Patent Description:
Electromagnetic fields are commonly used in medicine for diagnosis and therapy. One emerging EMF technology that has potential medical applications is plasmonics.

Plasmonics is the study of the interaction between an electromagnetic field and free electrons in a metal. Most applications of plasmonics to date have relied on the interaction of light with the metallic structures, followed by detection of the light at the same wavelength that is reflected or scattered from the structures. For example, the optical excitation of surface plasmons in metal nanoparticles has led to the emerging field known as molecular plasmonics. Recent advances in molecular plasmonics and nanofabrication techniques have enabled novel optical materials and devices with applications in biology and nanomedicine.

<CIT>) describe a metal nanoantenna for use in biosensing, which is arranged to exhibit at least two particle plasmon resonances or surface plasmon resonances which allows the use in a sensor for detection of low concentration biological components. The nanoantenna in this invention can have an asymmetric structural configuration and spectrally separated resonances.

<CIT>) claim a method for measuring concentration of a biological substance contained in a living body in which deterioration of the accuracy due to the reflected light and the interruption component is suppressed. Linear-polarised light is emitted to a particle chip implemented in the skin, which generates a surface enhances Raman scattering light which changes the polarisation direction to obtain generate a signal.

<CIT>) describe an apparatus and methods for analysing single molecule and performing nucleic acid sequencing. The claimed apparatus contains an assay chip including multiple pixels with sample wells which are configured to receive a sample which emits emission energy upon excitement. The emitted emission energy is directed in a particular direction through a refractive lens.

While reducing the present invention to practice, the present inventor has discovered that surface plasmons and surface plasmon-polaritons collected from electromagnetic radiation reflected from biological materials (e.g., cells. tissues) can be used to identify and type the biological materials.

Thus, the present invention provides a system which is capable of identifying and typing biological material via plasmon/plasmon-polariton signature unique to the biological material.

According to one aspect of the present invention there is provided a system for identifying biological materials comprising (a) a coherent light source for irradiating the biological materials; (b) a device for collecting light waves reflected from the biological materials and transforming the light waves to propagating nanoplasmonic waves; and (c) a processing module for extracting phase and amplitude information from the nanoplasmonic waves to provide a plasmotic signature of the biological material, and for identifying the biological material by comparing the phase and amplitude information to a database of plasmonic signatures;.

According to further features in preferred embodiments of the invention described below, the coherent light source irradiates the biological sample with a light having a wavelength of <NUM> - <NUM>.

According to still further features in the described preferred embodiments the device includes one or more (e.g. an array) of plasmonic nanoantennas.

According to still further features in the described preferred embodiments the device further includes a plasmonic waveguide coupled to the at least one nanoantenna.

According to still further features in the described preferred embodiments the device includes a Silicon layer attached to Silicon Oxide layer.

According to still further features in the described preferred embodiments the nanoantenna is embedded within the Silicon Oxide layer.

According to still further features in the described preferred embodiments the nanoantenna is <NUM> X <NUM> X <NUM> in size.

According to still further features in the described preferred embodiments the nanoantenna is fabricated from Gold, Silver or Aluminum.

According to still further features in the described preferred embodiments the nanoantenna is coated with a <NUM> - <NUM> protective layer fabricated from a polymer.

According to still further features in the described preferred embodiments the waveguide is fabricated from a nanoplasmonic Metal - Insulator - Metal sandwich.

According to still further features in the described preferred embodiments the waveguide includes an insulative layer of air, Silicone oxide, a polymer or a ceramic.

According to still further features in the described preferred embodiments the phase and amplitude information is extracted at a spatial resolution of <NUM> - <NUM>.

According to still further features in the described preferred embodiments the system further includes a nano-metric phase shifter for controlling a phase of the light waves reflected from the biological material via electrostatic charging of the nanoantenna.

According to still further features in the described preferred embodiments the phase and amplitude information is utilized to sense and image the biological materials.

According to another aspect of the present invention there is provided a system for treating biological material comprising: (a) a light source for producing a coherent light beam; (b) a device for transforming the coherent light beam into nanoplasmonic waves; and projecting the nanoplasmonic waves onto the biological material thereby treating it.

According to still further features in the described preferred embodiments the nanoplasmonic waves are of a wavelength suitable for disrupting a cellular membrane.

According to another aspect of the present invention there is provided a method of identifying biological material comprising: (a) irradiating the biological material with coherent light; (b) collecting light waves reflected from the biological material and transforming the light waves to nanoplasmonic waves; and (c) extracting phase and amplitude information from the nanoplasmonic waves and identifying the biological material based on the phase and amplitude information.

According to still further features in the described preferred embodiments the coherent light has a wavelength of <NUM> - <NUM>.

According to still further features in the described preferred embodiments the phase and amplitude information is utilized to sense and image the biological material.

According to still further features in the described preferred embodiments (b) is effected by a device including a nanoantenna coupled with a plasmonic MIM waveguide.

According to another aspect of the present invention there is provided a system for treating tissue comprising (a) a device for irradiating the tissue with an electromagnetic signal; and (b) a plurality of a nanoantenna particles each being linked to a chemical moiety targeted to the tissue and each being capable of undergoing plasmonic excitation when exposed to the electromagnetic signal.

According to still further features in the described preferred embodiments each of the nanoantenna particles further includes an agent being activatable to destroy the tissue when the nanoantenna particles are plasmonically excited.

According to still further features in the described preferred embodiments the electromagnetic signal is IR laser, visible laser or white light.

Although methods and materials similar to those described herein can be used in the practice or testing of the present invention, suitable methods and materials are described below. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting.

The invention is herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only, and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the invention may be embodied in practice.

The present invention is of a system which can be used to identify, type and treat biological material. Specifically, embodiments of the present invention can be used to identify pathological tissue or cells in vitro, or in vivo.

The principles and operation of the present invention may be better understood with reference to the drawings and accompanying descriptions.

Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details set forth in the following description or exemplified by the Examples.

Use of plasmonics in medicine has been previously suggested. Studies have shown that surface plasmons emitted from metallic nanostructures can be used to enhance fluorescence of fluorophore [<NPL>)] or to potentially treat cancerous tissue targeted by the metallic nanostructures (<NPL>).

While experimenting with various antenna-waveguide devices for collection of surface plasmons and plasmon-polaritons, the present inventor has uncovered that nanoplasmonic interferometry, obtained at multiple Metal - Insulator - Metal (MIM) plasmonic waveguides can be used to type biological material such as molecules, cells and tissues.

As is described in the Examples section which follows, collection of surface plasmon-polaritons using multiple antenna-waveguide devices provides several advantages over surface plasmon resonance (SPR) detection approaches and greatly facilitates identification (presence/absence and location), typing and treatment of biological material such as molecules, cells and tissues.

The present system can be used for in-situ or in-vivo localization, qualification and quantitation of biological material related to pathologies (e.g. abnormal cells, plaques, pathological organisms such as bacteria, viruses and the like).

As is further described hereinunder, the present system is configured for establishing multiple plasmonic wave patterns that are sensitive to nano metric changes in a detected volume. The system includes a miniaturized optical wave source which illuminates a volume using safe, low power electromagnetic radiation. The volume-reflected beams are subsequently transformed to nanoplasmonic waves with a complex mode diffraction pattern. Such a diffraction pattern is characterized by phase and amplitude information with spatial resolution on the order of <NUM>-<NUM>. When a detectable object (e.g. cell or a molecular structure) is present in the irradiated volume, a change in the diffraction/wave pattern characteristic of the object is observed.

Thus, according to one aspect of the present invention there is provided a system for identifying biological material. The system can be used to detect, identify and quantitate any biological material in any setting (in-vitro, in-situ and in-vivo). Examples of biological material include normal and abnormal cells, and tissues.

The system of the present invention includes a coherent light source for irradiating a volume that includes a biological material. The light source can produce electromagnetic radiation which can penetrate the biological material to a depth of <NUM> - <NUM>. Examples of suitable light sources include He-Ne, Nd-Yag and preferably Er-Yag lasers, with preferable wavelengths at or near IR at milliwatt power levels. White light, or other broadband sources can also be used by the present invention but such light requires additional processing power.

The present system also includes a device which is capable of transforming the light waves reflected from the interrogated volume to nanoplasmonic waves. Such a device can be a Plasmonic chip, which includes an array of nano-metallic devices (antennas coupled to waveguides) fabricated on a standard silicon (Si) wafer. An example of such a device is described in greater detail hereinbelow with reference to <FIG>.

The present system also includes a digital signal processor running a dedicated algorithm for extracting phase and amplitude information from the nanoplasmonic waves and identifying the biological material based on the phase and amplitude information. The phase and amplitude information extracted by the present system provide a signature which is tissue unique.

The wavelength and phase, which characterize the plasmonic mode, change as a function of the tissue type. Since the resolution of the present system is high (e.g. <NUM>) the present plasmonic technology identifies cells as well as subcellular structures. Identification of a tissue (tissue typing) depends on data related to the prevalence and spatial arrangement of different cellular components within the referenced volume. For each tissue, a specific plasmonic wave is excited, enabling detection of different tissues by excitation of different plasmons. For example, each wave period (the distance between two adjacent peaks) represents different plasmonic wavelength (λ) (<FIG>). Therefore, specific peak distributions can be used to represent different types of tissues.

As is described in the Examples section, which follows, different tissues/cells exhibit different peak distributions, and each corresponds to a specific plasmonic wavelength. For example, a muscle cell exhibits effective plasmonic wavelength of about <NUM> while a tumor cell exhibits a wavelength of about <NUM>.

By 'training' the present system against different tissue types, a specific signature can be correlated with each specific tissue type.

Once the present system is 'trained', it will be capable of identifying tissues solely based on the plasmonic signature.

Referring now to the drawings, <FIG> illustrates one embodiment of the present system which is referred to herein as system <NUM>.

System <NUM> includes a coherent light source <NUM> which is configured for directing a light beam <NUM> having a wavelength of <NUM> - <NUM> onto a volume <NUM> including the biological material (e.g. liquid suspension of cells or a tissue sample). Light source <NUM> can be an Er-Yag laser. Light source <NUM> can be used to probe or scan the volume. The beam scanning, can be performed mechanically via scanning probe or it can be done electronically via 2D materials as Graphene plasmonics phase shifters.

System <NUM> also includes a device <NUM> for collecting light waves <NUM> reflected from volume <NUM> and biological material contained therein.

<FIG> illustrate one embodiment of device <NUM> which is configured as a nanoantenna-waveguide array.

Device <NUM> includes nanoantenna elements <NUM> (<FIG>) sandwiched between a silicon layer <NUM> and a silicon Oxide layer <NUM>. Any number of elements <NUM> can be used in device <NUM> (<NUM> shown). Other configurations can include mechanical miniaturized motors or micro-mirror arrangements.

Elements <NUM> can be fabricated from gold, silver or aluminum (or combinations thereof) and configured as rectangles <NUM> × <NUM> × <NUM> in size. Additional shapes can be bowties and Yagi structures.

Elements <NUM> can be arranged as pairs (as shown in Figure 2a) with a distance between pairs selected from a range of <NUM>-<NUM>.

Elements <NUM> can be omnidirectional or directional antennas depending on the application requirements and system implementation.

Elements <NUM> can be coated with a <NUM>-<NUM> protective layer fabricated from a metal such as silver or gold.

Elements <NUM> are connected to waveguides <NUM> (<FIG>) to form a nanoantenna-waveguide construct. Waveguides <NUM> are arranged perpendicularly to elements <NUM> (as shown in <FIG>) or at any angle between <NUM>-<NUM> degrees. Waveguides <NUM> can be fabricated from a Metal-Insulator-Metal sandwich (e.g. Au - Air - Au) and are preferably rectangular in shape with dimensions of <NUM> X <NUM> X <NUM>.

Waveguides <NUM> can include an insulative layer of air, silicone oxide, a polymer a ceramic or any type of dielectric material with positive relative permittivity.

Device <NUM> can also include a nano-metric phase shifter <NUM> (<FIG>) for controlling the phase of light waves reflected from the biological material via electrostatic charging. A specific plasmonic phase shifter can be implemented by using an engineered layer of Graphene under each nanoantenna, connected to a DC voltage source which facilitates the electrostatic charging upon voltage application.

The nanoantenna, schematically shown in <FIG>, is an engineered device including three closely spaced metallic (Gold) nanorods. Two identical nanorods of length LArm are separated by a nanoscopic gap (s = <NUM>). A third nanorod, is positioned closer to the dipole (g = <NUM>). Fabrication was performed via electron beam lithography (EBL), ion beam sputtering (Ag, <NUM>) and liftoff with optimized beam doses. <FIG> shows a high-resolution scanning electron microscopy (HR-SEM) image of a fabricated nanoantenna, recorded at beam current of <NUM> nA and low accelerating voltage of <NUM> kV, for sub-nanometer imaging resolution. Nanoantenna with demotions of LArm = <NUM>, LC = <NUM>, s = <NUM> and g = <NUM> was fabricated. Moreover, as shown in <FIG>, the nano-arms and director can be fabricated with different widths. High-resolution nano-optical images were recorded while the devices are illuminated by a He-Ne laser at wavelength of <NUM>.

<FIG> shows high-resolution nano-optical mapping of a nanoantenna, recorded at s set lift height of <NUM> using high aspect ratio uncoated Si AFM tip with diameter of <NUM>. The numerical results are obtained using High Frequency Structure Simulator (ANSYS HFSS V15) based on the finite element method (FEM). Generally, the electric field is described by a 3D vector E = (Ex, Ey, Ez), where each field component Ei is characterized by both magnitude |Ei| and phase φi41.

<FIG> shows the vertical near-field component Re(Ez) = |Ez|cos(φz) where |Ez| is the near-field amplitude and φz the phase. The Ez field distribution appears very similar to the Nano optical map (<FIG>), exhibiting identical spatial phase distribution. <FIG> and 3f show the Ex and Ey components (respectively) of the optical near fields.

Device <NUM> of system <NUM> functions as follows. Light reflected off the probed volume and biological material contained therein is converted by elements <NUM> (nanoantennas) to surface plasmons (SPs) and surface plasmon polaritons (SPPs) propagating at waveguide <NUM>. The phase and period of these SPs and SPPs are strongly dependent on the probed sample. A nano-metric phase shifter tunes the received radiation pattern of nanoantennas <NUM> to achieve maximum array gain.

System <NUM> further includes a processing unit <NUM> (<FIG>) for processing the light collected by device <NUM> and extracting the phase and amplitude information contained therein. The operation of processing unit <NUM> is summarized in the flow chart shown in <FIG>.

The plasmonic signature derived by processing unit <NUM> can then be compared to a database of plasmonic signatures correlated with tissue/cell types to identify the tissue/cell present in the probed/scanned volume.

System <NUM> of the present invention can be used for qualifying and quantifying biological material in sample or in-vivo and thus can be used in a variety of applications, including, but not limited to, identifying:.

The present invention also encompasses use of a plasmonic beam system for treating biological tissue. Thus, according to another aspect of the present invention, there is provided a system for treating biological material. The system includes a light source for producing a coherent light beam and a device for transforming the coherent light beam into nanoplasmonic waves and projecting the nanoplasmonic waves onto the biological material thereby treating it. A typical system setup for performing photo therapy (thermal or light) is illustrated in <FIG>.

A plasmonic photo-thermal therapy (PTT) system can include a nano-device (Typical dimensions of - 500nmX500nmX200nm) carrying nanoantennas (similar to those described above), that are chemically linked to targeting chemical moiety - a cell specific 'ligand' that is capable of binding to desired cells. For example, a nanoantenna array can be covalently linked to an antibody or antibody fragment capable of binding tumorous tissue or a cancer cell, a chemotherapeutic and/or radiosensitising agent such as mitomycin C or an amino acid sequence for targeting to a specific cell compartment (e.g. nucleus).

The nano device can further include any drug/prodrug for local drug release/activation upon plasmonic excitation or a resonant material (such as Au, Graphene, Al and Si) for increasing the plasmonic response of the nanoantenna array.

The nano-device is injected into a tissue, and diffuses to the specific tissue/cell targeted by the ligand. Upon illumination with a light source (e.g. near IR laser, visible laser or a white light source), plasmonic resonance at the nanoantenna releases/activates the drug at the targeted cells or alternatively, the plasmonic resonance is amplified by the resonant material to generate a localized hot spot which thermally destroys the targeted cells.

Photodynamic therapy (PDT) is a similar approach which utilizes light instead of heat for treatment. This approach requires the use of a chemical compound - also known as photosensitizer - with a particular type of light to kill cancer cells. The photosensitizer in the tumor absorbs the light and generates reactive oxygen species (ROS) - such as hydroxyl radical, singlet oxygen, as well as peroxides - that destroy nearby cancer cells.

The present system can be embedded into a medical catheter and used as a tissue sensor in theranostics (diagnostic + therapeutic) applications. Such a catheter can further include a therapeutic unit for treating tissue via, for example, mechanical (cutting), thermal (RF ablation), cryogenic or photoactivation (e.g. PDT) modalities. Alternatively, system <NUM> can also be configured to also provide a therapeutic signal as is described hereinabove.

<FIG> illustrates one embodiment of a catheter <NUM> which includes a system <NUM> sensor. System <NUM> is fabricated on a silicon chip which is integrated into catheter <NUM> at a working tip <NUM>. Silicon waveguides <NUM> are used for on-chip signal collection and communication as is described hereinabove. Optical signals obtained from the tissue are communicated to an extracorporeal unit <NUM> via optical fiber <NUM>. The optical signal collected by system <NUM> is processed by extracorporeal unit <NUM> to identify cells of interest (e.g. malignant cells) in a tissue region scanned. Extracorporeal unit <NUM> can then guide the therapeutic unit to specifically treat such cells.

The nanoantennas of system <NUM> can be fabricated on a nanometric layer of a chemical substrate (for example on a water-soluble polymer such as vinyl alcohol polymer) which is delivered into the body. The formed nanoantennas can be released from the substrate at the site of treatment when exposed to physiological conditions (fluid, pH etc), physical pressure (exposure to ultrasound) and the like. When the nanoantennas of system <NUM> are released from the substrate they bind the targeted cell at maximum resolution of ~<NUM>, governed by the chemical ligand and device dimensions.

Additional objects, advantages, and novel features of the present invention will become apparent to one ordinarily skilled in the art upon examination of the following examples, which are not intended to be limiting.

Reference is now made to the following examples, which together with the above descriptions, illustrate the invention in a non limiting fashion.

A <NUM> weeks old male mouse (C57B) was euthanized by overdose anesthetics. A variety of tissues were collected including: striated muscle, cardiac muscle, adipose tissue (retroperitoneal fat), liver, spleen, lung, adrenal, kidney. Each tissue was kept in a separate tube over ice water until analyzed. Tissue characterization for each sample was done at least twice (collected from separate mice).

Two lines of human melanoma cells (Mel526, MEL624) (P <NUM>-<NUM>), and human keratinocyte cells (P <NUM>-<NUM>), representative of normal skin cells were cultured. The cell cultures were trypsinized, centrifuged at 3000RPM, and the pellet was used for analysis.

A mouse from a melanoma model generated by using the RET proto-oncogene was euthanized and a subcutaneous lesion was excised from the mouse's back, kept in a tube over ice water until analysis. MM cells were identified within the analyzed tissue, well discriminated from the other cells and medium which occupied the bolus.

A commercially available scanning near field optical microscope (SNOM) was utilized for scanning the samples and to collect the reflected plasmonic waves. During each step, the plasmonic mode characteristics were extracted using spatial Fourier transform (s-FFT) and the plasmonic waveguide dispersion properties to create a plasmonic image. The intensity map of the image represents the amplitude of the plasmonic wave.

The results for the various mouse tissue examined are shown in <FIG>. The plasmonic waves at the center of the MIM waveguides as a function of the distance from the nanoantenna (L) are presented, with the wave amplitude is normalized to 0dB. Different phase and plasmonic wavelength are observed for each examined tissue, enabling to differentiate different materials/signatures.

Cultured human metastatic melanoma (MM) cells from both lines (Mel526. MEL624) yielded identical plasmonic characteristics. The human MM cell is represented by a plasmonic wavelength of <NUM> (horizontal axis at the graph of <FIG>). The peak which represents the MM tissue (L=<NUM>) is <NUM>. 5dB higher compared with medium only. Thus, MM cells have a plasmonic signature at L=<NUM>, which is <NUM>. 5dB higher compared to the medium at the background (<FIG>). Experiments were also performed on pellets including a mixture of MM cells and human skin keratinocytes (ratio <NUM>:<NUM>) and MM cells and human skin keratocytes were identified based on their plasmonic signature (Keratinocyte signature shown in <FIG>). Using the plasmonic information obtained for MM cells and keratocytes enables identification of these cell types in any sample by using, for example, spatial scanning approaches.

The MM regions in an engineered mouse were mapped based on the plasmonic signature obtained from human MM cells. <FIG> presents the results of plasmonic analysis of mouse MM tumor cells based on Human MM cells plasmonic data. The bright regions of this intensity map represent mouse MM cells while dark regions represent lack of mouse MM cells.

<FIG> illustrates the plasmonic peak obtained from a sample containing mouse MM tumor cells mixed with mouse skin cells. The peak which represents the MM tissue (L=<NUM>) is 15dB higher compared with skin cells.

The results presented above suggested that melanosomes are cell components responsible for the unique plasmonic signature of MM cell. Melanosomes in human MM cell culture were tagged with a fluorescent marker (Bruder et al. Melanosomal Dynamics Assessed with a Live-Cell Fluorescent Melanosomal Marker.

<NPL>) in order to ascertain their role in generating the plasmonic signature obtained herein. MM cells from both cell cultures were assessed, including cells with tagged and untagged melanosomes.

NUDE mice, <NUM> weeks old females were supplied by Harlan - Envigo, Israel. Human melanoma cells (Mel <NUM>), at dose of 3x106 cells were injected subcutaneously. MM tumors were palpable after <NUM> weeks, and were excised surgically, as well as samples of normal skin.

<FIG> illustrate the results obtained using the plasmonic approach of the present invention.

Several additional plasmonic thumb printing of Human Melanoma cells were obtained in lab experiments, with the cells suspended in medium in a petri dish. The samples were illuminated by an unfocused coherent He - Ne laser and the reflected light was collected and converted to plasmon polaritons by the nanoantenna. The Plasmonic Thumb Printing (profile) of a specific cell type was extracted after removal of the host-material effect. Samples of Human MM cells suspended in medium were tested as shown in <FIG>. The analysis included two types of cell, with the first being an untreated Human MM Cells and the second is characterized by addition of phosphorous marking material attached to the cells' melanosomes. As observed, the two MM cell configurations exhibit distinguishable plasmonic signatures, thus providing further confirmation to the proficiency of the proposed system to distinguish nanoscale material and structural changes. <FIG> shows plasmonic imaging of human MM cells grown as a tumor in a NUDE mouse, obtained by post processing the plasmon signatures obtained by the proposed invention. The figure is obtained via similar process to <FIG>. The bright patterns represent the areas within the tested mouse, for which the signature correlation with isolated MM cells is higher than <NUM>%. This imaging mechanism forms the basis for plasmon - correlation based imaging with sub diffraction optical resolution. <FIG> shows the specific plasmonic thumb printing of a human MM (A line) and a mouse skin (B line) cells on the same chart. The figure is obtained via similar process to <FIG>. Similar to previous experiments detailed herein (<FIG>), the plasmonic signature of the MM Cell exhibits different signature compared with that of regular skin cells, with less fluctuating character and a significant peak for plasmon wavelength of <NUM>.

Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination.

Claim 1:
A system (<NUM>) for identifying biological material comprising:
(a) a coherent light source (<NUM>) for irradiating the biological material;
(b) a device (<NUM>) for collecting light waves reflected from the biological material and transforming said light waves to nanoplasmonic waves; and
(c) a processing module (<NUM>) for extracting phase and amplitude information from said nanoplasmonic waves to provide a plasmonic signature of the biological material, and for identifying the biological material by comparing said phase and amplitude information to a database of plasmonic signatures;
wherein the biological material is selected from the group consisting of tissues, cells, subcellular structures and plaques;
and wherein said device comprises at least one nanoantenna coupled with at least one plasmonic waveguide (<NUM>).