Microspiral
Resonators for Integrated Photonics Andrew W. Poon, Xianshu Luo, Hui Chen, Gustavo E. Fernandes and Richard K. Chang
Microspiral resonators allow for unidirectional lasing and the direct coupling of light to the device’s microcavity—two characteristics that aren’t possible with conventional microresonators. These novel-shaped resonators are now finding promising applications as waveguide-coupled passive devices and multiple-element cascaded-resonator switches.
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O
ptical microresonators that partially confine light by total internal reflection at the dielectric cavity sidewalls have long been regarded as versatile building blocks for photonic integrated circuits. However, conventionally symmetric microresonators with shapes that are two-dimensional (e.g., pillar, disk, or ring) or three-dimensional (sphere) cannot make unidirectional lasers. The cavity resonance modes, known as whispering-gallery modes (WGMs), can leak along the cavity’s curved sidewalls, radiating tangentially and nearly homogeneously. In order to efficiently in/out-couple light to the WGMs, scientists must impose evanescent field coupling via a narrow gap (roughly 0.1-0.3 mm for high-index-contrast semiconductor substrates). Although this can be done using advanced lithography, it is challenging to fabricate such separation gaps with high fidelity and high uniformity across a chip. For integrated photonics applications, it is therefore technologically relevant to find a way to design a microcavity that can emit unidirectionally and enable light to be in/out-coupled without imposing narrow separation gaps and while preserving high-Q resonances. Microspiral resonators address these issues.
Microspiral cavity designs The microspiral cavity shape can be described as a micropillar or disk with the radius linearly depending on the azimuthal angle f as r(f) = r0 (1 + ef/2p), where r0 is the radius at f = 0, and e is the change rate of the radius. The radius mismatch at f = 2p gives a notch of width r0e, which is typically a small fraction of the radius. Alternatively, the microspiral disk can be approximated by two semicircular-shaped disks of slightly
[ Microdisk resonators ]
Circular-shaped microdisk
Microspiral disk
Double-notch-shaped microdisk
[ Microdisk resonator-based filters ]
(a)
(b)
(c)
(a) Circular-shaped microdisk filter with evanescently coupled waveguides, (b) microspiral disk filter with a gapless direct-coupled waveguide on one side, and (c) doublenotch-shaped microdisk filter with gapless direct-coupled waveguides on both sides.
different radii r1 and r2 joined at one edge, such that the off-centered jointed disks give a notch of width 2|r2 – r1|. Microspiral-like resonators with two notches are attained with two semicircle disks with radii r1 and r2 joined on-center. The notch enables spatial overlap and mode-matching with the whispering gallery-like (WG-like) modes partially confined near the microspiral cavity rim. It is thus possible to directly couple lightwaves to the cavity modes via the notch without imposing an evanescent wave. This brings two major advantages. First, the microspiral cavity light can be preferentially out-coupled via the notch, with a unidirectional emission normal to the notch end-face. Second, the lightwave can be non-evanescently in/out-
coupled via a waveguide butt-coupled to the spiral notch.
Microspiral unidirectional lasers In 2003, some of us at Yale demonstrated unidirectional lasing emission from an InGaN multiple-quantum-well microspiral pillar. Using an optical ring-shaped beam to achieve maximum overlap with the WGMs, we pumped the micropillar from the top to obtain lasing emission at 404 nm with a spectrometer-limited linewidth of 5 nm. The lasing emission that emerged from the spiral notch was unidirectional; however, it made a substantial angle relative to the notch end-face. Our modeling revealed a WG-like mode-field distribution showing preferential out-coupling from the notch.
Facing page: Numerically simulated whispering-gallery-like resonance mode intensity pattern in a microspiral resonator.
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qICCD 0 330
Ring
Intensity [a.u.]
25
300
20 15
270 6
60 4
2
90
10 5
30
404 nm
0
240 364 nm 360
qICCD =308 380
400
Wavelength [nm]
5
10
ICCD
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[ Microspiral unidirectional lasers ]
Optics
However, the lasing emission direction can be affected by the quality of the InGaN material and the smoothness of the sidewalls. In follow-up experiments, we used high-quality InGaN samples and confirmed that the unidirectional lasing emission from the spiral notch can be normal to the notch end-face. Since our study in 2003, various research groups have reported unidirectional lasing emission from microspiral resonators, using optical or electrical pumping and different material systems, including polymers and semiconductors with quantum wells. In order to interpret the unidirectional lasing, one needs to first understand the resonance modes and their intensity patterns in microspiral resonators. In conventional symmetric microdisk or pillar resonators, clockwise (CW) and counterclockwise (CCW) traveling waves are degenerate. Thus, the lasing modes can equally build up in both propagations, resulting in standingwave lasing modes that eventually outcouple homogeneously. The microspiral cavity may support non-degenerate CW and CCW waves as the spiral shape breaks the cavity’s rotational symmetry. These waves, which miss the notch end-face, are partially diffracted near the inner corner of the notch, where some of the CW waves are converted into CCW ones. The CCW waves have larger loss due to Fresnel transmission at the flat face of the notch. The Fresnel reflection of the CCW waves is in the CW wave direction; consequently, the CW waves determine the Q of the resonant mode, which is rather insensitive to what is coupled to the flat face of the notch. Therefore, the much weaker CCW waves are associated with much higher loss, which prevents the buildup of CCW waves. However, the spectral width or the photon lifetime of the CCW wave is comparable to that of the CW wave. As long as the stronger intensity CW wave lives, and is partially converted to the CCW wave through diffraction at the inner corner of the notch, the much weaker CCW wave can have the same lifetime as the CW wave.
Integrate image
420 (b)
(a)
CW
(c)
Output intensity
(d)
CCW
(e)
(a) Lasing emission spectra upon ring-shaped pumping. (b) Far-field lasing emission patterns show the unidirectionality. The inset schematic depicts how the experimental data are obtained from integrating images of the emission from the micropillar sidewall. (c) Calculated electric field modulus of a quasi-bound state at size-parameter nkr0 = 200 and e= 0.10. (d), (e) Schematics of light propagations in a microspiral resonator for CW and CCW traveling waves. Dotted arrows: backward coupling due to the notch junction diffraction and end-face reflection. [From Appl. Phys. Lett. 83(9), 1710-12 (2003); reprinted with permission from the American Institute of Physics.]
Direct measurement of CW and CCW traveling waves In order to separately measure CW and CCW traveling waves in microspiral resonators, some of us at The Hong Kong University of Science and Technology have decided to use passive microspiral resonators and couple light to the traveling waves with an external light source. Instead of using an isolated microresonator, we integrated the microspiral resonator with two waveguides for the ease of in/out-coupling. The waveguide that is butt-coupled to the spiral notch enabled gapless direct coupling to the resonator. The other waveguide, which was laterally coupled to the resonator, enabled throughput transmission. Using such a structure, we could separately approach CW and CCW traveling waves with an external light source end-firing to each end of the side-coupled waveguide while measuring the transmissions at the other end. Such passive microspiral resonators can also act as optical filters.
Initially, we expected CW and CCW traveling waves to encounter different cavity losses (and thereby different Qs) due to their different tendencies to outcouple at the notch waveguide. But to our surprise, our finite-difference time domain (FDTD) simulations and experiments revealed that CW and CCW traveling-wave transmissions along the side-coupled waveguide were identical. The measured free-spectral range from both simulated and measured spectra was consistent with the disk circumference, indicating WG-like modes. The identical traveling-wave transmissions clearly suggest that CW and CCW traveling-wave resonances encounter exactly the same cavity losses. In hindsight, the observed identical transmissions can be expected from reciprocity relations: The transmissions in a linear medium are reciprocal upon interchanging the input and the output. These relations should apply to passive and active microresonators, regardless of their shape or size.
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Taking advantage of gapless nonevanescent coupling, we seamlessly joined two microspiral resonators via their notches, attaining a coupled microspiral structure with gapless non-evanescent inter-cavity coupling. The cavity light could partially transmit between the two spirals via the notch junction. Due to the structural asymmetry, the mode spatial overlaps between the two microdisks at the notch junction were not identical for CW and CCW configurations. There was a weak mode spatial overlap for the CW configuration and a strong mode spatial overlap for the CCW configuration. Specifically, the CW configuration only allowed weak forward coupling but
CW
CCW
(a)
(b)
CW
Norm. int. [dB]
(e) 0 -15 Q~6,000 FSR~12.4 nm
-10
Q~1,300
CW
1,480
Norm. int. [dB]
CCW
CCW
Field amplitude [a.u.]
Coupled resonators with gapless non-evanescent inter-cavity coupling
[ Measuring CW and CCW traveling waves ] Field amplitude [a.u.]
Nonetheless, reciprocal transmissions do not imply that CW and CCW traveling waves take the same cavity field distributions. In order to preserve reciprocity relations in a geometrically chiral structure, it is conceivable that CW and CCW traveling waves support different cavity field distributions (spatially non-degenerate) for the same cavity round-trip losses and phasematching condition. Parts (e) and (f ) of the figure to the right show the FDTD-simulated traveling-wave resonance field patterns at the same resonance wavelength for CW and CCW circulations. The resonance field patterns were asymmetric between CW and CCW configurations. This means CW and CCW traveling-wave modes are non-degenerate only in cavity field distributions while they preserve identical cavity resonances and losses. We verified the asymmetric resonance field distributions between CW and CCW traveling waves by probing the out-of-plane scattering intensity. These distributions hint to a cavity loss-balancing mechanism, which enables CW and CCW traveling waves to encounter identical total cavity losses and resonance conditions.
1,490 1,500 Wavelength [nm] (c)
1,510
CW
(f) CCW
10 mm
-20 -30 -40 1,535
Q~6,000
~400 nm FSR~7.4 nm
1,540 1,545 1,550 Wavelength [nm] (d)
1,555
(g)
(a-b) Schematics of microspiral resonator-based filter configurations with different input ports. (c) FDTD-simulated reciprocal throughput-port transmission spectra of a microspiral resonator filter with r 0 = 9.6 mm, r 0e = 0.4 mm, and an effective refractive index contrast of 3.13 to 1.63 for the TE polarization. (d) Measured reciprocal throughput-port transmission spectra (TE-polarized) for a device with r 0 = 24.6 mm and r 0e = 0.4 mm. (e-f) Simulated resonance field patterns for CW and CCW configurations at a resonance denoted in a green circle in (c). (g) Scanning electron micrograph of the fabricated microspiral filter in a silicon nitride-on-silica substrate. Zoom-in shows the notch junction region.
strong backward coupling, whereas the CCW configuration favored forward coupling but only allowed weak backward coupling. Moreover, the CW configuration’s FDTD-simulated resonance field pattern displayed a strong disparity between the coupled disks, while CCW configuration exhibited essentially uniformly distributed field patterns between the coupled disks. Despite the asymmetric field distributions, the throughput-port transmissions were reciprocal between CW and CCW configurations, as expected from reciprocity relations. On the other hand, the corresponding drop-port transmissions were not identical because the inter-cavity forward and backward coupling were asymmetric.
The significance of this coupled resonator structure is two-fold: First, the gapless non-evanescent inter-cavity coupling can relax the fabrication constraint for coupled microdisks in close proximity, and, second, the asymmetric forward and backward inter-cavity coupling opens up a new degree of freedom in coupledresonator device design. Like a potential barrier between two potential wells, the barrier is now dependent on the cavity light’s sense of circulations. By changing the light input port, we can selectively choose between strong forward-weak backward coupling and weak forwardstrong backward coupling. The most exciting device implications of such asymmetric inter-cavity coupling are perhaps yet to be imagined.
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[ Coupled microspiral resonators ]
Three-element coupledresonator optical switches
From microspiral to doublenotch-shaped microresonators Microspiral resonators with a single notch are certainly suitable for unidirectional lasing emission applications. However, they only enable a uni-port
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CCW
CW
(c)
CCW
(d) 10 mm
-10
Throughput (CW)
Throughput (CCW)
-20 Q~15,000
-30 -40
FSR~9.1 nm Q~6,500
(f) Norm. int. [dB]
CW
(b) Norm. int. [dB]
(a)
Field amplitude [a.u.]
The concept of gapless inter-cavity coupling can be extended to multi-element coupled resonators. One interesting structure is to directly couple a microspiral disk to a semicircle microdisk. As the microspiral shape comprises two semicircles, it is conceivable that light can be properly mode-matched with minimum impedance mismatch between the seamlessly jointed microspiral and semicircle disks. Based on this structure, our Yale group proposed wavelength and intensity switching in a three-element microspiralsemicircular coupled microdisk system. We fabricated a single quantum-well AlGaAs device grown by low-pressure metal organic vapor phase epitaxy. We simultaneously applied variable amplitude current pulses to each of the three coupled active microdisks. When we plotted the measured lasing emission spectra as a function of the injection current ISC-1 in the middle cavity, we saw two discrete operation states with different resonance wavelengths separated by an off-state as ISC-1 increases from 0 A/cm2 to 1,700 A/cm2. When ISC-1 = 0 A/cm2, the lasing emission was from the edge semicircle disk (SC-2) upon 1,700 A/cm2 current injection, giving the first on-state. When ISC-1 increased to about 250 A/cm2, the center semicircle disk entered its transparency. The net light output from the device consisted entirely of amplified spontaneous emission (ASE), corresponding to the off-state. As ISC-1 further increased to 750 A/cm 2, the device entered into a second on-state. This corresponded to lasing emission from the coupled semicircle disks. Thus, the center semicircle disk functioned as a control channel for the coupling between the microspiral and the edge of the semicircle disk.
-20 -30 -40 -50 Drop (CW)
~400 nm
(e)
1,545
Drop (CCW) 1,550 1,555 Wavelength [nm] (g)
(a-b) Coupled-microspiral resonator-based filters with gapless non-evanescent inter-cavity coupling. The insets show the asymmetric inter-cavity coupling, with weak forward-coupling for the CW propagation modes and strong forward-coupling for the CCW propagation modes. (c-d) FDTD-simulated resonance field patterns for CW and CCW traveling waves at the same resonance wavelength in coupled identical microspiral disks with r0 = 4.2 mm, r0e = 0.8 mm, and an effective refractive index contrast of 1.92 to 1.40 for the TE mode. (e) Scanning electron micrograph of the fabricated device. Zoom-in shows the inter-cavity coupling region. (f) Measured reciprocal throughput-port transmission spectra and (g) measured non-identical drop-port transmission spectra for CW and CCW configurations. The coupled microspiral resonators are designed identical with r0 = 19.6 mm and r0e = 0.4 mm in a silicon nitride-on-silica substrate. The FSR shown in the throughput-port transmissions is consistent with the circumference of a single microspiral disk. [From Opt. Express 15(25), 17313-22 (2007).]
device with gapless non-evanescent coupling. To enable gapless non-evanescent coupling for both input- and outputcoupling, we recently proposed a microdisk resonator featuring two notches—which we refer to as a doublenotch-shaped microdisk resonator. The microdisk resonator comprises two semicircle disks of slightly different radii, r1 and r 2, jointed at their centers, giving two equal notches with width |r1 – r 2|. Each notch was seamlessly jointed to a waveguide of the same width. Thus, the cavity light could be directly in/out-coupled via these notch-waveguides without relying on the evanescent field. The input-coupled lightwave from each notch-waveguide
could be partially out-coupled via the other one. The round-trip cavity light tended to bypass the input-coupled notch junction, and could be wavefront-matched with the input-coupled lightwave. The FDTD-simulated cavity field patterns displayed a WG-like mode-field distribution at an on-resonance wavelength. A traveling-wave field pattern between the two butt-coupled waveguides was at an off-resonance wavelength. From both numerical simulations and experimental demonstrations, we observed that, like microspiral resonators, the double-notch-shaped microresonators can preserve high-Q resonances.
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[ Multi-element coupled resonators ]
Summary and outlook
A.W.P. thanks his thesis advisor, Richard K. Chang, for all his immense inspirations over the years. X.L. acknowledges the financial support he received from the HKUST NANO Fellowship. The work by HKUST reported here has been substantially supported by the Research Grants Council of The Hong Kong Special Administrative Region (project # 618506). The nanofabrication on silicon chips was conducted
ISC-1
ASE
Laser
280 A/cm2
SC-1 Spiral
1700 A/cm2
SC-2 Intensity [a.u.]
250 mm (a) (a) Scanning electron micrograph of a three-elementcoupled microspiral-semicircle microdisks device on an AlGaAs substrate. (b) Laser emission spectrogram and a selected set of the corresponding spectra. The injection current density Isc-1 to the middle semicircle microdisk ranged from 0 A/cm2 to 1700 A/cm2. We note two discrete operation states of different lasing modes under different ranges of Isc-1. [From Opt. Lett. 33(6), 605-7 (2008).]
0
IS
500 1000 A/ cm 2 1500
C1
735 ] 730 [ nm 725 gth 720 elen v Wa (b)
[ Double-notch-shaped microresonators ] On-resonance
(a)
Off-resonance
Norm. int. [dB]
(b)
(c)
Field amplitude [a.u.]
Microspiral resonators and doublenotch-shaped microresonators can be game changers when it comes to using optical microresonators as active and passive components for photonic integrated circuit applications. The characteristic notches enable one to achieve gapless non-evanescent coupling to the microresonators, preserve high-Q resonances, and realize unidirectional lasing. Over the past five years, we have seen that such novel-shaped microresonators are delivering their promise not only as unidirectional microlasers but also as waveguide-coupled passive devices and multiple-element cascaded-resonator switches. With the addition of double-notchshaped microresonators, it should be possible to cascade multiple doublenotch-shaped microresonators to realize many-element devices and possibly even optical delay lines. Compared with the many-element cascaded-resonator optical waveguides that use evanescently coupled microdisks or micro-rings, our non-evanescently coupled-resonator devices should offer significantly better tolerance to fabrication imperfection. Hopefully these creative device structures with gapless coupling will soon find their place on photonic chips. t
-10
-20
-30
20 mm
-40
(d)
FSR~3.6 nm
Q~7,000
1,534 1,536 1,538 1,540 Wavelength [nm]
(e)
at the HKUST Nanoelectronics Fabrication Facility. The work by the Yale group was partially supported by the Defense Advanced Research Projects Agency Semiconductor Ultraviolet Sources Program under Space and Naval Warfare Systems Center contract N6600102-C-8017.
(a) Schematic of a doublenotch-shaped microdisk with gapless non-evanescent input/output coupling. (b-c) FDTD-simulated field patterns for on-resonance and off-resonance wavelengths in a double-notch-shaped microdisk with r1 = 10 mm, r2 = 9.2 mm, and an effective refractive index contrast of 3.13 to 1.63 for the TE mode. (d) Scanning electron micrograph of our fabricated device in a silicon-nitride-onsilica substrate. (e) Measured TE-polarized throughput transmission spectrum for a doublenotch-shaped microdisk with r1 = 50 mm and r2 = 49 mm.
Andrew W. Poon (
[email protected]), Xianshu Luo and Hui Chen are with the Photonic Device Laboratory in the department of electronic and computer engineering at The Hong Kong University of Science and Technology, Hong Kong, China. Gustavo E. Fernandes and Richard K. Chang are with the department of applied physics and Center for Laser Diagnostics, Yale University, New Haven, Conn., U.S.A. Member
[ Reference and Resources ] >> G.D. Chern et al. Appl. Phys. Lett. 83(9),
1710-2 (2003). >> M. Kneissl et al. Appl. Phys. Lett. 84(14), 2485-7 (2004). >> T. Ben-Messaoud et al. Appl. Phys. Lett. 86, 241110 (2005). >> A. Fujii et al. Jap. J. Appl. Phys. 44(34), L1091–L1093 (2005). >> A. Fujii et al. Jap. J. Appl. Phys. 45(31), L833–L836 (2006).
>> R. Audet et al. Appl. Phys. Lett. 91, 131106 (2007) .
>> C.M. Kim et al. Appl. Phys. Lett. 92,
>> G.D. Chern et al. Opt. Lett. 32(9),
>> X. Luo et al. in Conference on Lasers
1093-5 (2007). >> J.Y. Lee et al. Opt. Express 15(22),
14650-66 (2007). >> X. Luo et al. Opt. Express 15(25),
17313-22 (2007). >> G.E. Fernandes et al. Opt. Lett. 33(6),
131110 (2008). and Electro-Optics 2008 (IEEE and Optical Society of America, 2008), paper CTuNN7. >> X. Luo et al. in IEEE 5th International Conference on Group IV Photonics, Sorrento, Italy, September 2008.
605-7 (2008).
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