Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals.Here,we derive the equivalent techniq...Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals.Here,we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors.While the absorption has useful applications,it is primarily a loss process;conversely,the non-linear susceptibility is a crucial parameter for active photonic devices.For Si:P,we predict the hyperpolarizability ranges from χ^((3))/n_(3D)=2.9 to 580×10^(−38 )m^(5)/V^(2) depending on the frequency,even while avoiding resonance.Using samples of a reasonable density,n3D,and thickness,L,to produce thirdharmonic generation at 9 THz,a frequency that is difficult to produce with existing solid-state sources,we predict that χ^((3)) should exceed that of bulk InSb and χ^((3))L should exceed that of graphene and resonantly enhanced quantum wells.展开更多
Third-order non-linearities are important because they allow control over light pulses in ubiquitous high-quality centro-symmetric materials like silicon and silica.Degenerate four-wave mixing provides a direct measur...Third-order non-linearities are important because they allow control over light pulses in ubiquitous high-quality centro-symmetric materials like silicon and silica.Degenerate four-wave mixing provides a direct measure of the third-order non-linear sheet susceptibility x^(3)(where L represents the material thickness)as well as technological possibilities such as optically gated detection and emission of photons.Using picosecond pulses from a free electron laser,we show that silicon doped with P or Bi has a value of x^(3)Lin the THz domain that is higher than that reported for any other material in any wavelength band.The immediate implication of our results is the efficient generation of intense coherent THz light via upconversion(also a x^(3)process),and they open the door to exploitation of nondegenerate mixing and optical nonlinearities beyond the perturbative regime.展开更多
基金financial support from the UK Engineering and Physical Sciences Research Council[ADDRFSS,Grant No.EP/M009564/1]EPSRC strategic equipment grant no.EP/L02263X/1.
文摘Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals.Here,we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors.While the absorption has useful applications,it is primarily a loss process;conversely,the non-linear susceptibility is a crucial parameter for active photonic devices.For Si:P,we predict the hyperpolarizability ranges from χ^((3))/n_(3D)=2.9 to 580×10^(−38 )m^(5)/V^(2) depending on the frequency,even while avoiding resonance.Using samples of a reasonable density,n3D,and thickness,L,to produce thirdharmonic generation at 9 THz,a frequency that is difficult to produce with existing solid-state sources,we predict that χ^((3)) should exceed that of bulk InSb and χ^((3))L should exceed that of graphene and resonantly enhanced quantum wells.
基金We acknowledge financial support from the UK Engineering and Physical Sciences Research Council[ADDRFSS,Grant No.EP/M009564/1]the EPSRC National Research Facility,FELIX
文摘Third-order non-linearities are important because they allow control over light pulses in ubiquitous high-quality centro-symmetric materials like silicon and silica.Degenerate four-wave mixing provides a direct measure of the third-order non-linear sheet susceptibility x^(3)(where L represents the material thickness)as well as technological possibilities such as optically gated detection and emission of photons.Using picosecond pulses from a free electron laser,we show that silicon doped with P or Bi has a value of x^(3)Lin the THz domain that is higher than that reported for any other material in any wavelength band.The immediate implication of our results is the efficient generation of intense coherent THz light via upconversion(also a x^(3)process),and they open the door to exploitation of nondegenerate mixing and optical nonlinearities beyond the perturbative regime.
