three-dimensional chirped high-contrast grating hollow

Three-Dimensional Chirped High-Contrast Grating Hollow-Core WaveguideVolume 4, Number 5, October 2012

Yang Yue, Student Member, IEEELin Zhang, Member, IEEEXue Wang, Student Member, IEEEHao Huang, Student Member, IEEEWeijian Yang, Student Member, IEEEJames Ferrara, Student Member, IEEEVadim KaragodskyChristopher ChaseMoshe Tur, Fellow, IEEEConnie J. Chang-Hasnain, Fellow, IEEEAlan E. Willner, Fellow, IEEE

DOI: 10.1109/JPHOT.2012.22102791943-0655/$31.00 ©2012 IEEE

Three-Dimensional Chirped High-ContrastGrating Hollow-Core Waveguide

Yang Yue,1 Student Member, IEEE, Lin Zhang,1 Member, IEEE,Xue Wang,1 Student Member, IEEE, Hao Huang,1 Student Member, IEEE,

Weijian Yang,2 Student Member, IEEE,James Ferrara,2 Student Member, IEEE, Vadim Karagodsky,2

Christopher Chase,2 Moshe Tur,3 Fellow, IEEE,Connie J. Chang-Hasnain,2 Fellow, IEEE, and Alan E. Willner,1 Fellow, IEEE

1Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089 USA2Department of Electrical Engineering and Computer Sciences, University of California,

Berkeley, CA 94720 USA3School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel

DOI: 10.1109/JPHOT.2012.22102791943-0655/$31.00 �2012 IEEE

Manuscript received June 29, 2012; accepted July 21, 2012. Date of current version July 31, 2012. Thiswork was supported by the Defense Advanced Research Projects Agency (DARPA) iPhoD programunder Contract HR0011-09-C-0124. Corresponding author: Y. Yue (e-mail: [email protected]).

Abstract: A 3-D chirped high-contrast grating hollow-core waveguide (HCG-HW) exhibitshighly efficient 2-D (transverse and lateral) light confinement. Compared with step-indexones, laterally chirped HCG-HWs (graded index) can pronouncedly reduce the propagationloss ð9 10�Þ without compromising the lateral index contrast. Simulation results show that apropagation loss as low as 0.04 dB/cm can be achieved. For a chirped HCG-HW with a 6-�mcore height, it exhibits 30- and 141-nm spectral widths for 0.1- and 1-dB/cm loss requirements.The chirped HCG-HW also shows an ultralow nonlinear coefficient, which is on the order of10�5 =W/m.

Index Terms: Waveguides, engineered photonic nanostructures, gratings, subwavelengthstructures, optics.

1. IntroductionHollow-core waveguides (HWs), which guide light in a low-index air core, show promise forachieving low propagation loss, small chromatic dispersion, and negligibly low nonlinearity [1]–[3].All these features are quite significant for applications that require small distortion, such as true timedelay [4] and high-power ultrashort pulse delivery [5]. Moreover, HWs provide the possibility to filldifferent gaseous or liquid materials into the hollow core and potentially open up a host ofapplications, such as nonlinear optics, sensing, quantum optics, and biophotonics [6]–[13].

With the advance of integrated optics, it is highly desirable to make the waveguide elementcompact and even realize on-chip integration. During the past decade, integrated HWs have beendemonstrated using Bragg and antiresonant Fabry–Perot reflectors [14]–[18]. However, the loss ofon-chip hollow-core Bragg and antiresonant reflecting optical waveguides has remained high.Moreover, multiple-layer deposition tends to complicate the fabrication process. Recently publishedworks have shown that the ultrahigh reflectivity of high-contrast gratings (HCGs) can be used toenable low-loss waveguiding and achieve unique dispersion properties and ultralow nonlinearity in2-D waveguides [19], [20]. Moreover, the HCG-HWs tend to require fewer process steps than theothers and, thus, facilitate the fabrication [21].

Vol. 4, No. 5, October 2012 Page 1372

IEEE Photonics Journal Three-Dimensional Chirped HCG-HW

A 3-D HCG-HW can be formed by bonding two HCGs [21], [22]. Due to high reflectivity, the twoHCGs can confine the light in the transverse direction. In order to confine light laterally, Bcore[ andBcladding[ regions have to be created by changing grating parameters, which gives rise to anBeffective[ index difference. This lateral confinement might not be perfect and induce unwantedlosses. A laudable goal would be to find a structural design that reduces the losses due tononperfect lateral confinement.

In this paper, we propose and simulate the use of chirped gratings between the core and claddingregions in order to lower the propagation loss in the 3-D HCG-HW. Similar to a graded-indexconfiguration [23], the adiabatically chirped gratings can significantly reduce the interruptiveeffective index mismatch induced leakage through the interface between the core and claddingwithout compromising the lateral index contrast [24]. As a result, a 9 10� reduction in loss can beachieved, dropping the loss from 1.62 to 0.13 dB/cm after introducing the chirped gratings for awaveguide with a �10-�m core width and 5-�m core height. Using a wider core width ð�23 �mÞand optimized core height ð�6 �mÞ, the propagation loss can be further reduced to 0.04 dB/cm.The chirped HCG-HW with a 6-�m core height also exhibits a 30- and 141-nm bandwidth for G 0.1-and G 1-dB/cm propagation loss, respectively. Moreover, it can potentially achieve a very lownonlinearity ð�10�5 =W/mÞ.

2. Waveguide Structure and Mode PropertyThe schematic of a 3-D HCG-HW is depicted in Fig. 1(a), in which light propagates in the z-direction(parallel to the grating bars). It is formed by two parallel silicon-on-insulator wafers. Each wafer hasa 340-nm Si layer, a 2-�m SiO2 space layer on a Si substrate. The waveguide width ðW Þ and coreheight ðDÞ are 100 and 5 �m, respectively. There are three grating parameters that are highlyrelated with the grating reflectivity: period ð�Þ, air gap ðagÞ, and thickness ðtgÞ. The refractive indicesof silicon and silica are obtained according to the Sellmeier equation in our model [25]. At 1550 nm,they are 3.478 and 1.444, respectively.

Commercial software, GSolver 4.2, based on rigorous coupled-wave analysis (RCWA) [26], isused to calculate the HCG reflectivity and design grating parameters. The gratings on the twowafers can provide light confinement in the y -direction. In order to confine light in the x -direction, wechoose two different sets of grating parameters for the core and cladding regions to form a lateraleffective index difference. The grating parameters B� ¼ 1170 nm, ag ¼ 450 nm[ andB� ¼ 1080 nm, ag ¼ 410 nm[ for the core and cladding regions are chosen to achieve highreflectivity and large effective refractive index difference simultaneously. The grating thickness in allsimulations is 340 nm. With the above grating parameters, there is a 7:6� 10�4 effective refractiveindex difference between the core and cladding regions for a HCG-HW with a 5-�m core height.

Fig. 1. (a) Schematic of a 3-D HCG-HW consisting of two reflecting HCGs in the y -direction. Si high-index gratings are on top of a 2-�m SiO2 layer and Si substrate. Two different grating designs arechosen as core and cladding to provide the effective index difference and lateral confinement. Linearlychirped gratings along the x -direction are used to mitigate the effective refractive index mismatchinduced leakage. The light propagates in the z-direction with TE polarization. (b) TE field (power norm)distribution in the chirped HCG-HW.



The gratings are designed to achieve high reflectivity for the fundamental transverse electric (TE)mode (i.e., x -polarized). With grating parameter optimization, HCG-HW can achieve similarperformance for the fundamental mode in the transverse magnetic (TM) polarization and also for thecase that light propagates perpendicularly to the grating bars. By properly controlling the launchingcondition, the fundamental mode can be effectively excited [22]. Ncore and Nchirp are the number ofgrating periods in the middle core region and the number of grating periods in the chirped region atone side. As a result, the number of grating periods in the effective core region Neff core equals thesum of Ncore and Nchirp . In the simulation, the nonlinear refractive indices n2 are 4:5� 10�18 and2:6� 10�20 m2=W, for silicon and silica, respectively [27], [28]. Using a full-vectorial finite-elementmethod (FEM), with perfectly matched layer on the boundaries, we obtain the electromagnetic fieldof the TE mode and its propagation loss, while the nonlinear coefficient is computed using a full-vectorial equation [29]. From Fig. 1(b), we can see that the TE field is well confined within the aircore region.

The unique light confinement mechanism of HCG-HW also provides novel waveguidingcharacteristics. Fig. 2(a) shows the TE field (power norm) distributions at different wavelength inthe chirped HCG-HW. Typically, the mode field increases with wavelength in regular waveguide,while it decreases in the HCG-HW. This unique property is attributed to the wavelength dependenceof the effective refractive index difference between the core and cladding regions. We investigate theeffective refractive indices of the modes in the slab waveguides (light confinement only in they -direction), which are formed by uniform gratings as the core region (� ¼ 1170 nm, ag ¼ 450 nm) orthe cladding region (� ¼ 1080 nm, ag ¼ 410 nm). As shown in Fig. 2(b), the effective index differencebetween the core and cladding regions increases from 3:1� 10�4 to 2:2� 10�3 as wavelengthincreases from 1450 to 1600 nm. Consequently, the mode is confined tighter, and thus, the effectivemode area of the TE mode decreases from 117.8 to 61.9 �m2.

3. Chirped Grating and Effect on Propagation LossThe chirping profile of the grating is a key parameter to optimize for achieving desired features.Here, we investigate different parabolic chirping profiles, as shown in Fig. 3(a), for lowering thepropagation loss according to

�ðnÞ ¼ �core þ �clad

2� �core � �clad

2� signðn � ðN þ 1Þ=2Þ � n � ðN þ 1Þ=2

ðN þ 1Þ=2

��

��

k

(1)

where �core, �clad , and �ðnÞ are the periods of the grating in the core region, the grating in thecladding region, and the nth grating in the chirped region, respectively. N denotes the number of the

Fig. 2. (a) Wavelength dependence of the TE field (power norm) distribution in the chirped HCG-HW.(b) Effective index difference (between the core and cladding regions) and effective mode area of theTE mode as a function of wavelength from 1450 to 1600 nm.



grating period in the chirped region, while k is the chirp rate in the parabolic function. As the greendot line shown in Fig. 3(a), a linear profile has a chirp rate k ¼ 1.

Fig. 3(b) shows the effect of chirp rate on propagation loss of HCG-HW with Neff core ¼ 15. Forsmall Nchirp , a smooth chirp profile ðk � 0:8Þ gives the lowest loss. For the case with enough chirpedgratings, a chirp rate k � 1 gives the lowest loss. As k ¼ 1 brings relatively low loss for most cases,we use linearly chirped HCG-HW for the following study.

Fig. 4 shows the propagation loss at 1550 nm as a function of Nchirp for different Neff core. Here,Nchirp ¼ 0 stands for no chirped gratings between the core and the cladding (step-index case). TheHCG-HW with a larger core width has smaller loss as the evanescent field decreases exponentiallytoward the waveguide edge and gives reduced field intensity at the interface between the core andcladding. FEM simulation shows that the field leakage through the interface can be significantlyreduced by introducing chirped gratings. For a HCG-HW with Neff core ¼ 9, the loss can be reducedby �12� from 1.62 to 0.13 dB/cm after introducing the six linearly chirped gratings at both sides ofthe core region.

To take advantage of the inherent broad bandwidth in the optical domain, broadening the low-loss wavelength range for an on-chip element is of great importance. The propagation loss as afunction of wavelength for the 3-D chirped HCG-HW with a 5-�m core height is shown in Fig. 5(a).For this HCG-HW design, the minimal propagation loss is achieved between 1550 and 1560 nm.The wavelength location of low-loss window can be well controlled by choosing proper grating

Fig. 3. (a) Chirping profile for different chirp rate ðkÞ. (b) Propagation loss as a function of chirp rate forHCG-HW with 15 effective gratings in the core region.

Fig. 4. Propagation loss at 1550 nm as a function of the grating period number in the chirped regionðNchirpÞ for different numbers of periods in the effective core ðNeff core ¼ 9;15;21Þ. Nchirp ¼ 0 stands forno chirped gratings between the core and the cladding regions (step-index case).



parameters [19]. As shown in the figure, increasing Nchirp (larger core width) can reduce thepropagation loss and broaden the low-loss spectral width simultaneously. The 3-D HCG-HW with21 effective core grating periods ðNcore ¼ 3; Nchirp ¼ 18Þ exhibits a 20-nm spectral width from 1545to 1565 nm for G 0.1-dB/cm propagation loss. As shown in Fig. 6, chirping the gratings canpronouncedly increase the low-loss bandwidth, especially for small-core-width HCG-HW. For a1-dB/cm loss requirement, the waveguide can operate over 104 nm.

If a microelectromechanical system (MEMS) actuator is added to change the HCG-HW coreheight, large tunability of waveguide properties can be potentially achieved [14]–[16]. Thetransverse leakage is inversely proportional to D2 in 2-D HCG-HW [19]. Fig. 5(b) illustrates theimpact of core height on the propagation loss of 3-D chirped HCG-HW. With the decrease in coreheight, the effective index difference between the core and cladding regions increases and causesa larger leakage through the interface. While for larger core height, the effective refractive indexdifference decreases, the lateral confinement is not strong enough, which results in a larger lateralleakage. Therefore, there is a tradeoff between the leakage through the interface and lateralleakage. The optimal core height for the lowest loss is between 5 and 6 �m. For a HCG-HWðNcore ¼ 3; Nchirp ¼ 18Þ with a 6-�m core height, a propagation loss as low as 0.04 dB/cm can beachieved at 1550 nm. Simulation shows that the propagation loss can be further reduced for a widercore or a larger waveguide width.

Fig. 5. (a) Propagation loss as a function of wavelength from 1500 to 1600 nm for different grating periodnumber in the chirped region ðNchirp ¼ 6;12; 18Þ with fixed grating period number in the core regionðNcore ¼ 3Þ and core height ðD ¼ 5 �mÞ. (b) Propagation loss at 1550 nm as a function of waveguidecore height ðDÞ from 3 to 10 �m for different grating period number in the chirped regionðNchirp ¼ 6; 12;18Þ with fixed grating period number in the core region ðNcore ¼ 3Þ.

Fig. 6. G 1-dB/cm loss bandwidth as a function of grating period number of the effective core form 7 to21 step-index ðNchirp ¼ 0Þ and chirped ðNcore ¼ 3Þ HCG-HW with 5-�m core height.



From Fig. 5, we can see that introducing more chirped gratings can efficiently broaden thebandwidth and increase the core height tuning range for low-loss operation. To further explore theeffect of chirped gratings, the contour plot of propagation loss for the HCG-HW as a function ofwavelength and waveguide core height is shown in Fig. 7. In the figure, we can see that chirping thegrating between the core and cladding regions can efficiently broaden the low-loss window, whichmeans it can simultaneously broaden the operation range for wavelength and waveguide coreheight. For a chirped HCG-HW ðNcore ¼ 3; Nchirp ¼ 18Þ with a 6-�m core height, G 0.1-dB/cm losscan be maintained over a 30-nm spectral width. Moreover, one can achieve G 1-dB/cm loss over a141-nm wavelength range from 1452 to 1593 nm. Furthermore, as shown in the dark blue region ofFig. 7(b), G 0.1-dB/cm loss can be achieved with 2-�m core height tuning over 20-nm bandwidth.

4. Chromatic Dispersion and NonlinearityIn general, chromatic dispersion in the waveguide stems from material dispersion and waveguidedispersion. As light is efficiently confined within the air core region of the 3-D chirped HCG-HW,waveguide dispersion contributes mostly to the total chromatic dispersion. Fig. 8(a) shows thechromatic dispersion of the chirped HCG-HW ðD ¼ 5 �m; Ncore ¼ 3Þ with different grating periodnumber in the chirped region. We can see that increasing the number of the chirped gratings reduce

Fig. 7. Contour plot of propagation loss for the HCG-HW ðNcore ¼ 3Þ versus wavelength and core heightwith different number of chirped grating periods (a) Nchirp ¼ 6 and (b) Nchirp ¼ 18.

Fig. 8. (a) Chromatic dispersion as a function of wavelength from 1450 to 1600 nm for different gratingperiod number in the chirped region ðNchirp ¼ 6;12;18Þ with fixed grating period number in the coreregion ðNcore ¼ 3Þ and core height ðD ¼ 5 �mÞ. (b) Chromatic dispersion as a function of wavelengthfrom 1450 to 1600 nm for different waveguide core height ðD ¼ 3; 5; 7 �mÞ with fixed grating periodnumber in the core region ðNcore ¼ 3Þ and in the chirped region ðNchirp ¼ 12Þ.



not only the propagation loss but also the waveguide and total dispersion. At 1550 nm, thechromatic dispersion decreases from 1.37 to 1.08 ps/(nm km) after increasing Nchirp from 6 to 18.Another way of tuning the chromatic dispersion for HCG-HW is adjusting the waveguide coreheight, as it can efficiently control the degree of interaction between the guided mode and HCGs onthe wafer. Fig. 8(b) shows chromatic dispersion as a function of wavelength from 1450 to 1600 nmfor different waveguide core height with fixed grating period number in the core region ðNcore ¼ 3Þand in the chirped region ðNchirp ¼ 12Þ. As one can see, the dispersion at 1550 nm increases from0.5 to 4.5 ps/(nm km) by decreasing the waveguide core height from 7 to 3 �m. Consequently, wecan partially control the total dispersion of HCG-HW by adjusting the waveguide parameters fordifferent applications. Furthermore, an advanced grating profile might be able to extend thetailorability of the dispersion.

For many on-chip applications, a linear transfer function is highly desired to prevent the opticalwave from being distorted. HCG-HWs can potentially achieve this characteristic. From Fig. 9(a), wecan see that the nonlinear coefficients at 1550 nm are on the order of 10�5 =W/m and decrease withthe effective core width because a larger core width provides better light confinement in the hollowair region. This results in less interaction between the field and nonlinear materials. For a HCG-HWwith Neff core ¼ 21, a nonlinear coefficient as low as 5:5� 10�5 =W/m is achieved. The wavelengthdependence of the nonlinear coefficient for chirped HCG-HW is shown in Fig. 9(b). The nonlinearcoefficient of the chirped HCG-HW increases one order of magnitude as wavelength increases from1500 to 1600 nm. This is because with increased wavelength, the mode is confined tighter and,thus, more interaction with the silicon grating in the transverse direction. Moreover, one can see thatincreasing the chirped gratings can reduce the nonlinear coefficient, which is due to the reducedleakage through the core/cladding interface.

5. ConclusionIn conclusion, we propose and simulate a 3-D chirped HCG-HW. Simulation shows that HCG-HWpossesses novel waveguiding properties due to its unique light confinement mechanism. Thechirping profile of the grating is optimized to achieve low propagation loss. By adding adiabaticallychirped gratings, one can significantly ð9 10�Þ reduce the mode leakage through the interfacebetween the core and cladding without compromising the lateral index contrast. A propagation lossas low as 0.04 dB/cm can be achieved using HCG-HW with a �23-�m core width and a �6-�mcore height. The 3-D chirped HCG-HW also exhibits a 30- and 141-nm bandwidth for G 0.1- andG 1-dB/cm propagation loss, respectively. For a chirped HCG-HW ðNcore ¼ 3; Nchirp ¼ 18Þ,

Fig. 9. (a) Nonlinear coefficient at 1550 nm as a function of the grating period number in the chirpedregion ðNchirpÞ for different grating period number of the effective core ðNeff core ¼ 9;15;21Þ. Nchirp ¼ 0stands for no chirped gratings between the core and the cladding regions (step-index case). (b) Nonlinearcoefficient as a function of wavelength from 1500 to 1600 nm for different grating period number in thechirped region ðNchirp ¼ 6; 12; 18Þ with fixed grating period number in the core region ðNcore ¼ 3Þ.



G 0.1-dB/cm loss can be achieved with 2-�m core height tuning over 20-nm bandwidth. Thechromatic dispersion of HCG-HW can be partially controlled by adjusting the waveguide parameters.Furthermore, it can potentially provide an on-chip medium with ultralow nonlinearity ð�10�5 =W/mÞ.

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three-dimensional chirped high-contrast grating hollow

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