Surface-normal coupled four-wave mixing in a high contrast gratings resonator

Tianbo Sun; Weijian Yang; Connie Chang-Hasnain

doi:10.1364/OE.23.029565

1. Introduction

Nonlinear optical frequency conversion is important for many applications, including photonic switching, correlated photon pair generation, and narrow linewidth sources [1–5]. Recently, Four Wave Mixing (FWM) in silicon platform has received intense investigation due to the potential of integrating with electric/photonic circuits, scalable manufacturability, and a reasonably large third-order susceptibility in silicon [6]. FWM in silicon devices has been studied in slab waveguides, resonator structures, photonic crystal slow light waveguides etc [6–14]. These structures are mostly based on silicon waveguides, utilizing strong index contrast between core and cladding to achieve high transverse confinement. Enhanced optical intensity inside silicon due to mode confinement will then result in increased FWM efficiency. However, in such structures, laser input is usually coupled into in-plane waveguide structures from an off-chip source. The optical coupling loss between an optical fiber and the in-plane waveguide structures compromises the net conversion efficiency and total power consumption. Efficient coupling requires both optimized coupling structures (i.e. grating couplers or tapered waveguides) and accurate alignment, thus greatly increasing the system complexity [15, 16]. In addition, for practical applications, it is critical to develop devices with high efficiency at low pumping levels.

In this express, we present a novel Si-based on-chip high contrast grating (HCG) resonator and demonstrate resonance enhanced degenerate four-wave mixing. Theoretically and experimentally, the HCG resonator has been demonstrated to have high optical quality factor [17–19]. Furthermore, laser light can be directly coupled to the HCG resonator from a free space or fiber output with very high efficiency (~87% experimentally). A lower bound Q of 7330 was chosen in the experiment to allow a cavity linewidth ~210pm, within which the four-wave mixing process is enhanced by the resonance. The surface-normal input angle is designed to allow for easy alignment and setup robustness. High FWM conversion efficiency (−19.5dB) in this resonator has been demonstrated under low pumping power (~900µW).

2. High contrast gratings resonator

A high contrast grating (HCG) is a new class of optics with a wide range of designable properties resulting from a large contrast of refractive indices between the grating ribbons and their surroundings [19]. In this experiment, HCG is fabricated on a silicon-on-insulator (SOI) wafer. Schematic is shown in Fig. 1(a). Theoretically, we have previously shown that HCGs can be designed to have high-quality-factor resonance at surface-normal incidence angle [18, 19]. This can be understood as follows: When a plane wave hits the grating surface, it couples into waveguide array modes inside the gratings. Due to the large index contrast, there are only two waveguide array modes over a wide spectral range. The two modes mixes/couples strongly with each other at the input and exit planes, again due to a large index step between the grating plane and the exiting media. By properly choosing the thickness of the grating, constructive interference of the modes can be achieved, leading self-sustained optical energy or a high quality factor (Q-factor) [19]. We summarize the basic principle in the following. First, if we define $ρ$ as the coupling coefficient matrix between grating modes at the entrance/exit boundaries (assuming the same refractive index for the entrance and exiting media) and $φ$ as the propagation factor inside the grating through its thickness, and C is the vector representing a self-sustainable mode which satisfies the round-trip condition, thus:

C = ρ φ ρ φ C .

This equation provides an intuitive illustration of the resonance nature. The intrinsic quality factor (defined as center wavelength divided by full width half maxima) is calculated by

Q = \frac{2 π n_{g} t_{g}}{λ} | \frac{r}{1 - r^{2}} | .

where

t_{g}

is the thickness of the grating,

λ

is the wavelength of the incident light,

n_{g}

is the group index, and r represents the eigenvalues of matrix

ρ φ

[19]. This design algorithm bases on the assumption of periodic structure and plane wave excitation.

Fig. 1 (a) Schematic of HCG resonator. In this particular design, resonance is coupled by a surface normal plan wave input with TE polarization. Grating thickness t_g, period Λ and duty cycle are important parameters to determine the resonance wavelength and quality factor. (b) Top view of SEM image of gratings within a single fabricated HCG resonator. (c) Measured reflection spectrum for the HCG resonator. Linewidth shows 210pm, indicating Q ~7330. An absolute reflectivity (normalized by gold mirror) of 87% was achieved at the peak indicating a very high coupling efficiency.

Download Full Size | PDF

Devices are fabricated on an SOI wafer with a 500nm Si device layer and 3m buried oxide layer. A simple two-step fabrication process including optical lithography and silicon etching was used. We chose grating period (780nm) and barwidth (410nm), which can be easily fabricated with ASML300 deep UV stepper. Reactive ion etching (RIE) was performed for Si etching (Lam Research). In the scanning electron micrographs of the fabricated devices shown in Fig. 1(b) the HCG structure is evident and good fabrication accuracy is observed.

Measurement is performed to exam the optical quality factor (Q) of the fabricated devices. The single device we fabricated has a lateral size ~800µm x 800µm and input spot size is adjusted to be 20 µm diameter. In this scenario, the HCG is practically infinite compared to the spot size we used in the measurement. A tunable laser centered at 1550nm is used as the excitation and is set in a continuous sweeping mode between 1538nm and 1540nm at a rate of 40nm/sec. Laser light is adjusted to TE polarization (parallel to the grating bars). The power of the reflected light is recorded using a photodiode in real time and is synchronized to the laser sweep rate. Reflection spectrum is normalized to a near 100% gold mirror and then plot in Fig. 1(c). As high as 87% peak reflection was obtained, indicating an excellent surface-normal coupling efficiency. Theoretical predication shows that 100% reflection is expected at resonance wavelength [19]. Experiment results will be further increased if structure optimization is performed under Gaussian beam excitation. A linewidth ~210pm indicates that the Q for this device is ~7330, an excellent value for high FWM conversion efficiency with a reasonable detuning range.

One most important advantage of HCG resonator over the other on-chip resonators is the high coupling efficiency with single mode fiber output or free-space Gaussian mode. Figure 2(a) and (b) show the simulated mode pattern (intensity) at resonance for an HCG resonator under excitation of a Gaussian beam with a ~10 µm diameter (similar size with output from single mode fiber). Figure 2(a) shows a top view of the resonance sliced in the center of resonator. Excellent match of mode intensity profile with the input Gaussian beam contributes to the easy and efficient coupling from the input. Figure 3(b) shows the side view of the resonance mode inside one grating period of the cavity.

Fig. 2 Simulated resonance mode pattern (intensity): (a) Top view of the resonance inside HCG cavity, excited by Gaussian beam with 10𝜇𝑚 spot size. Large mode overlap with the input beam contributes to the easy and efficient coupling (~87%). (b) Side view of the resonance inside one period of the HCG resonator.

Download Full Size | PDF

Fig. 3 Schematic of the FWM measurement setup.

Download Full Size | PDF

3. Enhanced four-wave mixing experiment

In part 2, we demonstrated that an HCG can be a high Q resonator with easy and efficient coupling from an off-chip laser source. Now we show its application in degenerate four wave mixing (FWM). We consider the net conversion efficiency $η = P_{i d l e r} / P_{s i g n a l}$ by taking the ratio of idler output power and signal output power. This ratio can eliminate the difference caused by fluctuation from the experiment setup (i.e. coupling and laser fluctuation). Thus, the conversion efficiency under certain pumping power will serve as an important figure of merit to determine performance of FWM devices. Theoretically, the conversion efficiency for resonance enhanced FWM can be modeled using the following equation [20, 21]:

η = | γ P_{p} L^{'} |^{2} F E_{p}^{4} F E_{s}^{2} F E_{c}^{2} .

where

γ

is the third order nonlinear parameter,

P_{p}

is the pumping power,

L^{'}

is the effective optical length and

F E_{p}

,

F E_{s}

,

F E_{c}

are the field enhancement factors of pump, signal and idler respectively. This simple equation contains physics for both FWM and the resonator. To take the most advantage of cavity enhancement for FWM in the HCG resonator, the pumping laser is typically aligned to the center of resonance frequency. In the experiment, we place both pumping and signal inside the same cavity linewidth. Thus

F E_{p}^{2}

,

F E_{s}^{2}

and

F E_{c}^{2}

have the same Lorezian lineshapes with HCG cavity under first order estimation. When the pumping laser is fixed at the resonance wavelength, conversion efficiency

η

lineshape will be described by square of cavity lineshapes. Thus, the detuning linewidth will be roughly depending on1/Q.

Figure 3 shows the schematic of the experimental setup used to achieve the degenerate FWM in the HCG resonator. Two continuous-wave tunable lasers serve as the pump and signal source, respectively. A 50:50 optical fiber coupler combines the pump and signal prior to coupling them into HCG resonator. A 5x objective lens is used to adjust the laser spot size to achieve optimized coupling. The reflected beam and the generated signal are collected by the same objective and directed to an optical spectrum analyzer through a free space beam splitter. High coupling efficiency with simple alignment is enabled by the unique resonance mode of inside HCG as we discussed in section 2.

Figure 4(a) shows the observed FWM results in the HCG resonator. In this example, the pump wavelength is set at 1538.9nm, located at the center wavelength of the resonance (shown in Fig. 1(c)) to maximize the cavity enhancement. The signal laser is set at 70pm detuning. The idler shows up as a side band with frequency $υ_{i d l e r} = 2 υ_{p u m p} - υ_{s i g n a l}$ . The net conversion efficiency in this particular configuration is approximately −19.5dB at a low pumping power of ~900W.

Fig. 4 (a) Reflection beam spectrum taken from the OSA; −19.5dB conversion efficiency is achieved in this configuration. (b) Conversion efficiency as function of signal power. The slope of the Log-Log plot is nearly 2, indicating the idler signal is generated from FWM.

Download Full Size | PDF

Conversion efficiency as function of pumping power is plotted in Fig. 4(b). The slope of the linear fitted line (nearly 2) in the log-log plot indicates that the pulse at frequency $2 υ_{p u m p} - υ_{s i g n a l}$ is caused by FWM inside HCG resonator.

Next, we studied the FWM detuning characteristics inside the same device. In the measurement, the pumping laser and signal laser detuning were both placed within the resonance linewidth, with carefully controlled TE polarization. Two example series of idler measurements are presented in Fig. 5, with different pump and signal detuning wavelengths, respectively. In Fig. 5(a), the pump wavelength is set at center wavelength of the resonance (1538.9nm) with the signal detuning from −200pm to −70pm. In Fig. 5(b) signal wavelength is fixed with the pump detuning from −240pm to −70pm. In both series, the parametric idler is clearly observed as a side band to the cavity resonance, located at frequency_{$2 υ_{p u m p} - υ_{s i g n a l}$}.

Fig. 5 Wavelength detuning: (a) Signal detuning with pump fixed at resonance wavelength (1538.9nm). (b) Pump detuning with fixed signal laser.

Download Full Size | PDF

The phase matching condition for FWM in HCG resonator can be expressed in terms of the requirement fitting the idler frequency inside the resonance:

Δ υ = | υ_{i d l e r} - υ_{r e s} | < \frac{Δ υ_{F W H M}}{2} .

where

Δ υ_{F W H M}

is the resonance linewidth. Figure 6 shows conversion efficiency as a function of signal detuning wavelength (with pumping laser fixed at resonance frequency). The measurement results are plotted as red dots and a numerical fitting based on Eq. (3) is shown as a black dashed curve. Under first order estimation, the FWM detuning bandwidth roughly matches the HCG resonance linewidth. In our numerical fitting,

F E^{2}

is assumed to have a shape of Lorentzian function with peak ~7330.

L^{'}

is ~0.5µm.

Fig. 6 Conversion efficiency as a function of signal detuning. Red dots are measurement results. Black dashed line is from numerical simulation using Eq. (3).

Download Full Size | PDF

4. Discussion

To our knowledge, this is the first time that high Q resonance and four wave mixing are observed in a Si based HCG resonator. Compared with other on-chip Si resonators, aseptically those photonic crystal cavity with far-field optimization [22], HCG resonators gain benefits from direct and more efficient coupling from either free-space optics or fiber output. It reduces design complexity, area on chip and total power consumption. Highest Q we measured so far is ~7330, lower than the highest number reported in photonic crystal cavity [22] or ring resonator [23]. However, this number is mainly limited by the imperfection of etching (side wall roughness and 6o side wall angle). We are expecting 2 orders of improvement with optimized process.

On one hand, the peak conversion efficiency is strongly depending on resonance enhancement, which is proportional to cavity quality factor (Q). On the other hand, lineshape of conversion efficiency $η$ function is described by square of cavity linesape function, which is depending on1/Q. Thus, there is an obvious trade-off between detuning linewidth and peak efficiency. This trade-off may limit the practical use of resonance-enhanced FWM as wavelength conversion devices. One solution to overcome this problem is to employ a resonator array together with wavelength splitting device. Each resonator inside the array will be optimized for high efficiency at single wavelength. Resonance wavelength inside the array will be designed to vary with grating period and duty cycle, which can be easily defined in the lithography step [16]. By taking advantage of free-space operation, we can put the wavelength splitting device (i.e. diffraction gratings) in front of HCG resonators array. Different wavelength will be diffracted to the ‘right’ device inside the array. This will not increase the system cost because of the small HCG resonator footprint and coupling mechanism.

5. Summary

We observed resonance enhanced four-wave mixing in a surface-normal coupled silicon based high contrast grating (HCG) resonator, with an experimentally measured Q ~7000. We achieve a peak conversion efficiency of −19.5dB at a pumping power of ~900µW. Coupling efficiency is ~87% with an easily aligned and robust configuration. The device demonstrated here could have a small footprint and the potential to be built into a large array to increase the operation wavelength range.

Acknowledgment

This work was mainly supported by Department of Defense National Security Science and Engineering Faculty Fellowship awarded to C.C.H

References and links

1. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006). [CrossRef] [PubMed]

2. D. Klonidis, C. T. Politi, R. Nejabati, M. J. O’Mahony, and D. Simeonidou, “OPSnet: design and demonstration of an asynchronous high-speed optical packet switch,” J. Lightwave Technol. 23(10), 2914–2925 (2005). [CrossRef]

3. J. Ma and C. Jiang, “Design and analysis of all-optical switches based on fiber parametric devices,” Opt. Commun. 281(9), 2605–2613 (2008). [CrossRef]

4. K. Kawase, J. Shikata, K. Imai, and H. Ito, “Transform-limited, narrow-linewidth, terahertz-wave parametric generator,” Appl. Phys. Lett. 78(19), 2819–2821 (2001). [CrossRef]

5. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]

6. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

7. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005). [CrossRef] [PubMed]

8. R. Espinola, J. Dadap, R. Osgood Jr, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005). [CrossRef] [PubMed]

9. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006). [CrossRef] [PubMed]

10. M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011). [CrossRef] [PubMed]

11. J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18(15), 15484–15497 (2010). [CrossRef] [PubMed]

12. T. Baba, “Slow light in photonic crystal,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef] [PubMed]

13. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18(22), 22915–22927 (2010). [CrossRef] [PubMed]

14. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19(5), 4458–4463 (2011). [CrossRef] [PubMed]

15. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Beats, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006). [CrossRef]

16. O. Mitomi, K. Kasaya, and H. Miyazawa, “Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling,” IEEE J. Quantum Electron. 30(8), 1787–1793 (1994). [CrossRef]

17. Y. Zhou, M. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. Sedgwick, and C. J. Chang-Hasnain, “High-index-contrast gratin (HCG) and its application in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1485–1499 (2009). [CrossRef]

18. Y. Zhou, M. Moewe, J. Kern, M. C. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008). [CrossRef] [PubMed]

19. C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012). [CrossRef]

20. T. Gu, N. Petrone, J. F. McMillan, A. Van Der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012). [CrossRef]

21. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25(8), 554–556 (2000). [CrossRef] [PubMed]

22. S. L. Portalupi, M. Galli, C. Reardon, T. F. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18(15), 16064–16073 (2010). [CrossRef] [PubMed]

23. M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009). [CrossRef] [PubMed]

Surface-normal coupled four-wave mixing in a high contrast gratings resonator

Abstract

1. Introduction

2. High contrast gratings resonator

3. Enhanced four-wave mixing experiment

4. Discussion

5. Summary

Acknowledgment

References and links

Cited By

Figures (6)

Equations (4)

Optics Express