Abstract

We demonstrate optical gradient force-tunable directional couplers in free-standing silicon nitride slot waveguides. Utilizing device geometries optimized for strong optomechanical interactions allows us to control the optical transmission without the aid of a cavity. Static, wideband tuning as well as low-power optical modulation is achieved.

©2011 Optical Society of America

1. Introduction

Over the past years nanophotonic circuits have been established as a promising platform for realizing densely integrated optics [16]. To date a multitude of photonic components that split, couple and guide light on a chip have been demonstrated in silicon and related materials [710] and most optical components traditionally employed in fiber-based systems have been implemented using silicon nano-waveguides and resonators. Despite significant progress in the development of passive integrated optical circuits, which perform a given task based on geometrical design, tunable integrated devices that can be used to actively control light on a chip are more difficult to achieve.

A particularly important actively controlled optical component is an optical switch. Routing of optical signals can be achieved either with traditional electrical methods or also with optical approaches. All-optical switching has been demonstrated in III-V based material systems exploiting the refractive index change due to free-carrier generation by one- or two photon absorption processes [11,12]. Similarly, silicon based optical modulators have been realized [1317], relying on refractive index modulation through electrical carrier injection. In addition, thermal tuning can be employed to modify the refractive index locally via the thermo-optical effect [1820].

Recently it has been demonstrated that the gradient optical force provides an efficient mechanical degree of freedom to achieve tunable optical systems [2127]. As a result direct modulation in the optical domain can be achieved by exploiting opto-mechanical interactions in deformable photonic structures. Because nano-photonic components are size-matched to nano-mechanical resonators, the combination of both technologies provides a route for integrated opto-mechanical circuits. Instead of relying on electrical methods for device actuation and readout we showed previously that it is possible to generate sufficient optical force to set nano-mechanical resonators into motion [2123]. In addition, optomechanical interactions lead to mechanically induced nonlinearity in analogy to the Kerr effect, with prospect for tunable photonics [24]. Indeed, wavelength tuning through opto-mechanical effects was demonstrated in microring [25,26] and microdisk [27] resonators. Cavity enhancement provides strong interactions for wavelength routing, which is however restricted to the line-width of the optical resonator.

Here we demonstrate wideband tunable directional couplers whose coupling ratio is controlled by the gradient optical force in parallel waveguides. In order to obtain wide tuning with low optical input power we fabricate long free-standing devices from silicon nitride membranes. Embedding slot waveguides in integrated directional couplers allows us to observe dynamic control of optical signals. The interaction is strong enough that large tuning is achieved without making use of optical cavity enhancement. Static tuning over a wide wavelength range is realized in low-stress silicon nitride waveguides whereas high mechanical quality factors for low-power modulation are obtained in highly stressed nitride waveguides. Our results demonstrate flexible exploitation of gradient optical forces for controlling nanophotonic circuits.

2. Geometry and design of the opto-mechanical coupler

Our design goal is to maximize the gradient optical force to achieve large mode index change by mechanically displacing the devices [28]. As shown previously, slot waveguides are a viable route to realize strong field enhancement at the air-slot interace and generate large self-displacement in response to gradient optical forces inside the slot [2932]. Therefore we employ the slot-mode, whose refractive index is highly tunable, as a basis for tunable opto-mechanical devices.

In the slot waveguide design (Fig. 1a ) the effective refractive index of the propagating modes depends on the separation between the dielectric beams as shown for the x-component of the electrical field in Fig. 1b). Using finite-element simulations we calculate the dependence of the effective refractive index of a slot waveguide on the width of the dielectric beams and the air gap between them, for an input wavelength of 1550nm. The thickness of the silicon nitride layer is kept constant at 330nm. For high-stress silicon nitride we assume a refractive index of 2.0, which is used throughout the simulations in the following. Similar results are obtained for low-stress silicon nitride with refractive index of 2.2. When the waveguide width approaches ~200nm width the effective index of the propagating mode is close to the refractive index of the surrounding air and thus close to the waveguide cutoff. In order to obtain tight optical confinement it is thus preferable to work with wider waveguides. This is also important if waveguiding is to be achieved in un-released slot waveguides that still reside on the underlying SiO2 substrate.

 

Fig. 1 (a) Mode profile of a silicon nitride slot waveguide with a dielectric beam cross-section of 330 × 500nm2. Shown is the magnitude of the Ex component in (V/m) for waveguides separated by a gap of 200nm. (b) The dependence of the effective index of the slot waveguide mode on the width of the dielectric beams. Shown are simulations for waveguide separations from 50nm to 400nm.

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Because the effective index depends on the separation between the waveguides, the phase change acquired by a wave travelling along the slot waveguide will also be dependent on the separation. By continuously varying the gap size it is thus possible to modulate transmission through the waveguide by embedding the slot waveguide in a phase-sensitive photonic circuit. An optical tuning mechanism to realize the desired change in the gap is the gradient optical force. By exciting the slot mode in the waveguides an attractive optical force results, which pulls the dielectric beams together. The magnitude of the resulting optical force can be deduced from the gradient of the effective index of the slot mode (Fig. 1b) and the resulting group index (Fig. 2a )) [28,33]. The optical force (normalized to the optical power on the waveguide and the waveguide length) depends on both the waveguide width and the gap between the beams as shown in Fig. 2b).

 

Fig. 2 (a) Numerical simulation of the group index of a silicon nitride slot waveguide in dependence of wavelength. A slot gap of 200nm is assumed. (b) Calculation of the optical force between two coupled silicon nitride beams in dependence of waveguide separation, normalized to the input power and the beam length. By decreasing the waveguide width the magnitude of the optical force is increased, while a reduced gap leads to enhanced optical force.

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The gradient force decays strongly with increasing gap, therefore strong opto-mechanical interactions necessitate a small air gap. At the same time reducing the waveguide width leads to increased optical confinement in the air gap and thus larger optical forces. This trend is accompanied by a reduced group index at 1550nm wavelength.

Wider waveguides provide higher group index and thus larger amplification of the optical force [28,33], but also reduce gradients in the electrical field. Therefore there is an optimal set of parameters for real devices in terms of waveguide width and realizable waveguide separation.

3 All-optical modulation in tunable directional couplers

As mentioned above, all-optical modulation of device transmission can be realized by implementing a phase-sensitive photonic circuit containing a movable opto-mechanical device. A promising candidate for wideband optical modulation is a directional coupler, where two waveguides are placed in close enough proximity so that the optical modes supported by each waveguide are weakly coupled. Here we employ two free-standing slot waveguides to realize a tunable coupler, as shown schematically in Fig. 3a ).

 

Fig. 3 (a) Design of a photonic circuit for a tunable coupler employing coupled slot modes. The coupling length is tuned by varying the slot gap. The released parts of the waveguide cross the blue membrane area. The input signal is routed into either the through or drop port, depending on the beating gap. (b) The modal distribution along the coupled slot waveguides, obtained by FDTD simulation. Overlaid in green is the sinusoidal profile of the intensity along the top slot waveguide. (c) The calculated beating length for two coupled nitride slot waveguides of 500nm width and 200nm gap in dependence of the beating gap. (d) The calculated beating length for a beating gap of 730nm in dependence of the slot gap.

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Light is coupled into the device and then adiabatically into one of the slot modes. This slot mode is coupled to a transfer slot-mode, which acts as the drop port of the device. This design allows us to independently control the beating length and the magnitude of optical force in the slots: the two slot waveguides are used to modify the effective refractive index and can thus have a small gap; the separation between the two slot waveguides can be arbitrary and only influences the beating length. Hence force and extinction ratio can be adjusted separately. From the numerical simulations in the previous section we find that the minimum beam width of the free-standing region will be 500nm, when also un-released waveguides guide optical modes.

A reasonable slot gap for the slot waveguides which can be reliably fabricated for long, free-standing beams is 200nm. This choice of gap also accounts for the case when the dielectric beams are deflected under the influence of the optical force and thus show a reduced slot gap. In this geometry the optical force in each slot waveguide amounts to 1.83pN/μm/mW.

The beating length in the double-slot design (defined as the length light has to travel to completely transfer its power from one slot waveguide to the other) can be determined by examining the propagation constants of the coupled slot modes. Having obtained the effective indices for the even mode ne and the odd mode no the beating length Lb at a wavelength λ is given by

Lb=λ2(neno)
The calculated beating length in dependence of the beating gap gb is shown in Fig. 3b). For a desired beating length of 20μm, the slot waveguides need to be separated by a gap 730nm. A beating length of 20μm implies that the power switches waveguides 20 times for the 400μm long directional coupler. Complete power transfer from the through port of the coupler to the drop port of the coupler is achieved when the number of beatings is increased by one. When the optical force is applied, the slot gap will decrease, because the force is attractive. The resulting beating length, when the slot gap is changed, is shown in Fig. 3c).

In addition to a directional coupler design we also consider a simple Mach-Zehnder interferometer to verify our design concept. By employing the movable slot design the phase difference in each arm can be controlled by adjusting the slot gap. Because a change in the gap results in a change in the effective mode index as shown in Fig. 1b), a tunable phase change can be measured. All-optical tuning is then possible by employing a separate tuning light to control the optical force on the slot waveguide.

4. Fabrication of the nano-photonic circuits

To achieve large amplitude and low power tuning, we employ nano-photonic devices with free standing slot waveguides, up to several hundreds of microns long. To fabricate such long suspended structures, we rely on a membrane technique which allows us to realize long suspended beams through dry etching. The necessary silicon nitride membranes are defined by silicon micromachining techniques and then photonic components are fabricated subsequently across the membrane area. The complete fabrication process is described in the flow diagram shown in Fig. 4a ). First, 3.3um silicon oxide and 330nm LPCVD (Low-Pressure Chemical Vapor Deposition) silicon nitride were grown on both sides of a silicon wafer (425um thick). The silicon nitride serves as the light guiding layer and the silicon oxide serves as the low-index cladding layer. Devices made of both high-stress and low-stress silicon nitride were then fabricated from the membrane wafers. Since high-stress silicon nitride (stoichiometric) and low-stress silicon nitride have different Si-N composition ratios, a general atomic formula SixNy is used in Fig. 4a). Photolithography is used to define etching windows on the backside of the wafer. The silicon nitride at the backside was then etched by reactive ion etching (RIE) using fluorine chemistry and the silicon oxide underneath was removed by buffered oxide etchant (BOE). Photoresist is then removed and a protection polymer ProTEK® B3 (Brewer Science) is spun on the front side of the wafer to protect the silicon nitride from being etched in the subsequent KOH etching. The whole wafer was immersed in KOH solution (30%) at 85 °C for 6-7 hours until the silicon wafer was etched through. The etch rate of silicon was found to be dependent on the stress of the silicon nitride. The etch rate was higher for high-stress silicon nitride (~65um/hr) and lower for low-stress silicon nitride (~57um/hr). The front-side oxide layer was then removed by BOE and the ProTEK® layer was removed by. On the topside of the wafer, electron beam lithography was performed to define the photonic structures. ma-N 2403 (Microresist Technology) was used as e-beam resist. Finally the top silicon nitride layer was etched by RIE and the remaining ma-N resist was removed by O2 plasma.

 

Fig. 4 (a) Process flow diagram illustrating the fabrication process. (b) Optical micrograph of a fabricated Mach-Zehnder interferometer device. One arm of the interferometer crosses the membrane area to realize a free-standing slot waveguide. An SEM zoom-in image of the slot waveguide is shown in the inset. (c) Optical micrograph of a directional coupler device, showing two sets of grating couplers and the directional coupler crossing the grey membrane area. An SEM zoom-in image of the two coupled slot waveguides is shown in the inset.

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In Fig. 4b) and 4c) we show optical images of two fabricated devices. The device shown in Fig. 4b) is an example of a fabricated Mach-Zehnder interferometer device realized in low-stress silicon nitride. The device presented in Fig. 4c is a tunable directional coupler made of high-stress silicon nitride consisting of two coupled slot waveguides (the released waveguides are shown in the inset). At the input/output ports, focusing grating couplers were used to couple light from free-space into and out of the waveguides (labeled 1-4 in Fig. 4c).

5. Tunable Mach-Zehnder interferometer in low-stress silicon nitride

In order to confirm effective index modulation due to changes in the slot gap we first investigate a single slot waveguide embedded in a Mach-Zehnder interferometer (MZI) made of low-stress silicon nitride, as shown in Fig. 4b). The arms of the MZI have a path difference of 100μm, leading to characteristic fringes in the transmission spectrum due to the acquired phase difference in the longer arm. Transmission through the device was measured at different laser power level in atmospheric environment and the result is shown in Fig. 5a ). The black dashed line is a Gaussian fit to the transmission band of the grating coupler. As can be seen from the graph, the expected sinusoidal Mach-Zehnder fringes shift towards longer wavelengths when the laser power is increased. When the laser power is increased, the magnitude of the optical force acting on the slot waveguide in the released membrane area is increased. As a result, the beams are pulled together and the slot gap is reduced. This in turn increases the effective refractive index of the slot mode and thus shifts the fringe minimum to wider wavelengths.

 

Fig. 5 (a) The normalized transmission spectrum of a low-stress silicon nitride Mach-Zehnder interferometer device at various input laser power. Overlaid is the transmission band profile of the grating couplers, shown by the black dashed line. (b) The measured wavelength and phase shift in dependence of the laser power on the device. The linear fit to the data reveals a tuning sensitivity of 1.7nm/mW.

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The free spectral range (FSR) of the Mach-Zehnder interferometer was measured to be 7.8nm. Having obtained the FSR, the wavelength shift as well as the phase shift can be calculated and is shown in Fig. 5b). A linear tuning can be observed with a tunability of 1.7nm/mW.

6. Tunable directional coupler in low-stress silicon nitride

With good refractive index tunability demonstrated in the slot mode, we fabricated tunable directional coupler devices using low stress silicon nitride. In order to realize several fringes within the bandwidth of the on-chip grating couplers we design directional couplers with long coupling length (2.5mm) and small beating gap (300nm). Over the length of the device light coupled into the input port will switch multiple times between the directional coupler arms. The central portion of the device crosses a membrane area, thus leading to free-standing beams. The beating gap can be tuned via the optical force as outlined above, when the laser power is varied.

A fabricated device and the measuring setup are shown in Fig. 6a ) Using a tunable diode laser we measure the transmission in both the drop port and the through port. Figure 6b) shows the normalized transmission of the tunable directional coupler device. Laser light was coupled into the device at port 2 and transmission at port 3 (through port) and port 4 (drop port) were monitored with photodetectors (the port numbers are labeled in Fig. 6a)). The optical transmission is enveloped by the transmission profile of the grating couplers, with a 3dB bandwidth of roughly 70nm.

 

Fig. 6 (a) Optical micrograph showing the tunable directional coupler device made of low-stress silicon nitride and the schematic showing the measurement setup. (b) Normalized transmission spectrum of the tunable directional coupler device. The blue and red lines are the measured transmission from the through and drop port, respectively. The transmission curve is enveloped by a Gaussian fit (dashed black line) of the transmission band profile of the grating couplers. (c) and (d) Static tuning of the through port and drop port transmission as a function of control laser power at two different probe laser wavelength.

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When the coupling length of the device is kept constant the coupling ratio between the through and drop port is a function of only the beating length. Then with a total device length of L, the output power at the through port is given by

P(L)=P0cos2(πL2Lb)
As a result the power in the through port exhibits wavelength dependence as
P(λ)=P0cos2(π(neno)Lλ)
From the above equation it is apparent that in first order approximation the output power varies sinusoidally in λ, with a period given by ë02/L(ne(g)-no(g)), where ne(g) and no(g) are group indices of the even and odd modes. As can be seen from Fig. 6b), the transmission shows the expected sinusoidal dependence in λ, with the period slightly changing across the whole spectrum due to the dispersion of the group indices. The measured period of the device amounts to 5 nm around 1550 nm.

In order to demonstrate static tunability of the directional coupler device, a second control laser at wavelength of 1554.14 nm was coupled into the device at port 1 and the transmission at the through and drop ports was measured at a fixed probe wavelength with control laser power varied. WDM (Wavelength-Division Multiplexing) band stop filters were used to filter out the control light before the photo-detector. The control laser generates a static optical force on the free-standing optical waveguide beams. When the control power is varied, the magnitude of the optical force is increased and as a result the beating gap is increased. The results are presented in Fig. 6c) for a probe wavelength of 1547.5 nm. When the control laser is turned off, 70% of the input light is coupled out on the through port, whereas 30% of the probe light is transferred to the drop port. When the control laser power is increased the transmission in the through port is reduced and all the light is transferred to the drop port instead. As expected for a directional coupler, the drop and through port show complementary output behavior.

By adjusting the probe wavelength to a point of complete transmission in the through port the extinction ratio of the directional coupler can be measured. As shown in Fig. 6d) we obtain nearly 30dB extinction for a probe wavelength of 1558.3 nm. When the control laser power is increased the transmission in the drop port rises to 70%. By varying the control laser power it is therefore possible to adjust the coupling ratio from 0.1/99.9 to 70/30.

7. Dynamic response of devices realized in high-stress silicon nitride

In addition to the static response we also investigate the dynamic behavior of the directional coupler device. Here, to attain high speed and low mechanical loss, we utilize stoichiometric high stress silicon nitride which is known for its low optical absorption and high mechanical quality [34,35]. Figure 7a ) shows the normalized transmission of the device.

 

Fig. 7 (a) Normalized transmission spectrum of the tunable directional coupler device. The blue and red squares are the measured transmission data from the through and drop port, respectively. The solid blue and red lines show a sinusoidal fit of the transmission data. In the real device, the transmission curve is enveloped by the transmission band profile of the grating couplers, shown by the dashed black line. (b) The measurement setup used to characterize the performance of the directional coupler device. Time-domain traces are recorded on an oscilloscope, while the mechanical response in the frequency domain is obtained with a network analyzer. (c) The driven mechanical response of the directional coupler. Two resonance peaks corresponding to the in-plane motion of the slot waveguides are measured around 609kHz. (d) The measured modulated signal in the through and the drop port of the device.

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The measured results are plotted in squares, while the sinusoidal curves show the expected wavelength dependence of a typical directional coupler, i.e., the output power in the drop port and through port alternates periodically with input wavelength, as explained in previous section. As in Fig. 7a) the black dashed line shows a Gaussian fit to the transmission spectrum of the grating couplers. As expected, the device has shorter coupling length and so larger FSR compared to data shown in Fig. 6b. The dynamic response of device was then studied by a pump-probe scheme [21]. A pump laser at wavelength of 1554.14 nm was intensity-modulated and coupled into the device through port 1. This time-varying laser intensity exerts an oscillating optical force that drives the suspended waveguides into mechanical vibration. A probe laser at wavelength of 1510nm was coupled into the device at port 2 and the transmission was measured at the through port (port 3) and the drop port (port 4) with the pump light filtered out by a WDM band stop filter. The measurement was carried out in vacuum (1mTorr) in order to minimize air damping due to the mechanical motion. The measured driven mechanical response is shown in Fig. 7c), in amplitude (black) and phase (red).

Because the gap of the slot waveguide is much smaller than the beating gap between the two slot waveguides, the optical mode is mainly confined in the slot and therefore the attractive optical force acting within the slot dominates and the attractive/repulsive/beating force arising from cross-gap waveguide coupling becomes negligible [36]. Since the net optical force is attractive, only the in-plane 180°-out-of-phase coupled modes were excited, as illustrated in the insets of Fig. 7c). Note that the thermal time constant of the suspended waveguide (time required for the heat to diffuse from the middle of the waveguide to the support end) is in milli-second range and therefore at the frequency considered here (around 600kHz) the thermal-optical effect is negligible [37].

The mechanical quality factor Q of the resonance was calculated by fitting the response curve with a Lorentzian function. The mechanical Q was found to be around 30,000, which is not as high as the Q of similar silicon nitride nanostructure reported in the literature [34,35]. We attribute the reduced mechanical Q to the loose clamping, since in the device reported here the splitter and so the clamping point was also suspended (see Fig. 3a)). Nevertheless, when driven at resonance, the mechanical amplitude was enhanced by a factor of Q and so only little power is required to drive the structure into large motion. Modulation of the probe light in time domain is shown in Fig. 7d). In this measurement, pump light intensity as low as 3 μW was used to provide switching of up to 7% of the power of the probe light between the through and the drop ports.

8. Conclusion

In conclusion, we have demonstrated broadband static and dynamic wavelength tunability in silicon nitride photonic integrated circuits. By exploiting opto-mechanical interactions in free-standing slot waveguides we achieve all-optical tunable Mach-Zehnder interferometers and directional couplers. Employing a membrane fabrication technique allows us to realize ultra-long free-standing slot-waveguides. Because of the field and optical gradient enhancement in the slot waveguides strong gradient forces are generated. Our results provide an implementation of all-optical tuning through mechanically induced geometrical modifications. The obtained modulation amplitude demonstrates the feasibility of routing of optical signal via optomechanical effects.

Acknowledgements

This work was supported by DARPA/MTO ORCHID program through a grant from AFSOR (Grant No. FA9550-10-1-0297, managed by J. Abo-Shaeer), National Science Foundation Career award, Packard Foundation and a seedling grant from DARPA/MTO (Award No.W911NF-09-1-0410, managed by M. Haney, H. Temkin). W.H.P. Pernice would like to thank the Alexander-von-Humboldt foundation for providing a postdoctoral fellowship. The authors wish to thank Dr. Michael Rooks, Michael Power, James Agresta and Christopher Tillinghast for assistance in device fabrication.

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34. S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008). [CrossRef]  

35. K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010). [CrossRef]  

36. W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009). [CrossRef]   [PubMed]  

37. W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009). [CrossRef]  

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  28. W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
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  29. P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14(20), 9197–9202 (2006).
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    [Crossref] [PubMed]
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  35. K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
    [Crossref]
  36. W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
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    [Crossref]

2011 (1)

2010 (4)

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

C. Xiong, W. H. Pernice, M. Li, and H. X. Tang, “High performance nanophotonic circuits based on partially buried horizontal slot waveguides,” Opt. Express 18(20), 20690–20698 (2010).
[Crossref] [PubMed]

M. Li, W. Pernice, and H. Tang, “Ultrahigh-Frequency Nano-Optomechanical Resonators in Slot Waveguide Ring Cavities,” Appl. Phys. Lett. 97(18), 183110 (2010).
[Crossref]

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

2009 (9)

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnol. 4(6), 377–382 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical Kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[Crossref]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[Crossref] [PubMed]

P. Dong, L. Chen, Q. Xu, and M. Lipson, “On-chip generation of high-intensity short optical pulses using dynamic microcavities,” Opt. Lett. 34(15), 2315–2317 (2009).
[Crossref] [PubMed]

2008 (3)

J. Song, Q. Fang, S. H. Tao, T. Y. Liow, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Fast and low power Michelson interferometer thermo-optical switch on SOI,” Opt. Express 16(20), 15304–15311 (2008).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008).
[Crossref]

2007 (3)

2006 (4)

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

B. Jalali and S. Fathpour, “Silicon Photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[Crossref]

P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14(20), 9197–9202 (2006).
[Crossref] [PubMed]

2005 (4)

2004 (2)

2003 (1)

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

2002 (2)

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

2000 (1)

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

1992 (1)

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

Absil, P. P.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Almeida, V. R.

Anderson, P. A.

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Baets, R.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Barrios, C. A.

Beckx, S.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Bienstman, P.

Bogaerts, W.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Cao, W.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

Capasso, F.

Chen, L.

P. Dong, L. Chen, Q. Xu, and M. Lipson, “On-chip generation of high-intensity short optical pulses using dynamic microcavities,” Opt. Lett. 34(15), 2315–2317 (2009).
[Crossref] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[Crossref] [PubMed]

Chi, H.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Cocorullo, G.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

Craighead, H. G.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008).
[Crossref]

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Dong, P.

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Dumon, P.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Fang, Q.

Fathpour, S.

Ferraro, M. S.

Fong, K. Y.

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[Crossref] [PubMed]

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Foster, M. A.

Gaeta, A. L.

Goldhar, J.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[Crossref] [PubMed]

Greene, W.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Grover, R.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Haus, H. A.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Ho, P.-T.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Hodson, T.

Ibanescu, M.

Ibrahim, T. A.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Ippen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Jaenen, P.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Jalali, B.

Joannopoulos, J. D.

Johnson, F. G.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Johnson, S. G.

Kim, Y.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

Kwong, D. L.

Lee, S.

Li, J.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

Li, M.

C. Xiong, W. H. Pernice, M. Li, and H. X. Tang, “High performance nanophotonic circuits based on partially buried horizontal slot waveguides,” Opt. Express 18(20), 20690–20698 (2010).
[Crossref] [PubMed]

M. Li, W. Pernice, and H. Tang, “Ultrahigh-Frequency Nano-Optomechanical Resonators in Slot Waveguide Ring Cavities,” Appl. Phys. Lett. 97(18), 183110 (2010).
[Crossref]

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical Kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnol. 4(6), 377–382 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Lin, Q.

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[Crossref]

Liow, T. Y.

Lipson, M.

Little, B. E.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Lo, G. Q.

Loncar, M.

Luyssaert, B.

Manipatruni, S.

Ndi, F. C.

Ouzounov, D. G.

Painter, O.

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[Crossref]

Pan, W.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

Panepucci, R. R.

Parpia, J. M.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008).
[Crossref]

Pernice, W.

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

M. Li, W. Pernice, and H. Tang, “Ultrahigh-Frequency Nano-Optomechanical Resonators in Slot Waveguide Ring Cavities,” Appl. Phys. Lett. 97(18), 183110 (2010).
[Crossref]

Pernice, W. H.

Pernice, W. H. P.

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical Kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnol. 4(6), 377–382 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[Crossref]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Povinelli, M. L.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Prather, D. W.

Pruessner, M. W.

Rabinovich, W. S.

Rendina, I.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

Ritter, K.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Rooks, M.

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express 15(19), 11934–11941 (2007).
[Crossref] [PubMed]

Rosenberg, J.

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[Crossref]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Schmidt, B. S.

Sekaric, L.

Smythe, E. J.

Song, J.

Soref, R.

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Stievater, T. H.

Taillaert, D.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Tang, H.

M. Li, W. Pernice, and H. Tang, “Ultrahigh-Frequency Nano-Optomechanical Resonators in Slot Waveguide Ring Cavities,” Appl. Phys. Lett. 97(18), 183110 (2010).
[Crossref]

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

Tang, H. X.

C. Xiong, W. H. Pernice, M. Li, and H. X. Tang, “High performance nanophotonic circuits based on partially buried horizontal slot waveguides,” Opt. Express 18(20), 20690–20698 (2010).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical Kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[Crossref]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnol. 4(6), 377–382 (2009).
[Crossref] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Tao, S. H.

Thoen, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Toulouse, J.

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Van, V.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

Van Campenhout, J.

Van Thourhout, D.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in Silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

Verbridge, S. S.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008).
[Crossref]

Vlasov, Y.

Wiaux, V.

Wiederhecker, G. S.

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, “Broadband tuning of optomechanical cavities,” Opt. Express 19(3), 2782–2790 (2011).
[Crossref] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[Crossref] [PubMed]

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

Wouters, J.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

Xia, F.

Xiong, C.

C. Xiong, W. H. Pernice, M. Li, and H. X. Tang, “High performance nanophotonic circuits based on partially buried horizontal slot waveguides,” Opt. Express 18(20), 20690–20698 (2010).
[Crossref] [PubMed]

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Xu, Q.

P. Dong, L. Chen, Q. Xu, and M. Lipson, “On-chip generation of high-intensity short optical pulses using dynamic microcavities,” Opt. Lett. 34(15), 2315–2317 (2009).
[Crossref] [PubMed]

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Yu, M. B.

Appl. Phys. Lett. (6)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80(3), 416 (2002).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical Kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[Crossref]

C. Xiong, W. Pernice, M. Li, M. Rooks, and H. Tang, “Adiabatic embedment of nanomechanical resonators in photonic microring cavities,” Appl. Phys. Lett. 96(26), 263101 (2010).
[Crossref]

M. Li, W. Pernice, and H. Tang, “Ultrahigh-Frequency Nano-Optomechanical Resonators in Slot Waveguide Ring Cavities,” Appl. Phys. Lett. 97(18), 183110 (2010).
[Crossref]

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92(1), 013112 (2008).
[Crossref]

K. Y. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. 97(7), 073112 (2010).
[Crossref]

Electron. Lett. (1)

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, and R. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (4)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12(3), 323–325 (2000).
[Crossref]

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and H. Chi, “Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon. Technol. Lett. 15(1), 36–38 (2003).
[Crossref]

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002).
[Crossref]

J. Appl. Phys. (1)

W. H. P. Pernice, M. Li, and H. X. Tang, “Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

J. Lightwave Technol. (2)

Nat. Nanotechnol. (1)

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnol. 4(6), 377–382 (2009).
[Crossref] [PubMed]

Nat. Photonics (2)

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[Crossref]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[Crossref]

Nat. Phys. (1)

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[Crossref]

Nature (3)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Opt. Express (9)

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007).
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Opt. Lett. (4)

Other (1)

R. Soref, ” Recent Advances in Silicon Photonic Components,” in Integrated Photonics Research and Applications/Nanophotonics for Information Systems, Technical Digest (Optical Society of America, 2005), paper JWA1.

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Figures (7)

Fig. 1
Fig. 1 (a) Mode profile of a silicon nitride slot waveguide with a dielectric beam cross-section of 330 × 500nm2. Shown is the magnitude of the Ex component in (V/m) for waveguides separated by a gap of 200nm. (b) The dependence of the effective index of the slot waveguide mode on the width of the dielectric beams. Shown are simulations for waveguide separations from 50nm to 400nm.
Fig. 2
Fig. 2 (a) Numerical simulation of the group index of a silicon nitride slot waveguide in dependence of wavelength. A slot gap of 200nm is assumed. (b) Calculation of the optical force between two coupled silicon nitride beams in dependence of waveguide separation, normalized to the input power and the beam length. By decreasing the waveguide width the magnitude of the optical force is increased, while a reduced gap leads to enhanced optical force.
Fig. 3
Fig. 3 (a) Design of a photonic circuit for a tunable coupler employing coupled slot modes. The coupling length is tuned by varying the slot gap. The released parts of the waveguide cross the blue membrane area. The input signal is routed into either the through or drop port, depending on the beating gap. (b) The modal distribution along the coupled slot waveguides, obtained by FDTD simulation. Overlaid in green is the sinusoidal profile of the intensity along the top slot waveguide. (c) The calculated beating length for two coupled nitride slot waveguides of 500nm width and 200nm gap in dependence of the beating gap. (d) The calculated beating length for a beating gap of 730nm in dependence of the slot gap.
Fig. 4
Fig. 4 (a) Process flow diagram illustrating the fabrication process. (b) Optical micrograph of a fabricated Mach-Zehnder interferometer device. One arm of the interferometer crosses the membrane area to realize a free-standing slot waveguide. An SEM zoom-in image of the slot waveguide is shown in the inset. (c) Optical micrograph of a directional coupler device, showing two sets of grating couplers and the directional coupler crossing the grey membrane area. An SEM zoom-in image of the two coupled slot waveguides is shown in the inset.
Fig. 5
Fig. 5 (a) The normalized transmission spectrum of a low-stress silicon nitride Mach-Zehnder interferometer device at various input laser power. Overlaid is the transmission band profile of the grating couplers, shown by the black dashed line. (b) The measured wavelength and phase shift in dependence of the laser power on the device. The linear fit to the data reveals a tuning sensitivity of 1.7nm/mW.
Fig. 6
Fig. 6 (a) Optical micrograph showing the tunable directional coupler device made of low-stress silicon nitride and the schematic showing the measurement setup. (b) Normalized transmission spectrum of the tunable directional coupler device. The blue and red lines are the measured transmission from the through and drop port, respectively. The transmission curve is enveloped by a Gaussian fit (dashed black line) of the transmission band profile of the grating couplers. (c) and (d) Static tuning of the through port and drop port transmission as a function of control laser power at two different probe laser wavelength.
Fig. 7
Fig. 7 (a) Normalized transmission spectrum of the tunable directional coupler device. The blue and red squares are the measured transmission data from the through and drop port, respectively. The solid blue and red lines show a sinusoidal fit of the transmission data. In the real device, the transmission curve is enveloped by the transmission band profile of the grating couplers, shown by the dashed black line. (b) The measurement setup used to characterize the performance of the directional coupler device. Time-domain traces are recorded on an oscilloscope, while the mechanical response in the frequency domain is obtained with a network analyzer. (c) The driven mechanical response of the directional coupler. Two resonance peaks corresponding to the in-plane motion of the slot waveguides are measured around 609kHz. (d) The measured modulated signal in the through and the drop port of the device.

Equations (3)

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L b = λ 2 ( n e n o )
P ( L ) = P 0 cos 2 ( π L 2 L b )
P ( λ ) = P 0 cos 2 ( π ( n e n o ) L λ )

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