Generating mid-IR octave-spanning supercontinua and few-cycle pulses with solitons in phase-mismatched quadratic nonlinear crystals

We discuss a novel method for generating octave-spanning supercontinua and few-cycle pulses in the important mid-IR wavelength range. The technique relies on strongly phase-mismatched cascaded second-harmonic generation (SHG) in mid-IR nonlinear frequency conversion crystals. Importantly we here investigate the so-called noncritical SHG case, where no phase matching can be achieved but as a compensation the largest quadratic nonlinearities are exploited. A self-defocusing temporal soliton can be excited if the cascading nonlinearity is larger than the competing material self-focusing nonlinearity, and we define a suitable figure of merit to screen a wide range of mid-IR dielectric and semiconductor materials with large effective second-order nonlinearities $d_{\rm eff}$. The best candidates have simultaneously a large bandgap and a large $d_{\rm eff}$. We show selected realistic numerical examples using one of the promising crystals: in one case soliton pulse compression from 50 fs to 15 fs (1.5 cycles) at 3.0\mic is achieved, and at the same time a 3-cycle dispersive wave at 5.0\mic is formed that can be isolated using a long-pass filter. In another example we show that extremely broadband supercontinua can form spanning the near-IR to the end of the mid-IR (nearly 4 octaves).Comment: submitted to Optics Materials Express special issue on mid-IR photonic

Optical Cherenkov radiation by cascaded nonlinear interaction: an efficient source of few-cycle energetic near- to mid-IR pulses

When ultrafast noncritical cascaded second-harmonic generation of energetic femtosecond pulses occur in a bulk lithium niobate crystal optical Cherenkov waves are formed in the near- to mid-IR. Numerical simulations show that the few-cycle solitons radiate Cherenkov (dispersive) waves in the \lambda=2.2-4.5\mic range when pumping at \lambda_1=1.2-1.8\mic. The exact phase-matching point depends on the soliton wavelength, and we show that a simple longpass filter can separate the Cherenkov waves from the solitons. The Cherenkov waves are born few-cycle with an excellent Gaussian pulse shape, and the conversion efficiency is up to 25%. Thus, optical Cherenkov waves formed with cascaded nonlinearities could become an efficient source of energetic near- to mid-IR few-cycle pulses.Comment: Extended version of Nonlinear Optics 2011 contribution http://www.opticsinfobase.org/abstract.cfm?URI=NLO-2011-NTuA7. Submitted for Optics Express special issue for NLO conferenc

Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression

We study soliton pulse compression in materials with cascaded quadratic nonlinearities, and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible.Comment: 3 pages, 2 figures, published verison in Optics Letters. Contains revised equations, including an updated mode

Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched cascaded interactions

Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase-matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase-mismatch ensures an ultrafast nonlinear response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals.Comment: resubmitted, revised version, accepted for Phys. Rev. Let

A Phylogenetic Study of Vulnerable Batoid Species from the North Atlantic

Successful resolution of the nomenclature and taxonomy of batoid fish complicated by the high degree of morphological and ecological conservatism in this group. However, both mitochondrial DNA (mtDNA) and nuclear DNA (nDNA) phylogenies have been utilised to resolve batoid phylogenies and even to identify cryptic species. As a result, the number of ray species described in recent decades has dramatically increased- although questions still remain regarding the taxonomic status of many batoid species. In chapter one of this thesis, the importance of taxonomy in skate conservation and management is reviewed. In chapter two, control region (CR) and cytochrome oxidase I (COI) sequencing of the blue skate (Dipturus batis) and the flapper skate (Dipturus intermedius) from across the Northeast Atlantic was performed, in order to clarify their geographical distribution. Although now formally recognised as distinct species, before 2010 these two taxa were classified together as the critically endangered ‘common skate’, D. batis. Although this has important conservation implications, their protection is currently being hindered by a lack of spatiotemporal data. In the present study, the blue skate generally appears to be more common than the flapper skate, with a distribution extending from Rockall and Iceland to the Western Approaches and the Celtic Sea. Whilst the flapper skate appears most frequent around northern Scotland, the North Sea and Ireland, novel data also suggests that it may have once had a much wider distribution. For the first time, this species was identified in the Azores, where unique haplotypes were also isolated, potentially highlighting the genetic distinctiveness of the population in this region. In chapter three, nextRAD and mtDNA (concatenated CR and COI) sequencing were utilised to explore the phylogenetics of several vulnerable species of European skate. Whilst the current designation of the Madeiran skate (Raja maderensis) and the thornback ray (Raja clavata) as distinct species wasn’t fully supported, genetically distinct populations were identified in the Azores and surrounding seamounts. The presence of a cryptic Dipturus species in the Azores wasn’t supported, as suggested by previous work on the longnosed skate (Dipturus oxyrinchus). However, Azorean longnosed skate and flapper skate were distinct from their geographically proximate counterparts, and may represent distinct populations. The uniqueness of the Azores highlights the importance of seamounts as ‘hotspots’ of biodiversity, which has important implications for marine protected areas that include these batoid species as a protected feature. In addition to resolving these phylogenies, this thesis also offered an opportunity to comment on the utility of mtDNA and nextRAD sequencing for batoid phylogenetics, the latter of which has never been applied to skates and rays before

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (\textit{i.e.}, the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -- related to the difference between the SHG and the Kerr soliton numbers -- and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, which control the behaviour of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a $\beta$-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.Comment: 11 pages, 8 figures, resubmitted version, to appear in October issue of J. Opt. Soc. Am. B. Substantially revised, updated mode

Limits to compression with cascaded quadratic soliton compressors

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths $\lambda=1.0-1.3 \mu{\rm m}$ in a $\beta$-barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. However, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account.Comment: 16 pages, 5 figures, submitted to Optics Expres