1. Introduction

During the last years the potential of circularly shaped quantum dot (QD) microcavities (e.g. microdisks, micropillars) became more and more evident, not only for the investigation of fundamental phenomena of quantum electrodynamics [1,2], but also for practical use [3–5]. Their strengths are, for example, simple fabrication, low threshold lasing, high Q-modes, high β-factors, and a high integrability. Moreover, it was shown that those microcavities are able to support lasing of so called whispering gallery modes (WGM) with in plane k-vectors, which were extensively studied in QD microdisks under optical pumping and cryogenic temperatures [6]. Recently, they were reported to be excitable in electrically driven micropillars [7], and also in more broadened microposts and ring-shaped structures at room-temperature [8]. Ring devices have the advantage of an optimized mode to cavity volume. Since WGMs are confined to the sidewalls of the circular cavity, the inner region of a micropillar or micropost structure is not vital to sustain those lasing modes. It can thus be removed or omitted in order to reduce threshold current [9,10], and background radiation from spontaneous emission.

A WGM spectrum shows the classical pattern of squared wavelength distributed modes. The mode spacing is further inversely proportional to the resonator length, which corresponds to the circumference in case of a ring cavity. Thus, a combination of the inhomogeneously broadened gain spectrum of a six layer QD cavity [11], and a large ring diameter provide spectra that present a good basis to investigate a novel approach to suppress unwanted modes. By introducing subwavelength sized notches to the ring's sidewalls, the spectrum can be influenced [12], and periodical intervals of mode numbers can be disturbed. Single mode lasing was observed in studies with an etched grating stretching over the whole circumference of the resonator, a so-called microgear cavity [13]. Other possibilities for mode selection are combinations of rings with distributed Bragg reflectors (DBRs) [14–16] or waveguides and photonic crystals [17]. These more complex devices also allow a tuning of the emission wavelength.

In contrast, the method presented in this paper requires only a few notches arranged in a certain geometry and can therefore preserve multi-mode lasing with a determined wavelength spacing. This feature is very interesting in regard of applications based on distinct multi-color lasing, for example the terahertz (THz) emission from difference frequency generation (DFG). It was already proposed that micropost devices can make use of the strong non-linear optical properties of GaAs and use two near-infrared modes to generate THz radiation using a difference frequency scheme [18]. Using an appropriate selection mechanism, electrically driven microrings are able to sustain those IR modes on their own and would thus be a great step towards integrable, electrical THz devices. This would mean a significant advantage over common THz systems that either need optical pumping, work only at cryogenic temperatures, or have very low output powers.

In this letter, the basic concept of the proposed mode selection mechanism is discussed and supported by numerical modeling of the notched devices. By comparison of experimental emission spectra of unnotched and notched rings with 78µm inner and 80µm outer diameter (i.e. a 1µm wide ridge), the effect of a 90°, 60° and 45° notch geometry is demonstrated.

2. Theoretical modeling of the selection mechanism

Whispering gallery modes build up from circulating photons confined by total internal reflection at the outer sidewalls of the ring structure. The modes are degenerated, since the light can propagate in both circular directions, and they can be characterized by vertical, radial and azimuthal mode numbers (n, l, m accordingly). The layer structure and ring ridge width is chosen so that the following investigations can be restricted to n = 1, l = 1. Only transverse electric TE modes, with their electric field vector in plane with the cavity, can couple effectively to the dipole moment of the quantum dots and TM modes can be neglected [6].

2.1 Basic concept

The main idea of selecting modes by notching the sidewalls of a WGM ring laser is to introduce high losses to unwanted modes and thus suppressing their lasing ability. Figure 1 presents a not drawn to scale scheme of this principle using two notches with an offset angle of 90°, indicated by the black bars. The dashed concentric circles illustrate a ring with normalized diameter. One can recognize the mode distribution for TE_1,1,18 (a), TE_1,1,19 (b) and TE_1,1,20 (c) modes for undisturbed light propagation. The mode numbers are chosen quite low for the sake of clearness. The standing waves with even azimuthal mode number (a, c) will be almost unaffected by the thin notches, whereas the odd mode in the middle shows an intensity maximum at one notch position and will thus suffer from high scattering losses.

 

Fig. 1 Schematic mode distribution for notched rings with 90° offset angle. Does not account for influences of notches to propagation of the modes. (a) m = 18. (b) m = 19. (c) m = 20.

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The selection can be expanded to allowing only every forth mode to lase by introducing a third notch halfway between the two existing ones. In case of the TE_1,1,20 mode, this position is associated with a node so that this mode is not significantly afflicted by the notch. In contrast, the TE_1,1,18 mode shows an antinode there and will thus be suppressed. By a further bisection of the circular distance between the notches, one can obtain mode selection allowing for only every eighth, sixteenth etc. mode to reach the lasing regime. Analogous considerations for other offset angles result in Eq. (1) for the generalized calculation of the resulting effective free spectral range FSR_eff between the lasing modes.

2.2 Simulation

For a more detailed understanding of the notches' influence on the wave propagation, simulations of the mode distributions for an orthogonally notched ring were performed. The results are presented in Fig. 2. The upper row shows (from the left to the right) TE_1,1,18, TE_1,1,19 and TE_1,1,20 modes with positive parity. The lower row shows negative parity mode, accordingly. The simulation uses an effective index method (EIM) to account for the vertical mode confinement with a group index n_g = 3.67 and an internal absorption α_i = 2cm⁻¹. The remaining two-dimensional problem is numerically solved in frequency space with the boundary element method [22]. This approach is based on a Green function technique which transforms the 2D partial differential equation to a 1D integral equation defined along the boundary of the cavity. The integral equation is then discretized into N boundary points. In the case at hand N = 16000 is required for an accurate determination of the Q-factors. To simplify the illustration of the physics, a much smaller ring than the experimentally examined, with diameters of 2.56µm and 1.67µm is used. The notch width is taken to be 16nm and the depth is 160nm. As the precise shape of a notch is not important as long as its size is smaller than the wavelength [23], each notch is modeled by a Gaussian function.

 

Fig. 2 Simulated mode distributions for TE_1,1,18 (a, d), TE_1,1,19 (b, e) and TE_1,1,20 (c, f) modes of an orthogonally notched ring with positive (upper row) and negative parity (lower row).

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A displacement of the electric field is seen in the plots, which is most pronounced for modes where the maxima of the intensity coincide with notches. This displacement is a consequence of the interaction between the optical mode and the notches. All solutions are still radially single mode as there is only a single local maximum of the field in radial direction. However, if such a solution would be expanded in modes of the unperturbed ring (without notches), there would be a significant contribution not only from the mode with the lowest radial mode number, but also from excited modes with higher radial mode numbers. The contribution from the excited modes is a result of the pertubation induced by the notches.

By comparison of the modes' Q-factors, one can estimate which modes will be stimulated and which will not. As predicted in the introduction of the concept above, only two of the six examined modes, namely TE⁺_1,1,18 (a) and TE^-_1,1,20 (f), are truly undisturbed in their propagation, showing Q-factors of 89000 (a) and 64000 (f). Additionally, once again taking account of symmetry arguments, it becomes obvious that the undisturbed modes with mode numbers which are multiples of four will have negative, the other modes positive parity.

In contrast to the scheme of Fig. 1, both azimuthally odd numbered modes form in such a way that two intensity maxima are equally disturbed by the notches. This symmetry leads to Q-factors which are about 30 times smaller, i.e. 2600 (b) and 2400 (e), than the ones of the unimpaired modes, making it very hard to stimulate them. Thus they will not appear in the resulting spectrum, what leads to a duplication of the effective FSR. As expected from the model, the Q-factors of the TE^-_1,1,18 and TE⁺_1,1,20 modes are even stronger influenced, since each mode has two maxima at the notches' positions and the modes will thus also not reach laser threshold.

3. Processing of notched ring structures

The samples used for fabrication of ring lasers were grown by molecular beam epitaxy on a n-doped GaAs substrate, in order to be capable of backside contacting. An AlGaAs graded index separate confinement heterostructure (GRINSCH) surrounds six 5nm thick layers of InGaAs/InAs quantum dots separated by 40nm of GaAs. The QDs provide an inhomogeneously broadened gain so that several modes can be stimulated simultaneously. The structure is cladded with 1700nm of Al_0.4Ga_0.6As on both sides. The use of a quantum dot active region is beneficial in lasers where the active region has an open sidewall (which is the case for the ring lasers presented here), since lateral carrier diffusion and therefore non-radiative recombination at the sidewall is suppressed. Electron beam lithography and an electron cyclotron resonance Cl₂ /Ar plasma etching process was applied to define the notched ring shaped microresonators. Since the notches and the ring ridges are processed within the same step, a very precise positioning and size control of the notch is guaranteed. Figure 3(a) shows a scanning electron microscopy (SEM) image of a ring with 80 µm outer and 78 µm inner diameter after etching, and a corresponding width of 1µm. We did not investigate rings with a smaller width, since the optical mode also interacts with the inner circumference of the ring in these structures, leading to an increase of the optical losses. On the right hand side, a more detailed close-up of the upper edge of a ring sidewall with a notch is provided. The width is about 50nm and the depth amounts to 500nm over the whole 4.4µm height of the ring. The roughness on top of the ring is due to an intentionally incomplete removal of the Ni-mask. In a final step, the rings were embedded in benzocylobutene and covered by a full circle gold contact that allows comfortable contacting of single rings.

 

Fig. 3 SEM images. (a) Total view of a ring with 80 µm outer diameter. (b) Close-up of a notch.

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4. Experimental results

All samples were characterized at room temperature. Electric current was applied using a metal tip to contact individual microring lasers. To collect the emission of a device, the cleaved facet of a multimode optical fiber (core diameter 50µm) was brought close (~100µm) to the microring. A spectrum analyzer with a spectral resolution of 50pm is then used to investigate the optical output of the lasers. A typical normalized, integrated output characteristic of a ring with two orthogonally arranged 50/500nm notches is depicted in Fig. 4. The red line indicates the fitting to the linear region used for determination of the threshold current. The threshold current is 3.39mA, which differs by less than 10% from the value of an unnotched ring.

 

Fig. 4 Output power characteristic of a ring with 78µm inner and 80µm outer diameter. Two 50/500nm notches are placed under an angle of 90°.

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A comparison of emission spectra obtained from rings with 78µm inner and 80µm outer diameter, resulting in azimuthal mode numbers of approximately 730 to 760, and different notch symmetries is provided by Fig. 5. All spectra were taken at a heat sink temperature of 20°C and an injection current of 10mA. Graph (a) shows a reference spectrum of an unnotched ring, containing a broad band of modes which are all neighbors in azimuthal mode number. The spectra (b) to (d) feature successively growing effective FSRs from two to four times the adjacent mode distance, achieved by choosing 90°, 60° and 45° offset angles. The corresponding notch geometry is indicated by the red bars of the gray, not drawn to scale, circles on the right hand side of each spectrum. For achieving a fourfold mode spacing in (d), three notches were used to enforce the selection effect. The dashed red lines serve as guide for the eye and project the energies of the neighboring modes of the topmost spectrum onto the three lower spectra, indicating the approximate positions of suppressed modes. Since the high azimuthal mode numbers and the modes' energetic positions are very sensitive to variations in diameter, Fig. 5 does not account for the superimposed modes' azimuthal numbers to share the same divisors. As a consequence of variations in QD density and size distribution dependent on ring position on the sample, the energetic ranges and the normalized intensities of the spectra differ from each other. Thus, the peak energies occasionally deviate from the dashed red lines. The average FSR of the reference spectrum is 1.62 nm.

 

Fig. 5 Comparison of room temperature spectra of 80µm outer diameter rings with different notch symmetries taken at 10mA injection current. The dashed red lines are guides to the eye, indicating selected modes. (a) Unnotched reference spectrum. (b) Two notches with 90° offset angle. (c) Two notches with 60° offset angle. (d) Three notches with 45° offset angle.

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Figure 5(b) shows an effective FSR of $3.12\text{nm}=2\times 1.56\text{nm}$, (c) shows $5.05\text{nm}=3\times 1.68\text{nm}$and (d) shows $6.50\text{nm}=4\times 1.63\text{nm}$, which means that they vary by less than 2% from the expected values. In regard of applicability as THz source, especially the 45° assembly is very promising, since an appropriate resonator can sustain THz lasing from two near-IR modes with a difference in azimuthal mode number of four [18]. As the notches are very small in comparison to the THz-mode's wavelength, it will not suffer from significant, notch-induced losses.

5. Conclusion

Within this report a simple method to filter modes with certain azimuthal mode numbers from a WGM spectrum of a microring resonator by notching its sidewalls is introduced. The experimentally obtained spectra from rings with 80µm outer diameter clearly confirm this appraoch and the performed simulations. A six laxer QD microring cavity with broad gain spectrum supports the demonstration of selecting every second, third and fourth mode to reach the lasing regime using 90°, 60° and 45° offset angles, accordingly. Emission wavelengths in the region around 1230nm and appropriately chosen ring parameters result in FSRs of 1.62nm for the unnotched reference spectrum, 3.12nm for 90° notching, 5.05nm for 60° notching and 6.50nm for 45° notching.