Plasmonic lasers (spasers) generate coherent surface plasmon polaritons (SPPs) and could be realized at subwavelength dimensions in metallic cavities for applications in nanoscale optics. Plasmonic cavities are also utilized for terahertz quantum-cascade lasers (QCLs), which are the brightest available solid-state sources of terahertz radiation. A long standing challenge for spasers that are utilized as nanoscale sources of radiation, is their poor coupling to the far-field radiation. Unlike conventional lasers that could produce directional beams, spasers have highly divergent radiation patterns due to their subwavelength apertures. Here, we theoretically and experimentally demonstrate a new technique for implementing distributed feedback (DFB) that is distinct from any other previously utilized DFB schemes for semiconductor lasers. The so-termed antenna-feedback scheme leads to single-mode operation in plasmonic lasers, couples the resonant SPP mode to a highly directional far-field radiation pattern, and integrates hybrid SPPs in surrounding medium into the operation of the DFB lasers. Experimentally, the antenna-feedback method, which does not require the phase matching to a well-defined effective index, is implemented for terahertz QCLs, and single-mode terahertz QCLs with a beam divergence as small as are demonstrated, which is the narrowest beam reported for any terahertz QCL to date. Moreover, in contrast to a negligible radiative field in conventional photonic band-edge lasers, in which the periodicity follows the integer multiple of half-wavelengths inside the active medium, antenna-feedback breaks this integer limit for the first time and enhances the radiative field of the lasing mode. Terahertz lasers with narrow-beam emission will find applications for integrated as well as standoff terahertz spectroscopy and sensing. The antenna-feedback scheme is generally applicable to any plasmonic laser with a Fabry–Perot cavity irrespective of its operating wavelength and could bring plasmonic lasers closer to practical applications.
© 2016 Optical Society of America
A surface plasmon polariton (SPP) is a coupled state between electromagnetic (EM) field and electron plasma oscillations at the interface between a metal and a dielectric for which the EM field could be confined in subwavelength dimensions normal to the surface of the metal. Consequently, metallic cavities supporting SPP modes have been used to realize SPP lasers (also known as plasmonic lasers or spasers) with subwavelength dimensions [1–5]. The energy in a spaser can remain confined as coherent SPPs or it can be made to leak out from the spaser as radiation. In many targeted applications in integrated optics and nanophotonics, spasers are developed as nanoscale sources of coherent EM radiation and show interesting properties such as ultrafast dynamics for applications in high-speed optical communications. Parallel-plate metallic cavities supporting SPP modes are also utilized for terahertz quantum-cascade lasers (QCLs)  to achieve low-threshold and high-temperature performance  owing to the low loss of SPP modes at terahertz frequencies that are much smaller than the plasma frequency in metal. The most common type of plasmonic lasers with long-range SPPs, which include terahertz QCLs, utilize Fabry–Perot type cavities in which at least one dimension is longer than the wavelength inside the dielectric [8–11]. One of the most important challenges for such plasmonic lasers is their poor coupling to free-space radiation modes owing to the subwavelength mode confinement in the cavity, which leads to a small radiative efficiency and highly divergent radiation patterns. This problem is also severe for terahertz QCLs based on metallic cavities and leads to low-output power and undesirable omnidirectional radiation patterns from Fabry–Perot cavities [12,13].
A possible solution to achieve directionality of far-field emission from spasers is to utilize periodic structures with broad-area emission, which has been used for both short-wavelength spasers [14–19] as well as terahertz QCLs [20,21]. On chip phased-locked arrays [22,23] or metasurface reflectors composed of multiple cavities  have also been utilized for directional emission in terahertz QCLs. However, edge-emitting Fabry–Perot cavity structures with narrow cavity widths are more desirable, especially for electrically pumped spasers to achieve a small operating electrical power and better heat removal from the cavity (along the width of the cavity in the lateral dimension, through the substrate) for continuous wave (cw) operation. In this paper, we theoretically and experimentally demonstrate a new technique for implementing distributed feedback (DFB) in plasmonic lasers with Fabry–Perot cavities, which is termed an antenna-feedback scheme. This DFB scheme has no resemblance to the multitude of DFB methods that have been conventionally utilized for semiconductor lasers. The key concept is to couple the guided SPP mode in a spaser’s cavity to a single-sided SPP mode that can exist in its surrounding medium by periodic perturbation of the metallic cladding in the cavity. Such a coupling is possible by choosing a Bragg grating of appropriate periodicity in the metallic film. This leads to excitation of coherent single-sided SPPs on the metallic cladding of the spaser that couple to a narrow beam in the far field. The narrow-beam emission is due in part to the cavity acting like an end-fire phased-array antenna at microwave frequencies as well as due to the large spatial extent of a coherent single-sided SPP mode that is generated on the metal film as a result of the feedback scheme. Experimentally, the antenna-feedback method is implemented for terahertz QCLs for which the method is shown to be an improvement over the recently developed third-order DFB scheme for producing directional beams  since it does not require any specific design considerations for phase matching . The emitted beam is more directional and the output power is also increased due to an increased radiative field by virtue of this specific scheme.
2. ANTENNA-FEEDBACK SCHEME FOR PLASMONIC LASERS
Single-mode operation in spasers with Fabry–Perot cavities could be implemented in a straightforward manner by periodically perturbing the metallic film that supports the resonant SPP modes. The schematic in Fig. 1(a) shows an example of a periodic grating in the top metal cladding for a parallel-plate metallic cavity that could be utilized to implement conventional -th order DFB by choosing the appropriate periodicity. Since the SPP mode has a maximum amplitude at the interface of the metal and dielectric active medium, a periodic perturbation in the metal film could provide strong Bragg diffraction up to high orders for the counterpropagating SPP waves inside the active medium with incident and diffracted wave vectors and , respectively, such that27] and second-order [28,29] DFBs have been implemented to achieve robust single-mode operation. However, these conventional DFB techniques do not achieve directionality of far-field radiation in both directions. There is a phase mismatch for SPP waves on either side of metal claddings and destructive interference between successive apertures, as shown in Fig. 1(b) for propagating SPP waves. Therefore, no coherent single-sided SPP waves can be established on the metallic cladding in the surrounding medium, as demonstrated in Fig. 1(c). Consequently, 2D photonic-crystal DFB structures have been utilized for broad-area (surface) single-mode emission [30,31] for which diffraction-limited beams could be achieved at the expense of large cavity dimensions.
In contrast to conventional DFB methods in which periodic gratings couple forward and backward propagating waves inside the active medium itself, the antenna-feedback scheme couples a single-sided SPP wave that travels in the surrounding medium with the SPP wave traveling inside the active medium, as illustrated in Fig. 1(d). The SPP wave inside the active medium with incident wave vector is diffracted in the opposite direction in the surrounding medium with wave vector . For the first-order diffraction grating (), Eq. (1) results in
The antenna-feedback scheme leads to the excitation of a coherent single-sided SPP standing wave on the metallic cladding of the spaser, which is phase locked to the resonant-cavity SPP mode inside the active medium, as shown in Fig. 1(f). Both waves maintain the exact same phase relation at each aperture location, where they exchange EM energy with each other due to diffraction, as illustrated in Fig. 1(e). The SPP wave in the surrounding medium is excited due to scattering of the EM field at apertures that generate a combination of propagating quasi-cylindrical waves and SPPs [32,33] that propagate along the surface of the metal film. The scattered waves thus generated at each aperture superimpose constructively in only the end-fire () direction owing to the phase condition thus established at each aperture. For coupling to far-field radiation, the radiation is therefore analogous to that from an end-fire phased array antenna that produces a narrow beam in both the and directions.
A third-order DFB technique was recently shown to achieve emission in a narrow beam for terahertz QCLs with Fabry–Perot cavities . It can achieve high directionality for the radiated beam in both directions perpendicular to propagation as long as the effective propagation index of the SPP wave inside the active medium could be made by complex deep dry etching in the slits  or lateral corrugated geometry . The so-called phase-matching condition is possible for GaAs-based QCLs by cavity engineering  since the is close to 3.0. The antenna-feedback technique in this work offers a similar outcome as a perfectly matched third-order DFB with improved directionality as well as a novel outcoupling mechanism of the radiated beam from terahertz QCLs. It is to be noted that the antenna-feedback scheme is automatically phase matched and hence it could be utilized for any type of spaser without any restrictions on the required index in the active medium.
3. SIMULATION RESULTS
Figure 2 shows a comparison of the eigenmode spectrum of a terahertz QCL cavity with a conventional DFB, taking a third-order DFB as an example versus antenna-feedback gratings computed using a finite-element solver . The occurrence of bandgaps in the spectra is indicative of the DFB effect. In both cases, the lower-frequency band-edge mode is the lowest-loss mode by way of DFB action since the DFB modes result in a standing wave being established along the length of the cavity with an envelope shape that vanishes close to the longitudinal boundaries (end facets). For the antenna-feedback grating, a standing wave for the single-sided SPP wave is additionally established in air, as can be seen from the field plot of the band-edge mode in Fig. 2(b). In contrast, the third-order DFB leads to a negligible amplitude of the single-sided SPP wave in air, as mentioned previously and illustrated schematically in Fig. 1(c). For the dominant TM polarized (Ey) electric field of the antenna-feedback, the hybrid SPPs mode bound to the top metal layer consists of both quasi-cylindrical waves and SPPs, which are evanescent-fields with a free-space propagation constant. Particularly at long wavelengths, such as the mid infrared and THz regions, SPPs and quasi-cylindrical waves complexly mix with each other , contributing to the large spatial extent of the SPP mode in the surrounding medium, as shown in Fig. 2(b), which does not exist for any conventional DFB, such as first-order, second-order and third-order DFB. In addition, hybrid SPPs on top of metallic gratings and standing wave inside the laser cavity show clearly different periodicity, with the ratio of the free-space wavelength over the guided wavelength, which further confirms that the excitation of the coherent SPP wave on both sides of the top metallic surface contribute to the feedback and coupling mechanism with the antenna-feedback scheme. The absorbing boundaries at the longitudinal ends of the cavity  increase the relative loss of the modes that are further away from the band-edge mode, which helps in the mode discrimination and will lead to the excitation of the desired band-edge mode for the single-mode operation of the spaser. The active region and metal layers are modeled as lossless since the exact loss contribution due to each is not clear in literature for terahertz QCLs at cryogenic temperatures. If a lossy metal is used, the relative loss of various resonant modes for the DFB cavities are not impacted and neither are the mode shapes and the corresponding resonant frequencies. For the band-edge modes in Figs. 2(a) and 2(b), a loss of was estimated as a contribution from the absorbing boundaries. Consequently, the radiative (outcoupling) loss of the third-order DFB is as compared to for the antenna-feedback. The radiative loss of the third-order DFB is smaller since the band-edge mode has zeros of the radiative field () being located at each aperture since the grating period is an integer multiple of half-wavelengths in the GaAs/AlGaAs active medium (, where ). Such a low outcoupling efficiency is also existent in surface-emitting terahertz QCLs with a second-order DFB . For the cavity with antenna-feedback, the radiative loss is higher because the grating period is not an integer multiple of half-wavelengths inside the active medium () that leads to large amplitudes of the radiative field () in alternating apertures, as shown in the figure. As a consequence, the output power from terahertz QCLs with antenna-feedback should be greater than that with conventional DFB gratings, which is an additional advantage of the antenna-feedback scheme for terahertz QCLs. This was also verified experimentally from the measured output power. The recently developed second-order DFB QCLs with graded periodicity  achieve high-power emission for the same reason, i.e., a nonzero radiative field under the metallic apertures.
4. EXPERIMENTAL DEMONSTRATION OF ANTENNA-FEEDBACK FOR TERAHERTZ QCLs
Figure 3 shows the experimental results from terahertz QCLs implemented with antenna-feedback gratings. Details about the fabrication and measurement methods are presented in Supplement 1 (Section S1). Figure 3(b) shows representative - curves versus the heat-sink temperature for a QCL with . The QCL operated up to a temperature of 124 K. In comparison, multimode Fabry–Perot cavity QCLs on the same chip that did not include longitudinal or lateral absorbing boundaries operated up to . Light-current characteristics and spectra at a different bias with the Fabry–Perot cavity are shown in the Supplement 1 (Section S3). The temperature degradation due to the absorbing boundaries is relatively small and similar to previous reports of DFB terahertz QCLs . The inset shows the measured spectra at a different bias at 78 K. Most QCLs tested with different grating periods showed a robust single-mode operation except a close to peak bias when a second mode was excited for some devices at a shorter wavelength, which suggests that it is likely due to a higher-order lateral mode being excited due to spatial-hole burning in the cavity. A peak- power output of was detected from the antenna-feedback QCL measured directly at the detector without using any collecting optics. For comparison, a terahertz QCL with a third-order DFB (without phase matching) and similar dimensions was also fabricated on the same chip, which operated up to a similar temperature of and emitted a peak-power output of (see the Supplement 1, Section S3). The antenna-feedback gratings lead to a greater radiative outcoupling compared to conventional DFB schemes for terahertz QCLs, as discussed in the previous section.
Figure 3(c) shows the spectra measured from four different terahertz QCLs with antenna-feedback gratings of different grating periods . The single-mode spectra scales linearly with , which is the clearest proof that the feedback mechanism works as expected and the lower band-edge mode is selectively excited in each case. Using from Eq. (2), the effective propagation index of the SPP mode in the active medium is calculated as 3.59, 3.53, 3.46, and 3.33 for QCLs with of 21 μm, 22 μm, 23 μm, and 24 μm, respectively. The effective mode index decreases because a larger introduces larger sized apertures in the metal film since the grating duty cycle was kept the same for all devices. Consequently, a greater amount of field couples to the single-sided SPP mode in air for increasing , thereby reducing the modal confinement in the active medium that reduces the propagation index of the guided SPP mode further.
Experimental far-field beam patterns for antenna-feedback QCLs with varying designed parameters are shown in Fig. 4. Single-lobed beams in both lateral () and vertical () directions were measured for all QCLs. As shown in Fig. 4(b), the full-width half-maximum (FWHM) for the QCL with 70 μm width, is , which is the narrowest reported beam profile from any terahertz QCL to date. In contrast, previous schemes for emission in a narrow beam have resulted in divergence angles of using very long () cavities and a phased-matched third-order DFB scheme  and using broad-area devices with 2D photonic crystals  for single-mode terahertz QCLs, and  and  for multimode QCLs using metamaterial collimators. Figures 4(c) and 4(d) show representative beam patterns from QCLs with wider cavities of 100 μm width for the smallest and largest in the range of fabricated devices, respectively. The beam divergence is relatively independent of , as expected. More importantly, the measurements show that the wider cavities result in a slightly broader beam. Such a result is counter intuitive because typically a laser emits in a narrower beam as its cavity’s dimensions are increased due to an increase in the size of the emitting aperture. Such a behavior is unique for a spaser with antenna-feedback and is discussed along with the full-wave 3D FEM simulation of the beam pattern in the Supplement 1 (Section S2). It can be argued that the size of the beam could be further narrowed by utilizing narrower cavities for terahertz QCLs, which will be extremely beneficial to develop cw sources of narrow-beam coherent terahertz radiation.
In this paper, we have presented a novel antenna-feedback scheme to achieve single-mode operation and a highly directional far-field radiation pattern from plasmonic lasers with subwavelength apertures and Fabry–Perot type cavities. It is conceptually different from any other previously utilized DFB scheme for solid-state lasers, and is based on the phase locking of a single-sided SPP mode on (one of) the metal film(s) in the spaser’s cavity, with the guided SPP mode inside the spaser’s active medium. The phase locking is established due to strong Bragg diffraction of the SPP modes by periodically perforating the metal film in the form of a grating of holes or slits. The uniqueness of the method lies in the specific value of the grating’s period, which leads to the spaser’s cavity radiating like an end-fire phased-array antenna for the excited DFB mode. Additionally, coherent single-sided SPPs are also generated on the metal film that have a large spatial extent in the surrounding medium of the laser’s cavity, which could have important implications for applications in integrated plasmonics. Coherent SPPs with a large spatial extent could make it easy to couple SPP waves from the plasmonic lasers to other photonic components, and could also potentially be utilized for plasmonic sensing. Experimentally, the scheme is implemented in terahertz QCLs with subwavelength metallic cavities. A beam-divergence angle as small as is achieved for single-mode QCLs, which is narrower than that achieved with any other previously reported schemes for terahertz QCLs with periodic photonic structures. Compared with the third-order DFB method, the new antenna-feedback scheme is easier to implement for fabrication by standard lithography techniques without any other complex fabrication technique to precisely match a well-defined effective mode index, and achieves a superior radiative outcoupling owing to the fact that the grating period is not an integer multiple of half-wavelengths of the standing SPP wave inside the active medium. Terahertz QCLs with antenna-feedback could lead to the development of new modalities for terahertz spectroscopic sensing and wavelength tunability due to the access of a coherent terahertz SPP wave on top of the QCL’s cavity, possibilities of sensing and imaging at standoff distances of a few tens of meters, and the development of integrated terahertz laser arrays with a broad spectral coverage for applications in terahertz absorption spectroscopy.
National Science Foundation (NSF) (ECCS 1128562, ECCS 1351142, CMMI 1437168).
This work was performed, in part, at the Center for Integrated Nanotechnologies, a U. S. Department of Energy (DOE), Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U. S. DOE’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
A United States patent application (pending) for the described technology has been filed through Lehigh University (application number 14/984,652, filed on Dec. 30, 2015).
See Supplement 1 for the supporting content.
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