Sub-Diffraction Mode Characteristics In Nanolaser.

Abstract

Nanolasers are the key component in photonic integration and in this work we investigate the mode characteristics of an optically pumped Metal-Insulator-Semiconductor (MIS) plasmonic nanolaser structure at the sub-diffraction limit. The nanolaser structure consists of Ag/oxide/InGaAsP materials and operates at the telecom wavelength of 1330 nm. For two different oxides (Al2O3, MgF2) and waveguide sizes, mode-characteristic parameters such as effective refractive index, propagation loss, mode area and confinement factor are calculated. In addition, the threshold gain for each mode is investigated and the appropriate waveguide size according to the required threshold gain is estimated. Based on our calculations, the hybrid mode can propagate with low loss and sub-diffraction size in waveguides of 650 to 800 nm width.

Introduction

Active photonic components such as lasers and light-emitting diodes have important roles in modern optical devices. But like any other photonic component, they have a minimum size limit of half the wavelength, called the diffraction limit. This results in a minimum attainable volume of for photonic devices and, given the typical telecom wavelength, means a considerable size of hundreds of nanometers while electronic components are capable of integrating with sizes as small as tens of nanometers. To allow better integration capabilities and competition with their electronic counterparts, researchers have started to investigate new ways and possibilities of breaking the diffraction size limit in these photonic devices, leading to the emergence of the nanophotonic field.

One of the most promising fields of research in realizing these nanophotonic devices is the use of Surface Plasmon Polaritons (SPPs). SPPs can propagate on the surface of a metal waveguide that is only a couple of nanometers thick and could be used to realize nanoscale photonic components. However, the most important challenge in realizing these plasmonic devices is the high energy absorption loss in the metal, especially at high frequencies that considerably limit the propagation length (Lprop) of plasmonic modes to hundreds of nanometers. To overcome this challenge, researchers have studied active plasmonic devices with a gain medium to miniaturize the plasmonic losses. This has led to the introduction of plasmonic amplifiers and nanolasers.

Nanolasers using surface plasmons (SPASERs) have been demonstrated with different structures, from nanoparticles to nanowires and slab waveguides, and a frequency range of near ultra-violet to mid-infrared and even terahertz. One of the most promising of the structures reported to realize photonic integration is the plasmonic nanolaser using hybrid semiconductor structures, plane waveguides and quantum wells in active mediums. These nanolasers demonstrated a high modulation bandwidth with a three-dimensional confinement of the optical mode below the diffraction limit and a very small footprint. In this paper, we investigate the modal behaviors in an optically pumped hybrid Metal-Insulator(oxide)-Semiconductor (MIS) plasmonic nanolaser structure based on propagating long-range SPPs. The modal characteristics of the nanolaser around and below the diffraction limit for different propagating eigenmodes are investigated and parameters such as the effective refractive indices, propagation length, mode area of plasmonic and hybrid modes, and mode confinement factors are calculated. Using these parameters, the threshold optical gain for the lossless propagation of each eigenmode is determined and compared with the other modes. This analysis will lead to an estimation of the applicable size of a laser waveguide for operating at the desired telecom wavelength of 1330 nm.

Nanolaser structure and modal characteristics

In recent years, different structures with different performances have been proposed to realize the concept of plasmonic nanolasers but not all of these structures are suitable for photonic integration applications and, among them, structures based on nanowires and planar waveguides are the most promising candidates. According to our survey of previous work, it was obvious that structures with a laser diode configuration and using active gain media consisting of quantum wells have superior performance and a lower lasing threshold in comparison to structures using directly pumped dielectric nanowires or planar layers of dielectric as gain media. In addition, it was notable that the plasmonic contact area of a wider structure has a lower lasing threshold.

Accordingly, we chose a plasmonic nanolaser with a planar waveguide structure as the base structure for our study. The nanolaser has an MIS structure and can provide low-threshold lasing owing to its wide plasmonic contact area and Multiple Quantum Well (MQW) gain medium.

The active region is formed by an InGaAsP material system, a well-known and common four-element semiconductor material for active photonic devices operating in the telecom wavelength of 1. 3–1. 55 um. The radiation wavelength can be adjusted to the desired frequency by changing the component composition and stress levels of the Quantum Wells (QWs) and barrier layers. Silver was used for the metallic part of the plasmonic waveguide, which has a small permittivity imaginary part and can lower the plasmonic mode attenuation. For the guiding part of the plasmonic waveguide, two different oxide materials, Al2O3 and MgF2, were studied to investigate their refractive index in relation to the nanolaser gain. Al2O3 has a relatively high refractive index of 1. 75 (at 1330 nm) and MgF2 is transparent in the visible and infrared bands of the spectrum and has a lower refractive index of 1. 4 at 1330 nm.

The dielectric material is an InGaAsP semiconductor including four QW layers of 10 nm thickness and 15 nm barrier layers with different compositions, sandwiched between two InGaAsP spacer layers. The waveguide in the Z direction is 5 μm in length. The two spacer layers confine the optical mode inside the semiconductor waveguide region. Moreover, the bottom layer prevents the depletion of photo-generated electrons and holes in the metallic layer. It should be mentioned that a thick bottom spacer layer will prevent efficient coupling between the plasmonic modes and the quantum-well active region and there is a trade-off between nonradioactive losses and mode coupling in designing the nanolaser waveguide. As defined in the literature, plasmonic structures with oxides of higher refractive index have a larger effective mode index, a higher propagation loss and a smaller propagation length. It means that the plasmonic mode needs a higher marital gain to overcome the losses induced by the large imaginary part of the metal permittivity. On the other hand, there is a well-known trade-off between increasing the propagation length and decreasing the confinement factor that directly leads to shrinkage in the interaction of the plasmonic mode with the gain medium. Here we compare the plasmonic nanolaser performance for oxides of different refractive index, with MgF2 and Al2O3 being the low and high refractive index oxides, respectively, to determine the material most suitable for the nanolaser structure. First, the mode characteristics of the nanolasers with the two different oxides are calculated and compared. Theoretically, only the Transverse Magnetic (TM) mode can propagate on the surface of a pure plasmonic waveguide (metal-insulator). On the other hand, the semiconductor waveguide supports the propagation of Transverse Electric (TE) modes with the electric field parallel to the quantum-well axis. But in the hybrid plasmonic waveguide, a hybrid or quasi-TM mode (EH) can also propagate. Therefore, to investigate the modal behaviors of the structure, we choose three different modes, the first fundamental plasmonic mode (SPP0), the first hybrid mode (EH00) and the fundamental photonic mode. The fundamental photonic mode was created by placing the semiconductor waveguide on a quartz (n = 1. 53) substrate layer.

For the SPP0 and photonic eigenmodes, polarization (direction of white arrows) is mostly perpendicular or parallel, respectively, to the metal surface, and shows the propagation of the TM and TE modes. In the case of the hybrid EH00 eigenmode, polarization is a combination of these two pure modes, with perpendicular polarization near the metal surface and polarization parallel to the metal and quantum wells in the semiconductor waveguide core. This phenomenon will take the energy of the optical mode created by photons generated inside the quantum-well cavities and transfer it to the highly confined plasmonic mode, allowing the hybrid mode to travel below diffraction limits.

Results and Discussions

For plasmonic eigenmodes the majority of the electrical energy is concentrated in the oxide, with little intensity inside the metallic layer, and the remaining energy distributed in the semiconductor. For the photonic mode, the electrical energy is mostly inside the semiconductor. In the case of the hybrid modes, the electrical energy is present in both the oxide and the semiconductor. As discussed further below, this will increase both the confinement factor and the propagation length of the mode.

The field distribution and eigenmode refractive indices were calculated using the Finite Element Method in FEMLAB modeling software (COMSOL Inc. , Stockholm, Sweden). The hybrid modes are cut off at widths smaller than 450 nm. The photonic-mode loss was much smaller compared with the plasmonic modes and has been excluded from the plots. The parameters of the two plasmonic (SPP0) modes and the two hybrid modes are behaving similarly. As expected, and as apparent in Figure 4a, the first fundamental plasmonic mode (SPP0) doesn’t have a cutoff width. The hybrid modes are cut off below the 450 nm waveguide width, which indicates the minimum possible width for these modes to propagate inside the nanolaser. However, the photonic mode can propagate inside waveguides as small as 300 nm. Inside the Al2O3 layer, the plasmonic mode experiences higher loss compared to the MgF2 layer and has a smaller propagation length. It can be understood that the propagation loss for the EH00 hybrid modes decreases rapidly with wider waveguides and indicates more power in traveling as photonic mode than plasmonic. For each eigenmode, the effective mode index neff was evaluated as the real part of the complex mode refractive index in the waveguide, and the propagation loss and distance were obtained from its imaginary part. The mode area Am is evaluated as the ratio of the total energy and the maximum energy density for each mode. The confinement factor is defined as the ratio of the electrical density in the active area of the nanolaser and the whole-structure cross-sectional area in the X–Y plane

Photonic-mode gain has been depicted without scaling to show the small amount of gain needed for this mode. For waveguides wider than 600 nm, the plasmonic (SPP0) modes, as expected, need higher gain levels for lossless propagation as a result of higher propagation loss and a poor confinement factor. Propagation loss in small waveguides increments because more energy propagates inside the metal. In addition, the nanolaser structure using Al2O3 needs less gain to overcome the plasmonic mode losses than that using MgF2. For the hybrid modes, the threshold gain is nearly one order of magnitude (700 1/cm) smaller than that of the plasmonic modes and the choice of oxide material does not make a significant difference.

It should be mentioned that our results were derived assuming a loss-free semiconductor waveguide to match the approach of previous work. The inclusion of waveguide losses in our calculations makes a noticeable change, particularly in propagation length and Γ factor. Moreover, other parameters such as the quality and the Purcell factor will also contribute to the nanolaser performance and output and should be considered when trying to predict or simulate a plasmonic nanolaser structure output.

Conclusions

In summary, we have investigated the mode-characteristic parameters and gain threshold of a semiconductor plasmonic nanolaser with multiple InGaAsP quantum wells active layer at a wavelength of 1330 nm. Effective mode index, propagation loss, mode area and confinement factor for two different oxides (Al2O3, MgF2), three different propagating modes (SPP0, EH00 and photonic) and waveguide-width ranges of 100 nm to 900 nm were obtained and used to calculate the threshold gain. The results show that the SPP0 mode has no cutoff and propagates in waveguides as narrow as 100 nm or less, but the propagation loss increases rapidly. The plasmonic mode always propagates with a sub-diffraction mode area. Hybrid modes have a cutoff width near 450 nm and at waveguides broader than 650nm can propagate with losses one order of magnitude smaller than the plasmonic mode and, in addition, below the diffraction limit. For waveguides wider than 800 nm, this mode reaches the diffraction limit. The photonic mode needs a considerably lower threshold gain for lossless propagation but can only propagate above the diffraction limit.