Photonic Crystal Laser Yong-Hee Lee and In-Kag Hwang Department of physics, Korea Advanced Institute of Science and Technology
[email protected] Abstract Recent progress toward wavelength-scale photonic crystal lasers is summarized. To realize the ultimate laser, one needs to have a wavelength-scale photonic crystal cavity that is lossless. As a candidate for this ultimate laser, the two-dimensional unit-cell photonic crystal laser compatible with current injection is proposed. Experimental demonstration of the low-threshold two-dimensional photonic crystal lasers in the triangular lattice and the square lattice will be discussed. The very high quality factor in excess of 1,000,000 is theoretically predicted from the wavelength-scale resonator supporting the whispering-gallery-like photonic crystal mode.
1. Introduction Recently, the photonic crystal at optical regime has matured from a theoretical interest to realistic experimental problems, owing to the advancement of nanofabrication technologies. Generally, the lattice constant of a photonic crystal is about one-half of the wavelength of the light. In such a case, photons tend to interact very strongly with the periodically repeating structure through constructive or destructive interferences. Interestingly, the characteristics of this interaction can be artificially controlled by varying the lattice constant, the dielectric constant and the structure of the lattice. For example, one can create a novel optical material that has a ‘photonic band gap’, an energy region in which no electromagnetic wave can exist [1]. Remember that the ‘electronic band gap’ is the forbidden energy region for electrons in semiconductor ‘electronic’ crystals. However, unlike natural ‘electronic’ crystals, the ‘photonic’ counterpart can be designed, fabricated. In other words, the ‘man-made’ photonic crystal opens up the possibility of the photon control: it can be engineered to guide photons, to localize photons, or to modify the dispersion relation of photons. The concept of the photon confinement in multi-dimensions has attracted many scientists in search of the ultimate thresholdless laser. To realize the thresholdless laser, one needs to find a resonant cavity that satisfies two requirements. First of all, the cavity size should be extremely small on the order of a half wavelength. The fundamental limit of the mode volume that is allowed by nature is (λ/2n)3. In addition, the cavity should be able to confine photons effectively with low optical loss: the cavity should have a high quality (Q) factor. The physical dimension of the cavity determines the number of photon modes available for a given cavity. It can be argued that the best choice is the cavity allowing just one single mode. Then, all the photons generated inside the cavity are forced to funnel
through this single mode to come outside [2]. In fact, the larger quality factor encourages more efficient photon localization and, therefore, promotes stronger stimulated emission of photons from the excited atoms. 2. Nondegenerate Monopole Mode Unit-Cell PBG Laser The smallest possible cavity configuration imaginable from the photonic crystal is the unit-cell resonator where only one lattice point is filled. Then around this imperfection in the middle of the photonic band gap, photons tend to be localized. However, even from this unit-cell cavity, several resonant modes are found and some the modes are doubly degenerate. Several ways to lift this degeneracy have been suggested and demonstrated. However, it is believed that utilizing the truly nondegenerate mode is generally more advantageous to funnel most of photons into one and only one resonant mode. One way to lift the degeneracy is to use the cavity mode that is inherently nondegenerate. In this case, natural and efficient coupling with that sole mode is expected. One example of this genuine nondegenerate mode is the monopole mode. In the regular photonic crystal unit-cell cavities, this nondegenerate monopole mode is buried in the air band and cannot be found. However, if one decreases the size of the nearest air holes, the effective volume of the cavity is slightly enlarged as shown in Fig. 1(a) and this monopole mode can be pulled down into the middle of the photonic band gap where the photon confinement is stronger. The 2-D triangular PBG laser working in this monopole mode was realized with low threshold power of 0.3 mW [3]. It is interesting to note that this monopole mode has a node in the center of the cavity as shown in Fig. 1(b). Note that the monopole mode profile has good overlap with the central cavity region where optical gain is generated.
effective size of this square lattice PBG cavity is ~ 0.5 µm. The existence of this extremely small mode proves very effective photon confinement by the photonic band gap in the plane of the photonic crystal. In fact, this lowest whispering gallery mode turns out to have the large Q factor in excess of 100,000. Moreover, this mode has a node for both electric and magnetic fields at the center that can be conveniently used for electrical current pumping. As one can see in Fig. 2, the introduction of the central post does not degrade quality factor noticeably until the diameter of the post become 0.4 times the lattice constant [7].
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(c) (a) Fig. 1. 2D air-slab monopole mode PBG laser. (a) SEM picture, (b) calculated mode profile, (c) measured nearfield image.
3. Very High-Q Whispering-Gallery-like Nondegenerate PBG Laser
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Square lattice unit-cell photonic crystal laser: The twodimensional triangular photonic crystal is widely studied because it has a large photonic band gap. For the square lattice, the size of the band gap is small for the square lattice photonic crystal. However, the index contrast along the crystal direction is larger for the square photonic crystal than for the triangular photonic crystal. Therefore, photons can be confined more tightly in the photonic band gap of the square photonic crystal. Recently, we observed interesting photonic band gap lasers from the square lattice photonic crystal [5]. Here the characteristics of the resonant mode are vastly different from those of the triangular PBG lasers. The square lattice cavity with a single defect shows behaviors reminiscent of the whispering gallery mode in the lowest order (m=2). As shown in Fig. 2, the field pattern has the four-fold symmetry and the radial directions of the electric fields indicate the tangential directions of the propagation. Characteristically this field pattern corresponds to a closed-loop standing wave. This form of the mode is usually observed in circular microdisk lasers and named as the whispering gallery mode [6]. There usually exist a set of clock-wise and counter-clock-wise modes of the same frequency. However, when the diameter of the disk approaches 1.0 µm, the microdisk resonator becomes very lossy and unable to function as a laser. Note that the
Quality factor
Experimentally InGaAsP quantum wells are used as an active material whose photoluminescence peak is located near 1,550 nm. Rich photonic bandgap lasing modes are observed from various samples of different lattice constant and air hole size. Moreover, it is confirmed from the computer simulation that the introduction of a small post in the middle of the resonator does not introduce appreciable optical losses and, therefore, does not degrade the quality factor of the cavity appreciably. In other words, this middle post [4] can be used as an electrical wire through which electrical current can be supplied. So the electrical pumping of the single defect PBG laser can be practically feasible.
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Diameter of the post [d p / a] Fig. 2. 2-D air-slab square lattice PBG laser structure. (inset: SEM picture) The graph shows the quality factor of the whispering-gallery-like mode as a function of the size of the central post.
It is worth emphasizing that all the small cavity air-slab PBG lasers described above show low threshold less than 0.5-mW peak incident optical power under pulse pumping at 980 nm using an InGaAs laser diode. The main reason for this low threshold lasing is their extremely small mode volume and very small cavity loss. The lowest value of the threshold pump power is about 0.3 mW and about 30% of this incident power actually participates in the generation of electron-hole pairs in the light-emitting active region of InGaAs quantum wells. In fact, the threshold pumping condition is quite comparable to the transparency condition. The InGaAs quantum well and the InGaAsP material system are commonly employed because of their low surface recombination velocity. In most photonic crystals, the surface-to-volume ratio is large. Therefore, the carrier loss originating from this nonradiative surface recombination should be carefully taken care of. Triangular lattice hexapole mode photonic crystal resonator: The photonic crystal resonant mode reminiscent of the whispering gallery mode exists in the triangular lattice photonic crystal as well. Since the size of the photonic bandgap is large for the triangular lattice, this hexagonal mode could find broader application than the square lattice counter part. Just like the monopole mode, this hexapole mode is pulled down into the photonic bandgap from the air band by modifying the size
of the nearest-neighbor holes. In this case, the azimuthal mode number of this nondegenerate hexapole mode m is 3, because of the 3-fold symmetry of the triangular lattice. Using the finite difference time domain analyses, we investigated the hexapole mode of photonic crystal slab as a candidate for a high quality factor and small mode volume resonant mode. It is very encouraging to find that one can optimize structural parameters to achieve a very large quality factor in excess of 2,000,000 with small effective mode volume of cubic wavelength in material [8]. Interestingly, the largest Q value is observed when the radius of the nearest neighbor air hole (rm) is 0.26a, independent of the lattice constant (a) and the air hole size(r). This implies that the cancellation mechanism works best for the mode distribution when rm=0.26a. In fact, main features of the mode is determined by the rm, because the shape and the size of the nearest air holes determines the m=3 whispering gallery mode that best satisfies the condition of the 3-wavelength-long circumference. It is found, by Fourier-space investigation of resonant modes, that such a high quality factor from the hexapole mode is understood by the cancellation mechanism related to the hexagonally symmetric whispering-gallery-mode distribution and to the mode delocalization mechanism. For this resonant mode, the Purcell factor is evaluated to be larger than 10,000. The small mode volume of this resonant mode is mainly responsible for this record-high Purcell factor. If one can place a single quantum dot in this cavity, the strong coupling regime will be achieved even with an extremely small photon number.
Fig. 3 (a) Q factor and mode volume of the hexapole mode cavity. (b) k-space electric field intensity when rm=0.26 r, and (c) when rm=0.3 r.
4. Summary In summary, we demonstrated several examples of the possible wavelength scale photonic crystal resonators with the small mode volume and the high quality factor. We prefer to play with the nondegenerate photonic crystal mode with the central node through which carriers can be supplied. Up to now, all the demonstration is made through the optical pumping. Therefore, the issue still need to be addressed is that of the electrical pumping scheme together with the issue of the surface recombination. The wavelength-scale very high-Q cavity with a central node could be a good candidate for the ultimate thresholdless laser and on-demand single photon guns for the secret quantum communications. References 1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). 2. Y. H. Lee and H. Y. Ryu, "Custom crystals control photons," IEEE Circuit and Devices Magazine 18, 8 (2002). 3. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode twodimensional photonic bandgap laser,” Appl. Phys. Lett. 79, 3032 (2001). 4. H. G. Park, S. K. Kim, S. H. Kwon, G. H. Kim, S. H. Kim, H. Y. Ryu, S. B. Kim, and Y. H. Lee, "Single-mode operation of two-dimensional photonic crystal laser with central post," IEEE Photon. Technol. Lett. 15, 1327 (2003). 5. H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, “Square lattice photonic band gap unit cell laser operating in the lowest-order whispering gallery mode,” Appl. Phys. Lett. 80, 3883 (2002). 6. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289 (1992). 7. H. Y. Ryu, J. K. Hwang, and Y. H. Lee, "The smallest possible whispering-gallery-like mode in the square lattice photonic-crystal slab single-defect cavity," IEEE J. Quantum Electron. 39, 314 (2003). 8. H. Y. Ryu, M. Notomi, and Y. H. Lee, "High-qualityfactor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities" Appl. Phys. Lett. 83, 4294 (2003).
