WO2013049649A1 - Modulateur de phase basse tension et filtres accordables - Google Patents

Modulateur de phase basse tension et filtres accordables Download PDF

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Publication number
WO2013049649A1
WO2013049649A1 PCT/US2012/058030 US2012058030W WO2013049649A1 WO 2013049649 A1 WO2013049649 A1 WO 2013049649A1 US 2012058030 W US2012058030 W US 2012058030W WO 2013049649 A1 WO2013049649 A1 WO 2013049649A1
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Prior art keywords
photonic crystal
photonic
zero
phc
superlattice
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PCT/US2012/058030
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English (en)
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Chee Wei Wong
Serdar KOCAMAN
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The Trustees Of Columbia University In The City Of New York
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Publication of WO2013049649A1 publication Critical patent/WO2013049649A1/fr

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/122—Basic optical elements, e.g. light-guiding paths
    • G02B6/1225—Basic optical elements, e.g. light-guiding paths comprising photonic band-gap structures or photonic lattices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29346—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by wave or beam interference
    • G02B6/2935—Mach-Zehnder configuration, i.e. comprising separate splitting and combining means
    • G02B6/29352—Mach-Zehnder configuration, i.e. comprising separate splitting and combining means in a light guide
    • G02B6/29353—Mach-Zehnder configuration, i.e. comprising separate splitting and combining means in a light guide with a wavelength selective element in at least one light guide interferometer arm, e.g. grating, interference filter, resonator

Definitions

  • the disclosed subject matter generally relates to integrated optical systems. More particularly, the disclosed subject matter relates to a new design for a photonic crystal.
  • Integrated optical systems such as fiber optic communication systems, generally include filters, phase modulators, and delay lines, which allow for the processing and transportation of optical signals on-chip.
  • These components are often implemented as waveguides etched into silicon.
  • Filters are designed as periodic structures within waveguides
  • Phase modulators are designed as a combination of two waveguides which divide an optical wave, adjust the phase in one of the waveguides, and recombine the wave to create constructive or destructive interference.
  • Phase is often adjusted by introducing a certain path length difference or inserting an opto -electronic material in the waveguide which introduces phase delays proportional to an applied voltage.
  • Photonic crystals are patterned dielectric materials that have optical properties that are a function of their geometry; changing the shape will change the spectral response.
  • LHMs Left handed metamaterials
  • LHMs which was also characterized theoretically decades ago are artificial composites having both negative permittivity and permeability. These conditions allow LHMs to have negative refraction indices.
  • Their uncommon physical properties have sparked intense interest in these materials and many groups have been studied LHMs.
  • metallic based LHMs can also operate in optical frequencies, they have large optical losses.
  • photonic crystals can have effective negative index of refraction in a certain frequency range and this can lead to many applications such as zero phase delay lines and the subdiffraction imaging.
  • photonic crystals can have effective negative index of refraction in a certain frequency range and this can lead to many applications such as zero phase delay lines and the subdiffraction imaging.
  • a photonic crystal structure including a base body defining a photonic superlattice including alternating sections having lattice holes and sections excluding lattice holes, wherein a first Brillouin zone is defined by a section having lattice holes, and wherein a second Brillouin zone is defined by the photonic superlattice.
  • each section of the base body defining lattice holes includes hexagonal photonic crystals.
  • the section excluding lattice holes is a homogenous slab.
  • the first Brillouin zone is defined by a hexagonal photonic crystal lattice.
  • the first section including lattice holes is defined by a dimension di, and the section excluding lattice holes has a dimension d 2 .
  • the sum of di and d 2 equals a first superperiod.
  • said distance dl and distance d2 are selected to provide said photonic crystal with one or more passband.
  • said distance dl and distance d2 are selected to provide said photonic crystal with one or more stopband.
  • the photonic crystal can be a spectral filter, a band stop filter, a band pass filter.
  • said distance di and d 2 are selected to adapt said photonic crystal to act as a phase modulator.
  • said phase modulation is adapted to encrypt a first signal.
  • said phase modulation is adapted to decrypt a first signal.
  • said distance dl is about 2.56-4.03 ⁇ and said distance d2 is about 1.90-3.22 ⁇
  • the base body has a thickness within a range of about 13.38-21.75 ⁇ , the spacing of adjacent lattice holes is within a range of about 410 nm to about 430 nm, and the radius of the lattice holes is within a range of about 100 nm to about 120 nm.
  • said photonic crystal is a waveguide.
  • the photonic crystal can adapted to be integrated into an existing optical system.
  • the photonic crystal can be affixed to an integrated circuit.
  • said integrated circuit has a silicon substrate.
  • said photonic crystal is adapted to perform optical switching.
  • said plurality is arranged proximately to form an array.
  • the array can be adapted to perform passive image processing.
  • said photonic crystal is adapted to act as a delay line.
  • Figure 1 is a schematic representation of a photonic superlattice in accordance with the disclosed subject matter.
  • Figures 2(a) and (b) are band diagrams of the photonic crystal in accordance with the disclosed subject matter.
  • Figure 2(c) is a representation of the calculated effective index of refraction of the photonic crystal, in accordance with the disclosed subject matter.
  • Figures 3(a) and (b) are schematic representations of the device, in accordance with the disclosed subject matter.
  • Figures 4(a)- 4(e) are plots of transmission (a.u.) vs. wavelength in accordance with the disclosed subject matter.
  • Figure 4(f) is a plot of the calculated effective index of refraction for the superlattices in accordance with the disclosed subject matter.
  • Figure 7(a) illustrates transmission spectra calculated for different values of the disorder parameter ⁇ in which the structural disorder is introduced by randomly changing the radius of the holes in the photonic crystal sections of the superlattice in accordance with the disclosed subject matter.
  • Figure 7(b) illustrates transmission spectra calculated for different values of the disorder parameter ⁇ in which the structural disorder is introduced by randomly perturbing the location of the holes in accordance with the disclosed subject matter.
  • Figure 8(a) is a schematic of a Mach-Zelinder interferometer (MZI) in accordance with the disclosed subject matter.
  • Figures 8(b) and (c) are band diagrams of the photonic crystal of Figure 8(a) in accordance with the disclosed subject matter.
  • Figure 9(a) is a band diagram change of the photonic crystal with respect to radius (r/a) change, in which t/a has been kept constant at 0.744 in accordance with the disclosed subject matter.
  • Figure 9(b) is a band diagram change of the photonic crystal with respect to thickness (t/a) change, in which r/a has been kept constant at 0.279 in accordance with the disclosed subject matter.
  • Figure 9(c) is a band diagram change of the photonic crystal with respect to period (a) change in accordance with the disclosed subject matter.
  • Figure 10(a) is a transmission spectrum for the designs on the two arms of the MZI in Figure 8(a) in accordance with the disclosed subject matter.
  • Figure 10(b) illustrates transmission for designs of Figure 10(a) with 68 unit cells (UC) in which transmission is high for the wavelengths between 1580 and 1620 nm and low for the wavelengths between 1520 and 1560 nm, a high pass filter in accordance with the disclosed subject matter.
  • UC unit cells
  • Figure 10(c) illustrates transmission for designs of Figure 10(a) with 76 UC in which transmission is low for the wavelengths between 1580 and 1620 nm and high for wavelengths between 1520 and 1560 nm, a low pass filter in accordance with the disclosed subject matter.
  • Figure 10(d) is a transmission spectrum for the designs on the two arms of the MZI in Figure 8(a) in accordance with the disclosed subject matter.
  • Figure 10(e) illustrates transmission for designs of Figure 10(d) with 100 UC in which transmission is high for the band between 1535 and 1550 nm, a band pass filter in accordance with the disclosed subject matter.
  • Figure 10(f) illustrates transmission for designs of Figure 10(d) with 130 UC in which transmission is low for the band between 1535 and 1550 nm, a band reject filter, in accordance with the disclosed subject matter.
  • Figure 11(a) illustrates a transmission spectrum for the designs on the two arms of the MZI in Figure 8a in accordance with the disclosed subject matter.
  • Figure 11(b) illustrates an MZI transmission with the designs in Figure 11(a) on the two arms of the MZI in accordance with the disclosed subject matter.
  • Figure 12(a) is a schematic representation of an MZI in accordance with the disclosed subject matter.
  • Figure 12(b) is a SEM image of a sample, showing the photonic crystal layer only, in accordance with the disclosed subject matter.
  • Figure 12(b') is a zoomed-in image of the SEM of Figure 12(b) in accordance with the disclosed subject matter.
  • Figure 12(c) is a SEM image of a fabricated superlattice with seven superperiods (SP) in accordance with the disclosed subject matter.
  • Figure 12(d) is a SEM image of the Y-branch of the MZI in accordance with the disclosed subject matter.
  • Figure 12(d') is a zoomed-in image of SEM image of Figure 12(d) in accordance with the disclosed subject matter.
  • Figure 13(a) is a band diagram of the photonic crystal with the parameters given in Fig. 12(a)-(d) in accordance with the disclosed subject matter.
  • Figure 13(b) is a zoomed-in representation of the spectral domain of Figure 13(a) in accordance with the disclosed subject matter.
  • Figure 13(c) is a transmission spectrum of a device in accordance with the disclosed subject matter.
  • Figure 13(d) illustrates the influence of lattice disorder (parameter ⁇ ) on transmission spectra in accordance with the disclosed subject matter.
  • Figure 14(a) is a band diagram of a photonic crystal in accordance with the disclosed subject matter.
  • Figure 14(b) is a transmission spectrum for MZI transmission with 100 UC of photonic crystal on one arm and a homogeneous slab waveguide on the other arm compared with transmission spectrum for non-MZI photonic crystal with 60 photonic crystal UC in accordance with the disclosed subject matter.
  • Figures 15(a)-(d) illustrates output of the MZI with increasing number of superperiods in accordance with the disclosed subject matter.
  • Figures 16(a)-(d) illustrate FSR wavelength dependence corresponding to superlattices in Fig. 14(a)-(c) in accordance with the disclosed subject matter.
  • the superlattice can include alternating layers of hexagonal photonic crystals (PhCs) and homogeneous slabs.
  • the hexagonal PhC and the photonic superlattice have different symmetry properties, and therefore they also have different first Brillouin zones.
  • Figure 2a illustrates a band diagram of the PhC, with the parameters given in Fig. 1.
  • a first Brillouin zone of the hexagonal PhC is represented.
  • Figure 1, above represents a schematic of the Brillouin zones.
  • the TM-like photonic bands are depicted by lines 22, and the transverse electric (TE)-like photonic bands are depicted by lines 24.
  • the light cone is denoted by the lines 26.
  • Figure 2b represents a zoom-in of the spectral domain corresponding to experimental region of interest in Figure 2a. Experiments were performed in the spectral region marked by the two horizontal lines 28 (0.278-0.261 normalized frequency; 0.270 (dashed line 30) to 0.278 is negative index region).
  • Figures 3(a)-3(b) show a schematic representation of a device with 2 superperiods and the integrated Mach Zehnder Interferometer (MZI) is modified after introducing the third superperiod.
  • MZI Mach Zehnder Interferometer
  • the adiabatic region remains unchanged if Li is increased to Li+A and L2 is shortened by ⁇ /2, in both the input and output sides of the device, as illustrated in Figure 3(b).
  • the length L3 is increased to L3+ A/2. This procedure is used each time a superperiod (SP) is added to the structure.
  • SP superperiod
  • a common reference point is used for all devices that have the same ratio.
  • FIG. 3 a an integrated MZI of a device with 2 SPs and a channel waveguide is shown.
  • Figure 3(b) illustrates device modifications after the third superperiod is added. The length of the channel waveguide remains the same so as the effect of the additional superperiod is isolated.
  • the interferometer output intensity is given as:
  • phase 0 is the phase difference (or imbalance) between the modes propagating in the two arms (denoted by subscript 1 and 2).
  • n wg , n s i a b_i, n s i are the effective mode refractive indices of the channel waveguide, the adiabatic slab in arm 1, and the zero-index superlattice, respectively.
  • Li denotes the corresponding lengths.
  • the difference between the physical path length of the channel waveguides on both arms is designed to be equal to the physical path length of the tapering slab.
  • the mode indices n wg , n s i a b_i, n s i have different frequency dispersion.
  • the phase ⁇ s i a b _ wg ), arising , is maintained constant between different devices in each set of measurements by ensuring that the physical lengths and widths of the slabs are the same for each nano fabricated device. The remaining phase variation therefore is generated only by the photonic crystal superlattice If n s i is equal to zero, ⁇ 3 ⁇ is zero too, hence the total phase difference ⁇ in the interferometer arises only from the ⁇ wg component and is the same for all the devices in each set. Therefore, the sinusoidal oscillations in the transmission and the free spectral range are determined only by
  • ni and ri2 are the effective mode indices in the PhC and homogeneous (PIM) layers, respectively, at the corresponding wavelength.
  • the design includes 7 SPs for the devices with 7 unit cells of PhC and 5 SPs for those with 9 and 11 unit cells of PhC (these designs ensure a sufficient signal-to-noise ratio for the transmission measurements). In these experiments both the existence of the zero-n bandgap as well as its tenability were tested.
  • the effective index of the PIM layer, /3 ⁇ 4, is calculated numerically and for the asymmetric TM slab waveguide mode corresponds to, for example, 2.671 at 1550 nm.
  • Figure 4(d) presents similar information as Figure 2(a), but for superlattice ratio
  • NSOM near-field scanning optical microscopy
  • An exemplary NSOM is an aperture-type instrument, where the fiber is produced in National Chiao Tung University in Taiwan by use of thermal pulling method. A metal coating is used to create the aperture.
  • the NSOM fiber was then attached to a tuning fork sensor produced by Veeco Instruments. The detection is performed with a New Focus 2153 InGaAs femtowatt photoreceiver with lock-in amplification.
  • the NSOM instrument is a modified Veeco Aurora-3.
  • Coupling light into the zero-n superlattices is achieved by UV-curing adhesive bonding of a tapered lens fiber to the silicon input waveguide.
  • the input fiber was stably UV-epoxy bonded to the devices selected for the measurements.
  • Figures 5(a)-(b) represent near-field scanning optical microscopy of zero- n superlattices.
  • the scale bar in Figures 5 (a)-(b) is 2.5 ⁇ .
  • the input beam is impinging onto the structure from the right, which means that light scattering at the left facet of the device indicates light transmission.
  • the main effect consists of a small decrease of the zero-n superlattice transmission with increasing values of the disorder parameter a.
  • structural disorder induced by randomly changing the location of the holes has a much larger effect on the transmission spectra.
  • Figure 7(c) shows the expanded transmission spectra.
  • the structural disorder is introduced by randomly changing the radius of the holes in the PhC sections of the superlattice.
  • the structural disorder is generated by randomly perturbing the location of the holes.
  • chip-scale flat-top filters in near infrared wavelength using negative index photonic crystal based Mach Zehnder interferometers (MZI) are demonstrated.
  • high-pass, low-pass, band-pass and band reject filters are engineered by designing the photonic band diagram in terms of both band-gap and away from band-gap frequencies for different polarizations.
  • filters have tunable multi-level response for different sections of the spectrum. This configuration enables deterministic control of the bandwidth and the rejection ratio of the filters for integrated photonic circuits.
  • on-chip filter designs are described herein with photonic crystals by studying them in terms of the wavelengths at which they are transparent.
  • different kinds of filters can be realized based on their nontrivial phase effects coming from negative refractive characteristic in the transparent region.
  • the phase difference leading to interference originates from the imbalance in the refractive indices of two arms.
  • FIG. 8(a) illustrates a schematic of a MZI.
  • FIG. 8(b)-(c) The band diagram of the photonic crystal with a hole-to-lattice constant (r/a) ratio of 0.283 (r ⁇ 120 nm) is shown in Figures 8(b)-(c).
  • Figure 8(b) is a band diagram of the PhC with the parameters given in Figure 8(a), above.
  • Figure 8(b') inset represents first Brillouin zones of the hexagonal PhC.
  • the TM-like photonic bands are depicted in blue line 82 (darker).
  • the TE-like photonic bands are depicted in red line 84 (lighter).
  • the light cone is denoted by the green lines 86.
  • Figure 8(c) is a zoom-in of the spectral domain, corresponding to experimental region of interest. Experiments were performed in the spectral region marked by the two horizontal dashed lines 88. The effective refractive indices corresponding TM-like bands are determined from the relation (note that for the second band the effective index of refraction is negative since k decreases with co.
  • the two-dimensional (2D) hexagonal photonic crystal has a negative index within the spectral band of 0.27 to 0.278, in normalized frequency of ⁇ , or 1520 nm to 1566 nm wavelengths, such as reported earlier for near- field imaging.
  • the effective index of refraction is negative since k decreases with ⁇ .
  • the definition of this phase index of refraction is with respect to the wavevector in the first Brillouin zone as is understood in the art. Alternative definitions can also be used, such as the wavevector of the plane wave with the largest amplitude in the Fourier series decomposition of the Bloch mode.
  • the photonic crystal slabs are integrated with an interferometer, e.g., MZI, to facilitate the phase delay measurements.
  • an interferometer e.g., MZI
  • the imbalanced interferometer is designed such that after splitting from the Y-branch (Fig. (8a' ') right inset), a single-mode input channel waveguide adiabatically tapers (over ⁇ 400 ⁇ ) to match the width of the photonic crystal slabs.
  • the longitudinal direction of the superlattice coincides with the ⁇ - ⁇ axis of the hexagonal PhC.
  • a new design is provided for the photonic crystal band structure.
  • the band diagram in Fig. 8(b) is calculated by using RSoft's BandSOLVE that implements a numerical method based on the plane wave expansion of the electromagnetic field. 3D simulations were performed to calculate 30 bands, and for each band the corresponding values of the effective refractive index have also been determined. In all these numerical simulations a convergence tolerance of 10 ⁇ 8 has been used.
  • the photonic bands have been divided into transverse magnetic like (TM-like) and transverse electric like (TE-like), according to their parity symmetry.
  • the design parameters include the thickness of the slab, t, the radius of the holes, r, and the period of the photonic crystal, a, which is conventionally used as the normalization factor in the frequency axis.
  • the parameters t, r and a were varied one at a time with small incremental steps to cover the experimental range and the dependence of the band diagram to each of them was observed. Results of three simulations from each case are summarized in the Figures. 9(a)-(c). Note that, within the operating wavelength range (Fig. 8(c)) mainly there are two TM-like bands, one with positive refractive index and the other one with negative refractive index, and an almost complete TE-like bandgap. Thus the summary analysis here only shows TM polarization for the simplicity; however the dependence of the TE bands has also been studied.
  • a TM band diagram is shown, in which t/a has been kept constant at 0.744, with r variation where the bands shift to higher frequency with increasing r/a ratio, and the band gaps broaden since we plated with the dielectric contrast distribution.
  • the shifts in the TE bands were more than the shift in TM bands. This is due to the fact that TE modes are more planar than TM modes and are more sensitive to r/a change. As r/a increases, TE-like bands shifts more and both TE-like and TM-like band-gaps widen.
  • Results were plotted in wavelength in Fig. 9(c), rather than the normalized frequency.
  • the band diagram scales up with the period of the photonic crystal and bands shift to higher wavelength with increasing a.
  • t/a and r/a are changed together at the same rate so that effectively period variation is obtained.
  • the both bands scale with a and band-gaps widen as a increases.
  • FIG. 8(a) Devices were fabricated with the parameters selected by using the simulation results presented above.
  • the photonic crystal structures shown in Fig. 8(a) were fabricated with electron-beam lithography with ZEP520A (100%) positive tone e-beam resist and JEOL JBX6300FS electron-beam lithography system was used to expose the pattern.
  • an Oxford instruments Plasmalab 100 was used for performing cryogenic etching of silicon, employing an inductively coupled plasma reactive ion etcher (ICP-RIE). The chip was cleaved and mounted on the sample holder for measurements.
  • ICP-RIE inductively coupled plasma reactive ion etcher
  • Figures 10(a)-(f) present high-pass, low-pass, band-pass and band-reject filters experimentally.
  • Figure 10(a) individual transmission spectrum for the designs on the two arms of the MZI is shown.
  • the transmission is higher for the wavelengths between 1580 and 1620 nm and lower for the wavelengths between 1520 and 1560 nm, a typical response of a high pass filter. Furthermore, in Figure 10(c), with 76 unit cells of photonic crystal in both arms with same designs, the transmission is lower for the wavelengths between 1580 and 1620 nm and higher for the ones between 1520 and 1560 nm, thus a low pass filter.
  • FIG. 11(a) shows the spectrum for the designs on the two arms of the MZI illustrated in Figure 8(a).
  • the band-gap in the second design can require a greater number of unit cells to be formed; however, the transparent region is addressed herein.
  • Figure 11(b) shows the MZI transmission with the designs presented in Fig. 11(a), and with both 70 unit cells of photonic crystals, and transmission has three levels: The first level is between 1520 nm and 1560 nm where both designs have negative index values; the second level is between 1575 nm and 1590 nm where first design has positive index, second design has negative index; and the third level is between 1600nm and 1620 nm where both designs have positive index.
  • This filter with its multi-level response is broadly tunable can be used widely in integrated photonics such as a variable attenuator.
  • Integrated optical filters described herein can be designed by adjusting bandwidth and the rejection ratio for different parts of the spectrum via band diagram engineering in negative index photonic crystal slabs.
  • filtering operations on CMOS-fabricated devices can be controlled through, e.g., nontrivial phase effects in the transparent region of the photonic crystals, instead of the band gap.
  • optical beams propagating in path-averaged zero-index photonic crystal superlattices can have zero phase delay.
  • the nano fabricated superlattices include alternating stacks of negative index photonic crystals and positive index homogeneous dielectric media, where the phase differences corresponding to consecutive primary unit cells are measured with integrated Mach-Zehnder interferometers. These measurements demonstrate that at path- averaged zero-index frequencies the phase accumulation remains constant and equal to zero despite the increase in the physical path length.
  • the superlattice zero-n bandgaps remain invariant to geometrical changes of the photonic structure and have a center frequency which is deterministically tunable. The properties of the zero-n gap frequencies, optical phase, and effective refractive indices are described herein.
  • NIMs Negative-index metamaterials
  • metal-based NIMs dielectric-based photonic crystals
  • PhCs dielectric-based photonic crystals
  • a PhC can be obtained by cascading alternating layers of NIMs and positive-index materials (PIMs).
  • PIMs positive-index materials
  • This photonic structure ( Figure 12) has unique optical properties, including new surface states and gap solutions, unusual transmission and emission properties, complete photonic bandgaps, and a phase-invariant field for cloaking applications.
  • these binary photonic structures have an omnidirectional bandgap that is insensitive to wave polarization, incidence angle, structure periodicity and structural disorder. Such a gap exists because the path-averaged refractive index is equal to zero within a certain frequency band.
  • Near-zero-index materials are applicable to a number of applications, such as beam self-collimation, extremely convergent lenses and spontaneous emission control, strong field enhancement and cloaking devices.
  • the vanishingly small value of the refractive index of near-zero-index materials and their large phase velocity can reshape electromagnetic phase fronts emitted by optical antennae or, for highly directive antennas, transfer near-field phase information into the far-field.
  • the electromagnetic field In the near-zero-index regime, the electromagnetic field has an unusual dual character; that is, it is static in the spatial domain (the phase difference between arbitrary spatial locations is equal to zero), while remaining dynamic in the time domain, thus allowing energy transport.
  • FIG. 12(a) is a schematic of an MZI in accordance with the subject matter described herein.
  • Li ⁇ 850 ⁇ ; L 2 ⁇ 250 ⁇ ; L 3 is initially zero and is incremented by additional SPs in the phase measurements.
  • this gap is formed when the spatially averaged index is zero, it is insensitive to superlattice period variations as long as the condition of zero average index is satisfied. This property also implies that the total phase accumulation upon beam propagation in the superlattice cancels at wavelengths corresponding to the zero-n gap.
  • FIG. 12 The photonic structures examined for zero- n gaps (Fig. 12) consist of dielectric PhC superlattices with alternating layers of negative -index PhC and positive-index homogeneous slabs 30 .
  • Figures 12(b)-(d) illustrate scanning electron microscopy (SEM) images of the fabricated device.
  • Figure 12(b') is a zoomed-in image.
  • Figure 12(d) is a SEM image of the Y-branch
  • Figure 12(d') is a zoomed- in image of the Y-branch.
  • the PhC band structure is shown in Figures 13(a) and (b) with geometrical parameters from averaged fabricated samples (hole-to-lattice constant (r/a) ratio of 0.283 and a 3 ⁇ 4 423 nm).
  • This two-dimensional (2D) hexagonal PhC has a negative index within the spectral band of 0.270-0.278, in normalized frequencies of ⁇ /2 ⁇ , or wavelengths from 1 ,520 nm to 1 ,566 nm.
  • the phase index of refraction is defined with respect to the wave vector in the first Brillouin zone.
  • Alternative choices can be used, such as the wave vector of the plane wave with the largest amplitude in the Fourier series decomposition of the Bloch mode.
  • Figure 13(a) is a band diagram of the PhC with the parameters given in Fig. 12 (for a schematic of the Brillouin zones, see Fig. 1).
  • the TM-like photonic bands 134 and TE- like photonic bands 132 and light cone 136 are depicted in a similar manner as Figures 2(a)- (b) and 8(b)-(c) hereinabove.
  • Figure 13(b) is a zoomed-in representation of the spectral domain corresponding to the experimental region of interest. Experiments were performed in the spectral region delineated by two horizontal lines 138 (normalized frequency, 0.278- 0.261).
  • the longitudinal direction of the superlattice coincides with the ⁇ - ⁇ axis of the hexagonal PhC.
  • the ID binary superlattice and the hexagonal PhC have different symmetry properties and therefore different first Brillouin zones (see, Fig. l).
  • the PhC has two transverse-magnetic (TM)-like bands, one with a positive refractive index and the other with a negative refractive index, and an almost complete transverse-electric (TE)-like bandgap.
  • the experiments spanned 1,520 nm to 1,620 nm, with the negative refractive index band existing for wavelengths up to 1,570 nm.
  • the effective refractive index of the PhC region was obtained from the band diagram (Fig, 13(a)-(b)) and the PIM layer index computed from the asymmetric TM slab-waveguide mode effective index (for example, at 1,550 nm the mode index is 2.671).
  • the length ratio between the PIM and PhC sections of the superlattice was set to 0.78. As such, the zero-n gap should occur at 1,552.6 nm.
  • PhC structures integrated with MZIs were examined for phase-delay measurements.
  • the phase difference leading to interference originates from the physical length difference between the two arms, but in integrated photonic circuits this delay can easily be modulated by the imbalance in the refractive indices of two arms.
  • the unbalanced interferometer is designed so that after splitting from the Y-branch (Fig. 12(d)); a single-mode input channel wave-guide adiabatically tapers (over -400 ⁇ ) to match the width of the superlattice structures.
  • Figure 14(a) illustrates the band diagram shifts to lower frequency when the rla ratio changes.
  • the accumulated phase difference between the two arms is almost independent of wavelength, except for a steep variation that again corresponds to a steep refractive index change (moving from band to band).
  • the transmission spectra have two spectral domains, 1,525-1,550 nm and 1,580-1,615 nm, where the interference transmission is rather constant (line 147 in Fig. 14(c)) with ⁇ 14 dB transmission difference between the two domains (for high spatial resolution images, see Figures 6).
  • the total phase accumulation in the superlattices is zero.
  • a single-mode channel waveguide was used for the MZI reference arm. Owing at least in part to the large imbalance between the tapering slab and the channel waveguide, a series of high- visibility interference fringes can be observed at the output and used to determine the phase delay by analysing the fringe spectral locations and peak-to-peak free spectral range (FSR).
  • FSR peak-to-peak free spectral range
  • the taper length was designed to have a large number of fringes within the measurement window. With this approach the uncertainty of transmission and coupling losses (and the resulting normalization by the individual device transmissions) could be avoided when determining the phase differences between devices.
  • the MZI was modified so that when a SP was added to the superlattice, the length of the adiabatic transition arms was increased by ⁇ 2, making the horizontal single-mode channel waveguides shorter (from Z 2 to Z 2 - ⁇ 2), at both the input and output sides of the device arm in Fig. 12(a) (for a schematic illustration, see Fig. 3).
  • This change is compensated by adding the same length to the vertical part (from L3 to L3 + ⁇ 2 on both sides in Fig. 12(a)).
  • the only phase difference between devices is due to the additional SPs.
  • the phase difference between the waves propagating in the two arms of the MZI is given by
  • n sla b, n wg and n & ⁇ are the refractive indices of the tapering slab, the channel waveguide and the superlattice, respectively. These have different frequency dispersions, and therefore different functional dependence on the probed wavelength.
  • Z, sl and Z s i a b are the physical lengths of the superlattice and the tapering slab (total -850 ⁇ ).
  • FIG. 16(a) shows the FSR values for each of the devices examined— specifically, the spectral spacing between the transmission minima is calculated and the spectral spacing versus centre wavelength between the two neighbouring minima is plotted.
  • Figures 16(a)-(d) illustrate FSR spectral spacing between the transmission minima versus centre wavelength between the two neighbouring minima, extracted from the data in Figures 14(a)-(d).
  • phase difference is independent of the length of the superlattice (see also equation 2); this further proves that a zero phase difference is observed and not a multiple of 2 ⁇ .
  • n x ⁇ -njc « x 4.56 ⁇
  • n x A > uc « x 5.87 ⁇
  • the only possible solution is that the multiple is equal to zero.
  • both the FSR (Fig. 16(c),(d)) and absolute wavelength values (Fig. 15(c),(d)) overlap in the zero- n spectral domain, proving the zero phase variation across the superlattices.
  • One of the main properties of zero- n bandgaps is their remarkable robustness against effects induced by structural disorder.
  • Engineered control of the phase delay in these near-zero refractive index superlattices can be implemented in chip-scale transmission lines and interferometers with deterministic phase array and dispersion control and has significant technological potential in phase-insensitive image processing, phase-invariant fields for electromagnetic cloaking, lumped elements in optoelectronics, information processing, and engineering of radiation wavefronts to pre-designed shapes.
  • Numerical simulations The band diagram in Fig. 13(a) was calculated using RSoft's BandSOLVE, a commercially available software that implements a numerical method based on the plane wave expansion of the electromagnetic field. Three-dimensional simulations were performed to calculate 30 bands.
  • the photonic bands were divided into TM-like and TE-like, according to their parity symmetry.
  • the path-averaged index of the superlattice was calculated using the negative effective index of the second TM-like band and the effective modal index of the homogeneous asymmetric slab waveguide.
  • the transmission spectra were determined using MIT's MEEP49, a freely available code based on the finite-difference time-domain (FDTD) method. In all numerical simulations a uniform computational grid of 40 grid points per micrometer was used. This ensured that the smallest characteristic length of the system (e.g., the diameter of the holes) contained at least 10 grid points.
  • the transmission spectra corresponding to a specific geometry of the photonic superlattice were determined by normalizing the transmission spectrum of use photonic superlattice to the transmission spectrum of the homogeneous structure that was obtained by replacing the PhC regions with homogeneous slabs.
  • a typical simulation run on 64 Intel® Xeon processors was performed in ⁇ 7h.
  • a JEOL JBX6300FS electron-beam lithography system was used to expose the pattern, followed by development in amyl acetate for 90 s, and rinsing with isopropyl alcohol (IPA) for 45 s to completely remove the developer (amyl acetate) residue.
  • IPA isopropyl alcohol
  • an Oxford instruments Plasmalab 100 was used to perform cryogenic etching of the silicon 50 using an inductively coupled plasma reactive ion etcher (ICP-RIE).
  • ICP-RIE inductively coupled plasma reactive ion etcher
  • the wafer was placed in 1165 resist remover for ⁇ 4 h to completely remove the remainder of the resist.
  • the chip was cleaved and mounted on the sample holder for measurements.
  • An in-line fibre polarizer with a polarization controller was used to couple TE light from an amplified spontaneous emissions source (ranging from 1,520 nm to 1,620 nm) into the waveguide via a tapered lensed fibre.
  • a second tapered lensed fibre collected the transmission from the waveguide output, and the signal was sent to an optical spectrum analyser (OSA).
  • OSA optical spectrum analyser

Abstract

La présente invention porte sur une structure de cristal photonique comprenant un corps de base définissant une hétérostructure photonique comprenant des sections alternées ayant des trous de réseau et des sections excluant des trous de réseau, une première zone de Brillouin étant définie par une section ayant des trous de réseau, et une seconde zone de Brillouin étant définie par l'hétérostructure photonique.
PCT/US2012/058030 2011-09-30 2012-09-28 Modulateur de phase basse tension et filtres accordables WO2013049649A1 (fr)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060081171A1 (en) * 2003-06-19 2006-04-20 Yasushi Enokido Method for producing photonic crystal and photonic crystal
US20060119853A1 (en) * 2004-11-04 2006-06-08 Mesophotonics Limited Metal nano-void photonic crystal for enhanced raman spectroscopy
US20070172235A1 (en) * 2006-01-23 2007-07-26 Snider Gregory S Compute clusters employing photonic interconnections for transmitting optical signals between compute cluster nodes

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060081171A1 (en) * 2003-06-19 2006-04-20 Yasushi Enokido Method for producing photonic crystal and photonic crystal
US20060119853A1 (en) * 2004-11-04 2006-06-08 Mesophotonics Limited Metal nano-void photonic crystal for enhanced raman spectroscopy
US20070172235A1 (en) * 2006-01-23 2007-07-26 Snider Gregory S Compute clusters employing photonic interconnections for transmitting optical signals between compute cluster nodes

Non-Patent Citations (1)

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Title
KOCAMAN, S. ET AL.: "Zero phase delay in negative-refractive-index photonic crystal superlattices", NATURE PHOTONICS, vol. 5, 10 July 2011 (2011-07-10), pages 499 - 505 *

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