Stable optical frequency reference has been studied for decades [90, 91] and has revo- lutionized many application areas such as communication, time keeping, low noise mi- crowave generation, and basic science[26, 92, 93]. Such optical frequency references ben- efit from high optical Q factor or equivalently long optical storage time. Fabry-Perot cavi- ties [94, 95, 96], absorption spectral-hole burning in cryogenically cooled crystals [97, 98], and long-delay-line interferometers [99, 100] are examples of such stable optical reference systems. Allan deviation (i.e. fractional frequency instability, which is a standard measure of frequency stability) of 1x10 −16 at 1 s averaging  has been attained from the state- of-the-art Fabry-Perot optical cavities. In these systems, a narrow resonator line for laser locking is created by high-finesse-mirrors and the resonance frequency is immune to ther- mal fluctuations by using low-thermal-expansion housings and low-thermal-noise mirror coating [95, 94, 96, 101, 102]. However, these optical frequency reference systems remain as laboratory systems, because they are rather bulky and sometimes use cryogenic systems. While pursuing the ultimate stabiltiy, there has been a continuing need for portable optical frequency references. Bench-top or rack-mount optical frequency systems with Hz- level linewidth is developed by miniaturizing Fabry-Perot optical cavity[103, 104]. Besides miniaturization of conventional Fabry-Perot optical cavity, attention has naturally turned towards miniature devices such as ultra-high optical-Q, solid-state resonator systems based on silica [105, 106, 107] and crystalline fluoride materials [108, 109, 110]. Besides the compact size of these devices, their reduced mass can offer improved performance with respect to shock and acceleration. Some systems are chip-based and there is the possibility of integration with other components. These compact solid-state microresonators are also demonstrated as optical reference cavities [111, 112, 113].
Nonlinearoptics (NLO) can potentially overcome this limitation. At high field strengths nonlinear contributions become significant allowing nonlinear optical techniques to be used, for example second-harmonic generation (SHG) or sum-frequency generation (SFG). Compared to linear techniques, NLO techniques exhibit richer selection rules due to the higher-order tensors involved.  Because of the lower symmetry of interfaces, NLO and particularly SHG may be used as interface-specific probes. Buried interfaces are still accessible provided that light penetrates the overlayers. In the dipole approximation the media symmetry can make certain techniques interface (SHG, FHG) or bulk (THG) specific. SHG theory was nominally well developed in 1960s and 1970s. [8, 7, 9] However, weak signals, typically one second-harmonic photon per 10 13 − 10 17 incident photons, pre-
S eU m eier e q u a tio n s a n d th e r m a l d e p e n d e n c e o f p rin c ip a l re fra c tiv e in d ices In early times, a set of Sellmier ecpiations was m easured by Chen et a/., using the least angle deflection m ethod, they m easured the three principal refractive indices at 16 wavelengths from A =1.064 fim to A=0.2537 //,m, but the crystal tem perature was not men tioned. Shortly thereafter, a num ber of Sellmeier equations for LBO were published, and those can be seen in Refs. [43, 42, 44]. Among them , the Sellmeier equations published by Chen, and by Kato have been regarded as being in good agreem ent with exper im ental results. In particular for short wavelength generation (>240 nm ), the Sellmeier equations presented by K ato gives m ore accurate predictions th an others. To have a set of Sellmeier equations suitable for the deep uv spectral region, Chen et <il. have m ade further modifications based on their sum-frequency mixing experim ents down to the shortest wavelength of 187.7 nm. In our work, we have adopted th e Sellmeier equations given in Ref. through all of the phase-m atching calculations.
expressions are used to obtain the observed harmonic fields. Another method is the Green-function approach, where the NLO problem is solved using the classical E&M Green-function formalism in terms of s- and p- polarized vector waves. This leads to generated fields written as functions of the Fresnel coefficients of the interfaces . The polarizable bond model calculates SHG in terms of the energy resonances associated with the linear response , and in fact picks up only part of the total response, the quadrupole contribution. Other methods such as quantum-mechanical evaluation of polarizabilities from band structure, and simple listings of Fourier coefficients of intensity anisotropies observed as the sample is rotated during exposure to a fixed wavelength, are also used in some applications.
Hollow-core fiber is a versatile medium for the optical light transmission. Hollow core and large mode area result in exceptional transmission properties that allow a large number of applications in linear optics, despite multimode guidance. Telecommunication system: hollow-core fibers guide light mostly in air, so that light propagation experiences smaller nonlinearity and GVD. These features are useful for delivering data accurately over a long distance. The unique advantages of hollow-core fibers are perfectly suitable for high-speed data transmission system. Information transmission through the air leads to the lowest time of delay. As the light propagates faster in the air than any medium, therefore reducing the latency substantially which makes the hollow-core fiber a strong candidate for use in telecommunication systems [15, 39].
that exhibit both extremely low linear and, perhaps more importantly, low nonlinear optical loss 173,174 ). Although Hydex – similar to silicon oxynitride – has a lower nonlinearity than silicon, very high Q ring resonators can be achieved (> 10 6 ), which greatly enhances the SFWM 98,175,176 . The emission of pairs for heralded single-photon sources was demonstrated over a 200 GHz multifrequency comb compatible with the ITU frequency grid for dense wavelength division multiplexed optical networks 97 . This would allow the transmission of quantum states over fibre-optic networks, as well as the use of standard telecom filters to route the different wavelengths and deterministically separate signal and idler photons. The high Q factor yielded photon pairs with narrow linewidths – compatible with quantum memories (~150 MHz). Very recently , the emission of entangled photons was also reported, with the multifrequency nature of the emitted signal idler pairs being exploited to enable an on-chip source of four-photon time-bin entangled states 92 (Fig. 5). In moderate refractive index materials such as Hydex, fibre-to-chip coupling can be extremely efficient; this coupling has allowed the use of self-pumping techniques with optical amplifiers to avoid the need for expensive external tuneable lasers, which is important for practical applications 97,177 . Advanced time-bin entanglement circuits have also been reported in ultralow-loss
Optical microcavities confine light to small mode volume due to resonant recirculation . In whispering-gallery-mode (WGM) optical microcavities, light circulates around the boundary of a dielectric microcavity due to total internal reflection, in analogy to acoustic waves circulating around a round enclosure (e.g., the St Paul’s Cathedral in London and the Echo Wall of Temple of Heaven in Beijing). Maintaining a large photon storage time, or equivalently high Q factors in optical cavities, are critical in many scientific and technological applications of microcavities, including cavity QED , cavity optomechanics , biosensing [4, 5], microresonator-based frequency combs , and narrow-linewidth laser sources [7, 8]. To achieve high Q factor in WGM cavities, it relies on the use of low-absorption dielectrics (to reduce material absorption loss) and the creation of very smooth dielectric surfaces (to reduce surface scattering loss). Although crystalline resonators currently have the highest Q factors on the order of 10 10 and 10 11 [9–11], for silicon-chip-based devices, microtoroid silica cavities provide the highest Q factors on the order of several hundred million . Microtoroid resonators combine low material loss of silica with a reflow technique in which surface tension is used to smooth lithographic and etch-related blemishes. However, reflow smoothing makes it very challenging to fabricate larger-diameter ultrahigh-Q (UHQ) resonators or to leverage the full range of integration tools and devices available on silicon.
Albanis, V., Dhanjal, S., MacDonald, K., Petropoulos, P., Offerhaus, H. ., Richardson, D. ., … Zheludev, N. . (2000). The light-induced structural phase transition in confining gallium and its photonic applications. Journal of Luminescence, 87-89, 646–648. Available at: http://dx.doi.org/10.1016/s0022-2313(99)00340-3
From afar, fabrication of nanoscale optical components can appear to be predominantly mo- tivated by the same forces that have driven developments in the microelectronics industry, where we have become accustomed to equating smaller with more powerful. Unsurpris- ingly, to a large degree this intuition is correct. Optical chips containing dense arrays of devices have the potential for high bandwidth data processing, and already play a role in the telecommunications industry [1, 2, 3]. However, as a scientist, the motivation for minitur- ization can come from elsewhere: the desire to study optical eﬀects that cannot be observed easily, if at all, without the help of wavelength scale conﬁnement of light. Reassuringly, these two views of optical miniturization are not in conﬂict. Instead, these interests drive each other: Novel chip-scale optical phenomena often ﬁnd applications in practical devices, and the usefulness of a scalable, integrated optical platform is not lost on physicists wanting to study increasingly complex systems.
While less is known of molecular structure-NLO activity relationships for third-order properties than for second-order properties, it has been established with organic compounds that increase in Ji-delocalization possibilities (e.g. progressing from small molecules to jt- conjugated polymers), the introduction of strong donor and acceptor functional groups, controlling chain orientation, packing density, and conformation, and increasing dimensionality can all result in increased cubic nonlinearity. Where applicable, similar trends are seen with the ruthenium acetylide complexes, although in many instances error margins are large (note that many of the small donor-acceptor acetylide complexes were designed for optimizing second-order rather than third-order NLO response). Negative real components of the nonlinearities (yreai) are observed in many instances and significant imaginary components ( Y i m a g ) are seen for almost all complexes, consistent with two-photon effects contributing to the observed molecular nonlinearities. Two-photon absorption (TPA) is a third-order NLO property that is of interest for applications in multiphoton microscopy, optical limiting, and optical data storage, and for which structure-activity trends are identical with those for Y i m a g . Cubic nonlinearities for these acetylide complexes increase significantly on progression from monometallic linear (“one-dimensional”) complex to bimetallic linear complex, trimetallic octupolar (“two-dimensional”) complex,53’54 and nonametallic dendritic complex74 without significant loss of optical transparency. For these complexes, TPA similarly increases substantially on progression to larger 7t-delocalizable compounds, TPA cross-sections for the dendritic examples being of the same order of magnitude as the best organic compounds.
Optical power limiting (OPL) has attracted considerable interest with applications such as the protection o f sensors from damage resulting from exposure to high energy laser pulses. In principle, the direct two-photon absorption process is suitable for optical limiting, but practical estimates show that power limiting properties o f existing materials (even those with the largest two-photon absorption coefficients) are insufficient for the most important applications, namely, the protection of sensors from laser pulses of duration of the order of nanoseconds. Another important process which affords optical limiting behaviour is reverse saturable absorption (RSA). If a substantial proportion o f the population o f molecules is excited from the ground state to the excited state, then the absorption o f the material is no longer the same as that o f the population o f ground state molecules. A common phenomenon is saturable absorption (absorption bleaching), i.e. increase o f sample transmission as the ground state molecules are depleted. In order for reverse saturable absorption to take place, it is necessary that the excited state molecules exhibit a higher absorptivity at a given wavelength than the ground state molecules. The RSA phenomenon is thus a "photodarkening" effect. The difference between the RSA process and two-photon absorption is that the two-photon absorption is virtually instantaneous whereas processes involving intermediate absorbing states exhibit certain kinetic behaviour, which is
Abstract Entangled optical quantum states are essential towards solving questions in fundamental physics and are at the heart of applications in quantum information science. For advancing the research and development of quantum technologies, practical access to the generation and manipulation of photon states carrying significant quantum resources is required. Recently, integrated photonics has become a leading platform for the compact and cost- efficient generation and processing of optical quantum states. Despite significant advances, most on-chip non- classical light sources are still limited to basic bi-photon systems formed by two-dimensional states (i.e. qubits). An interesting approach bearing large potential is the use of the time or frequency domain to enabled the scalable on- chip generation of complex states. In this manuscript, we review recent efforts in using on-chip optical frequency combs for quantum state generation and telecommunications components for their coherent control. In particular, the generation of bi- and multi-photon entangled qubit states has been demonstrated, based on a discrete time domain approach. Moreover, the on-chip generation of high-dimensional entangled states (quDits) has recently been realized, wherein the photons are created in a coherent superposition of multiple pure frequency modes. The time- and frequency-domain states formed with on-chip frequency comb sources were coherently manipulated via off-the- shelf telecommunications components. Our results suggest that microcavity-based entangled photon states and their coherent control using accessible telecommunication infrastructures can open up new venues for scalable quantum information science.
produce photon pairs through sFWM. This requires the use of a bright pump which has to be ltered out from the generated radiation. This stage is usually accomplished o chip by the use of interference lters, Arrayed Waveguide Gratings (AWG) or Fiber Bragg Gratings (FBG) (see e.g., Ref.). The lter itself constitutes another building block of the experiment. Next, the generated radiation is manipulated in in- terferometric structures which allow to create well dened quantum states to be eventually fed o chip for further manipulation. These includes the use of delay lines, beamsplitters, AWGs etc. Up to now, a network which integrates all these functionalities on a chip has not been yet demonstrated. Functions that can not be easily integrated, such as the delay lines or lters, have been supplied by external optical components. In this chapter, the design and the simulation of most of the main building blocks for integrated quantum networks is reported. The goal is to produce the rst network in which all the functionalities are integrated, and the only external components required to perform the experiment are the pump laser and the photon counters. In the rst section the sources are discussed. These are based on sFWM in racetrack resonators or in straight waveguides. The pump ltering stage and its roboustness to fabrication defects is discussed later. Interferometers, AWGs and delay lines are covered at the end of the chapter. In this chapter, the design of the integrated quantum photonic chip is presented. Its fabrication is underway.
Wafer-scale processing techniques allow precise dimensional at the nano-scale level, and are the foundation of modern microelectronics. The potential of these techniques in the domain of optics, and in particular optical microcavities, has been extensively investigated in the early 1990, and have led to the demonstration of a variety of chipbased optical microcavities concepts. Microdisk cavities were among the first chip- based microcavities demonstrated. Since then, a variety of other confinement geometries, such as vertical micro-posts or photonic crystal defect cavities have been demonstrated. The small mode volume and high-Q factor of these structures, can be used in a variety of fundamental and applied studies. In addition the wafer- scale nature allow possible integration with complementary optical, mechanical or electrical functionality. Reported Q-factor results have ranged from 13,000 in InGaAs microdisks, to 130,000 in polymer rings, to a record value of more than 3 million in a silica microdisk  and described in thesis chapter 8.
Quantum photonics is a rapidly developing platform for future quantum network applications. Waveguide-based architectures, in which embedded quantum emitters act as both nonlinear elements to mediate photon–photon inter- actions and as highly coherent single-photon sources, offer a highly promising route to realize such networks. A key requirement for the scale-up of the waveguide architecture is local control and tunability of individual quantum emitters. Here, we demonstrate electrical control, tuning, and switching of the nonlinear photon–photon interaction arising due to a quantum dot embedded in a single-mode nano-photonic waveguide. A power-dependent waveguide transmission extinction as large as 40 2% is observed on resonance. Photon statistics measurements show clear, voltage-controlled bunching of the transmitted light and antibunching of the reflected light, demonstrating the single- photon, quantum character of the nonlinearity. Importantly, the same architecture is also shown to act as a source of highly coherent, electrically tunable single photons. Overall, the platform presented addresses the essential requirements for the implementation of photonic gates for scalable nano-photonic-based quantum information processing.
transfer from the fiber to the cavity is achievable. Tobias Kippenberg and I have used this fact to observe nonlinear stimulated Raman scattering in a silica microsphere, with optical thresholds below 100 microwatts, by far a record value over other types of Raman lasers . However, the use of silica microspheres is not ideal for applications, as not only does this structure possess a complicated (but well-understood) mode and lasing spectrum, but their fabrication process does not lead to easy integration onto a microelectronic chip. Previous microcavities, which are easily controllable and integrable do not, however, possess the high- quality factors necessary to enable low threshold nonlinear operation [23, 24]. Deniz Armani and I developed a process to merge the integrability and control of planar microfabricated res- onators, with the high quality factors of silica microspheres. The resultant structures consist of a toroidally shaped silica cavity supported on a silicon chip . These structures were also found to have advantages over spherical cavities by the ability to modify the toroidal geom- etry [26, 27]. However, the modal properties are not easily solvable in this cavity structure. Numerical characterization of the optical properties of these structures indicates benefits over spherical cavities, which have been experimentally verified.
This study focuses on optical solitons in fiber optics. It can be modeled into two mathematical equations, which are nonlinear Schrödinger (NLS) equation and forced nonlinear Schrödinger (fNLS) equation. The first chapter includes the background of study, the statement of problem, objectives of study, scope of studies and significance of study, which is explained in details.
Parallel developments in both computer technologies and symbolic softwares have greatly contributed to solve lots of problems defined in various fields covering applied mathematics, physics and many engineering fields. A diverse class of effective methods have successfully been introduced to study this class of equations, for example [3, 10–15]. On the other hand some of the commonly used approaches, for solving nonlinear evolution equations, are: The ansatz [16–18], modified simple equation , the first integral [20,21], ( G G 0 )-expansion , sine-Gordon expansion [23, 24]. Furthermore, some other excellent works like Kudryashov methods , a modified form of Kudryashov and functional variable methods [26–28] have been done by different researchers. In [29–32], the auxiliary equation, the improved tan( φ(η) 2 )-expansion methods and the exp function approach have been explored for discrete and fractional order PDEs as well. Ali and Hassan , Hosseini et al.  and Zayed and Al-Nowehy  all have utilized the exp a function method to explore the exact solutions
For picoliter- to nanoliter-scale sample volumes, the surface-to-volume ratio of the sample becomes significant and results in a large heat loss. In this situation even the surrounding air becomes a significant source of heat loss. Therefore, to improve the thermal isolation of chip calorimeters, it is necessary to employ vacuum insulation, which is never realized by the up-to-date chip calorimeters even though it is common for conventional calorimeters. We built an on-chip vacuum chamber surrounding the Parylene fluidic structure. Parylene has very low gas permeability and good mechanical strength, and these attributes enable us to apply vacuum across the thin-film microfluidic channel walls. We find that 2 μm thick Parylene layer provides enough mechanical strength and physical isolation of the sample under vacuum.
Capillary electrophoresis (CE) suffers from a relatively small sensitivity—at least in case of optical detection transversely to the capillary axis due to the small capillary inner diameters in the range of 50 - 100 µm. Different concepts like bubble, U-, or Z-cells have been used to tackle that problem already in the nineties of the last century. But the U- and Z-cells have typically been extra cells with larger inner channel diameters and no optimization for optical waveguiding and the bubble cell per se did not allow for optical waveguiding. In the case of on-chip capillary electrophoresis (chip-CE) a U-cell can be implemented quite easily on the chip. Here we show how leaky optical waveguiding can be employed to improve optical detection. Proper U-channel design and prepa- ration by wet-chemical etching of the fused silica sub- and superstrate, making the U-channel bend a part of the optical input lens system, can help to achieve high coupling efficiency with loss coeffi- cients around 2 dB and low waveguiding loss.