Ultrafast all-optical modulation in a silicon nanoplasmonic resonator

M. P. Nielsen; A. Y. Elezzabi

doi:10.1364/OE.21.020274

1. Introduction

Diffraction limits photonic devices to dimensions far in excess of typical modern nanoscale electronic modules. Through photon-surface plasmon interactions at metal-dielectric interfaces, nanoplasmonic waveguides and devices are capable of nanoscale footprints below the light diffraction limit. The nanoscale optical mode confinement and subwavelength bending radii of nanoplasmonic waveguides give rise to high integration densities and more efficient access to higher order nonlinearities. Indeed, nanoplasmonic waveguides enable more than just increased mode confinement, but also enable an overall reduction of the device dimensions. This has led to their proposal as a lead contender for providing the basis for the next generation of chip-scale computing platforms offering ultrafast operation capabilities [1]. A number of innovative nanoplasmonic waveguiding configurations have been proposed including: long range surface plasmon polariton waveguides [2], dielectric loaded surface plasmon polariton waveguides [3], metal-dielectric slab waveguides [4], and metal-insulator-metal (MIM) waveguides [5]. More recently, the hybrid metal-insulator-semiconductor-insulator-metal (MISIM) waveguide [6] have been proposed to overcome the inherent trade-off between reducing propagation losses and increasing optical mode confinement in traditional nanoplasmonic waveguides.

A requirement for compatibility with complementary metal-oxide-semiconductor (CMOS) processes and the possibility of integrating electronics and plasmonics on the same chip is the use of a silicon-based plasmonic platform. Previous approaches to signal modulation in silicon-based plasmonics have included charge redistribution through an applied electric field [7,8] and above band gap photogenerated free-carrier modulation [9–11]. However, the reliance on a driving electrical signal to produce the applied electric field for charge redistribution limits the modulation bandwidth to that of the electronic components. This negates one of the primary advantages of using plasmonic circuitry instead of conventional electronics. While photogenerated free-carrier modulation retains this high-bandwidth operation advantage, above band gap radiation in silicon requires the on-chip integration of non-silicon based routing buses and waveguides to distribute and deliver the pump pulses. To overcome this constraint, one can turn to exploiting silicon’s nonlinearities. The two-photon absorption (TPA) process allows ultrafast free-carrier photogeneration using a pump wavelength within the telecommunication band from 1300 to 1600nm. Since TPA is an intensity dependent process, the enhanced signal confinement provided by nanoplasmonic waveguides increases the efficiency of carrier generation. By further enhancing the signal confinement through the use of a resonator, the device footprint can be reduced to the nanoscale.

In this investigation, we explore the viability of ultrafast all-optical modulation in a silicon MISIM nanoring resonator using TPA. Carriers generated by degenerate TPA from a pump pulse at 1.35-1.44µm modify the complex refractive index of the nanoring resonator, modulating the resonant characteristics of the nanoring and modulating the transmission of a probe pulse at 1.53-1.58µm. Three separate devices are explored to examine how the thickness of the insulator layers and the nanoring dimensions influence the light modulation characteristics. Signal modulation of up to 13.1dB was obtained with an off-on switching time of 2ps using a modest pump pulse energy of 16.0pJ in a compact 1.4µm² device footprint.

2. Devices

The nanoring resonator devices and associated coupling waveguides presented are formed of Ag/HfO₂/Si/HfO₂/Ag MISIM nanoplasmonic waveguides. Such devices would be fabricated by first lithographically defining a mask on an oxygen implanted SOI wafer, and dry etching through the device layer to define the silicon elements. Following this, the HfO₂ dielectric spacer can be deposited conformally through atomic layer deposition (ALD). Finally, a second lithography step can be used to deposit silver around the structure though sputtering and lift-off processes. Although the indirect bandgap nature of silicon normally limits the carrier recombination time to timescales of nanoseconds, it has been shown that through ion implantation of oxygen into silicon, the introduction of carrier recombination centers reduces the carrier recombination lifetime to 600fs [13]. The silicon core in the MISIM nanoplasmonic waveguides is taken as oxygen doped silicon with a carrier recombination time of τ_r = 1ps to enable terahertz modulation bandwidth.

Schematics of the three presented devices, hereafter denoted as Device A, Device B and Device C, are depicted in Figs. 1(a)-1(c) along with their broadband spectral responses calculated within the 1.3-1.6µm wavelength range. Figures 1(d) and 1(e) depict the input modes for the input bus waveguides of the devices. All three devices are formed of 100nm wide by 340nm tall Si waveguides surrounded by hafnium oxide (HfO₂) dielectric spacers and silver sidewalls. By varying the HfO₂ dielectric spacer layer from 10nm in Device A to 20nm in Device B and Device C, it is possible to discern the influence of the spacer layer on device performance. Similarly, by varying the outer radii of the nanorings from 540nm in Device A and Device B to 1µm in Device C, the influence of the nanoring radii can be determined. These radii allow for compact device footprints as small as 1.4µm². The MISIM nanoplasmonic waveguides are aperture coupled to the nanorings via a 200nm wide and 50nm deep silicon opening. To characterize the modulation properties of the devices, 400fs FWHM probe pulses, comparable to the lifetime of the nanoring resonances, are injected at the input port with a pulse energy of 6.4fJ and centered at resonances (depicted in Fig. 1) at 1.53µm, 1.58µm, and 1.55µm for Device A, Device B and Device C, respectively. To modulate the probe pulses, 400fs FWHM pump pulses are injected at the input port with various pulse energies ranging from 6.4fJ to 64pJ and centered at resonances (depicted in Fig. 1) at 1.35µm, 1.37µm, and 1.44µm for Device A, Device B and Device C, respectively.

Fig. 1 Schematic diagrams and broadband spectral response with pump and probe pulse resonances for (a) Device A, (b) Device B, and (c) Device C. Electric field intensity distribution for the fundamental TE modes of the MISIM waveguides for (a) Device A and (b) Devices B and C.

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3. FDTD formulation

To assess the proposed nanoring resonators as all-optical switch devices, self-consistent 2-D finite difference time domain (FDTD) simulations incorporating the nonlinear two-photon absorption (TPA) process, free-carrier absorption (FCA), and plasma dispersion effects (PDE) in silicon were conducted. In the standard Yee algorithm for the FDTD method used here, the electric displacement field D is calculated from Ampère’s equation, and the electric field E is calculated from both D and the polarization P by $D = ε_{0} E + P$ . For Ag and HfO₂, the polarization is calculated through auxiliary differential equations using a multi-pole Lorentzian fit to the refractive index values from [14] and [15], respectively. The polarization for silicon, on the other hand, is divided into linear and nonlinear components, $P = P_{l i n e a r} + P_{T P A} + P_{F C A} + P_{p l a s m a}$ , where the linear component is calculated through an auxiliary differential equation using a multi-pole Lorentzian fit to the refractive index values from [16] and the nonlinear components are calculated using the method derived in [17] as follows. Silicon’s Kerr and Raman nonlinearities are neglected for this investigation as they are much weaker than the TPA and carrier effects for the time duration, length scales, and pulse energies under consideration [18,19]. With the change in optical intensity, I, due to TPA, $d I / d L = - β_{T P A} I^{2}$ , where β_TPA = 0.8cm/GW [20] is the TPA coefficient and L is the interaction length, the nonlinear polarization due to TPA, $P_{T P A} = ε_{0} χ_{T P A} E$ , can be calculated from:

χ_{T P A} = i \frac{c_{0} n_{0} β_{T P A}}{ω} I = - \frac{c_{0}^{2} ε_{0} n_{0}^{2} β_{T P A}}{i ω} {| E |}^{2},

which can be discretized through the use of the substitution –iω by ∂/∂t into:

χ_{T P A}^{n + 1} = χ_{T P A}^{n} - \frac{c_{0}^{2} ε_{0} n_{0}^{2} β_{T P A} Δ t}{2} {| E^{n + 1 / 2} |}^{2} ≅ χ_{T P A}^{n} - \frac{c_{0}^{2} ε_{0} n_{0}^{2} β_{T P A} Δ t}{4} [{| E^{n + 1} |}^{2} + {| E^{n} |}^{2}],

where χ_TPA is the nonlinear susceptibility due to TPA, c₀ is the speed of light, n₀ = 3.48 is the refractive index of silicon at 1.55µm, ε₀ is the permittivity of free space, ω is the angular frequency, n is the discretized step index, and Δt is the time step. The dependence of

χ_{T P A}^{n + 1}

on E^{n + 1} requires iteration for self-consistency. The free-carrier concentration, N_f, equivalent to both the electron, N_e, and the hole, N_h, concentrations, is calculated through the rate equation:

\frac{d N_{f}}{d t} = \frac{1}{2 ℏ ω} (- \frac{d I}{d z}) - \frac{N_{f}}{τ_{r}} = \frac{c_{0}^{2} ε_{0}^{2} n_{0}^{2} β_{T P A}}{8 ℏ ω} {| E |}^{4} - \frac{N_{f}}{τ_{r}},

which can be discretized into:

N_{f}^{n + 1 / 2} = \frac{2 τ_{r} - Δ t}{2 τ_{r} + Δ t} N_{f}^{n - 1 / 2} + \frac{τ_{r} Δ t}{2 τ_{r} + Δ t} \frac{c_{0}^{2} ε_{0}^{2} n_{0}^{2} β_{T P A}}{4 ℏ ω} {| E^{n} |}^{4},

where τ_r = 1ps is the free-carrier recombination time in oxygen doped silicon. The generated free-carriers then lead to FCA and plasma dispersion effects. The change in optical intensity due to FCA is

d I / d L = - σ_{F C A} N_{f} I

leads to the polarization due to FCA of:

P_{F C A} = i ε_{0} ε_{i F C A} E = - \frac{c_{0} ε_{0} n_{0} σ_{F C A} N_{f}}{i ω} E,

where

σ_{F C A} = 3.6 \times 10^{- 21} [m^{2}] {(λ [μ m] / 1.55)}^{2}

[21] is the free-carrier absorption cross-section. The plasma dispersion polarization arising from the free-carrier refractive index change is:

P_{p l a s m a} = ε_{0} ε_{r P l a s m a} E = ε_{0} 2 n_{0} Δ n_{p l a s m a} E,

where

Δ n_{P l a s m a} = [- 8.8 \times 10^{- 22} N_{e} - 8.5 \times 10^{- 18} N_{h}^{0.8}] {(λ [μ m] / 1.55)}^{2}

[22].

This allows the relationship between D and E for silicon to be rewritten as:

\tilde{D} = D - P_{L i n e a r} = ε_{0} E [2 n_{0} Δ n_{p l a s m a} - \frac{c_{0} n_{0} σ_{F C A} N_{f}}{i ω} - \frac{c_{0}^{2} ε_{0} n_{0}^{2} β_{T P A}}{2 i ω} {| E |}^{2}]

Discretizing through the substitution of –iω by ∂/∂t and rearranging to solve for E^{n + 1} yields:

E^{n + 1} = \frac{g^{-} (E^{n + 1})}{g^{+} (E^{n + 1})} E^{n} + \frac{{\tilde{D}}^{n + 1} - {\tilde{D}}^{n}}{ε_{0} g^{+} (E^{n + 1})},

where,

g^{\pm} (E^{n + 1}) = 2 n_{0} Δ n_{p l a s m a} (E^{n + 1}) \pm \frac{c_{0} n_{0} σ_{F C A} N_{f}^{n + 1 / 2} Δ t}{2} \pm \frac{c_{0}^{2} ε_{0} n_{0}^{2} β_{T P A} Δ t [{| E^{n + 1} |}^{2} + {| E^{n} |}^{2}]}{8} .

As with Eq. (3), Eq. (8) must be solved with iteration. In this case, the maximum number of iterations was set to six to ensure accuracy without compromising simulation performance.

4. Results

To characterize the three devices, a 400fs FWHM pump pulse was injected at the input port at various pulse energies and the device was probed with the 400fs FWHM 6.4fJ probe pulse. Figure 2(a) depicts Device A at the probe resonance at 1.53µm, without injection of the pump pulse. When the 16.0pJ pump pulse at 1.35µm generates free-carriers inside the nanoring, it causes a shift of the nanoring’s resonant characteristics, thus, moving the probe pulse ‘off’ resonance and away from the minimum transmission. Figure 2(b) shows Device A after the pump pulse has shifted the probe resonance away from the probe 1.53µm resonant wavelength. The time dynamics for the average carrier concentration generated in the nanoring for Device A at several pump pulse energies are depicted in Fig. 2(c). The carrier density increases within the first 400fs and decays within 1ps. During this time, it is expected that the nanoring resonance will shift and revert back to its original state. Figure 3 depicts the ultrafast response of the devices under various pump energy excitations. Maximum transmission is obtained for a 400fs delay between pump and probe pulses, as this corresponds to the free-carrier concentration reaching its maximum value. The broader resonances associated with the smaller nanorings in Device A and Device B (pump at 1.37µm, probe at 1.58µm) result in more of the spectral contents of the probe pulse to fall within the nanoring resonator’s bandwidth, thus leading to transmission minimum on the order of a few percent for the ‘off’ state. Figure 4(a) shows how the lower transmission minimum leads to a greater on-off modulation amplitude for Device A and Device B compared to Device C (pump at 1.44µm, probe at 1.55µm) which has a 51% narrower resonance as shown in Fig. 1(f). The thinner (10nm) HfO₂ spacer layers in Device A confine more of the pump energy to the silicon core, leading to greater modulation of up to 13.1dB at lower pump pulse energies. As the pump pulse energy is increased above 31.3pJ, the modulation amplitude plateaus and decreases due to increased FCA and non-degenerate TPA between the pump and probe pulses. At higher pump energies, the pump begins to experience increased FCA from its leading edge, hence the maximum nanoring carrier concentration [Fig. 4(b)] increases slowly with pump energy. Another cause of the plateau behaviour of the signal response is that, similarly to the probe pulse, the leading edge of the pump pulse shifts the pump resonance before the trailing edge reaches the device. The plateau behaviour at higher pump energies is also illustrated in Fig. 4(c) for the maximum resonance shift of the nanorings. An important characteristic of any signal modulating device is its switching time. Here, the devices’ switching time is defined as the time over which the signal reaches 3dB over its initial value. As depicted in Fig. 4(d), this value is very dependent on the ring geometry with smaller rings having longer switching times due to their lower ‘off’ state transmission. It can be seen that using smaller nanorings with thinner dielectric spacer layers enables more efficient and stronger modulation capabilities. Using a modest pump pulse energy of 16.0pJ, Device A achieved 13.1dB modulation amplitude with an ultrafast switching time of only 2ps. The required energy formodulation could be further reduced by utilizing shorter pump pulses in smaller nanorings with thinner dielectric spacer layers.

Fig. 2 Intensity plots for Device A with the 400fs FWHM probe pulse centered at 1.53µm (a) ‘on’ resonance and (b) after the pump pulse has turned it ‘off’ resonance at 16.0pJ. (c) Average carrier concentration in the nanoring for Device A at pump pulse energies of 31.3pJ (green solid line), 16.0pJ (red dashed line), and 5.8pJ (blued dotted line).

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Fig. 3 Ultrafast response of the devices as a function of the signal delay between pump and probe pulses for (a) Device A, (b) Device B, and (c) Device C at pump pulse energies of 31.3pJ (green solid line), 16.0pJ (red dashed line), and 5.8pJ (blued dotted line).

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Fig. 4 Effect of increased pump pulse energies up to 64pJ for Device A (blue diamonds and solid line), Device B (red squares and dashed line), and Device C (green triangles and dotted line) on (a) modulation amplitude, (b) maximum carrier concentration in the nanoring, (c) maximum resonance shift, and (d) switching time for the respective probe pulses.

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5. Conclusion

Self-consistent FDTD simulations incorporating TPA, FCA, and plasma dispersion are utilized to examine ultrafast all-optical modulation in silicon-based MISIM nanoring resonators. With a modest pump pulse energy of 16.0pJ, a 13.1dB modulation amplitude was obtained with a switching time of only 2ps with a compact 1.4µm² device footprint. It is shown that the modulation amplitude is maximized for smaller nanorings and thinner dielectric spacer layers due to the broader device bandwidth.

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Ultrafast all-optical modulation in a silicon nanoplasmonic resonator

Abstract

1. Introduction

2. Devices

3. FDTD formulation

4. Results

5. Conclusion

References and links

Cited By

Figures (4)

Equations (9)

Optics Express