CN108493770B - Simulation method for photon pair source associated with electric pumping Bragg reflection waveguide - Google Patents
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Abstract
The invention discloses a simulation method of an electric pumping Bragg reflection waveguide associated photon pair source, which comprises the following steps: designing a quantum well region structure and a Bragg reflection waveguide structure in a spontaneous parameter down-conversion process to obtain an electric injection laser consisting of 2 structures; calculating a phase matching tuning curve in the conversion process under the spontaneous parameters according to the Bragg reflection waveguide structure, and finely adjusting the structure parameters to enable the position of the degenerate pumping wavelength to be close to the peak gain wavelength of the quantum well; and calculating the injection current of the electric injection laser, a relation curve of the injection current and the internal optical power and a power density spectrum of the Bragg waveguide spontaneous parameter down-conversion process by the finely adjusted Bragg reflection waveguide structure, and further determining the generation efficiency of the associated photon pair. The invention realizes the systematic geographic theory analysis of the characteristics of the electric injection associated photon pair source and meets various requirements in practical application.
Description
Technical Field
The invention relates to the field of integrated quantum optics, in particular to a simulation method for an electric pumping Bragg reflection waveguide associated photon source.
Background
The related photon pair source is an important resource in quantum optical information processing, and has been widely applied to the fields of quantum key distribution, quantum invisible state transfer, quantum imaging, quantum storage and the like.
The associated photon pairs have both optical and electrical pumping generation mechanisms. The principle of generating the associated photon pair by optical pumping includes two kinds of second-order optical nonlinear effect and third-order optical nonlinear effect by utilizing nonlinear crystal, and is not suitable for integrated mass production. Electrically pumped correlated photon pair source a quantum dot dual exciton radiating diode and a bragg reflective waveguide integrated correlated photon pair source. The electric pumping Bragg reflection waveguide correlation photon pair source integrates a quantum well laser and a Bragg reflection waveguide converted under a spontaneous parameter into a whole by simultaneously utilizing the gain characteristic and the nonlinear characteristic of a quantum well material to generate a correlation photon pair.
Spontaneous parametric down-conversion is considered one of the most efficient methods for the nonlinear process of correlated photon pair generation, which exploits the second-order nonlinear effect of materials to achieve pump light (λ)p) In thatTE (transverse electric) polarized signal light (lambda) is generated simultaneously under the condition of satisfying II-type phase matchings) And TM (transverse magnetic) polarized idler frequency light (lambda)i). Semiconductors are ideal materials for realizing integrated systems, and semiconductor materials such as AlGaAs, GaInP and the like have higher second-order nonlinear coefficients, which provides a material basis for large-scale integration of the source by the electron injection correlated photons.
In 2014, the french Sara Ducci research group implemented electrical injection using AlGaAs material systems in bragg to produce correlated photon pair sources around a wavelength of 1.55 μm. However, the photon pair source associated with the electrically pumped bragg reflection waveguide has the problems of high threshold current, low efficiency of photon pair generated by electrical injection and the like, and the application of the photon pair source associated with the electrical pumping is directly influenced.
In summary, it is urgent to establish a set of simulation methods for the source of the photon pair associated with the electrically pumped bragg reflection waveguide, and systematically analyze these problems to further improve the characteristics of the source of the associated photon pair.
Disclosure of Invention
The invention provides a simulation method of an electric pumping Bragg reflection waveguide associated photon pair source, which realizes the systematic geographic theory analysis of the characteristics of an electric injection associated photon pair source, meets various requirements in practical application and is described in detail as follows:
a simulation method of an electrically pumped bragg reflector waveguide associated photon pair source, the simulation method comprising the steps of:
designing a quantum well region structure and a Bragg reflection waveguide structure in a spontaneous parameter down-conversion process to obtain an electric injection laser consisting of 2 structures;
calculating a phase matching tuning curve in the conversion process under the spontaneous parameters according to the Bragg reflection waveguide structure, and finely adjusting the structure parameters to enable the position of the degenerate pumping wavelength to be close to the peak gain wavelength of the quantum well;
and calculating the injection current of the electric injection laser, a relation curve of the injection current and the internal optical power and a power density spectrum of the Bragg waveguide spontaneous parameter down-conversion process by the finely adjusted Bragg reflection waveguide structure, and further determining the generation efficiency of the associated photon pair.
The electric injection laser includes:
the device comprises a lower electrode, an N-type substrate, an N-type Bragg waveguide layer, a single quantum well layer or a multi-quantum well layer, a P-type etching barrier layer, a P-type Bragg waveguide layer, a P-type protective layer and an upper electrode.
The design of the quantum well region structure specifically comprises the following steps:
selecting a material with a second-order nonlinear coefficient larger than a certain threshold value as a quantum well region material, determining well region thickness, material components of a quantum well and a barrier, and determining a substrate material with a corresponding structure; calculating the trap depth of the quantum trap under stress;
calculating discrete energy levels and wave functions of electrons and holes in the z direction; calculating a hole energy band structure with a mixing effect in the x and y directions;
calculating the state density of a valence band, the transition momentum matrix element and the Fermi level under the given carrier concentration according to the hole energy band structure;
the linear gain coefficient of the quantum well is calculated and the wavelength position of the peak gain is found.
The Bragg reflection waveguide structure for designing the conversion process under the spontaneous parameter specifically comprises the following steps:
selecting a material of the Bragg waveguide reflecting layer according to the thickness and the material of the waveguide core layer, and designing the thickness of the Bragg reflecting layer meeting the condition of 1/4 wavelength Bragg waveguide;
establishing a structural model in COMSOL software according to the thicknesses of the Bragg core layer and the reflecting layer, and solving effective refractive indexes at the conversion wavelength under different pumping wavelengths and spontaneous parameters to obtain the dispersion characteristic of the structural model;
by means of the dispersion characteristic and the class II phase matching condition, the structural model is solved, the pump light wavelength and the down-conversion light wavelength of spontaneous parameter down-conversion can be achieved, and a phase matching tuning curve is obtained.
The thickness of the waveguide core layer is specifically as follows:
and calculating the thickness of the waveguide core layer according to the pump wavelength by taking the wavelength corresponding to the peak gain obtained by designing the quantum well region as the pump wavelength converted under the spontaneous parameter.
The degenerate pump wavelength specifically is:
making signal light lambda in spontaneous parametric down-conversionsAnd idler light lambdaiOnly the pump light wavelength of one set of solutions.
The technical scheme provided by the invention has the beneficial effects that:
1. the Bragg reflection waveguide of the electric pump is integrated with the associated photon pair source, and the large-scale integration of the associated photon pair source can be realized by utilizing the high-second order nonlinear characteristic of a semiconductor material;
2. the simulation method provided by the invention can be used for analyzing the laser gain characteristic and the spontaneous parameter down-conversion efficiency of the associated photon pair source;
3. the invention provides a theoretical basis for designing the source of the associated photon pair generated by the electrically pumped Bragg waveguide, and the characteristics of the generated associated photon pair can be improved through system geographic theory analysis.
Drawings
FIG. 1 is a flow diagram of a method for electrically pumping Bragg reflection waveguide-associated photon-to-source simulation;
FIG. 2 is a schematic diagram of a structure of an electrically pumped Bragg reflector waveguide associated with a photon pair source;
FIG. 3 is a schematic diagram of z-directed energy levels of a source of photon pairs associated with an electrically pumped Bragg reflector waveguide;
FIG. 4 is a schematic representation of a conduction band electron wavefunction of an electrically pumped Bragg reflector waveguide with respect to a photon-to-source;
FIG. 5 is a schematic diagram of a heavy hole wave function associated with a photon-pair source for an electrically pumped Bragg reflector waveguide;
FIG. 6 is a schematic diagram of the light hole wave function of an electrically pumped Bragg reflector waveguide associated photon pair source;
FIG. 7 is an xy-direction hole band structure (E-k) of an electrically pumped Bragg reflector waveguide associated photon pair sourcexy) A schematic diagram;
FIG. 8 is a schematic diagram of the hole state density of an electrically pumped Bragg reflector waveguide associated photon pair source;
FIG. 9 is a schematic diagram of an element of a transition momentum matrix between a conduction band first energy level (C1) and a heavy hole first energy level (HH1) of an electrically pumped Bragg reflector waveguide associated with a photon pair source;
FIG. 10 is a schematic of the linear gain of an electrically pumped Bragg reflector waveguide in relation to a photon-to-source;
FIG. 11 is a schematic diagram of the dispersion characteristics of electrically pumped Bragg reflector waveguides with respect to photons versus the source;
FIG. 12 is a schematic diagram of phase matching tuning curves associated with an electrically pumped Bragg reflector waveguide for a photon-to-source configuration;
FIG. 13 is a graph showing the relationship between the source injection current and the internal optical power of photons associated with an electrically pumped Bragg reflector waveguide (intrinsic loss α)i＝20cm-1injection efficiency of carriers etai20%, 30%, and 40%, respectively);
FIG. 14 is a schematic diagram of a power density spectrum of an electrically pumped Bragg reflector waveguide associated photon-to-source down-conversion process;
FIG. 15 is a graph of the efficiency of photon pair generation associated with an electrically pumped Bragg reflector waveguide with a source of photon pairs (intrinsic loss α)i＝20cm-1injection efficiency of carriers etai20%, 30%, and 40%, respectively).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
The embodiment of the invention provides a simulation method for an electrically pumped Bragg reflection waveguide associated photon pair source, which is an associated photon pair source integrating a quantum well laser and a Bragg reflection waveguide. The waveguide adopts different light limitation and light guide mechanisms for pump light and down-conversion light modes to realize II-class phase matching in the spontaneous parameter down-conversion process: the pump laser is in a Bragg mode (TEB transverse electric Bragg mode), and is limited and guided by utilizing Bragg reflecting layers on two sides of the quantum well region, so that the pump laser mode is mainly limited in the quantum well, and is quickly attenuated in the Bragg reflecting layers; signal light (lambda) generated under spontaneous parameterss) And idler (λ)i) Being totally inverse with mutually perpendicular polarizationsAnd the emission modes are respectively TE (transverse electric) polarization and TM (transverse magnetic) polarization, and total internal reflection limitation is performed by using a combination of low-high-low refractive index formed by the barrier region of the quantum well and the first group of periodic structures, so that the effective refractive index of the spontaneous parametric down-conversion light mode is close to the refractive index of the material of the barrier region of the quantum well.
Example 1
The embodiment of the invention mainly comprises two parts when designing the electric pumping Bragg reflection waveguide correlation photon pair source, firstly determining the quantum well region of the electric injection laser as the core layer of the whole electric pumping Bragg reflection waveguide, and then designing the Bragg waveguide structure for realizing the spontaneous parameter down-conversion process. As described in detail below in conjunction with fig. 1, the model design theory includes:
101: designing a quantum well region structure and a Bragg reflection waveguide structure in a spontaneous parameter down-conversion process to obtain an electric injection laser consisting of 2 structures;
the electric injection laser comprises a lower electrode, an N-type substrate, an N-type Bragg waveguide layer, a single quantum well layer or a multi-quantum well layer, a P-type etching barrier layer, a P-type Bragg waveguide layer, a P-type protective layer and an upper electrode.
102: calculating a phase matching tuning curve in the conversion process under the spontaneous parameters according to the Bragg reflection waveguide structure, and finely adjusting the structure parameters to enable the position of the degenerate pumping wavelength to be close to the peak gain wavelength of the quantum well;
103: and calculating the injection current of the electric injection laser, a relation curve of the injection current and the internal optical power and a power density spectrum of the Bragg waveguide spontaneous parameter down-conversion process by the finely adjusted Bragg reflection waveguide structure, and further determining the generation efficiency of the associated photon pair.
The design of the quantum well region structure in step 101 specifically comprises:
selecting a material with a second-order nonlinear coefficient larger than a certain threshold value as a quantum well region material, determining well region thickness, material components of a quantum well and a barrier, and determining a substrate material with a corresponding structure; calculating the trap depth of the quantum trap under stress;
calculating discrete energy levels and wave functions of electrons and holes in the z direction; calculating a hole energy band structure with a mixing effect in the x and y directions;
calculating the state density of a valence band, the transition momentum matrix element and the Fermi level under the given carrier concentration according to the hole energy band structure;
the linear gain coefficient of the quantum well is calculated and the wavelength position of the peak gain is found.
The bragg reflection waveguide structure for designing the conversion process under the spontaneous parameter in step 101 is specifically as follows:
selecting a material of the Bragg waveguide reflecting layer according to the thickness and the material of the waveguide core layer, and designing the thickness of the Bragg reflecting layer meeting the condition of 1/4 wavelength Bragg waveguide;
establishing a structural model in COMSOL software according to the thicknesses of the Bragg core layer and the reflecting layer, and solving effective refractive indexes at the conversion wavelength under different pumping wavelengths and spontaneous parameters to obtain the dispersion characteristic of the structural model;
by means of the dispersion characteristic and the class II phase matching condition, the structural model is solved, the pump light wavelength and the down-conversion light wavelength of spontaneous parameter down-conversion can be achieved, and a phase matching tuning curve is obtained.
Further, the simulation method further comprises: and calculating the thickness of the waveguide core layer according to the pump wavelength by taking the wavelength corresponding to the peak gain obtained by designing the quantum well region as the pump wavelength converted under the spontaneous parameter.
The degenerate pumping wavelength in step 102 is specifically:
making signal light lambda in spontaneous parametric down-conversionsAnd idler light lambdaiOnly the pump light wavelength of one set of solutions.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
In summary, the bragg reflection waveguide of the electric pump selected in the embodiment of the present invention integrates the correlated photon pair source, and the large scale integration of the correlated photon pair source can be realized by using the high second order nonlinear characteristic of the semiconductor material; the simulation method provided by the invention can be used for analyzing the laser gain characteristic and the spontaneous parameter down-conversion efficiency of the associated photon pair source.
Example 2
The scheme of example 1 is further described below in conjunction with a specific design flow, which is described in detail below:
201: the whole structure of the electric injection laser consists of a quantum well region and a Bragg waveguide in the conversion process under spontaneous parameters;
selecting proper quantum well structure parameters to enable the electric injection laser to generate larger gain near the required pumping wavelength, wherein the whole structure of the electric injection laser is composed of a quantum well region and a Bragg waveguide in the conversion process under spontaneous parameters, namely the whole structure of the electric injection laser comprises: the device comprises a lower electrode, an N-type substrate, an N-type Bragg waveguide layer, a single quantum well layer or a multi-quantum well layer, a P-type etching barrier layer, a P-type Bragg waveguide layer, a P-type protective layer and an upper electrode.
The formula for calculating the linear gain coefficient g of the electric injection laser is as follows:
wherein e is the electron electric quantity, omega is the photon angular frequency, nrWhich is the refractive index of the material,
is Planck constant, c is the speed of light in vacuum, ε0Is a vacuum dielectric constant, m0For free electron mass, LzIn terms of the well region thickness,
an element of a transition momentum matrix from the nth energy level of the conduction band to the mth energy level of the valence band, EcvThe transition energy of the conduction band energy level and the valence band energy level, τinIs the interband electron relaxation time, fc、fvFermi distributions of conduction and valence bands, respectively; k is the photon wave vector, dk is the differential to the wave vector k, and the whole expression is the result of the integration in k-space.
202: designing a quantum well region of an electric injection laser;
203: designing a Bragg reflection waveguide structure in a conversion process under a spontaneous parameter;
and calculating the thickness of a Bragg waveguide core layer and the thickness of a Bragg waveguide reflecting layer according to the pumping wavelength, wherein the core layer is made of the quantum well region (comprising a well region and a barrier region), and the Bragg reflecting waveguide structure is also used as a Bragg waveguide layer of the laser.
204: calculating a phase matching tuning curve in the conversion process under the spontaneous parameters according to the Bragg reflection waveguide structure, and finely adjusting the structure parameters to enable the position of the degenerate pumping wavelength to be close to the peak gain wavelength of the quantum well;
searching for a tuning curve to degenerate the pump wavelength (i.e. to make the signal light lambda in spontaneous parametric down-conversion)sAnd idler light lambdaiOf pump light having only one set of solution wavelengths lambdap) The structural parameters are tuned such that the location of the degenerate pump wavelength is near the quantum well peak gain wavelength.
In specific implementation, the simulation method further includes: and judging whether the position of the degenerate pumping wavelength is near the quantum well peak gain wavelength, if so, executing the step 205, and if not, executing the step 202 again.
205: and calculating the associated photon pair generation efficiency of the Bragg reflection waveguide structure after fine adjustment.
Calculating a relation curve between the injection current and the internal optical power of the electric injection laser according to the structural parameters determined in the step 204, wherein the relation curve satisfies the following relation:
wherein, Pinternalinternal power, η, of pump light for electric injection lasersiefficiency of carrier injection, αiis an intra-cavity loss, αmFor cavity mirror loss, IthIs the threshold current, I is the injection current.
Further, calculating to obtain a power density spectrum of the conversion process under the Bragg reflection waveguide spontaneous parameter:
Δk＝βp-βs-βi
wherein, Ps(i)Signal light (idler) power, P, generated for spontaneous parametric down-conversionpIs the pump light power, d is the second order nonlinear coefficient, L is the waveguide cavity length, nsRefractive index of material of signal light, niRefractive index of material being idler, npRefractive index of material, lambda, for pump lights(i)Is the wavelength of the signal light (idler light), lambdai(s)is the wavelength of the idler light (signal light), βpis the propagation constant of the pump light, betasis a propagation constant of signal light, βiIs the propagation constant of the idler light, AIThe three-wave interaction area in the spontaneous parametric down-conversion process.
And further determining the generation efficiency of the correlated photon pair of the Bragg reflection waveguide structure after fine adjustment according to the integration result of the power density spectrum of the pump light power and the spontaneous parameter down-conversion process.
The step 202 of designing the quantum well region of the electrical injection laser specifically comprises the following steps:
1) selecting the material with larger second-order nonlinear coefficient as the quantum well region material, determining the well region thickness LzThe quantum well and the barrier material, and simultaneously determining the substrate material of the corresponding structure;
2) calculating the trap depth of the quantum trap under stress;
3) calculating discrete energy levels and wave functions of electrons and holes in the z direction;
4) calculating the hole band structure (E-k) in the x, y directions taking into account the band mixing effectxy)；
5) According to the hole band structure (E-k)xy) Calculating the state density of the valence band, the transition momentum matrix element and the Fermi level under the given carrier concentration;
6) for computing quantum wellsLinear gain coefficient g (ω), and finding the wavelength position λ of the peak gainp。
Further, the step 203 of designing the bragg reflection waveguide structure in the spontaneous parametric down-conversion process specifically includes:
1) the wavelength λ corresponding to the peak gain obtained by designing the quantum well region in step 202pAs a pump wavelength for conversion under spontaneous parameters, the thickness of the waveguide core layer is calculated according to the pump wavelength
(i.e. the thickness of the core layer is the thickness of the quantum well region, including the thickness of the well region and the barrier region), ncRefractive index of the material of the core layer (here, the refractive index of the material of the barrier layer in the quantum well structure), neffAt a wavelength of λpThe effective refractive index of (d);
2) selecting the material of the Bragg waveguide reflecting layer according to the thickness and the material of the waveguide core layer, and designing the condition k meeting the 1/4 wavelength Bragg waveguideidiThickness d of pi/2 Bragg reflection layeri，kiFor pump light lambdapWave vector at the ith layer;
3) establishing a structural model in COMSOL software according to the parameters obtained by the design in the step 2), and solving effective refractive indexes at the conversion wavelength under different pumping wavelengths and spontaneous parameters to obtain the dispersion characteristic of the structural model;
the COMSOL software is well known to those skilled in the art, and the embodiments of the present invention will not be described herein.
4) The structural model is solved according to the dispersion characteristic and the class II phase matching condition to realize the pump light wavelength (lambda) converted under the spontaneous parameterp) And down-converting the wavelength of light (lambda)i，λs) And obtaining a phase matching tuning curve.
The class ii phase matching condition is well known to those skilled in the art, and is not described in detail in the embodiments of the present invention.
In summary, the present invention establishes a simulation method for electrically pumping the bragg reflection waveguide and associating the photon pair source through the above steps 201 to 205, and provides a theoretical basis for the system for further improving the characteristics of the electrically injected and associated photon pair source.
Example 3
The following detailed description of the design process of the schemes in examples 1 and 2 is provided with specific parameters, and is described in detail below:
taking the quantum well region material being GaInP/InGaAlP and the bragg reflection layer material being AlGaAs as an example, the structure of the electrically pumped bragg reflection waveguide associated photon pair source is designed and obtained according to the above embodiment, as shown in fig. 2, the following components are sequentially provided from bottom to top:
1) a lower electrode Au;
2) n-type GaAs substrate: the doping type is N type, the doping element is Si, the thickness is 1.4 μm, and the doping concentration is 2 × 1019cm-3；
3) N-type bragg reflective layer: the doping type is N type, the doping element is Si, the N type Bragg reflection layer is formed by two materials alternately, 6 groups are formed, and 12 layers are formed:
Al0.95Ga0.05as (subscript 0.95 represents 95 mol% of AlAs in the ternary compound, subscript 0.05 represents 5 mol% of GaAs in the ternary compound, and the subscripts of the following ternary compounds have similar meanings), thickness of 199.5nm, and Al content0.55Ga0.45As thickness was 103.5 nm.
The material composition and doping concentration of each layer from bottom to top are as follows: al (Al)0.95Ga0.05As(2×1018cm-3)，Al0.55Ga0.45As(1.82×1018cm-3)，Al0.95Ga0.05As(1.65×1018cm-3)，Al0.55Ga0.45As(1.48×1018cm-3)，Al0.95Ga0.05As(1.3×1018cm-3)，Al0.55Ga0.45As(1.13×1018cm-3)，Al0.95Ga0.05As(9.6×1017cm-3)，Al0.55Ga0.45As(7.88×1017cm-3)，Al0.95Ga0.05As(6.16×1017cm-3)，Al0.55Ga0.45As(4.44×1017cm-3)，Al0.95Ga0.05As(2.72×1017cm-3)，Al0.55Ga0.45As(1×1017cm-3)；
4) Quantum well: barrier regions In from bottom to top0.50Ga0.36Al0.14P (115.7 nm thick) (subscript 0.50 indicates 50 mol% of InP in the quaternary compound, subscript 0.36 indicates 36 mol% of GaP in the quaternary compound, subscript 0.14 indicates 14 mol% of AlP in the quaternary compound, and the subscripts in the quaternary compound have similar meanings), well region Ga0.41In0.59P (thickness 5nm), barrier In0.50Ga0.36Al0.14P (thickness 115.7nm), undoped;
5) p-type bragg reflector: the doping type is P type, the doping element is C, the P type Bragg reflection layer is formed by two materials alternately, 6 groups and 12 layers are formed in total.
Al0.55Ga0.45As thickness of 103.5nm and Al0.95Ga0.05As, 199.5nm thick. The material composition and doping concentration of each layer from bottom to top are as follows: al (Al)0.55Ga0.45As(1×1017cm-3)，Al0.95Ga0.05As(2.72×1017cm-3)，Al0.55Ga0.45As(4.44×1017cm-3)，Al0.95Ga0.05As(6.16×1017cm-3)，Al0.55Ga0.45As(7.88×1017cm-3)，Al0.95Ga0.05As(9.6×1017cm-3)，Al0.55Ga0.45As(1.13×1018cm-3)，Al0.95Ga0.05As(1.3×1018cm-3)，Al0.55Ga0.45As(1.48×1018cm-3)，Al0.95Ga0.05As(1.65×1018cm-3)，Al0.55Ga0.45As(1.82×1018cm-3)，Al0.95Ga0.05As(2×1018cm-3)；
6) P-type etching barrier layer: the doping type is P type, and the doping elements are C and In0.48Ga0.42Al0.10P with a thickness of 10nm and a doping concentration of 7 × 1018cm-3；
7) P-type GaAs protective layer: the doping type is P type, the doping element is C, the thickness is 230nm, and the doping concentration is 2 multiplied by 1019cm-3；
8) And an upper electrode Au.
Wherein the quantum well comprises a well region (Ga)0.41In0.59P) and barrier region (In)0.50Ga0.36Al0.14P), the bragg reflection waveguide includes: the GaAs substrate, the Bragg reflector of N type, the Bragg reflector of P type, P type etching barrier layer, P type GaAs protective layer. The lower electrode Au and the upper electrode Au are used for realizing electric injection excitation to generate pumping laser.
The embodiment of the present invention is described by taking the doping concentration, the thickness, the doping element, and the like as examples, and when the embodiment is specifically implemented, the value is not limited, and is set and selected according to the requirements in practical application.
Example 4
The following detailed description of the design process of the schemes in examples 1 and 2 is provided with specific parameters, and is described in detail below:
1) GaInP and InGaAlP have higher second-order nonlinear coefficients and are ideal materials for realizing conversion under spontaneous parameters, so that GaInP and InGaAlP are respectively selected as materials of a well region and a barrier region of a laser;
2) AlGaAs is selected as a material of a Bragg reflection layer, and GaAs is taken as a substrate material;
3) according to the research on the characteristics of the strained quantum well laser, the TE polarized light (transverse electric polarization) generated under the compressive strain has larger gain, so that the material component Ga of the well region with the compressive strain is selected0.41In0.59P (strain amount is epsilon-0.65%), selecting barrier zone material component In without strain0.50Ga0.36Al0.14P, well region thickness Lz＝5nm；
4) Root of herbaceous plantThe well depth under the well region compressive strain (epsilon ═ 0.65%) is calculated according to the structural parameters of the quantum well region as follows: conduction band electron trap depth: delta Ec0.1243eV, valence band heavy hole well depth: delta Ehh0.0669eV, valence band light hole well depth: delta Elh＝0.1204eV；
5) Solving the schrodinger equation in the z direction to obtain a z-direction energy level value and a wave function, as shown in fig. 3, 4, 5 and 6, wherein the obtained first energy level of the conduction band is as follows: ec1.859eV, heavy hole first energy level: eh1-4.6meV, heavy hole second energy level: eh2-65.9meV, light hole first energy level: el1＝-75.9meV；
6) Considering the band mixing effect between valence bands, solving the Schrodinger equation of the xy direction of the valence bands by using Luttinger Hamilton quantity to obtain the xy direction cavity energy band structure (E-k)xy) As shown in fig. 7;
7) the hole band structure (E-k) calculated in step (6)xy): calculating the hole state density:
(wherein, k isxyIs the wave vector of the xy direction of the pump light, LzIs well z-direction thickness) as shown in fig. 8; calculating an element | R of a transition momentum matrix between a first energy level of a conduction band (C1) and a first energy level of heavy holes (HH1)cv|2＝<Ψc|-er|Ψv>2(Ψc、ΨvWave functions of a conduction band and a valence band, respectively, e is an electron quantity, and r is a position operator), as shown in fig. 9; calculation of given injected carrier concentration of 8 × 1018cm-3Fermi energy level of hour: conduction band fermi level Efc1.977eV, valence band Fermi level Efv＝-9.1meV；
8) The linear gain coefficient of the quantum well was calculated as shown in fig. 10, and the wavelength position of the peak gain was found to be λp654nm (concentration of injected carriers 8 × 10)18cm-3)。
9) Wavelength lambda corresponding to peak gain obtained by designing quantum well regionp654nm as pump wavelength for spontaneous parametric down-conversionCalculating the thickness of the waveguide core layer according to the wavelength
The thickness of a quantum well region (comprising a well region and a barrier region) is determined, and the thickness of the barrier region is determined to be 115.7 nm;
10) since AlGaAs is a common material for bragg reflective waveguides, the embodiments of the present invention select the high and low refractive index materials of the 1/4 wavelength bragg waveguide reflective layer as: al (Al)0.55Ga0.45As and Al0.95Ga0.05As, the thickness of each layer of the Bragg reflection layer is 1/4 of the transverse transmission constant of the pump mode, i.e. kidiPi/2, resulting in a thickness of 103.5nm and 199.5nm for the two materials, respectively;
11) establishing the waveguide model by COMSOL software, selecting a ridge waveguide to transversely limit an optical mode field, and calculating the effective refractive index of a pumping wavelength of 651-654 nm and a down-conversion wavelength of 1200-1400 nm to obtain the dispersion characteristic of the structure, as shown in FIG. 11;
12) the three wavelengths converted under the spontaneous parameters satisfy: 1/lambdap＝1/λs+1/λiAnd np/λp＝ns/λs+ni/λiSolving the system of equations can obtain the wavelength (lambda) of the pump light which can realize spontaneous parametric down-conversionp) And down-converting the wavelength of light (lambda)i，λs) And a phase matching tuning curve is obtained as shown in fig. 12. By fine-tuning the structural parameters, the degenerate pumping wavelength of 653.1nm is obtained and is positioned near the peak gain wavelength of 654nm of the quantum well;
13) according to the analysis, a relation curve (α) of the injection current and the internal optical power of the laser is calculatedi＝20cm-1injection efficiency of carriers eta i20%, 30% and 40% respectively), power density spectrum of Bragg waveguide spontaneous parameter down-conversion process, associated photon pair generation efficiency curve (α)i＝20cm-1injection efficiency of carriers eta i20%, 30%, 40%, respectively) as shown in fig. 13, 14, and 15, respectively.
The embodiments of the present invention are described only by taking the injection efficiency of the carriers, the degenerate pumping wavelength, the thickness of the material, and the like as examples, and in the specific implementation, the values are not limited, and are set and selected according to the requirements in practical applications.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (5)
1. A simulation method for an electrically pumped Bragg reflection waveguide associated photon pair source is characterized by comprising the following steps:
designing a quantum well region structure and a Bragg reflection waveguide structure in a spontaneous parameter down-conversion process to obtain an electric injection laser consisting of 2 structures;
calculating a phase matching tuning curve in the conversion process under the spontaneous parameters according to the Bragg reflection waveguide structure, and finely adjusting the structure parameters to enable the position of the degenerate pumping wavelength to be close to the peak gain wavelength of the quantum well;
calculating the injection current of the electric injection laser, a relation curve between the injection current and the internal optical power and a power density spectrum of the Bragg waveguide spontaneous parameter down-conversion process by the finely adjusted Bragg reflection waveguide structure, and further determining the generation efficiency of the associated photon pair;
wherein, the design quantum well region structure specifically comprises:
selecting a material with a second-order nonlinear coefficient larger than a certain threshold value as a quantum well region material, determining well region thickness, material components of a quantum well and a barrier, and determining a substrate material with a corresponding structure; calculating the trap depth of the quantum trap under stress;
calculating discrete energy levels and wave functions of electrons and holes in the z direction; calculating a hole energy band structure with a mixing effect in the x and y directions;
calculating the state density of a valence band, the transition momentum matrix element and the Fermi level under the given carrier concentration according to the hole energy band structure;
the linear gain coefficient of the quantum well is calculated and the wavelength position of the peak gain is found.
2. The method of claim 1, wherein the electrical injection laser comprises:
the device comprises a lower electrode, an N-type substrate, an N-type Bragg waveguide layer, a single quantum well layer or a multi-quantum well layer, a P-type etching barrier layer, a P-type Bragg waveguide layer, a P-type protective layer and an upper electrode.
3. The method according to claim 1, wherein the designing of the bragg reflection waveguide structure for the spontaneous parametric down-conversion process specifically comprises:
selecting a material of the Bragg waveguide reflecting layer according to the thickness and the material of the waveguide core layer, and designing the thickness of the Bragg reflecting layer meeting the condition of 1/4 wavelength Bragg waveguide;
establishing a structural model in COMSOL software according to the thicknesses of the Bragg core layer and the reflecting layer, and solving effective refractive indexes at the conversion wavelength under different pumping wavelengths and spontaneous parameters to obtain the dispersion characteristic of the structural model;
by means of the dispersion characteristic and the class II phase matching condition, the structural model is solved, the pump light wavelength and the down-conversion light wavelength of spontaneous parameter down-conversion can be achieved, and a phase matching tuning curve is obtained.
4. The method according to claim 3, wherein the waveguide core layer has a thickness of:
and calculating the thickness of the waveguide core layer according to the pump wavelength by taking the wavelength corresponding to the peak gain obtained by designing the quantum well region as the pump wavelength converted under the spontaneous parameter.
5. The method according to claim 1, wherein the degenerate pump wavelength is specifically:
making signal light lambda in spontaneous parametric down-conversionsAnd idler light lambdaiOnly the pump light wavelength of one set of solutions.
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