CN114859625B - Nonlinear crystal structure design method for realizing spontaneous parametric down-conversion process - Google Patents
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- 235000019796 monopotassium phosphate Nutrition 0.000 description 3
- QBLDFAIABQKINO-UHFFFAOYSA-N barium borate Chemical compound [Ba+2].[O-]B=O.[O-]B=O QBLDFAIABQKINO-UHFFFAOYSA-N 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
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- 229910000402 monopotassium phosphate Inorganic materials 0.000 description 2
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- PJNZPQUBCPKICU-UHFFFAOYSA-N phosphoric acid;potassium Chemical compound [K].OP(O)(O)=O PJNZPQUBCPKICU-UHFFFAOYSA-N 0.000 description 2
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Abstract
The invention relates to a nonlinear crystal structure design method for realizing a parametric down-conversion process, which comprises the following steps: s1: according to the actual requirement, determining that the wavelengths of the entangled light o light and the entangled light e light are lambda o、λe respectively, and further determining the wavelength lambda p of the required pump light, and the material and the size of the nonlinear crystal; and then determining a crystal cutting angle beta according to a phase matching mode: s2: the front surface inclination angle psi of the nonlinear crystal is equal to the discrete angle alpha of the e ray; s3: and (3) preparing a cuboid-shaped nonlinear crystal according to the material and the size of the nonlinear crystal determined in the step (S1), and cutting the front surface of the cuboid-shaped nonlinear crystal according to the front surface inclination angle psi calculated in the step (S3) to finally obtain the required nonlinear crystal structure. The invention can reduce the influence caused by deflection of the double refraction effect and has higher accuracy.
Description
Technical Field
The invention belongs to the technical field of quantum entanglement light sources, and particularly relates to a nonlinear crystal structure design method for realizing a spontaneous parametric down-conversion process.
Background
In recent years, quantum entanglement light sources have been rapidly developed, and have been widely used in quantum detection imaging, quantum computing, quantum key distribution, invisible state transfer, metering, safe time transfer and the like, and the core of these technologies is entangled photon pairs prepared by two-photon entanglement sources. The entangled photon pair prepared by the spontaneous parametric down-conversion (Spontaneous Parametric Down Conversion, SPDC) process has higher purity and higher brightness, so that the entangled photon pair is the most mature and most commonly used method for preparing the entangled photon pair by the existing two-photon entangled source.
SPDC exploits the second order nonlinear effect of nonlinear crystals to produce entangled photon pairs. In the nonlinear action process of the optical field and the crystal, after one pump light wave passes through the nonlinear crystal, another 2 beams of parametric light with lower frequency are generated under a certain probability, wherein one beam of parametric light is called signal light, and the other beam of parametric light is called idle light. The SPDC process is a three-wave mixing process of the above 3-beam light in a nonlinear crystal, which satisfies the energy conservation and momentum conservation, i.e., the "phase matching" condition. Because of the birefringence effect of nonlinear crystals, the refractive indices of light with different polarization directions in the crystals are also different, so that it is necessary to select an appropriate crystal as a down-conversion crystal to satisfy phase matching, thereby realizing the SPDC process. Common nonlinear materials include barium metaborate (barium metaborate, BBO), potassium dihydrogen phosphate (potassium dihydrogen phosphate, KDP), and the like.
In the SPDC process, collimated pump laser is normally incident into a nonlinear crystal cut into a cuboid traditional structure, but due to the birefringence effect of the nonlinear crystal, the pump light vertically incident into the crystal deflects at a certain angle, which affects the satisfaction of phase matching conditions and the quality of generated entangled photon pairs, and in a specific experimental process, in order to make generated signal light and idle light propagate on a horizontal plane, the propagation direction of the pump light, the angle of a wave plate, the placement direction of the crystal and the like need to be finely adjusted, the adjustment process is complex, and the accuracy is poor. .
Disclosure of Invention
The technical problems to be solved are as follows:
The invention aims to reduce the influence caused by deflection of the birefringence effect when the pump light is incident to the crystal by carrying out structural design on the nonlinear crystal for realizing the SPDC process, thereby improving the quality of phase matching conditions and the quality of the generated entangled photon pairs.
The invention provides a nonlinear crystal structure design method for realizing an SPDC process, which cuts a small part of a traditional cuboid structure to form an inclined plane with a small angle so as to realize that e light can propagate along a horizontal plane after entering a nonlinear crystal, thereby reducing the influence caused by deflection due to a double refraction effect and having higher accuracy.
The technical scheme adopted is as follows:
In order to realize propagation of pump light in the horizontal direction after vertical incidence to the front surface of the crystal in the spontaneous parametric down-conversion process, the material, the size, the cutting angle beta and the front surface inclination angle psi of the nonlinear crystal need to be determined, and the specific method is as follows:
s1: according to the actual requirement, determining that the wavelengths of the entangled light o light and the entangled light e light are lambda o、λe respectively, and further determining the wavelength lambda p of the required pump light, and the material and the size of the required nonlinear crystal; determining a crystal cutting angle beta of the nonlinear crystal according to a phase matching mode, wherein beta is an included angle between the optical axis direction and the horizontal direction of the nonlinear crystal;
s2: in order to realize that the pump light vertically enters the front surface of the nonlinear crystal and then propagates along the horizontal direction, the front surface inclination angle psi of the nonlinear crystal is equal to the discrete angle alpha of e light, wherein the front surface inclination angle psi is an included angle between the front surface of the nonlinear crystal and the vertical direction, the discrete angle alpha of e light is an included angle between the e light and the normal of e light, and then the size of the front surface inclination angle psi is obtained based on a calculation formula of the discrete angle alpha;
S3: designing according to the material, the size and the crystal cutting angle beta of the nonlinear crystal determined in the step S1 to obtain a cuboid nonlinear crystal, and cutting the front surface of the cuboid nonlinear crystal according to the front surface inclination angle psi calculated in the step S3 to finally obtain the required nonlinear crystal structure.
Further, in step S2, when the pump light is perpendicularly incident on the nonlinear crystal front surface, the wave normal directions of the o-light and the e-light generated in the nonlinear crystal are the same, and both are perpendicular to the nonlinear crystal front surface; meanwhile, due to normal incidence, the o light propagation direction does not deflect, the o light is in the same direction as the normal of the o light wave, the optical axis orientation has a certain included angle with the nonlinear crystal surface, and due to the birefringence effect of the nonlinear crystal, the discrete angle alpha between the e light and the normal of the e light wave meets the following conditions:
Wherein θ is the angle between the e light wave normal and the crystal optical axis; the refractive index n o、ne,no of the entangled light in the nonlinear crystal is calculated according to the wavelength lambda o、λe of the entangled light and the material of the nonlinear crystal, n o changes along with the change of the wavelength o of the light in the crystal, namely, n o＝f1(λo);ne is satisfied as the refractive index of the e light in the nonlinear crystal, and n e also changes along with the change of the wavelength e of the light in the crystal, namely, n e＝f2(λe is satisfied.
Further, in step S1, the entangled photon pair prepared by the spontaneous parametric down-conversion process satisfies:
Further, in step S2, the nonlinear crystal is made of a negative uniaxial crystal material, so that n e<no, that is, tan α <0, α <0 indicates that the angle between the e ray and the optical axis is greater than the angle θ between the normal of the e ray and the optical axis, so that the e ray is far away from the optical axis than the normal of the e ray; and because the normal line of the e light wave is consistent with the direction of the o light, the alpha angle is the included angle between the e light and the o light;
Further, based on the geometric relationship between the angles, it is known that: ψ=β - θ, i.e., θ=β - ψ, and ψ= |α|; substituting the inclination angle into the calculation formula of the dispersion angle to obtain a relation formula which is satisfied by the front surface inclination angle psi:
The magnitude of the front surface tilt angle ψ can be calculated.
The two-photon entanglement source comprises a laser, a beam shaping module and a nonlinear crystal, wherein the nonlinear crystal is prepared by adopting the nonlinear crystal structure design method for realizing the spontaneous parametric down-conversion process.
Further, the laser emits pump light with a frequency of omega p and a wavelength of lambda p.
Further, the beam shaping module comprises a small hole, a convex lens, a wave plate and a polarization beam splitter, and is used for shaping the pump light emitted by the laser to keep a state with good collimation and consistent polarization direction, and then the pump light is incident into the nonlinear crystal.
The invention has the beneficial effects that:
(1) According to the invention, the front surface of the crystal is obliquely cut at a specific angle according to the parameters of the nonlinear crystal, such as the pump light, the signal light and the idle light, so as to ensure that the pump light propagates along the horizontal direction after entering the crystal, and the propagation direction of the pump light is accurately regulated through the crystal structure design, thereby improving the quality of phase matching.
(2) The method improves the cuboid traditional structure of the nonlinear crystal in the two-photon entanglement source by carrying out structural design on the nonlinear crystal, effectively reduces the influence of the birefringence effect on the change of the propagation direction of the pumping light when the pumping light enters the nonlinear crystal, has simple method and simple and convenient operation, and is suitable for engineering application.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of the components of a two-photon entanglement source according to the present invention;
FIG. 2 is a schematic diagram of phase matching in a nonlinear crystal according to the present invention;
FIG. 3a is a schematic diagram of a nonlinear crystal cuboid structure in a conventional scheme
FIG. 3b is a diagram illustrating the deviation of pump light in the SPDC process in the conventional scheme
FIG. 4a is a schematic diagram of a nonlinear crystal structure in the present invention
FIG. 4b is a schematic diagram of the SPDC process implemented by the nonlinear crystal in the present invention
FIG. 5 is a schematic view showing the process of making pump light incident on nonlinear crystal
FIG. 6 is a block diagram showing a structural design flow of a nonlinear crystal according to the present invention
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
Typically, the two-photon entanglement source comprises a laser, a beam shaping module, a nonlinear crystal and other components, and a block diagram of the specific components is shown in fig. 1. The laser emits pumping light with the frequency omega p and the wavelength lambda p, the initial pumping light is shaped by utilizing optical devices such as a small hole, a convex lens, a wave plate, a polarization beam splitter and the like in the beam shaping module, so that the initial pumping light is kept in a state of good collimation and consistent polarization direction, and then the pumping light is incident into a nonlinear crystal, and the preparation of entangled photon pairs is completed by realizing an SPDC process.
In the SPDC process, after a pump light with a frequency of ω p passes through a nonlinear crystal, another 2 beams of parametric light with a lower frequency are generated with a certain probability, wherein one beam of parametric light is called signal light (with a frequency of ω s), and the other beam of parametric light is called idle light (with a frequency of ω i). The SPDC process is a three-wave mixing process of the above 3 lights in a nonlinear crystal, which satisfies the energy conservation and momentum conservation, i.e. "phase matching" condition, expressed as: omega p＝ωs+ωi,kp＝ks+ki. Wherein k p、ks and k i are wave vectors of pump light, signal light and idle light, respectively. In order to obtain entangled photon pairs with higher purity and better quality, the spectrum of the signal light and the spectrum of the idle light need to be basically consistent, namely, the following conditions are satisfied: omega s＝ωi. In addition, the pump light is generally incident to the crystal, so that the pump light propagates in the crystal along the horizontal direction, and the propagation direction of the generated entangled photon pair is also the same as that in a horizontal plane, and the separation angle between the entangled photon pair and the pump light is the same, so that the detection, collection and utilization of the entangled photon pair prepared by the rear end of the crystal are facilitated. A schematic diagram of phase matching in a nonlinear crystal is shown in fig. 2.
In implementing SPDC, collimated pump laser light is typically used to perpendicularly impinge on a nonlinear crystal cut into a cuboid structure. Because of the condition constraint of the phase matching mode, only very light (Extraordinary Rays, abbreviated as e light) can realize the SPDC process in general, so that the pumping light emitted by the laser is basically filtered out by an ordinary ray (Ordinary Rays, abbreviated as o light) part after passing through the beam shaping module, and only the e light is left to enter the nonlinear crystal. However, due to the birefringence effect of the nonlinear crystal, the pump light can deflect at a small angle after entering the crystal, and at the moment, the propagation direction of the pump light in the crystal is not parallel to the horizontal plane, so that the generated signal light and idle light are not parallel to the horizontal plane, and the detection, collection and utilization of the prepared entangled photon pair by the rear end are inconvenient, as shown in fig. 3; in a specific experimental process, in order to make the generated signal light and idle light propagate on a horizontal plane, fine adjustment needs to be performed on the propagation direction of the pump light, the angle of the wave plate, the placement direction of the crystal and the like, the adjustment process is complex, and the accuracy is poor.
The invention provides an improved nonlinear crystal structure design method for realizing an SPDC process, which cuts a small part of a traditional cuboid structure to form an inclined plane with a small angle so as to realize that e light can propagate along a horizontal plane after entering a nonlinear crystal, thereby reducing the influence caused by deflection due to a double refraction effect and having higher accuracy as shown in figure 4.
In the specific process of the nonlinear crystal structure design, firstly, the wavelength lambda o、λe of entangled light is determined according to the requirement, and then the wavelength lambda p of pump light, the material and the size of the nonlinear crystal are determined; the crystal cutting angle beta is determined according to the phase matching mode, and the determination of the material, the size and the crystal cutting angle beta of the nonlinear crystal is obtained by the prior known method based on the required entangled light, the designed optical path and other parameters.
According to the required wavelength lambda o、λe of the entangled light and the material of the nonlinear crystal, the refractive index n o、ne of the entangled light in the nonlinear crystal is calculated, the calculated n o、ne and beta are substituted into a derived functional relation formula about e light propagation dispersion angle, an included angle phi between the front surface of the nonlinear crystal and the vertical direction is calculated, and finally the material, the size, the crystal cutting angle beta and the front surface inclination angle phi of the nonlinear crystal are determined, so that the structural design of the nonlinear crystal is completed, as shown in fig. 6.
When the pump light vertically enters the nonlinear crystal, the wave normal directions of o light and e light in the crystal are the same and are vertical to the surface of the crystal; meanwhile, due to vertical incidence, the o light propagation direction is not deflected, and the o light is in the same direction as the normal of the o light wave. The optical axis orientation and the crystal surface have a certain included angle, and a dispersion angle alpha between the e light ray and the normal line of the e light wave meets the following conditions due to the double refraction effect of the nonlinear crystal:
Wherein n o is the refractive index of o light in the nonlinear crystal, n o varies in the crystal with the variation of the wavelength of o light, i.e. satisfies n o＝f1(λo), where λ o is the wavelength of o light; n e is the refractive index of e light in the nonlinear crystal, and n e also varies in the crystal with the variation of e light wavelength, i.e., satisfies n e＝f2(λe), where λ e is the wavelength of e light, and the magnitudes of n o and n e can be calculated by the formulas of n o and n e described above.
Entangled photon pairs are typically prepared by the SPDC process to satisfy: Where lambda p is the wavelength of the pump light. A schematic of the fresnel plot for this process is shown in fig. 5.
According to the energy conservation and momentum conservation conditions of the SPDC process, the nonlinear crystal needs to adopt a negative uniaxial crystal material (n e<no), and after tan alpha is deduced to be less than 0, alpha is less than 0, and the included angle between the e light ray and the optical axis is larger than the included angle theta between the normal of the e light wave and the optical axis, so that the e light ray is far away from the optical axis than the normal of the e light wave; and because the normal line of the e light wave is consistent with the o light, the alpha angle is the included angle between the e light ray and the o light ray.
In order to realize the propagation of the pump light in the horizontal direction after the pump light is incident on the crystal, the included angle psi between the front surface of the nonlinear crystal and the vertical direction is required to be equal to the discrete angle alpha between the e light ray and the e light wave normal, namely, the discrete angle alpha between the psi and the e light ray and the e light wave normal is equal to the discrete angle alpha between the psi and the e light wave normal, namely, the phi alpha I is required to be satisfied; the geometrical relationship according to each angle can be known: ψ=β - θ, where β is the cutting angle of the crystal, i.e., the angle between the optical axis direction and the horizontal direction; it can be deduced that: θ=β - ψ, and substituting it into the formula of the discrete angle can obtain a relational expression that the included angle ψ satisfies:
The angle phi between the front surface of the nonlinear crystal and the vertical direction satisfies a functional relation, and the value of the front surface inclination angle can be finally calculated according to the relation.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. While still being apparent from variations or modifications that may be made by those skilled in the art are within the scope of the invention.
Claims (8)
1. The method is characterized in that in the spontaneous parametric down-conversion process, in order to realize that pump light vertically enters the front surface of a nonlinear crystal and then propagates along the horizontal direction, the material, the size, the cutting angle beta and the front surface inclination angle psi of the nonlinear crystal need to be determined, and the specific method is as follows:
s1: according to the actual requirement, determining that the wavelengths of the entangled light o light and the entangled light e light are lambda o、λe respectively, and further determining the wavelength lambda p of the required pump light, and the material and the size of the required nonlinear crystal; determining a crystal cutting angle beta of the nonlinear crystal according to a phase matching mode, wherein beta is an included angle between the optical axis direction and the horizontal direction of the nonlinear crystal;
S2: in order to realize that the pump light vertically enters the front surface of the nonlinear crystal and then propagates along the horizontal direction, firstly, the front surface inclination angle psi of the nonlinear crystal is equal to the discrete angle alpha of e light, wherein the front surface inclination angle psi is an included angle between the front surface of the nonlinear crystal and the vertical direction, the discrete angle alpha of the e light is an included angle between the e light and the normal of the e light wave, and then, the size of the front surface inclination angle psi is obtained based on a calculation formula of the discrete angle alpha;
s3: designing according to the material, the size and the crystal cutting angle beta of the nonlinear crystal determined in the step S1 to obtain a cuboid nonlinear crystal, and cutting the front surface of the cuboid nonlinear crystal according to the front surface inclination angle psi calculated in the step S2 to finally obtain the required nonlinear crystal structure.
2. The method according to claim 1, wherein in step S2, when the pump light is perpendicularly incident on the front surface of the nonlinear crystal, the directions of wave normals of o-light and e-light generated in the nonlinear crystal are the same and are perpendicular to the front surface of the nonlinear crystal; meanwhile, due to normal incidence, the o light propagation direction does not deflect, the o light is in the same direction as the normal of the o light wave, the optical axis orientation has a certain included angle with the nonlinear crystal surface, and due to the birefringence effect of the nonlinear crystal, the discrete angle alpha between the e light and the normal of the e light wave meets the following conditions:
Wherein θ is the angle between the e light wave normal and the crystal optical axis; the refractive index n o、ne,no of the entangled light in the nonlinear crystal is calculated according to the wavelength lambda o、λe of the entangled light and the material of the nonlinear crystal, n o changes along with the change of the wavelength o of the light in the crystal, namely, n o＝f1(λo);ne is satisfied as the refractive index of the e light in the nonlinear crystal, and n e also changes along with the change of the wavelength e of the light in the crystal, namely, n e＝f2(λe is satisfied.
3. A nonlinear crystal structure design method for realizing a spontaneous parametric down-conversion process according to claim 1, wherein in step S1, entangled photon pairs prepared by the spontaneous parametric down-conversion process satisfy:
4. A method for designing a nonlinear crystal structure for implementing a spontaneous parametric down-conversion process according to claim 2 or 3, wherein in step S2, the nonlinear crystal is made of a negative uniaxial crystal material, so that n e＜no, i.e. tan α < 0, the discrete angle α < 0 indicates that the angle between the e ray and the optical axis is larger than the angle θ between the normal of the e ray and the optical axis, so that the e ray is far away from the optical axis than the normal of the e ray; and because the normal line of the e light wave is consistent with the direction of the o light ray, the dispersion angle alpha is the included angle between the e light ray and the o light ray.
5. The method for designing a nonlinear crystal structure for implementing a spontaneous parametric down-conversion process according to claim 4, wherein the geometric relationship between the angles is obtained based on: ψ=β - θ, i.e., θ=β - ψ, and ψ= |α|; substituting the inclination angle into a calculation formula of the dispersion angle alpha to obtain a relation formula which is satisfied by the front surface inclination angle psi:
The magnitude of the front surface tilt angle ψ can be calculated.
6. A two-photon entanglement source comprising a laser, a beam shaping module and a nonlinear crystal, wherein the nonlinear crystal is prepared by a nonlinear crystal structure design method for realizing a spontaneous parametric down-conversion process according to any one of claims 1 to 5.
7. The two-photon entanglement source according to claim 6, wherein said laser emits pump light with a frequency of ω p and a wavelength of λ p.
8. The two-photon entanglement source according to claim 6 or 7, wherein said beam shaping module comprises a pinhole, a convex lens, a wave plate and a polarization beam splitter, and shapes the pump light emitted from said laser to maintain good collimation and uniform polarization direction, and then to be incident into said nonlinear crystal.
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| CN113238427B (en) * | 2021-05-26 | 2022-05-31 | 南京邮电大学 | Device and method for preparing polarization, frequency and time slice three-degree-of-freedom super-entanglement |
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| CA3012946A1 (en) * | 2018-07-31 | 2020-01-31 | Oz Optics Ltd. | Fiber-based broadband polarization-entangled photon source |
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| 纠缠光子源的性能模型与实验实现;王冬阳;吴俊杰;刘英文;杨学军;;计算机工程与科学;20201015(第10期);50-57 * |
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