0074] This modelling validates that phase-delayed coupling can achieve single-mode operation across a broad range of pump powers in large arrays. Although multiple modes and complex dynamical solutions exist in such arrays, phase-delayed coupling effectively suppresses them and allows a single mode with the lowest threshold to dominate the system.Laser Systems Providing Single Mode Operation Through Phase Delayed Coupling

[0075] Embodiments of the present disclosure provide laser systems which provide a plurality of lasers, configured such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers with a non-zero phase delay.

[0076] Such laser systems comprise a plurality of lasers or, put another way, an array of lasers. Lasers in the array are coupled to each other with phase delayed coupling, that is to say the lasers in the array are coupled with a non-zero phase delay. The principles set out hereincan be applied to laser arrays comprising any number of lasers, for example arrays of five or more lasers, or arrays of ten or more lasers.

[0077] Each laser in the laser array may be coupled with only one other laser or only a small number of other lasers (for example with its nearest neighbour or nearest neighbours in the array) or may be coupled with a larger number of other lasers in the array.

[0078] Without wishing to be bound to any particular theory, it is thought that (in line with the explanation above) configuring the laser system to provide phase delayed coupling between lasers of the laser array gives rise to single mode operation and / or supresses multimode operation. Providing phase-delayed coupling increases the linear gain difference between different modes, which is preferential to single mode operation. Moreover, phase delayed coupling makes other lasing modes unstable, which increases the threshold for the onset of multimode operation. This in turn allows for high power operation of the laser array whilst maintaining single-mode emission from the laser system.

[0079] The phase delayed coupling between the lasers of the laser array can be achieved in any number of ways and arises when the effective propagation distance for radiation coupling the lasers is the order of the wavelength of the radiation emitted by the laser system. It can be implemented by, for example, using a waveguide near the individual lasers, with light coupled between lasers of the laser array using the waveguide. Alternatively, for example, the lasers of the array could be configured such that the light is coupled to one or more other lasers of the laser array through free space, with or without additional optics provided in the optical path between the lasers to direct the radiation coupling the lasers.

[0080] Multimode operation is suppressed through the phase delayed coupling between the lasers of the laser array. This is in contrast to prior art approaches which (for example) enhance gain for a particular mode of the laser array by imposing a specific defined periodicity across the entire laser array, which periodicity has a specific relationship to the spatial mode of the individual lasers in the array. Such prior art techniques will be highly sensitive to the position of each laser of the array and the precise dimensions of the lasers themselves. The suppression of multimode operation through phase delayed coupling, on the other hand, does not rely on precise control of placement of the lasers within the array, nor the dimensions of the lasers themselves. This in turn allows for looser manufacturing tolerance as compared to prior art approaches to supressing multimode operation.

[0081] Exemplary embodiments will now be described with reference to the drawings. The embodiments described below are based on arrays of nanolaser structures (that is, laser structures with dimensions of a few pm or less). It will be appreciated, however, that the principles explained herein would be applicable to many different types of laser structures, so long as a plurality of lasers is provided, and each laser is coupled to at least one other laser with a non-zero phase delay.

[0082] The phase delay, <|), is defined as the phase acquired by radiation when propagating between the lasers. In the context of phase delayed coupling between a first and second laser system, phase delay is defined as the relative phase of the light that is coupled from a laser to a lasing mode, relative to the phase of the laser. That is to say, for two lasers within a laser system, the phase delay of the coupling from the first laser to the second laser is the relative phase of the light that reaches the second laser from the first laser, relative to the phase of the lasing mode in the first laser.

[0083] As explained above, a non-zero phase delay can be achieved by configuring a laser system with a plurality of lasers, each laser being coupled to at least one other laser by an exchange of laser radiation. The effective propagation distance for the coupling radiation is on the order of a wavelength of the radiation, and is non-negligible, that is to say, greater than zero.

[0084] It will also be appreciated that, in terms of phase, a phase value of 2TT can be equivalent to a phase of 0. Therefore, where the phase delay between adjacent lasers of the laser array is an integer multiple of 2TT, a non-zero phase delay may not be provided. As such, the laser system may be designed such that the phase delay is not an integer multiple of 2TT. That is to say, the effective phase delaydefined as phase delay modulo 2TT, may be designed to be greater than zero:

[0085] In general, a non-zero phase delay is one in which the phase delay <|) (or effective phase delay in the coupling between lasers in the laser array is large enough to separate the threshold of the lasing modes of the system, thereby supressing multimode operation of the laser system so as to enable single mode emission from the laser system. It will be appreciated that hereinafter where a phase delay is referred to, it may also be read as the effective phase delay defined above.

[0086] For example, the minimal value of phase delay to give rise to a separation of the threshold of the lasing modes of the system (i.e. the non-zero phase delay) may be a value of <t> > 0.01TT. In other examples the value may be <|) > 0.1TT. In other examples, the value may be <t> > TT / 3.

[0087] Phase delayed coupling between lasers of the laser array can be provided, for example, by using a waveguide near the lasers of a laser array. Radiation from each laser can be coupled into the waveguide, for example by evanescent field coupling. The radiation can propagate through the waveguide and be coupled into at least one other laser of the laser array again, for example, by evanescent field coupling. The coupling radiation, having propagated a finite distance through the waveguide, will have acquired a non-zero phase delay. Thereby, phase delayed coupling between the lasers of the laser array can be provided. Alternatively, coupling between the laser structures may be provided by radiation propagating in free space, arranging the laser structures a suitable distance from each other to provide the required phase delay in the coupling.

[0088] Figures 5 to 7 show different exemplary configurations to provide phase delayed coupling between nanolasers in a nanolaser array.

[0089] Figures 5a and 5b show a free-space coupling configuration. Figure 5a shows a side view (i.e. a cross-sectional view in the x-z plane) of the configuration and Figure 5b shows a top- down view (i.e. a plan view in the x-y plane) of the configuration. Lasers 100 are provided on substrate 300. The lasers are spaced apart from each other. Radiation emitted from each laser 100 can, depending on the configuration, propagate through the free space between the lasers 100, and / or propagate at the surface of the substrate 300. That is to say, the radiation coupling the lasers 100 together propagates through free space between the lasers or is guided at the interface between the substrate 300 and free space. By providing a sufficient distance between the lasers, a non-zero phase delay is acquired as the radiation propagates between the lasers 100.

[0090] Figures 6a and 6b show a first waveguide coupling configuration. Figure 6a shows a side view of the configuration and Figure 6b shows a top-down view of the configuration. Lasers 100 are provided on waveguide 200 which is in turn provided on, or in, substrate 300. That is to say, the lasers 100, waveguide 200 and substrate 300 are stacked in the z-direction. Radiation can be coupled from the lasers 100 into the waveguide 200. The radiation will propagate throughthe waveguide 200 and couple the lasers 100 together. A non-zero phase delay is acquired by the coupling radiation as it travels through the waveguide 200.

[0091] Figures 7a and 7b show a second waveguide coupling configuration. Figure 7a shows a side view of the configuration and Figure 7b shows a top-down view of the configuration. Lasers 100 are provided on substrate 300. Waveguide 200 is also provided on substrate 300, positioned to the side of lasers 200 (in the horizontal, x-y, plane). As with the first waveguide coupling configuration, radiation can be coupled from the lasers 100 into the waveguide 200. The radiation will propagate through the waveguide 200 and couple the lasers 100 together. A non-zero phase delay is acquired by the coupling radiation as it travels through the waveguide 200.Array Configurations

[0092] Different coupling array configurations can be provided, examples of which are illustrated in Figures 8 to 15.

[0093] Figure 8 shows an arrangement wherein the plurality of lasers 100 is provided as a regular array which extends across a horizontal (x-y) plane on substrate 300. Coupling is effected by free space propagation of radiation between the lasers 100. The lasers are spaced apart such that the free space propagation distance between adjacent lasers of the laser array provides a non zero phase delay. It will be appreciated that additionally, or alternatively, the coupling radiation might propagate at the interface between the substrate 300 and free space. That is to say, the radiation is confined to the surface of the substrate 300 but otherwise free to propagate between lasers 100 of the array.

[0094] It will be appreciated that the lasers 100 need not be provided in a regular periodic arrangement, but instead could be arranged as an aperiodic array. That is to say, the lasers can be arranged as a quasi-random array (or disordered array). The spacing between the lasers of the laser array 100 can vary across the array, with the propagation distance between adjacent lasers provided by the separation being sufficient to provide a non zero phase delay.

[0095] Rather than using free-space propagation of radiation to couple lasers of the laser array 100 to each other, in certain embodiments (examples of which are described below with reference to figures 10 to 15), coupling between lasers of the laser array 100 can be effected by a waveguide structure 200. In such examples, generally, because the coupling radiation is confined to the waveguide structure 200, the effective propagation distance between the lasers can be controlled by the dimensions of the waveguide (i.e. the length of the waveguide between adjacent lasers) and also the material of the waveguide. A waveguide with a higher refractive index will provide agreater effective optical propagation distance for the coupling radiation, and therefore impart a greater phase delay in the coupling. The cross-sectional structure of a waveguide can, generally, also contribute to the effective refractive index. Therefore, in some embodiments, the cross- sectional structure of each waveguides in the waveguide structure is configured to control the phase delay imparted by the waveguide structure 200 to the coupling between lasers of the laser array 100.

[0096] Figures 9a and 9b respectively show a top-down and side-on view of an arrangement where the plurality of lasers 100 is provided as a regular array above a planar waveguide structure 200. The planar waveguide structure extends across a plane below the laser array 100 in the z- direction. The waveguide 200 is disposed upon (and extends across) a surface of the substrate 300 in the x-y plane. The coupling radiation may be coupled from each laser of the laser array 100 into the waveguide 200 below the laser, propagate through the waveguide, and be coupled into adjacent and surrounding lasers of the laser array 100 to provide phase delayed coupling.

[0097] Alternatively, as shown in Figure 9c, the waveguide structure could be designed to surround each of the lasers of the laser array 100, with the laser array 100 and waveguide structure 200 disposed on the substrate 300. The coupling radiation may be coupled from each laser of the laser array 100 into the waveguide 200 beside the laser (i.e. horizontally, in the x-y plane), propagate through the waveguide, and be coupled into adjacent and surrounding lasers of the laser array 100 to provide phase delayed coupling.

[0098] Figure 10 shows an arrangement where the plurality of lasers 100 is provided as a regular array above a lattice-like waveguide structure 200. The waveguide structure 200 comprises a set of linear waveguides 210, comprising a first set of linear waveguides 210a extending in the x-direction and a second set of linear waveguides 210b extending in the y- direction, wherein the first set of linear waveguides 210a intersects with the second set of linear waveguides 210b. It will be appreciated that, whilst in Figure 10 the first and second sets of waveguides are orthogonal to each other, this need not be the case - the first and second sets of waveguides can extend across the x-y plane in different directions, and at non-orthogonal angles to each other. Byway of this configuration, each laser of the laser array 100 can be coupled to (at least) its nearest neighbours in the x-direction and (at least) its nearest neighbours in the y- direction.

[0099] Figure 11 shows an arrangement where the waveguide structure 200 comprises a linear waveguide 200 which is folded across the plane of the substrate 300 to provide a ‘snakelike’ waveguide structure. Coupling across all lasers of the laser array 100 will be effected by asingle linear waveguide structure and thus the spacing between a given pair of lasers of the laser array 100 along the linear waveguide 200 will determine the phase delay imparted to the coupling radiation exchanged between those lasers.

[0100] Figure 12 shows an arrangement wherein the waveguide structure 200 provides a plurality of waveguides 220, each waveguide coupling together two (and only two) lasers of the laser array 100. Each of the waveguides 220 is offset, in a plane parallel to the substrate 300, from a pair of lasers of the laser array 100 and has a length corresponding to the separation of the lasers from each other. Waveguides 220a extend in the x-direction and couple together a laser of the laser array 100 to one of its nearest neighbours in the x-direction. Waveguides 220b extend in the y-direction and couple together a laser of the laser array 100 to one of its nearest neighbours in the y-direction. As such, this arrangement may be understood as a two-dimensional nearest neighbour coupling arrangement, whereby each laser of the laser array 100 is coupled only to each of its nearest neighbours in the x- and y-directions by way of waveguides 220.

[0101] Figure 13 shows an arrangement wherein the waveguide structure 200 provides a plurality of waveguides 230 which each couple a laser of the laser array 100 to one of its nearest neighbours in either the x- or y-direction. Each of the waveguides 230 is offset, in a plane parallel to the substrate 300, from a pair of lasers of the laser array 100 and has a length corresponding to the separation of the lasers from each other. Each laser is coupled to, at most, two other lasers of the laser array 100, such that the plurality of waveguides 230 of the waveguide structure 200 provides chain-like coupling of the lasers to each other, with each laser coupled to its two nearest neighbours within the chain.

[0102] Figure 14 shows an arrangement, which is similar to that of figure 11 , except for the waveguide 200 being offset, in the x-y plane (i.e. in a plane parallel to the substrate 300), from the lasers of the laser array 100.

[0103] Figure 15 shows an arrangement in which the lasers of the laser array 100 are arranged in an aperiodic manner. That is to say the lasers of the laser array 100 are not regularly spaced across the substrate but instead the lasers are arranged as a quasi-random array (or disordered array) across the surface of the substrate. The waveguide structure 200 provides a plurality of waveguides 240 which each couple together two lasers of the laser array 100. Each of the waveguides 230 is offset, in the x-y plane (i.e. in a plane parallel to the substrate 300), from a pair of lasers of the laser array 100 and has a length corresponding to the separation between the two lasers to which it is adjacent.Laser structures, gain media, and pumping arrangements

[0104] In any of the arrangements outlined above, the lasers of the laser array 100 can be any of a number of different laser configurations. It will be appreciated that the laser structures and laser gain medium can be selected depending on the desired properties of the radiation output from the laser system, in particular the wavelength and power range of light output from the system.

[0105] Depending on the laser structure and laser gain medium, the laser array 100 might operate within a number of different wavelength ranges.

[0106] For example, each laser of the laser array 100 may be a disk laser. Alternatively, each laser may be a microring laser. Alternatively, each laser may be a laser with a pillar structure. Alternatively, each laser may be a vertical cavity surface-emitting laser (VCSEL). Alternatively, each laser may be a photonic crystal surface-emitting laser.

[0107] For any of the arrangements and laser types described above, the lasers may comprise a suitable laser gain medium. The laser gain medium will dictate the output properties of the laser system, in particular the wavelength of the output radiation. As a further example, the laser gain medium may be a semiconductor laser gain medium such as cadmium selenide, cadmium sulphide, gallium arsenide, indium gallium arsenide, or aluminium gallium arsenide, or another semiconductor material, or a mixture of semiconductor materials. The laser gain medium may be a quantum dot laser gain medium, for example comprising semiconductor quantum dots. As yet another example, the laser gain medium may be a doped insulator medium, for example a crystal or glass doped with neodymium, ytterbium, erbium or the like. As yet another example, the laser gain medium may be an organic dye in a polymer or a perovskite.

[0108] It will be appreciated that the laser structures and gain media discussed above are examples only, and the principles disclosed herein can be applied to arrays of different types of lasers, the structure and gain medium of which can be selected based on desired output properties as is known in the art.

[0109] Generally, the laser system may also comprise a pumping means (not shown) which provides pump energy to the plurality of lasers. For example, the pumping means may be an optical pumping means, with a light source (such as a laser diode) used to provide radiation with a suitable wavelength to pump the laser gain medium employed in the laser system. Pump radiation can be delivered to the laser system by means of free space optics. For example, the optical pumping means may comprise a lens or system of lenses to project the pump radiationonto the laser array. Alternatively (or additionally) the optical pumping means might be configured to provide non-uniform optical pumping across the plurality of lasers. To this end, a digital micromirror device or a spatial light modulator might be used. The non-uniform pumping allows for the gain of different lasers across the plurality of lasers to be varied. The non-uniform gain across the different lasers of the plurality of lasers can in turn allow for mode selection.

[0110] Alternatively, the pump radiation might be delivered to the lasers of the laser array 100 using a pump delivery waveguide structure. The waveguide structure may be the same waveguide structure 200 used to provide phase delayed coupling between the lasers of the laser array 100. Alternatively, a separate pump delivery waveguide structure (not shown) might be provided on the substrate 300.

[0111] As an alternative to optical pumping, an electrical pumping means may be employed, with the laser system configured such that an electrical current can be provided to the lasers of the laser array 100, the electric current exciting the gain medium of the lasers.Methods of generating laser radiation

[0112] Any of the laser systems described above can be used in a method of generating laser radiation. Each laser of the laser array 100 will be coupled to at least one other laser of the plurality of lasers with a non-zero phase delay, and the laser array 100 will be operated to generate laser radiation. Operating the laser array may comprise pumping the lasers of the laser array 100 with an optical or electrical pumping means to give rise to the emission of laser radiation. Coupling each laser to other lasers of the laser array 100 with phase delayed coupling suppresses multimode operation, such that operating the plurality of lasers gives rise to single mode operation across the laser array 100.Experimental Results

[0113] Single mode operation of a laser array through phase delayed coupling was observed experimentally using a 14x14 array of nanolasers with a ring cavity structure, which provided single-mode lasing operation at 622.35 nm. A top-down electron microscope image of the laser array structure is shown in Figure 16. The rings were made of silicon nitride (Sisl^ ) with an embedded layer of CdSe / CdS quantum dots as the gain medium.

[0114] The rings were of 10 pm diameter, 2 pm width, 120 nm height and the gap between adjacent rings was designed to be 60 nm. The quantum dot layer was not etched through, with a 20 nm layer as part of the ring and 70 nm unetched below.

[0115] The unetched 70 nm depth of the quantum dot layer acts as a planar waveguide connecting the individual ring lasers. Due to the 60 nm separation of the lasers, and the effective refractive index of the quantum dot material, the lasers are coupled with a non-zero phase delay.

[0116] The array was pumped by a TEEM Power-Chip laser (532 nm wavelength, 400 ps pulse width) via a digital micromirror device (AJD-4500, all 912x1140 mirrors of the device were in the ON-state) and a 20x objective lens (Nikon CFI60).

[0117] The lasing emission was focused through a cylindrical lens and the spectrum was analysed using a grating spectrometer (Princeton Instruments lsoplane-320) with a CCD camera (Princeton Instruments Pixis 400). Figure 17 shows the recorded spectrum, with a sharp line at 622.35 nm, indicating single mode operation.

[0118] These results indicate that single mode operation of an array of nanolasers can be achieved by way of phase delayed coupling between the lasers of the array.

Claims

Claims1. A laser system comprising: a plurality of lasers, configured such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers with a non-zero phase delay.

2. The laser system of claim 1, wherein the plurality of lasers comprises at least five lasers, preferably wherein the plurality of lasers comprises at least ten lasers.

3. The laser system of claim 1 or claim 2, wherein, in operation, the non-zero phase delay suppresses multimode operation of the laser system so as to enable single mode emission from the laser system.

4. The laser system of any of claims 1 to 3, wherein the laser system is configured to provide single mode emission, wherein the array is configured such that the non-zero phase delay is sufficiently high that, for at least one mode other than the single laser mode, that other mode is unstable above its lasing threshold.

5. The laser system of any of claims 1 to 4, wherein the lasers of the plurality of lasers are arranged as a periodic array.

6. The laser system of any of claim 1 to 4, wherein the lasers of the plurality of lasers are arranged as an aperiodic array.

7. The laser system of any of claims 1 to 6, wherein the lasers are arranged such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers through free space coupling.

8. The laser system of any of claims 1 to 6, further comprising a waveguide structure, wherein each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers through the waveguide structure.

9. The laser system of claim 8, wherein the waveguide structure comprises a plurality of waveguides, each waveguide coupling one of the plurality of lasers to only one other laser of the plurality of lasers.

10. The laser system of claim 8, wherein the waveguide structure comprises a linear waveguide which is configured to couple each of the plurality of lasers to at least one other laser of the plurality of lasers.

11. The laser system of claim 10, wherein the linear waveguide is folded within a two- dimensional plane.

12. The laser system of claim 8, wherein the waveguide structure comprises an array of linear waveguides, wherein each linear waveguide of the array of linear waveguides is configured to couple two or more of the plurality of lasers together.

13. The laser system of claim 12, wherein the array of linear waveguides comprises a first set of waveguides which extend in a first horizontal direction, and a second set of waveguides which extend in a second horizontal direction, preferably wherein the first and second horizontal directions are orthogonal to each other.

14. The laser system of claim 8, wherein the waveguide structure comprises a planar waveguide which is configured to couple each of the plurality of lasers to at least one other laser of the plurality of lasers.

15. The laser system of any of claims 8 to 14, wherein the waveguide structure is horizontally displaced from the plurality of lasers.

16. The laser system of any of claims 8 to 14, wherein the waveguide structure is horizontally aligned with the plurality of lasers and is vertically displaced from the plurality of lasers.

17. The laser system of any preceding claim, further comprising a planar substrate extending in a horizontal direction, wherein the plurality of lasers are disposed on the substrate.

18. The laser system of claim 14, wherein the lasers are arranged such that each laser of the plurality of lasers is coupled to at least one other laser of the plurality of lasers via the surface of the substrate.

19. The laser system of claim 17, when dependent upon any of claims 8 to 16, wherein the waveguide structure is disposed on the substrate.

20. The laser system of any preceding claim, wherein each laser of the plurality of lasers is one of: a disk laser; a microring laser; a laser with a pillar structure; a vertical cavity surface-emitting laser (VCSEL); and a photonic crystal surface-emitting laser.

21. The laser system of any preceding claim, wherein each laser has at least one dimension of less than 10 pm, preferably wherein each laser has at least one dimension of less than 1 pm.

22. The laser system of any preceding claim, further comprising a pumping means configured to provide pump energy to the plurality of lasers.

23. The laser system of claim 22, wherein the pumping means is an electrical pumping means.

24. The laser system of claim 22, wherein the pumping means is an optical pumping means.

25. The laser system of claim 24, wherein the optical pumping means is configured to provide non-uniform optical pumping across the plurality of lasers, preferably wherein the optical pumping means comprises one of: a digital micromirror device; and a spatial light modulator.

26. The laser system of any preceding claim, wherein the non-zero phase delay modulo 2TT is greater than 0.

27. A method of generating laser radiation, the method comprising: providing a plurality of lasers; coupling each laser to at least one other laser of the plurality of lasers with a non-zero phase delay; and operating all of the plurality of lasers to generate the laser radiation.

28. The method of claim 27, wherein coupling each laser to at least one other laser of the plurality of lasers with a non-zero phase delay is to suppress multimode operation of the laser system, and wherein operating all of the plurality of lasers comprises providing the laser radiation with a single mode.

29. The method of claim 27 or of claim 28, wherein the method is performed using a laser system of any one of claims 1 to 26.

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