Tuning four-wave mixing through temperature in ethanol-filled photonic crystal fiber

In this paper, continuous tuning of four-wave mixing bands in an ethanol-filled photonic crystal fiber is investigated. A wide tuning range of the parametric bands, from 745 nm to 920 nm (signal) and from 1260 nm to 1710 nm (idler), is achieved through the thermo-optic effect. This corresponds to a frequency tuning range higher than 2000 cm−1; such wide range can be particularly useful in applications that require broadband wavelength conversion, e.g., CARS microscopy. Numerical calculations are in good agreement with experimental measurements.

Control of the chromatic dispersion of photonic crystal fibers for supercontinuum and photon pairs generation

The interplay between chromatic dispersion and nonlinear effects is crucial for an efficient exploitation of non linear propagation in photonic crystal fibers (PCF). Once a PCF preform has been prepared, changing the parameters that control the fabrication process it is possible to adjust the dispersion properties of the fiber. In addition, it is particularly useful to develop postprocessing techniques that enable a fine adjustment of the dispersion along a section of PCF. The tapering of PCF, using a fusion and pulling technique, has been established as a rather useful technique to engineer the dispersion properties along tens of centimeters. Some of our recent experiments demonstrate that…

Vector description of higher-order modes in photonic crystal fibers

We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCF's. Unlike conventional fibers, PCF's exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCF's are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these high…

Unified description of dispersive wave emission in normal and anomalous dispersion regimes

We present a novel theoretical framework where dispersive wave emission in normal and anomalous dispersion is interpreted based on four-wave mixing processes. It is a powerful tool for designing supercontinuum sources along analytical guidelines.

Cantor-like fractal photonic crystal waveguides

Abstract We propose a new class of one-dimensional (1D) photonic waveguides: the fractal photonic crystal waveguides (FPCWs). These structures are photonic crystal waveguides (PCWs) etched with fratal distribution of grooves such as Cantor bars. The transmission properties of the FPCWs are investigated and compared with those of the conventional 1D PCWs. It is shown that the FPCW transmission spectrum has self-similarity properties associated with the fractal distribution of grooves. Furthermore, FPCWs exhibit sharp localized transmissions peaks that are approximately equidistant inside the photonic band gap.

A robust and efficient method for obtaining the complex modes in inhomogeneously filled waveguides

In this paper, we present a computational simulation of the complex wave propagation in inhomogeneously filled waveguides with lossless and lossy dielectrics. We use a biorthonormal-basis method as a numerical technique. The behavior of complex modes in different waveguides whose characterization with other methods involves some difficulties is analyzed. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 218–222, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10875

Polarization Modulation Instability in All-Normal Dispersion Microstructured Optical Fibers with Quasi-Continuous 1064 nm Pump

Polarization modulation instability (PMI) is a form of modulation instability that can exist in weakly birefringent optical fibers [1]. Sidebands can be generated by this effect when a polarization mode of the birefringent fiber is excited with an intense optical pump. The polarization state of the sidebands is orthogonal to the polarization of the pump signal. PMI has been observed in microstructured optical fibers (MOFs). PMI was reported in a large-air-filling fraction MOF that was pumped in the normal dispersion regime with visible light [2]. The coherent degradation of femtosecond supercontinuum light generated in all-normal dispersion (ANDi) MOFs due to PMI was recently investigated […

Analysis of the irradiance along different paths in the image space using the Wigner distribution function

Abstract The intensity distribution along different paths in the image space of an optical system is described in a two-dimensional phase-space domain in terms of the Wigner distribution function. This approach is useful for an efficient analysis of the performance of optical imaging systems suffering from spherical aberration. The good performance of the method is shown in some numerical simulations.

Supercontinuum generation in silicon waveguides relying on wave-breaking

Four-wave-mixing processes enabled during optical wave-breaking (OWB) are exploited in this paper for supercontinuum generation. Unlike conventional approaches based on OWB, phase-matching is achieved here for these nonlinear interactions, and, consequently, new frequency production becomes more efficient. We take advantage of this kind of pulse propagation to obtain numerically a coherent octave-spanning mid-infrared supercontinuum generation in a silicon waveguide pumping at telecom wavelengths in the normal dispersion regime. This scheme shows a feasible path to overcome limits imposed by two-photon absorption on spectral broadening in silicon waveguides.

Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals

We consider periodic multilayers combining ordinary positive index materials and dispersive metamaterials with negative index in some frequency range. These structures can exhibit photonic band gaps which, in contrast with the usual Bragg gaps, are not based on interference mechanisms. We focus on effects produced by the interaction between non-Bragg gaps of different nature: a) the zero averaged refractive index, b) the zero permeability and c) the zero permittivity gaps. Our analysis highlights the role played by the unavoidable dispersive character of metamaterials. We show that the degree of overlap between these bands can be varied by a proper selection of the constructive parameters, …

Four Wave Mixing in Photonic Crystal Fibers:<br /> Tuning Techniques

We present an experimental and numerical study of four-wave mixing in photonic crystal fibers. Our objective is the development of tuning techniques based on tailoring de dispersion of the fibers. We demonstrate wide tuning ranges.

Spectral coherence in microresonator combs

We provide a quantitative analysis of the coherence in microresonator frequency combs. We show how to achieve coherent transform-limited pulses on-chip without actively manipulating the pump setting conditions in the course of comb formation.

Fabrication of polarizing photonic crystal fibres and photonic crystal fibre tapers: Applications

We report the fabrication of an anisotropic photonic crystal fibre with polarization properties and photonic crystal fibre tapers for supercontinuum generation. The anisotropy of the fibre was created by enlarging four airholes next to the silica core. Different polarization regimes as a function of the geometric parameters, including polarizing behaviour at 1.55 mum, were obtained. In the second part of the paper, we report the fabrication of photonic crystal fibre tapers. We present experimental results on supercontinuum generation in photonic crystal fibre tapers using quasi-continuous pump pulses of 7 ns duration at 532 nm and at 1064 nm.

Polarization Modulation Instability in All-Normal Dispersion Microstructured Optical Fibers with sub-ns Pumping

The advent of microstructured optical fiber (MOF) technology gave a significant boost to research in nonlinear optics. MOFs have the advantage of high nonlinearity and designable dispersion, which makes this type of fiber an excellent platform for efficient generation of nonlinear effects. In the last years, MOFs exhibiting normal dispersion at any guiding wavelength (ANDi fibers) aroused the interest because of the possibility of using them for the generation of coherent and recompressible supercontinuum (SC) light. In this contribution, we present our recent results regarding the generation of the polarization modulation instability (PMI) effect in ANDi MOFs in the quasi-CW pump regime at…

Measurement of the soliton number in guiding media through continuum generation.

No general approach is available yet to measure directly the ratio between chromatic dispersion and the nonlinear coefficient, and hence the soliton number for a given optical pulse, in an arbitrary guiding medium. Here we solve this problem using continuum generation. We experimentally demonstrate our method in polarization-maintaining and single-mode fibers with positive and negative chromatic dispersion. Our technique also offers new opportunities to determine the chromatic dispersion of guiding media over a broad spectral range while pumping at a fixed wavelength. (C) 2020 Optical Society of America

Towards an analytical framework for tailoring supercontinuum generation.

A fully analytical toolbox for supercontinuum generation relying on scenarios without pulse splitting is presented. Furthermore, starting from the new insights provided by this formalism about the physical nature of direct and cascaded dispersive wave emission, a unified description of this radiation in both normal and anomalous dispersion regimes is derived. Previously unidentified physics of broadband spectra reported in earlier works is successfully explained on this basis. Finally, a foundry-compatible few-millimeters-long silicon waveguide allowing octave-spanning supercontinuum generation pumped at telecom wavelengths in the normal dispersion regime is designed, hence showcasing the p…

Tapering photonic crystal fibres for supercontinuum generation with nanosecond pulses at 532nm

Experimental results on supercontinuum generation in photonic crystal fibre tapers using pump pulses of 7 ns duration at 532 nm are presented. Photonic crystal fibre tapers with the first wavelength of zero dispersion around 532 nm were fabricated. The generation of supercontinuum was investigated in normal and anomalous dispersion regimes. Supercontinuum spectra spanning more than 400 nm in the visible region are reported.

Dispersion-to-spectrum mapping in nonlinear fibers based on optical wave-breaking

In this work we recognize new strategies involving optical wave-breaking for controlling the output pulse spectrum in nonlinear fibers. To this end, first we obtain a constant of motion for nonlinear pulse propagation in waveguides derived from the generalized nonlinear Schrödinger equation. In a second phase, using the above conservation law we theoretically analyze how to transfer in a simple manner the group-velocity-dispersion curve of the waveguide to the output spectral profile of pulsed light. Finally, the computation of several output spectra corroborates our proposition.

Comparative analysis of spectral coherence in microresonator frequency combs

Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in u…

Inverse dispersion engineering in silicon waveguides

We present a numerical tool that searches an optimal cross section geometry of silicon-on-insulator waveguides given a target dispersion profile. The approach is a gradient-based multidimensional method whose efficiency resides on the simultaneous calculation of the propagation constant derivatives with respect to all geometrical parameters of the structure by using the waveguide mode distribution. The algorithm is compatible with regular mode solvers. As an illustrative example, using a silicon slot hybrid waveguide with 4 independent degrees of freedom, our approach finds ultra-flattened (either normal or anomalous) dispersion over 350 nm bandwidth in less than 10 iterations.

Waveguiding properties of a photonic crystal fiber with a solid core surrounded by four large air holes

The polarization-dependent guiding properties of a hexagonal-lattice photonic crystal fiber with a solid-core surrounded by four large air holes are investigated. The appearance of a polarization dependent cutoff frequency, together with several parameters as the birefringence, the modal effective area, the group velocity dispersion and the polarization dependent loss are analyzed. A collection of fibers with different structural parameters were fabricated and characterized. An effective anti-guide structure from at least 450 nm to 1750 nm, a polarizing fiber with a polarization dependent loss of 16 dB/m at 1550 nm, and an endlessly singlemode polarization-maintaining fiber with group biref…

Wide wavelength-tunable passive mode-locked Erbium-doped fiber laser with a SESAM

Abstract In this work we present a simple polarization-maintaining wavelength-tunable passive mode-locked Erbium-doped fiber laser with a semiconductor saturable absorber mirror (SESAM) as a mode locker. The cavity includes a Sagnac interferometer-based fiber optical loop mirror (FOLM) as a wide wavelength-tunable filter. Tunable mode-locking was experimentally achieved in the range of 1543.2 nm to 1569.5 nm by thermally adjustment of FOLM wavelength reflection. The output pulses have a repetition rate of 11.16 MHz with pulse duration about 0.9 ps. The experimental results were confirmed by numerical simulations.

Dispersion-optimized multicladding silicon nitride waveguides for nonlinear frequency generation from ultraviolet to mid-infrared

Nonlinear frequency conversion spanning from the ultraviolet to the mid-infrared (beyond 2.4 μm) is experimentally demonstrated in multicladding silicon nitride (𝑆𝑖𝑋𝑁𝑌) waveguides. By adjusting the waveguide cross-section the chromatic dispersion is flattened, which enhances both the efficiency and the bandwidth of the nonlinear conversion. How accurately the dispersion is tailored is assessed through chromatic dispersion measurements and an experiment/simulation comparison of the dispersive waves' wavelength locations. Undesirable fluctuations of both the refractive index and the dimensions of the waveguide during the fabrication process result in a dispersion unpredictability of at l…

Broadband dispersion compensation using inner cladding modes in photonic crystal fibers.

A photonic crystal fiber is optimized for chromatic dispersion compensation by using inner cladding modes. To this end, a photonic-oriented version of the downhill-simplex algorithm is employed. The numerical results show a dispersion profile that accurately compensates the targeted dispersion curve, as well as its dispersion slope. The presented fiber has a simple structure, while radiation losses can be reduced simply by adding a few more air-hole rings. Fabrication tolerances are also considered showing how fabrication inaccuracies effects can be overridden by just adjusting the compensation length.

Inverse photonic-crystal-fiber design through geometrical and material scalings

Geometrical and material - i.e., external and internal - scaling symmetries are exploited to obtain approximated analytical expressions for the mode effective index, group index, and chromatic dispersion of a scaled fiber. Our results include material refractive index scaling that changes the numerical aperture. First, the analytical expressions are successfully tested with a conventional step index fiber in a broadband range of wavelengths, from 1 to 2 mu m. Then, we establish a procedure to adapt the analytical expressions to photonic crystal fibers (PCFs) and illustrate its application in a triangular PCF with circular holes. These adapted analytical expressions show good agreement with …

Triply resonant coherent four-wave mixing in silicon nitride microresonators

The generation of multiple tones using four-wave mixing (FWM) has been exploited for many applications, ranging from wavelength conversion to frequency comb generation. FWM is a coherent process, meaning that its dynamics strongly depends on the relative phase among the waves involved. The coherent nature of FWM has been exploited for phase-sensitive processing in different waveguide structures, but it has never been studied in integrated microresonators. Waveguides arranged in a resonant way allow for an effective increase in the wavelength conversion efficiency (at the expense of a reduction in the operational bandwidth). In this letter, we show that phase shaping of a three-wave pump pro…

Modeling spectral correlations of photon-pairs generated in liquid-filled photonic crystal fiber

The generation of photon-pairs with controllable spectral correlations is crucial in quantum photonics. Here we present the design of a photonic crystal fiber to generate widely-spaced four-wave mixing bands with spectral correlations that can be tuned through the thermo-optic effect after being infiltrated with heavy water. We present a theoretical study of the purity of the signal (idler) photon generated as a function of temperature, pump spectral linewidth and the length of the fiber. 511-6/18-8876 CIIC155/2019 APN-624 TEC2016- 76664-C2-1-R PROMETEO/2019/048

Source linewidth effects in temporal imaging of Gaussian Schell-model pulses

A transform-limited Gaussian pulse generated from an externally modulated stationary source is launched within a temporal imaging system composed of a second-order dispersion followed by a time lens and a subsequent quadratic dispersion. We consider the effect of the statistical properties of the emitted light for temporal imaging. In particular, it is shown that the design parameters that ensure a received signal with the minimum root-mean-square (rms) width achievable, which is called the temporal image of the incident pulse, are strongly dependent on the coherence properties of the input waveform. Finally, limitations on the temporal resolution of the setup are highlighted and a realisti…

Analysis of Inhomogeneously Dielectric Filled Cavities Coupled to Dielectric-Loaded Waveguides: Application to the Study of NRD-Guide Components

In this paper, we present two contributions. First, we develop a computationally efficient technique for the full-wave characterization of inhomogeneously dielectric-filled cavities connected to inhomogeneously dielectric-loaded waveguides. This method is based on the expansion of the electromagnetic field within the cavity in terms of their solenoidal and irrotational modes. The presented formulation allows the treatment of hybrid modes in the waveguide ports, where the definition of a characteristic modal impedance or admittance is not possible. The multimode scattering matrix of the structure is computed throughout an efficient implementation of the orthonormal-basis method for the calcu…

Switching dynamics of dark-pulse Kerr comb states in optical microresonators

Dissipative Kerr solitons are localized structures that exist in optical microresonators. They lead to the formation of microcombs --- chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion microresonators. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we report the discovery of reversible switching between coherent dark-pulse Kerr combs, whereby distinct states can be accessed deterministically. Furt…

Endlessly single-mode heat-sink waveguide

Recently, a new form of optical fiber, the photonic crystal fiber, has been reported. This fiber has a hexagonal array of submicrometer air holes running along its length and a lattice site without a hole (a line defect) in its center. The defect acts as a core, confining light that travels along the fiber as a guided mode. This structure can be endlessly single mode, never supporting more than one confined mode no matter what the diameter of the core or the wavelength of the light. Having discovered this effect experimentally and provided a qualitative explanation for the observed behavior, we present here a planar version of this fiber. Periodic arrays of parallel planar fins are placed o…

Hot-cavity spectroscopy of dark pulse Kerr combs in microresonators

Kerr frequency combs are generated through cascaded four-wave mixing in high-Q microresonators [1]. These devices are pumped with a continuous-wave laser and modulational instability (MI) is responsible for the growth of the initial comb lines. Since it is easier to satisfy the MI phase matching condition in the anomalous dispersion regime, most studies on Kerr combs have focused on anomalous dispersion microresonators. However, coherent microresonator combs can also take place in the normal dispersion regime. In these combs, phase matching is attained with the aid of the mode coupling between transverse modes of the microresonator [2]. One particularly interesting comb state that operates …

Sloped-wall thin-film photonic crystal waveguides

The effect of the slope of the groove walls in the behavior of thin-film one-dimensional photonic crystal waveguides is extensively studied. In this respect, we point out its influence on the modal dispersion relations and then on the bandgap structure in general. Likewise, we also prove the lack of accuracy in the evaluation of the bandgap edges when material dispersion is ignored. The extreme importance of both facts, the wall slope and the material dispersion, in the analysis and design of realistic photonic crystal devices is emphasized. In particular, we exploit the wall slope as a new design parameter. By suitably choosing the value of the above parameter, sloped-wall photonic crystal…

Differential toolbox to shape dispersion behavior in photonic crystal fibers.

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabric…

Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals

We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability \mu or the electric permittivity \epsilon of the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when \mu= 0 or when \epsilon= 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to \mu = 0 occurs only for TE polarized waves, whereas a gap corresponding to \epsilon = 0 occurs only for TM polarized waves. These band gaps are …

Polarization Modulation Instability in Dispersion-Engineered Photonic Crystal Fibers

Generation of widely spaced polarization modulation instability (PMI) sidebands in a wide collection of photonic crystal fibers (PCF), including liquid-filled PCFs, is reported. The contribution of chromatic dispersion and birefringence to the net linear phase mismatch of PMI is investigated in all-normal dispersion PCFs and in PCFs with one (or two) zero dispersion wavelengths. Large frequency shift sidebands are demonstrated experimentally. Suitable fabrication parameters for air-filled and liquid-filled PCFs are proposed as guidelines for the development of dual-wavelength light sources based on PMI.

General measurement technique of the ratio between chromatic dispersion and the nonlinear coefficient

Measuring the nonlinear coefficient γ of any guiding medium, regardless of the sign and magnitude of its group-velocity dispersion parameter β 2 , is challenging because of the lack of general solutions of the nonlinear Schrodinger equation (NLSE). Indeed, existing approaches typically need to disregard chromatic-dispersion effects to determine γ [1] . Here we propose an all-encompassing approach to measure the ratio β 2 /γ and prove our method in polarization-maintaining (PM) and single-mode (SM) fibers with positive and negative β 2 .

Wideband tuning of four-wave mixing in solid-core liquid-filled photonic crystal fibers

We present an experimental study of parametric four-wave mixing generation in photonic crystal fibers that have been infiltrated with ethanol. A silica photonic crystal fiber was designed to have the proper dispersion properties after ethanol infiltration for the generation of widely spaced four-wave mixing (FWM) bands under 1064 nm pumping. We demonstrate that the FWM bands can be tuned in a wide wavelength range through the thermo-optic effect. Band shifts of 175 and over 500 nm for the signal and idler bands, respectively, are reported. The reported results can be of interest in many applications, such as CARS microscopy.

Wavelength shift of four-wave mixing bands in photonic crystal fibers pumped in the normal dispersion regime

The generation of correlated photon pairs plays a central role in several quantum mechanics applications, such as quantum information, and cryptography [1]. Correlated photon pairs can be generated inside an optical fiber through the parametric process of degenerated four-wave mixing (FWM) [2]. In this paper we report the results of two different experiments where wavelength shift of FWM bands in normal dispersive PCFs is investigated.

Designing a photonic crystal fibre with flattened chromatic dispersion

Using a full-vector modal method, the authors have identified a region of nearly zero flattened chromatic dispersion in a specially designed photonic crystal fibre. The approach permits an accurate control of the dispersion features of these fibres in terms of their structural parameters.

Smooth and stable supercontinuum generation with standard photonic crystal fibers

We identify some simple-to-fabricate photonic crystal fibers, with only two families of air-hole sizes, which provide a wide, smooth and highly-coherent supercontinuum.

Switching Dynamics of Dark Solitons in Kerr Microresonators

Dissipative Kerr solitons (DKS) are localized structures in optical resonators that arise from a double balance between dispersion and Kerr effect, and linear loss and parametric gain [1]. The periodic nature of DKS corresponds to frequency combs. DKS can be generated in high-Q microresonators for diverse applications, from coherent communications to precision frequency synthesis [1]. Most studies of DKS have focused on microresonator cavities operating in the anomalous dispersion regime, where the waveforms correspond to bright soliton pulses. Coherent microresonator combs can also be formed in the normal dispersion regime [2]. The time-domain waveform corresponds to a localized dark-pulse…

Analytical evaluation of chromatic dispersion in photonic crystal fibers

We present a two-dimensional modal approach for the evaluation, in an analytical manner, of chromatic dispersion in any kind of optical fiber. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical procedure to calculate its derivatives. The proposed formulation takes into account the effective anisotropy of the interfaces and allows us to deal with microstructured fibers, in general, and specifically with realistic photonic crystal fibers (PCFs), including arbitrary spatial refractive-index distributions of dispersive and absorbing materials. This fast and accurate numerical technique is extremely useful for both analysis an…

Broadband Tuning of Polarization Modulation Instability in Microstructured Optical Fiber through Thermal Heating

Broadband tuning of polarization modulation instability in microstructured optical fibers is reported. Tunability is achieved by simultaneous birefringence-dispersion changes through thermal heating. 906 cm-1 frequency tunability range is attained.

Spectral broadening enhancement in silicon waveguides through pulse shaping

Spectral broadening in silicon waveguides is usually inhibited at telecom wavelengths due to some adverse effects related to semiconductor dynamics, namely, two-photon and free-carrier absorption (FCA). In this Letter, our numerical simulations show that it is possible to achieve a significant enhancement in spectral broadening when we properly preshape the input pulse to reduce the impact of FCA on spectral broadening. Our analysis suggests that the use of input pulses with the correct skewness and power level is crucial for this achievemen This work was financially supported by the Plan Nacional Investigación, Desarrollo e Innovación (I+D +I) under the research project TEC2008-05490, by…

Experimental and theoretical study of the nonlinear birefringence in the formation process of vector solitons in a total polarization control ring cavity bias twist fiber

Abstract In this work, we present the numerical and experimental investigation of the polarization dynamics in a free birefringence mode-locked fiber laser. The laser includes a double-pass Erbium-doped fiber amplifier and 20-m long bi-twisted fiber at a twist rate of ± 6 turns m−1 to mitigate both, linear and circular birefringence effects. We found ellipticity changes due to nonlinear birefringence in the 20-m long fiber during pulse formation and propagation. In contrast with previously reported works, the inclusion of bi-twisted fiber allows investigate the nonlinear effects independently from the linear ones. The experimental behavior was confirmed by numerical simulations based on spl…

Designing the properties of dispersion-flattened photonic crystal fibers

We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCF's). This analysis includes a thorough description of the dependence of the fiber geometrical dispersion on the structural parameters of a PCF. The interplay between material dispersion and geometrical dispersion allows us to established a well-defined procedure to design specific predetermined dispersion profiles. We focus on flattened, or even ultraflattened, dispersion behaviors both in the telecommunication window (around 1.55 microm) and in the Ti-Za laser wavelength range (around 0.8 microm}. We show the different possibilities of obtaining normal, anomalous, and zero dispersion curves…

Space-time analogy for partially coherent plane-wave-type pulses.

In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength w…

Extremely efficient evaluation of chromatic dispersion in realistic photonic crystal fibers

We present a fast and accurate procedure for the evaluation of chromatic dispersion in photonic crystal fibers. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical approach to calculate its derivatives.

Design of All-Normal Dispersion Microstructured Optical Fiber on Silica Platform for Generation of Pulse-Preserving Supercontinuum Under Excitation at 1550 nm

We investigated numerically the possibility of all normal dispersion fiber design for near-infrared supercontinuum generation based on a standard air-silica microstructure. The design procedure includes finding of target dispersion profile and subsequent finding of appropriate geometrical fiber design by inverse dispersion engineering. It was shown that the tailoring of dispersion profile could increase the spectral width of generated supercontinuum while maintaining perfect spectral flatness. Conditions necessary for wide and flat supercontinuum generation as well as restrictions imposed by chosen materials were discussed. As a result of design and optimization procedure, an air-silica des…

Effective Fresnel-number concept for evaluating the relative focal shift in focused beams

We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.

Role of dispersion on zero-average-index bandgaps

We consider periodic multilayers combining ordinary positive index materials and dispersive metamaterials with negative index in some frequency ranges. These structures can exhibit photonic bandgaps which, in contrast with the usual Bragg gaps, are not based on interference mechanisms. Changing the dispersion models for the constituent metamaterial, we investigate its role in the production of zero-average-index bandgaps. In particular, we show the effect of each constitutive parameter on both bandgap edges. Finally, we give some approximated analytical expressions in terms of average parameters for the determination of the upper and lower limits of the zero-average refractive-index bandgap…

m-bonacci metamaterial multilayers: location of the zero-average index bandgap edges

We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positiveindex materials and dispersive metamaterials with negative index in a certain frequency range. When the volume-averaged refractive index of the nonperiodic multilayer equals zero, the structure does not propagate light radiation and exhibits a forbidden band. We identify some analytical expressions to determine the upper and lower limits of the above zero-average refractive-index bandgap. We recognize that these limits are not explicitly dependent on the geometrical parameters of the stack of layers. © 2009 Optical Society of America. Fil: Monsoriu, J.A.. Universidad Politécnica de Valencia;…

Broadband tuning of polarization modulation instability in microstructured optical fibers

The wideband tuning of strong bands generated through polarization modulation instability (PMI) in microstructured optical fibers (MOFs) is reported. Tunability is achieved by exploiting the dependence of the phase-matching condition on the fiber’s chromatic dispersion and birefringence, which is particularly sensitive when the fiber is pumped near the zero-dispersion wavelength. MOFs designed to accomplish PMI phase-matching when they are infiltrated with ethanol and pumped at 1064 nm were designed and fabricated. Taking advantage of the large thermo-optic coefficient of ethanol, both chromatic dispersion and birefringence were varied through temperature. Wavelength shifts from 937 nm to 8…

Supercontinuum generation with 532 nm quasi-continuum pulses in photonic crystal fibre tapers

We report experimental results on supercontinuum generation in PCF tapers using quasi-continuous pump pulses of 7 ns duration at 532 nm. SC generation in normal and anomalous dispersion regimes are presented. Introduction Supercontinuum generation (SC) in photonic crystal fibres (PCF), fibre tapers, and PCF tapers has been demonstrated in the past with pump pulses of fs, ps, and tenths of ns duration [1-2]. Here, we present experimental results on SC generation in PCF tapers using quasi-continuous pump pulses of 7 ns duration at 532 nm. Fabrication of the PCF tapers The PCF from which the tapers were made, was a large-air-hole PCF ("cobweb" PCF) with two rings of air holes around a solid si…

Broadband Tuning of Four-Wave Mixing Bands Using Photonic Crystal Fibers

We present an experimental study of the shift with temperature of widely-spaced FWM parametric bands generated in an ethanol-inflltrated photonic crystal fiber. We report broadband tuning of 175 nm and over 500 nm for the signal and idler bands, respectively, achieved through the thermo-optic effect. Numerical calculations were carried out and show good agreement with experimental data.

Analysis of whispering gallery modes resonators: wave propagation and energy balance models

Electromagnetic whispering gallery modes (WGM) are surface waves guided by the curvature of an interface. Microspheres, microdisks and microcylinders –as for example standard optical fibers– are high quality microresonators for the WGM. In fact, they can be regarded as compact and small ring resonators. Here, we present a comparison between wave propagation and energy balance models, stablishing the equivalence and discussing the basic characteristics of these two complementary approaches.

Nonlinearity measurement undergoing dispersion and loss

Accurate knowledge of the nonlinear coefficient is extremely important to make reliable predictions about optical pulses propagating along waveguides. Nevertheless, determining this parameter when dispersion and loss are as important as nonlinear effects brings both theoretical and experimental challenges that have not yet been solved. A general method for measuring the nonlinear coefficient of waveguides under these demanding conditions is here derived and demonstrated experimentally in a kilometer-long standard silica fiber pumped close to 2 µm.

Shaping the supercontinuum spectral profile

We numerically recognize a procedure for shaping, at least to some extent, the spectral profile of the supercontinuum (SC) generated by soft-glass photonic crystal fibers (PCFs). As example, we identify a PCF geometry that provides an ultrawide (over an octave) and very flat SC when pumped with pulsed light parameters corresponding to a commercially available Er-doped femtosecond fiber laser.

Ultrahigh-birefringent squeezed lattice photonic crystal fiber with rotated elliptical air holes.

We report an experimental realization of a highly birefringent photonic crystal fiber as a result of compressing a regular hexagonal structure. The experimental measurements estimate a group birefringence of approximately 5.5x10(-3) at 1550 nm in good agreement with the numerical results. We study the influence of compressing the regular structure at different directions and magnifications, obtaining a method to realistically enhance the phase birefringence while moderating the group birefringence.

Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method

A general theoretical formulation to analyze inhomogeneously filled waveguides with lossy dielectrics is presented in this paper. The wave equations for the tranverse-field components are written in terms of a nonself-adjoint linear operator and its adjoint. The eigenvectors of this pair of linear operators define a biorthonormal-basis, allowing for a matrix representation of the wave equations in the basis of an auxiliary waveguide. Thus, the problem of solving a system of differential equations is transformed into a linear matrix eigenvalue problem. This formulation is applied to rectangular waveguides loaded with an arbitrary number of dielectric slabs centered at arbitrary points. The c…

Nonlinear coefficient measurement in highly dispersive fibers

We present a novel approach for measuring nonlinear coefficients in fibers with significant pulse broadening. We perform a proof-of-concept demonstration for 200-m-long polarization-maintaining and single-mode fibers pumped at 1060 nm with ps pulses.

Nearly zero ultraflattened dispersion in photonic crystal fibers.

We present a procedure for achieving photonic crystal fibers with nearly zero ultraflattened group-velocity dispersion. Systematic knowledge of the special guiding properties of these fibers permits the achievement of qualitatively novel dispersion curves. Unlike the behavior of conventional fibers, this new type of dispersion behavior permits remarkably improved suppression of third-order dispersion, particularly in the low-dispersion domain.

Widely Tunable Polarization Modulation Instability in D2O-Filled Microstructured Optical Fiber

Polarization modulation instability (PMI) is a nonlinear effect in which two pump photons with identical polarization propagating in a nonlinear medium give rise to two new photons of different frequency and orthogonal polarization with respect to the pump photons [1] . In this work, we report the experimental demonstration of broad spectral tuning of PMI generated in solid-core microstructured optical fibers (MOF) that were previously infiltrated with heavy water (D 2 O). MOFs were designed and fabricated with the appropriate dispersion characteristics to produce widely spaced PMI spectral bands when they were filled with D 2 O and pumped at 1064 nm. Heavy water was chosen due to suitable …

Supercontinuum generation in silicon waveguides based on optical wave-breaking

We theoretically find the third order dispersion that optimizes the spectral broadening induced by optical wave-breaking. It produces supercontinuum spectra spanning beyond 2=3 of an octave in a silicon waveguide pumping at 1550 nm.

A Refractive Index Sensor Based on the Resonant Coupling to Cladding Modes in a Fiber Loop

We report an easy-to-build, compact, and low-cost optical fiber refractive index sensor. It consists of a single fiber loop whose transmission spectra exhibit a series of notches produced by the resonant coupling between the fundamental mode and the cladding modes in a uniformly bent fiber. The wavelength of the notches, distributed in a wavelength span from 1,400 to 1,700 nm, can be tuned by adjusting the diameter of the fiber loop and are sensitive to refractive index changes of the external medium. Sensitivities of 170 and 800 nm per refractive index unit for water solutions and for the refractive index interval 1.40-1.442, respectively, are demonstrated. We estimate a long range resolut…

Vector Description of a Realistic Photonic Crystal Fiber

Polarization Modulation Instability in All-Normal Dispersion Microstructured Optical Fibers With Quasi-Continuous Pump

We report the experimental observation of the polarization modulation instability (PMI) effect in all-normal dispersion (ANDi) microstructured optical fibers (MOFs) with quasi-continuous pumping. The small unintentional birefringence (~10-5), that any realistic non-polarization maintaining MOF exhibits, contributes to this nonlinear effect. PMI can produce two sidebands whose polarization state is orthogonal to the polarization of the pump. In this work, only one type of PMI process is observed, i.e., when the pump is polarized along the slow axis of the fiber and sidebands are generated in the fast axis mode. This PMI process was studied experimentally in two ANDi fibers with different dis…

Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers

We theoretically identify some photonic-crystal-fiber structures, made up of soft glass, that generate ultrawide (over an octave) and very smooth supercontinuum spectra when illuminated with femtosecond pulsed light. The design of the fiber geometry in order to reach a nearly ultraflattened normal dispersion behavior is crucial to accomplish the above goal. Our numerical simulations reveal that these supercontinuum sources show high stability and no significant changes are detected even for fairly large variations of the incident pulse. Ministerio de Ciencia e Innovación (TEC2008-05490) and Generalitat Valenciana (GV/2007/043).

Supercontinuum spectral control

Supercontinuum (SC) generation in photonic crystal fibers (PCFs) is a cutting-edge phenomenon extensively studied in recent years [1]. SC has found many scientific and technological applications. The control of the SC spectral characteristics is crucial in most of them. A pioneering attempt in this direction was reported in Ref. [2]. We point out that SC is typically generated by accessing the anomalous dispersion regime of the fiber, i.e., when the group velocity dispersion (GVD) coefficient is lower than zero, β 2 ≪0. The recent achievement of soft-glass PCFs, namely, PCFs made up of a transparent material that shows higher nonlinear response than the widely used fused silica, opens new p…

Inverse dispersion design in silicon waveguides

We present a numerical tool to find the cross-section geometry of silicon-oninsulator waveguides that leads to a target dispersion profile. In < 10 iterations, we achieve geometries providing ultraflattened dispersion over 350 nm bandwidth.

Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media.

We propose a numerical method for analyzing extensively the evolution of the coherence functions of nonstationary optical pulses in dispersive, instantaneous nonlinear Kerr media. Our approach deals with the individual propagation of samples from a properly selected ensemble that reproduces the coherence properties of the input pulsed light. In contrast to the usual strategy assuming Gaussian statistics, our numerical algorithm allows us to model the propagation of arbitrary partially coherent pulses in media with strong and instantaneous nonlinearities.

Biorthonormal-basis method for the vector description of optical-fiber modes

This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

Ultralow chirp photonic crystal fiber Mach-Zehnder interferometer

A photonic crystal fiber Mach-Zehnder interferometer design was optimized to obtain high performance and ultralow chirp. Two long-period gratings were used to excite the cladding modes, and the rich structure of the cladding was tailored to obtain a slightly chirped free spectral range, as required by the Telecommunication Standardization Sector of the International Telecommunication Union (ITU-T) Norm G.694.1. Finally, a fabrication tolerance analysis was performed. The advantages of the proposed device are an ultralow chirp, high bandwidth, and fabrication robustness tolerance.

Microstructured Optical Fiber on the Silica Platform for pulse-maintaining 2-octave supercontinuum in short-wavelength infra-red

Numerical design of all normal dispersion fiber for SWIR supercontinuum generation based on standard air-silica microstructure is presented. We increase the spectral width of generated supercontinuum up to 2 octaves while maintaining perfect spectral flatness by tailoring the dispersion profile.

Switching dynamics of dark-pulse Kerr frequency comb states in optical microresonators

Dissipative Kerr solitons are localized structures that exist in nonlinear optical cavities. They lead to the formation of microcombs - chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion cavities. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we explore dark-pulse Kerr combs generated in normal dispersion optical microresonators and report the discovery of reversible switching between coherent dar…

Donor and acceptor guided modes in photonic crystal fibers.

We present a triangular photonic-crystal-fiber structure that exhibits guided modes simultaneously above and below the first conduction band. We achieve this configuration by decreasing the size of one of the airholes (the defect) in a specific triangular lattice. More generally, we analyze the behavior of guided modes that depends on the size of the defect. Defects generated by decreasing or increasing the size of one of the holes produce donor or acceptor guided modes, respectively, in analogy with impurity levels in solid-state crystals. We conclude that the guiding mechanism for both donor and acceptor modes is produced by a unique phenomenon of multiple interference by a periodic struc…

Tunable Four-wave Mixing Light Source Based on Photonic Crystal Fibers with Variable Chromatic Dispersion

We present a detailed experimental study of fourwave mixing tuning in photonic crystal fibers that were filled either with ethanol or with heavy water. It is demonstrated that wide tuning ranges can be achieved in both cases through the variable chromatic dispersion generated by thermo-optic effect. Tunability of the signal band from 745 nm to 919 nm, and of the idler band from 1260 nm to 1759 nm is demonstrated with a pump at 1064 nm. Numerical calculations were carried out and show good agreement with experimental measurements. We present a detailed experimental study of fourwave mixing tuning in photonic crystal fibers that were filled either with ethanol or with heavy water. It is demon…