Slot Effect Meaning

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A slot-waveguide is an optical waveguide that guides strongly confined light in a subwavelength-scale low refractive index region by total internal reflection.

A slot-waveguide consists of two strips or slabs of high-refractive-index (nH) materials separated by a subwavelength-scale low-refractive-index (nS) slot region and surrounded by low-refractive-index (nC) cladding materials.

Schematic 2D slot-waveguide. Light propagates in the z-direction
Schematic 3D slot-waveguide. Light propagates in the z-direction

Principle of operation[edit]

The principle of operation of a slot-waveguide is based on the discontinuity of the electric field (E-field) at high-refractive-index-contrast interfaces. Maxwell’s equations state that, to satisfy the continuity of the normal component of the electric displacement fieldD at an interface, the corresponding E-field must undergo a discontinuity with higher amplitude in the low-refractive-index side. That is, at an interface between two regions of dielectric constants εS and εH, respectively:

DSN=DHN
εSESN=εHEHN
nS2ESN=nH2EHN

where the superscript N indicates the normal components of D and E vector fields. Thus, if nS<<nH, then ESN>>EHN.

E-field profile of a 2D slot-waveguide. E-vector is parallel to the y-axis
E-field distribution of a 3D slot-waveguide. Major E-field component is parallel to the x-axis

Given that the slot critical dimension (distance between the high-index slabs or strips) is comparable to the exponential decay length of the fundamental eigenmode of the guided-wave structure, the resulting E-field normal to the high-index-contrast interfaces is enhanced in the slot and remains high across it. The power density in the slot is much higher than that in the high-index regions. Since wave propagation is due to total internal reflection, there is no interference effect involved and the slot-structure exhibits very low wavelength sensitivity.[1]

Invention[edit]

The slot-waveguide was born in 2003 as an unexpected outcome of theoretical studies on metal-oxide-semiconductor (MOS) electro-opticmodulation in high-confinement silicon photonic waveguides by Vilson Rosa de Almeida and Carlos Angulo Barrios, then a Ph.D. student and a Postdoctoral Associate, respectively, at Cornell University. Theoretical analysis [1] and experimental demonstration [2] of the first slot-waveguide implemented in the Si/SiO2 material system at 1.55 μm operation wavelength were reported by Cornell researchers in 2004.

Since these pioneering works, several guided-wave configurations based on the slot-waveguide concept have been proposed and demonstrated. Relevant examples are the following:

In 2005, researchers at the Massachusetts Institute of Technology proposed to use multiple slot regions in the same guided-wave structure (multi-slot waveguide) in order to increase the optical field in the low-refractive-index regions.[3] The experimental demonstration of such multiple slot waveguide in a horizontal configuration was first published in 2007.[4]

In 2006, the slot-waveguide approach was extended to the terahertz frequency band by researchers at RWTH Aachen University.[5] Researchers at the California Institute of Technology also demonstrated that a slot waveguide, in combination with nonlinear electrooptic polymers, could be used to build ring modulators with exceptionally high tunability.[6] Later this same principle enabled Baehr-Jones et al. to demonstrate a mach-zehnder modulator with an exceptionally low drive voltage of 0.25 V[7][8]

In 2007, a non-planar implementation of the slot-waveguide principle of operation was demonstrated by researchers at the University of Bath. They showed concentration of optical energy within a subwavelength-scale air hole running down the length of a photonic-crystal fiber.[9]

Recently, in 2016, it is shown [10] that slots in a pair of waveguides if off-shifted away from each other can enhance the coupling coefficient even more than 100% if optimized properly, and thus the effective power coupling length between the waveguides can significantly be reduced. Hybrid slot (having vertical slot in one waveguide and horizontal slot in the other) assisted polarization beam splitter is also numerically demonstrated. Though, the losses are high for such slot structures, this scheme exploiting the asymmetric slots may have potential to design very compact optical directional couplers and polarization beam splitters for on-chip integrated optical devices.

The slot waveguide bend is another structure essential to the waveguide design of several Integrated micro- and nano-optics devices. One of the benefits of waveguide bends is the reduction of the footprint size of the device. There are two approaches based on the similarity of Si rails width to form the sharp bend in slot waveguide, which are the symmetric and asymmetric slot waveguides [11].

Fabrication[edit]

Planar slot-waveguides have been fabricated in different material systems such as Si/SiO2[2][12][13] and Si3N4/SiO2.[14] Both vertical (slot plane is normal to the substrate plane) and horizontal (slot plane is parallel to the substrate plane) configurations have been implemented by using conventional micro- and nano-fabrication techniques. These processing tools include electron beam lithography, photolithography, chemical vapour deposition [usually low-pressure chemical vapour deposition (LPCVD) or plasma enhanced chemical vapour deposition (PECVD)], thermal oxidation, reactive-ion etching and focused ion beam.

In vertical slot-waveguides, the slot and strips widths are defined by electron- or photo-lithography and dry etching techniques whereas in horizontal slot-waveguides the slot and strips thicknesses are defined by a thin-film deposition technique or thermal oxidation. Thin film deposition or oxidation provides better control of the layers dimensions and smoother interfaces between the high-index-contrast materials than lithography and dry etching techniques. This makes horizontal slot-waveguides less sensitive to scattering optical losses due to interface roughness than vertical configurations.

Fabrication of a non-planar (fiber-based) slot-waveguide configuration has also been demonstrated by means of conventional microstructured optical fiber technology.[9]

Applications[edit]

A slot-waveguide produces high E-field amplitude, optical power, and optical intensity in low-index materials at levels that cannot be achieved with conventional waveguides. This property allows highly efficient interaction between fields and active materials, which may lead to all-optical switching,[15]optical amplification[16][17] and optical detection [6] on integrated photonics. Strong E-field confinement can be localized in a nanometer-scale low-index region. As firstly pointed out in,[1] the slot waveguide can be used to greatly increase the sensitivity of compact optical sensing devices [18][19][20][21][22][23][24] or to enhance the efficiency of near-field optics probes.At Terahertz frequencies, slot waveguide based splitter has been designed which allows for low loss propagation of Terahertz waves. The device acts as a splitter through which maximum throughput can be achieved by adjusting the arm length ratio of the input to the output side.[25]

References[edit]

  1. ^ abcAlmeida, Vilson R.; Xu, Qianfan; Barrios, Carlos A.; Lipson, Michal (2004-06-01). 'Guiding and confining light in void nanostructure'. Optics Letters. The Optical Society. 29 (11): 1209–11. doi:10.1364/ol.29.001209. ISSN0146-9592. PMID15209249.
  2. ^ abXu, Qianfan; Almeida, Vilson R.; Panepucci, Roberto R.; Lipson, Michal (2004-07-15). 'Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material'. Optics Letters. The Optical Society. 29 (14): 1626–8. doi:10.1364/ol.29.001626. ISSN0146-9592. PMID15309840.
  3. ^Feng, N.-N.; Michel, J.; Kimerling, L.C. (2006). 'Optical Field Concentration in Low-Index Waveguides'. IEEE Journal of Quantum Electronics. Institute of Electrical and Electronics Engineers (IEEE). 42 (9): 883–888. doi:10.1109/jqe.2006.880061. ISSN0018-9197. S2CID46700811.
  4. ^Sun, Rong; Dong, Po; Feng, Ning-ning; Hong, Ching-yin; Michel, Jurgen; Lipson, Michal; Kimerling, Lionel (2007). 'Horizontal single and multiple slot waveguides: optical transmission at λ = 1550 nm'. Optics Express. The Optical Society. 15 (26): 17967–72. doi:10.1364/oe.15.017967. ISSN1094-4087. PMID19551093.
  5. ^Nagel, Michael; Marchewka, Astrid; Kurz, Heinrich (2006). 'Low-index discontinuity terahertz waveguides'. Optics Express. The Optical Society. 14 (21): 9944–54. doi:10.1364/oe.14.009944. ISSN1094-4087. PMID19529388.
  6. ^ abBaehr-Jones, T.; Hochberg, M.; Wang, Guangxi; Lawson, R.; Liao, Y.; Sullivan, P. A.; Dalton, L.; Jen, A. K.-Y.; Scherer, A. (2005). 'Optical modulation and detection in slotted Silicon waveguides'. Optics Express. The Optical Society. 13 (14): 5216–26. doi:10.1364/opex.13.005216. ISSN1094-4087. PMID19498512.
  7. ^Baehr-Jones, Tom; Penkov, Boyan; Huang, Jingqing; Sullivan, Phil; Davies, Joshua; et al. (2008-04-21). 'Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25V'. Applied Physics Letters. AIP Publishing. 92 (16): 163303. doi:10.1063/1.2909656. ISSN0003-6951.
  8. ^Witzens, Jeremy; Baehr-Jones, Thomas; Hochberg, Michael (2010-07-26). 'Design of transmission line driven slot waveguideMach-Zehnder interferometers and application to analog optical links'. Optics Express. The Optical Society. 18 (16): 16902–28. doi:10.1364/oe.18.016902. ISSN1094-4087. PMID20721082.
  9. ^ abWiederhecker, G. S.; Cordeiro, C. M. B.; Couny, F.; Benabid, F.; Maier, S. A.; et al. (2007). 'Field enhancement within an optical fibre with a subwavelength air core'. Nature Photonics. Springer Science and Business Media LLC. 1 (2): 115–118. doi:10.1038/nphoton.2006.81. ISSN1749-4885.
  10. ^Haldar, Raktim; Mishra, V; Dutt, Avik; Varshney, Shailendra K (2016-09-09). 'On-chip broadband ultra-compact optical couplers and polarization splitters based on off-centered and non-symmetric slotted Si-wire waveguides'. Journal of Optics. IOP Publishing. 18 (10): 105801. doi:10.1088/2040-8978/18/10/105801. ISSN2040-8978.
  11. ^Al-Tarawni, Musab A. M.; Bakar, A. Ashrif A.; Zain, Ahmad Rifqi Md.; Tarawneh, Mou’ad A.; Ahmad, Sahrim Hj. (2019-02-08). 'Enhancing the performance of strip and 180-deg slot waveguide bends for integrated optical waveguide modulator'. Optical Engineering. SPIE-Intl Soc Optical Eng. 58 (2): 027104. doi:10.1117/1.oe.58.2.027104. ISSN0091-3286. S2CID126965871.
  12. ^Baehr-Jones, Tom; Hochberg, Michael; Walker, Chris; Scherer, Axel (2005-02-21). 'High-Q optical resonators in silicon-on-insulator-based slot waveguides'. Applied Physics Letters. AIP Publishing. 86 (8): 081101. doi:10.1063/1.1871360. ISSN0003-6951.
  13. ^Schrauwen J., Van Lysebettens J., Vanhoutte M., Van Thourhout D. et al., 'Iodine enhanced focused ion beam etching of silicon for photonic device modification and prototyping (2008)', International Workshop on FIB for Photonics, 1st, Proceedings (2008)
  14. ^Barrios, C. A.; Sánchez, B.; Gylfason, K. B.; Griol, A.; Sohlström, H.; Holgado, M.; Casquel, R. (2007). 'Demonstration of slot-waveguide structures on silicon nitride / silicon oxide platform'. Optics Express. The Optical Society. 15 (11): 6846–56. doi:10.1364/oe.15.006846. ISSN1094-4087. PMID19546997.
  15. ^Barrios, C.A. (2004). 'High-performance all-optical silicon microswitch'. Electronics Letters. Institution of Engineering and Technology (IET). 40 (14): 862-863. doi:10.1049/el:20045179. ISSN0013-5194.
  16. ^Barrios, Carlos Angulo; Lipson, Michal (2005). 'Electrically driven silicon resonant light emitting device based on slot-waveguide'. Optics Express. The Optical Society. 13 (25): 10092–101. doi:10.1364/opex.13.010092. ISSN1094-4087. PMID19503222.
  17. ^A. Armaroli, A. Morand, P. Benech, G. Bellanca, S. Trillo, 'Comparative Analysis of a Planar Slotted Microdisk Resonator,' Lightwave Technology, Journal of , vol.27, no.18, pp.4009,4016, Sept.15, 2009
  18. ^Barrios, Carlos Angulo (2006). 'Ultrasensitive Nanomechanical Photonic Sensor Based on Horizontal Slot-Waveguide Resonator'. IEEE Photonics Technology Letters. Institute of Electrical and Electronics Engineers (IEEE). 18 (22): 2419–2421. doi:10.1109/lpt.2006.886824. ISSN1041-1135. S2CID32069322.
  19. ^Barrios, Carlos A.; Gylfason, Kristinn B.; Sánchez, Benito; Griol, Amadeu; Sohlström, H.; Holgado, M.; Casquel, R. (2007-10-17). 'Slot-waveguide biochemical sensor'. Optics Letters. The Optical Society. 32 (21): 3080–2. doi:10.1364/ol.32.003080. ISSN0146-9592. PMID17975603.
  20. ^Dell'Olio, Francesco; Passaro, Vittorio M. (2007). 'Optical sensing by optimized silicon slot waveguides'. Optics Express. The Optical Society. 15 (8): 4977–93. doi:10.1364/oe.15.004977. ISSN1094-4087. PMID19532747.
  21. ^Barrios, Carlos A.; Bañuls, María José; González-Pedro, Victoria; Gylfason, Kristinn B.; Sánchez, Benito; et al. (2008-03-28). 'Label-free optical biosensing with slot-waveguides'. Optics Letters. The Optical Society. 33 (7): 708–10. doi:10.1364/ol.33.000708. ISSN0146-9592. PMID18382525.
  22. ^Robinson, Jacob T.; Chen, Long; Lipson, Michal (2008-03-13). 'On-chip gas detection in silicon optical microcavities'. Optics Express. The Optical Society. 16 (6): 4296–301. doi:10.1364/oe.16.004296. ISSN1094-4087. PMID18542525.
  23. ^Witzens, Jeremy; Hochberg, Michael (2011-03-29). 'Optical detection of target molecule induced aggregation of nanoparticles by means of high-Q resonators'. Optics Express. The Optical Society. 19 (8): 7034–61. doi:10.1364/oe.19.007034. ISSN1094-4087. PMID21503017.
  24. ^Ghosh, Souvik; Rahman, B. M. A. (2017). 'An Innovative Straight Resonator Incorporating a Vertical Slot as an Efficient Bio-Chemical Sensor'(PDF). IEEE Journal of Selected Topics in Quantum Electronics. Institute of Electrical and Electronics Engineers (IEEE). 23 (2): 132–139. doi:10.1109/jstqe.2016.2630299. ISSN1077-260X. S2CID10903140.
  25. ^Pandey, Shashank; Kumar, Gagan; Nahata, Ajay (2010-10-22). 'Slot waveguide-based splitters for broadband terahertz radiation'. Optics Express. The Optical Society. 18 (22): 23466–71. doi:10.1364/oe.18.023466. ISSN1094-4087. PMID21164689.
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This information applies to the American Steel Industry.

Holes and Slots

Standard Holes

Standard hole sizes for bolts are made 1/16-in. larger in diameter than the nominal size of the fastener body. This provides a certain amount of play in the holes, which compensates for small misalignment’s in hole location or assembly, and aids in the shop and field entry of fasteners. In the absence of approval by the engineer for use of other hole types, standard holes shall be used in high strength bolted connections.

Slot Effect Meaning Definition

Although most holes for high-strength bolts are made 1/16-in. larger in diameter than the bolt body, certain conditions encountered in field erection require greater adjustment than this clearance can provide and approval from the engineer is required.

Slot effect meaning synonyms

The maximum sizes of holes for bolts are given in the table below, except that larger holes, required for tolerance on location of anchor bolts in concrete foundations, are permitted in column base details.

Standard holes shall be provided in member-to-member connections, unless oversized, short-slotted or long-slotted holes in bolted connections are approved by the designer. Finger shims up to 1/4-in. may be introduced into slip-critical connections designed on the basis of standard holes without reducing the allowable shear stress of the fastener.

Oversize and Slotted Holes

When approved by the engineer, oversize, short slotted holes or long slotted holes may be used subject to the following joint detail requirements:

(1) Oversize holes may be used in any or all plies of connections in which the allowable slip resistance of the connection is greater than the applied load. Oversized holes shall not be used in bearing-type connections. Hardened washers shall be installed over oversized holes in an outer ply.

(2) Short slotted holes may be used in any or all plies of connections designed on the basis of allowable stress on the fasteners provided the load is applied approximately normal (between 80 and 100 degrees) to the axis of the slot. Short slotted holes may be used without regard for the direction of applied load in any or all plies of connections in which the allowable slip resistance is greater than the applied force. Washers shall be installed over short-slotted holes in an outer ply; when high strength bolts are used, such washers shall be hardened.

(3) Long slotted holes may be used in one of the connected parts at any individual faying surface in connections designed on the basis of allowable stress on the fasteners provided the load is applied approximately normal (between 80 and 100 degrees) to the axis of the slot. Long slotted holes may be used in one of the connected parts at any individual faying surface without regard for the direction of applied load on connections in which the allowable slip resistance is greater than the applied force. Where long-slotted holes are used in an outer ply, plate washers or a continuous bar with standard holes, having a size sufficient to completely cover the slot after installation, shall be provided. In high-strength bolted connections, such plate washers or continuous bars shall not be less than 5/16-in. thick and shall be of structural grade material, but not be hardened. If hardened washers are required for use of high-strength bolts, the hardened washers shall be placed over the outer surface of the plate washer or bar.

Slot Effect Meaning Synonym

(4) Fully inserted finger shims between the faying surfaces of load transmitting elements of connections are not to be considered a long slot element of a connection.

Nominal Hole Dimensions

Anchor Bolt Holes

Meaning

Hole sizes for steel-to-steel structural connections are not the same as hole sizes for steel-to-concrete anchorage applications. In the case of steel-to-steel connections, the parts are made in a shop under good quality control, so standard holes (bolt diameter plus 1/16″), oversized holes (bolt diameter plus 3/16″), and short and long-slotted holes can be used quite successfully. However, the field placement of anchorage devices has long been subject to more permissive tolerances (and often, inaccuracies that exceed those tolerances anyway and may require consideration by the structural Engineer of Record).

AISC published Steel Design Guide Series 1, Column Base Plates back in the early 1990s. At that time, it was recognized that the quality of foundation work was getting worse and worse. To allow the erector (and designer) greater latitude when possible, the permissible hole sizes in base plates were increased. These same larger hole sizes were included in the 2nd ed. LRFD Manual. The values there are maximums, not a required size. Smaller holes can be used if desired. Plate washers are generally required with these holes because ASTM F436 washers can collapse into the larger-sized holes, even under erection loads.

The larger hole sizes are primarily intended for the majority of base plates that transfer only axial compression from the column into the foundation. The anchor rods don’t usually do much after erection in that case.

Slot Effect Definition

To allow for misplaced bolts, holes in base plates are oversized. The AISC Manual of Steel Construction recommends the following oversized hole diameters for each bolt diameter:

Anchor Bolt Hole Dimensions

AISC, Steel Design Guide Series 1, Column Base Plates, suggests that using oversize holes meeting these criteria may still not accommodate field variations in anchor bolt placement and suggests adding 1/4 in. to the hole diameter listed. The guide recommends using a heavy plate washer over the holes. The AISC Structural Steel Educational Council cites the following example: “If bolts are misplaced up to 1/2 inch, the oversized base plate holes normally allow the base plate and column to be placed near or on the column line. If the bolts are misplaced by more than 1/2 inch, then corrective work is required.”

Based on AISC oversize holes, the AISC Structural Steel Educational Council recommendations, and concrete contractor anchor-bolt placement techniques, ASCC (American Society of Concrete Contractors) concrete contractors recommend the following tolerance for each bolt location:

  • 3/4-in. and 7/8-in. diameter bolts: ±1/4 in.
  • 1-in., 1-1/4-in., and 1-1/2-in. diameter bolts: ±3/8 in.
  • 1-3/4-in., 2-in., and 2-1/2-in. diameter bolts: ±1/2 in.

Slot Effect Meaning Dictionary

End of article.