We have studied the coherent intercavity coupling of the evanescent fields of two microdisk terahertz quantum-cascade lasers. The electrically controllable optical coupling of the single-mode operating lasers has been observed for cavity spacings up to 30 µm. The strongest coupled photonic molecule with 2 µm intercavity spacing allows to conditionally switch the optical emission by the electrical modulation of only one microdisk. The lasing threshold characteristics demonstrate the linear dependence of the gain of a quantum-cascade laser on the applied electric field.
© 2009 Optical Society of America
Photonic integrated circuits are faster, providing more bandwidth and having lower power consumption compared to their electronic counterparts. Merging optics and electronics for future optical circuits [1, 2] is still an open challenge mainly due to the lack of a chip based platform providing photon sources and manipulation units at once. Hybrid solutions are on the way [3, 4] to bridge between sources and circuits, but the efficient coupling into photonic circuits remains still a problem to be overcome.
The III–V material system is well suited for fully functional optoelectronics, as it combines both optical and electronic functions. GaAs based compact and unipolar mid-infrared  and terahertz (THz)  emitting lasers called quantum-cascade lasers (QCLs) have already been realized. The light amplification within the cascaded semiconductor heterostructure is based on intersubband (ISB) transitions, i.e. transitions between levels quantized along one dimension. Quantum-cascade microlasers with in-plane highly directional , in-plane unidirectional , or surface [9, 10] emission as well as active photonic crystals [11, 12, 13] have also been established, providing the basic building blocks for light manipulation and waveguiding. Hence, photon sources and waveguides are already established in the THz spectral range, but the optical intercavity coupling has not been studied so far.
In this Letter we investigate for the first time the electrically controlled coherent optical coupling between whispering-gallery modes (WGMs). The linear combination of the optical fields allows to create so called photonic molecules (PMs) . Compared to former realizations of PMs, e.g. microspheres [15, 16] or semiconductor microcavities [14, 17], PMs based on microdisk THz-QCLs differ in several important aspects from these approaches. First, THz-PMs comprise an electrically pumped optical gain enabling fast electrically controlled mode tuning and switching. Second, the plasmonic mode confinement permits sub-wavelength sized cavities. This allows to study the optical coupling of just two single modes and the precise control over the resonance frequency. And third, the combination of gain switching and exact spatial cavity configuration offers a precise control over the resulting mode configuration and on chip integration.
2. Device design, fabrication and measurement scheme
The investigated PMs consist of two THz-QCLs having each a cylindrical resonator as shown in Fig. 1, i.e. a microdisk cavity, with the same nominal dimensions of radius R=45 µm and height H=16.2 µm. The varying spacings between the microdisks result in different coupling strengths. The spacing x will be included in the terminology as PM-x.
The active gain region of the microdisks is based on a four well/barrier GaAs/Al0:15Ga0:85As heterostructure , which has been repeated 271 times during the growth to achieve a large modal gain. The heterostructure is embedded between two metal layers serving as electrical contacts and allowing for strong vertical mode confinement (λ≫H), whereas the lateral confinement is provided by the impedance mismatch between the gain material and the air. Details of the design, growth, and processing can be found elsewhere .
The emitted optical power of the PMs has been measured in a closed light pipe equipped with a Ga doped Ge (Ge:Ga) detector. Hence, the whole 2π emitted optical power is guided to the detector. The PMs were operated in pulsed-mode with 100 ns short pulses and double modulated at 100 Hz with a duty-cycle of 50 % to allow for the detection with a Ge:Ga detector. The current-voltage characteristics have been measured in continuous-wave mode operation with a voltage source resolution of 1 mV and a current sense resolution of 10 µA.
3. Finite-difference time-domain calculations
Full 3-D finite-difference time-domain (FDTD) simulations have been performed to reveal the properties of the PM modes. A custom-made code  was employed for this purpose, which includes several enhancements over the classical FDTD, such as a Maxwell-Bloch module for two-level quantum systems.
Two types of simulations have been performed to reveal the detailed field configurations. First, simulations with forced symmetry/antisymmetry have been performed for the case of two active devices, i.e. devices with the same net gain . The modes are labelled by a pair (x;y), indicating a symmetric (SYM) or antisymmetric (ASYM) field configuration with respect to the symmetry planes perpendicular (x) or parallel (y) to the molecule axis. (ASYM;y) modes are pushed further inside the resonator compared to (SYM;y) modes, resulting in different effective optical paths causing higher emission frequencies for the (ASYM;y) modes as shown in Fig. 2(a–d). The purpose of the second set of simulations is to verify and illustrate the possibility of starting a single laser in the presence of an heavily absorbing device nearby . An amplitude growth has been obtained for distances of 10 and 20 µm having field distributions presented in Fig. 2(e,f). The mode is well localized in the active cavity but couples also into the passive cavity, i.e. the cavity with net loss. However, the field maxima in the active cavity are much smaller than in the passive cavity. Hence, the lasing emission is still possible due to the strong mode confinement and in addition controllable by changing the net loss of the passive cavity.
4. Experimental results and discussion
The optical intercavity coupling between microdisks forming a PM has a strong impact on the electrical and optical characteristics as shown in Fig. 3. A single, uncoupled microdisk exhibits the typical current density-applied field characteristics due to ISB tunneling and lasing emission , i.e. a kink at the onset of the lasing emission labelled FON and a negative differential resistivity regime above the maximum lasing emission between FMAX and FOFF in Fig. 3(a). Compared to that, the PM-2 and the PM-30 exhibit higher current densities starting below FON up to well above FOFF. This is a consequence of the strong optical intercavity coupling. The PM-40 does not show such an increase indicating that the strong optical coupling is limited to ≈30 µm.
Fig. 3(b) shows the optical emitted power of a single microdisk and several PMs. The PM-2 depicts the same qualitative behaviour and the same threshold current density JON of a single microdisk, i.e. (J 1+J 2)/2=JON, reflecting that a PM-2 acts as a single cavity QCL.
The PM-6 and the PM-12 exhibit emission already at J 1=0, i.e. the single peak gain of the second microdisk is larger than the loss of the coupled system. The emission of these PMs is decreasing around J 1≈10 A/cm2 due to the carrier injection into the other microdisk leading to ISB absorption. The lasing emission of these PMs recover exactly at J 1=JON, i.e. the additional loss is balanced by the gain.
Fig. 4 shows the electrical control of the lasing emission of four PMs. The unique possibility to externally control the gain/loss of each cavity of a PM allows to tune the spatial mode configuration. The strongest coupled system shown in Fig. 4(a) lases only if both cavities provide gain. This electrically controlled purely optical conditional switching represents a logical AND operation. All weaker coupled systems exhibit lasing also if only one microdisk is biased beyond the lasing threshold field FON, which is an equivalent to a logical OR operation. Adding a NOT operation by electrically inverting the applied field of a single microdisk completes the set of necessary basic operations, i.e. a logical AND, OR, and NOT, to perform any complex logical operation with a network of optically coupled THz laser.
The general transition from the strongly to the weakly coupled PM by increasing the spacing between the microdisks from 2 to 20 µm is directly reflected by the change from the trapezoid-shaped to the cross-shaped optical emitted power shown in Fig. 4(a–d).
The onset of the optical emission of the PM-2 is linearly and equally dependent on the applied electric fields F 1 and F 2 below FMAX, i.e. below the onset of the negative differential resistivity regime. Hence, (i) the gain of a single THz-QCL is proportional to the applied field above as well as below the threshold field with the same slope  and (ii) the alignment of the energy levels is achieved well before the lasing threshold field FON. Beyond FMAX the gain reduces with increasing applied field which requires both applied fields to increase linearly to maintain lasing emission. Thus, the gain of a single THz-QCL is inverse proportional to the applied field above FMAX, i.e. in the negative differential resistivity regime. The lasing emission of the PM-2 extends beyond FOFF and is limited by the onset of the gain reduction in the other microdisk at FMAX.
The decrease in the coupling efficiency allows for additional lasing in the regions between FON and FOFF as shown in Fig. 4(b–d). The lasing emission in Fig. 4(b) is strongly dependent at F 1≈3.7 kV/cm as already discussed in Fig. 3(b). The injected carriers in the other microdisk cause an increase in the ISB absorption of the optically coupled system. The increase of the spacing to 12 µm leads to a pronounced increase of the single microdisk lasing areas extending the available lasing range. Finally, the optical emission of the PM-20 shown in Fig. 4(d) covers almost only the whole applied electric field range of two independent microdisks between FON and FOFF. Hence, the crossed-like emission indicates the strong reduction of the mutual coupling.
In summary, we have demonstrated the coherent evanescent field coupling of two THz emitting microdisk lasers representing a PM. The electrical characteristics demonstrate mutual coupling up to 30 µm intercavity spacing which is comparable to the intracavity lasing wavelength. As a consequence of carrier lifetimes in the picosecond range THz-PMs can be operated with 100 ns short pulses performing extremely fast electrically gated optical modulation as well as logical AND and OR operations. The characteristics of the optical emitted power demonstrate a linear control of the ISB gain by the applied electric field.
THz emitting PMs might have a great potential for sub-wavelength photonic devices which can be easily realized by standard lithography. Hence, they might find their way into photonics as applications for highly sensitive gas sensors using the evanescent coupled fields with electrical readout or coherently coupled laser arrays with vertical outcoupling for power emission and possible beam shaping and steering. On chip integration of these electrically controllable discrete elements as couplers, filters, gates or flip-flops might allow the realization of complex plasmonic circuits.
This work was partly supported by the Austrian Science Fund (SFB-ADLIS, SFB-IRON), the Austrian Nano Initiative project (PLATON), the EC (POISE), the Lithuanian State and Studies Foundation (contract No C-07004), and the Society for Microelectronics (GME, Austria).
1. Le Nguyen Binh, Photonic Signal Processing: Techniques and Applications (CRC Press, FL, USA, 2007). [CrossRef]
4. H. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and Ch. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photon. 2, 622–626 (2008). [CrossRef]
6. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor heterostructure laser,” Nature 417, 156–159 (2002). [CrossRef] [PubMed]
7. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-Power Directional Emission from Microlasers with Chaotic Resonators,” Science 280, 1556–1564 (1998). [CrossRef] [PubMed]
8. G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 211112 (2005). [CrossRef]
9. L. Mahler, A. Tredicucci, F. Beltram, Ch. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nature Photon. 3, 46–49 (2009). [CrossRef]
10. E. Mujagic, Ch. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, and G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95, 011120 (2009). [CrossRef]
12. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174–178 (2009). [CrossRef] [PubMed]
13. A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17, 941–946 (2009). [CrossRef] [PubMed]
14. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998). [CrossRef]
15. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-Binding Photonic Molecule Modes of Resonant Bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999). [CrossRef]
16. Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, “Fine structure of coupled optical modes in photonic molecules,” Phys. Rev. A 70, 051801 (2004). [CrossRef]
17. A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phys. Lett. 86, 041112 (2005). [CrossRef]
18. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003). [CrossRef]
19. V. Tamošiūnas, Z. Kancleris, M. Dagysa, R. Simniskisa, M. Tamosiunienea, G. Valusisa, G. Strasser, and K. Unterrainer, “Finite-Difference Time-Domain Simulation of Mid- and Far-Infrared Quantum Cascade Lasers,” Act. Phys. Pol. A 107, 179–183 (2005).
20. The Yee cell size was set to 1.4 µm and the average relative dielectric constant of the heterostructure was set to 11.75 based on the better fitting of the spectra with earlier single cavity simulations. The material small signal gain maximum for the active devices and the small signal loss maximum for the absorbing devices were set to 10.7 cm-1 and 107 cm-1 at 2.63 THz, respectively.
21. C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Resonant Tunneling in Quantum Cascade Lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998). [CrossRef]
22. J. Kröll, J. Darmo, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and Karl Unterrainer, “Phase-resolved measurements of stimulated emission in a laser,” Nature 449, 698–701 (2007). [CrossRef] [PubMed]