1. Introduction

The miniaturization of semiconductor laser waveguides is a key point toward the development of low power consumption sources and the implementation of high density systems in integrated circuit. However, the reduction of the waveguide lateral size strongly affects the laser beam directionality, fundamental feature for most of the applications. The diffraction law governs the beam divergence, fixing the limit to waveguide dimensions suitable for a narrow emission in edge-emitting lasers. In this work we present a mean to overcome this limit: THz laser waveguide with sub-wavelength lateral size, emitting in a narrow single lobe are reported.

Light waveguides, where the mode is strongly confined in a one dimensional structure with sub-wavelength area, are generally called photonic-wires. They are mostly used as passive components, integrated in complex systems for sensing or circuit integration [1,2]. Similar structures, when used as active devices, are denominated photonic-wires lasers [3–5]. In this work we present a photonic-wire laser operating at THz frequencies designed to overcome the diffraction limit of sub-wavelength waveguides. For this purpose, the out-coupling aperture for the laser light has been moved from the facet to the waveguide surface and the field distribution has been engineered to keep the emission direction along the device length (See Fig. 1 ). A periodic array of apertures has been implemented along the waveguide to extract single frequency radiation from the active medium; at the same time the periodicity d has been designed to be ~λ/2 in order to provide the suitable phase distribution for light emission along the waveguide. This approach can be seen as good alternative to the velocity matching of the propagation mode to the vacuum, proposed in Ref [4] for similar structures. Besides, the surface emission from sub-wavelength apertures has been avoided since the field distribution in this case requires two dimensional structures to enable a narrow laser beam; in this configuration, indeed, the beam divergence of one dimensional waveguides is governed by the laser length and by its width [6–8].

 

Fig. 1 Schematic of waveguides emitting from the facet and from the surface along the arrows direction. Calculated beam divergence in the case of the emission along the blue arrows (diffraction limit) and along the red arrow (phased array).

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The active medium used in this work is a THz quantum cascade lasers (QCL) [9–11]: the design is based on a four wells active region with a phonon resonant extraction mechanism emitting at ~3THz [12]. Due to the long emission wavelength of these sources (~100µm), it is relatively easy to achieve the sub-wavelength regime with conventional optical-lithography fabrication techniques. The commonly used waveguide for THz QCL is very similar to microstrip antenna: the active medium is confined between two metal layers placed at a distance of ~10µm, smaller than λ/n (~30µm), where n is the refractive index of the structure [13–15]. In our previous work [16] an efficient design to extract single mode frequency from these waveguides has been presented: the combination of a third order periodic structure with a strong refractive index contrast grating provides the good mode matching condition for the radiation out-coupling. To push this approach to the sub-wavelength miniaturization, the key point has been the implementation of a different waveguide design for a convenient fabrication process and optimized laser performance in this regime. The periodic array has been realized as a lateral corrugated grating [17,18]: thanks to the opened features of the waveguide, an efficient rescaling for the fabrication process down to sub-wavelength dimensions has been achieved. Moreover this geometry offers the possibility of implementing wider waveguides, where no absorbing lateral regions are needed: the appropriate design can indeed selectively enhance the losses of the parasitic high-order lateral modes and enable the operation of the device on the fundamental ones. 3-D finite element simulations have been carried out to design the suitable grating for the efficient out-coupling of the desired frequency in the gain region of the active medium [16].

To avoid long and complex simulation routines, an analytical model has been developed to evaluate the radiation emission: a further optimization of the waveguide design in terms of beam divergence has then been possible. Indeed, our photonic-wire can be easily compared to an end-fire microwave antenna array and a similar formalism can be used to calculate the emission pattern of the laser [19,20]. The role of the independent microwave emitters is taken by the apertures in the waveguide. The far field emission is then the result of the field from each aperture multiplied by the array factor, representing the phase shift between each period due to the geometry of the waveguide. An important role is played by the metal layer below the waveguide that can reflect the radiation incoming with a certain angle; this effect has been included in the calculation adding another array symmetric to the previous respect to the array length. Given the geometry of the system and the field distribution, this model can obviously easily be extended to different kinds and more complex periodic waveguides. As it will be shown in the following, our model yields a better agreement with the experimental results as compared to standard Fourier- transform calculations.

Illustrative results are shown in Fig. 1 calculated beam divergence for the edge emitting phased array (red curves) are compared with the diffraction theory valid for standard edge and surface emitting devices (blue curves); the propagation of fundamental lateral mode has been considered. For the waveguide design implemented in this work, narrow laser beam in the sub-wavelength regime is predicted: narrower beams correspond to increasing values of the device length. Lasers with low electrical power consumption and low divergence are then expected for devices 5-10λ long.

2. Device fabrication and experimental results

The laser devices have been processed using standard procedure for the double metal THz waveguide and the grating has been defined using inductively coupled plasma dry-etching based on Cl₂ Ar chemistry at 60°C and a low temperature grown (120°C) SiN mask. A typical device is show in Fig. 2(a) the waveguide width is 15µm/5µm for the wide/narrow region. The two last periods of the grating have larger dimensions to allow the wire bonding for the electrical connections. The light-current-voltage curves for different temperature are presented in Fig. 2(b) and 2(c) for a device composed of 10 periods; the measurements have been performed both in pulsed and continuous mode operation.

 

Fig. 2 a) SEM photo of the device. Light-Voltage-Current characteristic in pulsed (a) and continous-wave operation (b) for a waveguide 15μm/5μm for the wide/narrow part.

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The operating current are in the range from 20 to 30mA: these values are much lower than for standard devices. The output power at 10K is more than 1.5mW and more than 1mW at the nitrogen temperature, both in pulsed and continuous mode operation. The slope efficiency at 10K is 150mW/A and the dynamic range is 40%; the emission frequency is single mode with a side mode suppression ratio of 3 decades (Inset Fig. 2(c)). Due to the very low electrical power dissipation, the maximum operating temperature in continuous mode is 110K, only 10K lower than the value measured for pulsed operation. Besides, the beam emission has been measured recording the light intensity with a pyroelectric detector over a sphere around the device at a distance of 6 cm. Devices with different lengths and widths have been studied and compared with results obtained from our analytical approach based on the antenna theory; results are reported in Fig. 3 . The emission divergence for the wire laser, whose characteristic have been presented above (in Fig. 2), is only 22° for the α and 30° for the β direction (See inset Fig. 3 for the angles notation). A narrower beam has been obtained for structure with the same width but an increased number of periods (15 periods): the beam divergence decrease to a value of 15° for the α and 18° for the β direction as expected from calculations. To further prove our model a structure with the same length (15 periods) but different width has been tested (50µm/15µm for the wide/narrow region). The increasing of the waveguide width of a factor 3 does not yield a narrower beam, as expected if the light would have been out-coupled from the facet, but it leads to similar beam divergences as predicted by our model.

 

Fig. 3 Comparison between calculated (left side) and measured (right side) beam pattern for different waveguide widths and lengths. First line: 15μm/5μm wide, 10 periods long waveguide. Second line: 15μm/5μm wide, 15 periods long waveguide. Third line: 50μm/16μm wide, 15 periods long waveguide. Inset: schematic of the angles notation.

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Due to the favorable extraction mechanism of this waveguide design, good laser performances have been obtained also for the wider waveguides (50µm/15µm for the wide/narrow region). The device is shown in Fig. 4(a) . The light-current-voltage curves in continuous wave are reported in Fig. 4(b). The output optical power at 10K is 11mW with a slope efficiency is of more than 230mW/A for a single mode emission. The maximum operating temperature is 80K in continuous-wave, a good value for double-metal waveguide; on the other side this result is lower than what presented for the wire waveguide, where the benefit of a low electrical power consumption has been demonstrated. In Fig. 4(c) it is also presented the tuning of the laser frequency with the grating period, greatly desirable for applications.

 

Fig. 4 a) SEM photo of the device b) Light-Voltage-Current characteristic in continuous-wave operation for a waveguide of 50μm/15μm for the wide/narrow part. c) Tuning of the laser frequency with the grating period going from 35μm to 43μm.

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3. Conclusions

In conclusion in this work we presented a successful gratin design to improve performance of photonic-wire laser. This idea could be applied to any frequency, both for passive and active element. Moreover at the terahertz frequency it could represents a valid approach to be combined with the results recently reported in ref [21], to achieve a high power, tunable source, with a narrow beam emission.