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We report and analyze the supermode switching with current injection found for coherently-coupled dual-element vertical cavity surface emitting laser arrays. The output power, spectral characteristics, and far-field mode profile are measured for a range of bias current operating conditions. The coupling-induced enhanced output power from an in-phase or out-of-phase supermode is confirmed when approximately equal currents are injected into each array element. We observe that the coherent supermode switches from out-of-phase to in-phase supermode with increasing equal current injection. The switching is found to be consistent with coupled mode theory and a 1-dimensional spatial supermode model. The calculated modal gain of the out-of-phase and in-phase array supermodes are consistent with the observed switching of the coherent supermodes.

Coherently coupled microcavity lasers have desirable properties for emerging applications. We use 2-dimensional complex refractive index waveguide modeling of 2-element photonic crystal vertical cavity surface emitting laser arrays to analyze their supermodes. The complex modal effective indices are used in turn to calculate the complex coupling coefficient between the laser array elements. An analysis of the effects of array design parameters, such as photonic crystal period, fill-factor, or confinement, to engineer the coupling coefficient for the desired properties is given and example designs for 850 nm arrays are presented.

We present fabrication of dielectric micro-optical elements on VCSELs and characterization of emitted orbital angular momentum modes. Spiral phase plates are fabricated on the top facet of oxide-confined VCSELs using grayscale photolithography and dry etching silicon nitride. The refractive index of silicon nitride film is characterized using ellipsometry and atomic force microscopy is used to verify the fidelity of fabricated dielectric micro-optical elements. Orbital angular momentum modes with on-axis null are experimentally demonstrated. A novel circular rotation of intensity with propagation in the near-field is observed and is analyzed using Fresnel transfer function simulations.

The multi-mode vertical-cavity surface-emitting lasers (MM-VCSELs) with different photonic crystal (PhC) designs in core and cladding regions are compared for transmitting the complex formatted QAM-OFDM data over 100-m OM5 multi-mode fiber (MMF). Among the designs with using flat core/cladding (denoting as Coreflat/Cladflat) and/or PhC core/cladding (denoting as Corephc/Cladphc) for the MM-VCSEL, the Coreflat+Cladflat VCSEL with the highest threshold current and large emission aperture provides the highest differential quantum efficiency of 0.11 and output power of 2 mW, whereas the Coreflat+Cladphc2 VCSEL with two periods of cladding PhC reveals the lowest threshold current of 2 mA, the highest modulation bandwidth of 15 GHz, the lowest relative intensity noise peak of -126 dBc/Hz and background level of -143 dBc/Hz. After pre-compensation, the Coreflat+Cladphc2 VCSEL chip can achieve the highest OFDM bandwidth of 18 GHz for 72-Gbit/s transmission in the BtB case. With additionally adding 1 period of core PhC, the Corephc1+Cladphc2 VCSEL possesses a single-mode lasing spectrum to facilitate the suppression of modal dispersion after MMF propagation. Hence, the Corephc1+Cladphc2 VCSEL exhibits the same bit rate of 60 Gbit/s as compared to the Coreflat+Cladphc2 VCSEL after 100-m OM5-MMF. After improving the analog bandwidth for waveform synthesis, the data rate of Coreflat+Cladphc2 VCSEL can successfully deliver 76-Gbit/s and 72-Gbit/s single-band 16-QAM OFDM data streams for BtB and 100-m OM5 MMF conditions via the pre-leveling technology. To date, the ultimate raw data rate achieves 92-Gbit/s with employing the multi-band QAM-OFDM data format.

Effective engineering and exploitation of coherently coupled vertical cavity surface emitting laser arrays will benefit from simple and fast characterization of the optical coupling and coherence. We propose a Fourier method of analyzing beam profiles as an alternative to the prior beam visibility analysis and show that the mode suppression ratio and phase between a pair of supermodes can be extracted. Our analysis enables fast quantitative determination of the array coherence and supermode characteristics.

Coherently-coupled 2x1 vertical cavity surface emitting laser arrays enable formation of two anti-guided supermodes which create a photon-photon resonance that increases the modulation bandwidth. We report 50 Gbps data rate from 850 nm VCSEL arrays.

We report progress on phased 850 nm vertical-cavity surface-emitting laser arrays that can be designed to operate reliably through control of individual injection current to each laser element. In this manner, nearly all fabricated arrays can be biased to be mutually phase locked. This paper attempts to visualize and characterize the locking region between two neighboring lasers by measuring far-field visibility to create a two-dimensional visibility map. Experimental data show that the locking region can be shifted or changed by ambient temperature, asymmetric array design, and fabrication imperfections. Additionally, the relative intensity noise and harmonic distortion are measured to characterize the dynamic behavior of coherently coupled laser arrays in the locking region. Two-dimensional maps of total relative intensity noise and total harmonic distortion are created to visualize laser array dynamics in the locking region. The data show that the laser array must be carefully designed, biased, and modulated within the locking region to achieve an output signal with low noise, low distortion, and improved modulation performance.

We consider the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers. The extended stability and the varying asymmetry of these modes allows for the introduction of a rich set of interesting modulation response features, such as sharp resonances and anti-resonance as well as efficient modulation at very high frequencies exceeding the free running relaxation frequencies by orders of magnitude., 6 pages, 5 figures

We experimentally demonstrated enhanced digital modulation of coherently coupled vertical-cavity surface-emitting laser arrays. Mutually coherent behavior of $2\times 1$ proton-implanted index-confined photonic crystal vertical-cavity phased laser arrays is characterized using a novel digital modulation scheme. Far-field interference fringe visibility is used to estimate the degree of coherence between two coherently coupled laser cavities, and a visibility map is created to visualize the dependence of laser array coherence on the injection current bias. The visibility map indicates that a dual-channel in-phase modulation scheme can preserve the laser array in mutual coherence while under digital modulation. Experimentally, the high-speed digital modulation signal up to 36 Gb/s is supplied to both laser elements simultaneously. The resulting eye diagram is shown to be improved under coherent-coupling conditions.

Coherent optical coupling in VCSEL arrays introduces novel and desirable behaviors that can manifest themselves in many ways. We explore some of these behaviors using common characterization techniques but using large datasets, and show how we use computational data analysis methods to analyze datasets in an automated and scalable manner.

Machine learning is used to estimate the coherent-coupling power enhancement from 2 × 1 VCSEL arrays and serves to identify coherent non-Hermitian operation.

A coupled 2x1 microcavity laser array is experimentally investigated. We show that the spectral mode profile can identify the coherent region and is consistent with the coupled power enhancement.

We present fabrication of silicon nitride integrated micro-optical elements on VCSELs using grayscale photolithography and dry etching. The optical characteristics of VCSELs with spirals are investigated.

The coupling coefficient of a 2×1 optically coherent microcavity laser array can be experimentally determined. We show the extracted coupling coefficient varies for arrays depending on in-phase or out-of-phase coherent operation, in agreement with theory.

We train autoencoder artificial neural networks on simulated multimodal images and their corresponding modal power coefficients to reconstruct the component modal profiles and obtain a network capable of modal decomposition.

We present novel orbital angular momentum (OAM) modes from a 2x1 coherently coupled VCSEL array. An 8-phase spiral phase plate is used on both elements to generate coupled OAM modes. Far-field mode profiles calculated using Huygens principle are distinctly different for independent versus coherent operation.

Various surface-etched, laterally structured waveguide designs were simulated to achieve improved modal dis-crimination, selection, and direct mode engineering in broad-area diode lasers. These designs have been fabricated in InP/InGaAsP edge-emitting lasers.

A laser phased array capable of 1D beam-steering can be adapted to scanning a path in 2D using free-space optics or integrated phase plates.

Coherently coupled 2-element laser diode arrays near the modal exceptional point have equal photon-photon and carrier-photon resonances with indistinguishable supermodes. Experimentally the relative intensity noise is suppressed near the exceptional point.

Laser array dynamics of coupled microcavity laser arrays operated near a modal exceptional point is studied using coupled laser rate equations. Tuning the laser array near exceptional point results in rejection of common-mode interference.

The modulation properties of two-element photonic crystal ion-implanted coherently coupled vertical cavity surface emitting laser arrays emitting at 850 nm are reported. Single mode emission into either the in-phase or out-of-phase supermode and significant modulation bandwidth enhancement are obtained for both operating conditions. We model our device as a monolithically integrated, mutually optically injection-locked laser system and show that the phase detuning and injection ratio between array elements are critical parameters influencing modulation bandwidth. Comparison of our experimental measurements to our model is consistent with mutual injection locking. Modulation bandwidth greater than 30 GHz and up to 37 GHz is consistently found for several array designs. We show the modulation response can be tailored for different applications.

We show that optical coupling can be achieved reproducibly and with high yield by resonance tuning the elements of substrate-emitting and top-emitting vertical-cavity surface-emitting laser arrays. The resonance tuning is enabled by electrical isolation of the lasing elements in the array, which in this paper is done by post fabrication processing. Prior to electrical isolation, the laser arrays exhibit incoherent optical properties. Using resonance tuning, both in-phase and out-of-phase coherent modes are observed.

Starting from the desired modal field we solve for the supporting waveguide refractive index structure within a semiconductor diode laser. Specifically we analyze the problem of maximizing far-field on-axis intensity and discuss the practical aspects of waveguide design.

When operated in the coherently coupled regime, microcavity laser diode arrays have an electrical signature in their differential series resistance. The mechanism of this effect is explained using a complex coupling coefficient in coupled mode rate equation theory.

Bandwidth enhancement in phased laser arrays is explained using small-signal frequency-domain analysis on coupled mode rate equations. In-phase modulation of asymmetric arrays produces bandwidth enhancement in agreement with experimental measurements.

The analysis and characteristics of photonic crystal coherently coupled 2x1 VCSEL arrays are reported.

The complex component of the coupling coefficient κ = κ r + i κ i, used to describe the coupling between adjacent semiconductor microcavity laser diodes, is studied. The complex component κ i represents the gain or loss difference between the coherent in-phase and out-of-phase array supermodes obtained from two laterally coupled lasers. Steady-state analysis reveals that the threshold of the preferred coherent supermode is lower than that of an individual laser mode in proportion to κ i. We show that the complex component κ i can be experimentally extracted from a simple output power vs current measurement. Furthermore, the change in the lasing threshold at the onset of optical coupling perturbs the differential resistance of the coupled lasers. Therefore, an electrical signature of optical coupling can be detected in the diode array series resistance.

We analyze the lateral modes of dielectric waveguides that include refractive index corrugations parallel the direction of light propagation. We show that we can engineer the resulting far-field profile arising from structure waveguide modes, leading to improved modal discrimination and brightness.

We present a new experimental procedure for the measurement of the complex coupling coefficient in 2×1 coherent VCSEL arrays. The coupling coefficient is found with non-zero imaginary component, which manifests as an increase of output power and lower threshold while coherently coupled as compared to incoherent operation.

A 2×1 coherent ion-implanted photonic crystal vertical-cavity surface-emitting phased laser array is digitally modulated at 36 Gb/s for error-free transmission. A dual-channel modulation scheme is implemented and digital modulation enhancement arising from coherence is studied.

Coupled semiconductor arrays are inherently non-Hermitian optical systems. We use a comprehensive coupled rate equation analysis to elucidate the unique properties of coherent 2×1 photonic crystal VCSEL arrays.

Coherently coupled 2×1 vertical cavity laser arrays are shown to exhibit unchanged near-field intensity profile with unequal current injection and associated far-field beam steering. The energy transfer to maintain equal near-field intensity between the cavities is shown to be consistent with parity-time symmetry.

Coupled semiconductor laser arrays are naturally non-Hermitian optical systems. We show that in a weakly coupled semiconductor laser array, the control for gain/loss is dominated by the nonlinearities, rather than simply following the pump profile.

A 3x1 vertical-cavity surface-emitting laser array is resonantly tuned to multiple coherent modes. Experimental near-field and far-field coherent modes profiles are characterized and simulated. The center element bias demonstrates control of the coherent mode.

We show the first theoretical analysis of the coupling coefficient in passive index-antiguided coupling. Both magnitude and sign of the coupling coefficient are controlled by the inter-element distance and index, enabling novel photonic applications.

We report direct modulation of 2x1 proton-implanted index-confined photonic crystal coherently-coupled VCSEL array operating error free at 36 Gb/s. The high-speed modulation is attributed to modulation-bandwidth enhancement.