CN114488552A - Space-time vector light field generation device and method - Google Patents
Space-time vector light field generation device and method Download PDFInfo
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- CN114488552A CN114488552A CN202210025308.6A CN202210025308A CN114488552A CN 114488552 A CN114488552 A CN 114488552A CN 202210025308 A CN202210025308 A CN 202210025308A CN 114488552 A CN114488552 A CN 114488552A
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- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/28—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
- G02B27/286—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising for controlling or changing the state of polarisation, e.g. transforming one polarisation state into another
Abstract
The invention relates to a space-time vector light field generating device and a method thereof, wherein the device comprises a first light splitting element, a first optical collimating element, a first quarter wave plate, a phase regulating element, a second quarter wave plate, a second optical collimating element and a second light splitting element which are sequentially arranged, wherein the distance between the first optical collimating element and the first light splitting element is equal to the distance between the first optical collimating element and the phase regulating element and is equal to the focal length of the first optical collimating element. The distance between the second optical collimating element and the second light splitting element is equal to the distance between the second optical collimating element and the phase adjusting element, and is equal to the focal length of the second optical collimating element. The second quarter-wave plate and the first quarter-wave plate are mirror-symmetrical with respect to the phase adjusting element. The space-time vector light field generating device and the method can be used for generating the space-time vector light field with complex polarization distribution in a space-time domain.
Description
Technical Field
The invention relates to the technical field of optics, in particular to a space-time vector light field generating device and method.
Background
Optical field refers to an electromagnetic field of optical frequency having a specific distribution in the time domain and in the spatial domain. In general, the study of the light field can be divided into the study of the light field distributed in the transverse x-y plane, i.e. the study of the light beam; the optical field distributed in the time domain, i.e. the study of the optical pulses, and the three-dimensional wave packet having a specific distribution in the x-y plane and in the time domain, respectively. For three-dimensional wave packets that are not coupled in the spatio-temporal domain, the light field can be expressed in the form of E (x, y, t) ═ E (x, y) · E (t).
In recent years, scientists find that a three-dimensional wave packet coupled in a space-time domain can have unique space-time propagation characteristics and physical characteristics, and is of great significance to research on novel light quantum devices, novel light quantum communication and basic physics, and a space-time light field becomes a new research hotspot. For example, a spatiotemporal light field with a specific distribution may achieve a significant anomalous spatiotemporal refraction phenomenon. The light field can ' break ' the old Snell's law in the process of propagation, and propagate with controllable group velocity after passing through the interface. The space-time light field can provide new possibility for the technical application of novel remote sensing, underground imaging, optical synchronization, phased array radar and the like.
Generating a novel space-time light field requires a novel light field regulation and control technology, and the traditional space-time light field regulation and control technology relies on implementing phase regulation and control or intensity regulation and control on the space-time light field by utilizing a phase regulation and control element to generate the space-time light field with the polarization state being a linear polarization state. Moreover, a means for regulating and controlling the polarization of the space-time light field is lacked, and the space-time vector light field with complex polarization distribution in a space-time domain is difficult to generate.
Disclosure of Invention
In view of the above, it is desirable to provide a space-time vector light field generating apparatus and method capable of generating a space-time vector light field having a complicated polarization distribution in a space-time domain.
A space-time vector light field generating device comprises a first light splitting element, a first optical collimation element, a first quarter wave plate, a phase regulating element, a second quarter wave plate, a second optical collimation element and a second light splitting element which are sequentially arranged, wherein the distance from the first optical collimation element to the first light splitting element is equal to the distance from the first optical collimation element to the phase regulating element and is equal to the focal length of the first optical collimation element;
the distance between the second optical collimating element and the second light splitting element is equal to the distance between the second optical collimating element and the phase adjusting element and is equal to the focal length of the second optical collimating element;
the second quarter wave plate and the first quarter wave plate are mirror symmetric with respect to the phase adjustment element.
Further, the first light splitting element and the second light splitting element are reflective gratings, transmissive gratings or triple prisms.
Further, the first optical collimating element and the second optical collimating element are cylindrical lenses or cylindrical mirrors.
Further, the phase control element is a spatial light modulator or a customized phase panel.
A method of spatio-temporal vector light field generation, the method comprising:
the collimated space-time light field is transmitted to a space-time vector light field generating device and sequentially passes through a first light splitting element, a first optical collimating element, a first quarter wave plate and a phase regulating element;
making the fast axis of the first quarter-wave plate and the y axis form an angle of +45 degrees;
and selecting the phase regulating element as a reflective device, regulating the phase regulating element to apply phase regulation on the light field in the y direction in the polarization direction, returning the light field after the light field is reflected by the phase regulating element according to the original path, and reconstructing the light field into a collimated space-time vector light field through the first quarter-wave plate, the first optical collimating element and the first light splitting element.
Furthermore, after passing through the space-time vector light field generating device, the light field obtains polarization rotation in a space-time domain and obtains an additional phase, and the angle of the polarization rotation and the size of the phase are half of the applied phase of the phase regulating element.
Further, the method further comprises:
selecting the phase regulating element as a transmission type device, adjusting the phase regulating element to perform phase regulation on an optical field in the y direction along the polarization direction, and enabling the optical field to transmit through the phase regulating element;
making the fast axis of the second quarter-wave plate and the y axis form an included angle of-45 degrees;
the light field is reconstructed into a collimated space-time vector light field through the second quarter-wave plate, the second optical collimation element and the second light splitting element.
Further, the obtained polarization rotation and the obtained phase of the light field in the time-space domain are obtained by the relationship between the magnitude of the polarization rotation and the applied phase of the phase control element:
thereby obtaining:
in the formula: einThe method is a Jones matrix form of a spatial frequency domain light field obtained after an incident light field passes through a first light splitting element and a first optical collimation element, wherein the light field is assumed to be linearly polarized light along the y direction, after the light field enters a vector light field regulator, the light field respectively passes through a first quarter wave plate with a + 45-degree included angle between a fast axis and the y axis, a phase regulating element for regulating the phase of the light field along the y direction along the polarization direction, and a second quarter wave plate with a-45-degree included angle between the fast axis and the y axis, R (theta) is a rotation matrix, M (theta) is a rotation matrixQWPRepresenting the phase retardation imposed by the quarter-wave plate, MpRepresenting the phase applied by the phase-regulating element, thetapSpatial phase applied to phase-regulating elements, EoutIs an emergent space-time vector light field;
the first quarter-wave plate, the phase regulating element and the second quarter-wave plate form a vector light field regulator, and a light field E is emitted after passing through the vector light field regulatoroutWill obtain a magnitude of thetapA polarization rotation of 2 and additionally a magnitude of θpA phase of/2; when the incident light field has a certain chirp state, the spatial phase theta applied by the phase control elementpWill be mapped to the light field in the spatio-temporal domain, producing a spatio-temporal vector light field.
Further, the regulation applied by the vector light field regulator may be expressed by the following jones matrix:
thus, the method can obtain the product,
the above formula shows that the vector light field regulator can implement polarization rotation regulation and control on any incident light field to enable the polarization state of the incident light field to rotate thetap2 and additionally obtains a magnitude of thetapPhase of/2.
Further, by the first light splitting element, the vector light field regulation applied by the vector light field regulator is mapped to a time-space domain to generate a time-space vector light field, and the mapping relation is as follows:
Ein(x′，y′)＝Ein(x，a·kGDD·t)；
where a denotes the spectral coefficient of the generator with respect to the incident light field, determined by the first light-splitting element and the first optical collimating element, kGDDDetermining the chirp state of the optical field for the chirp coefficient;
when k isGDD>0, the light field is in a positive chirp state, and the applied vector light field regulation and control map the mode of positive mapping to a space-time light field to generate the space-time vector light field;
when k isGDD<0, the light field is in a negative chirp state, and the applied vector light field regulation and control map the space-time light field in a reverse mapping mode to generate the space-time vector light field;
when k isGDD0, the field is in a zero chirp state and the applied vector field modulation will be one-dimensional fourier transformedThe mapping mode maps to a spatio-temporal light field, producing a spatio-temporal vector light field.
The space-time vector light field generating device and the method can be used for generating the space-time vector light field with complex polarization distribution in the space-time domain, realize the regulation and control of the space-time vector light field in the space-time domain and can be used for generating the complex space-time vector light field. By utilizing the chirp state of the incident light field, the mapping of any polarization state to the space-time domain of the space-time light field in different modes is realized, wherein the space vector light field regulation and control are directly mapped to the space-time domain polarization state distribution of the space-time light field to generate the space-time vector light field.
Drawings
FIG. 1 is a diagram of a spatio-temporal vector light field generation apparatus of an embodiment;
FIG. 2 is a flow diagram of a spatio-temporal vector light field generation method according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, in an embodiment, a space-time vector light field generating apparatus includes a first light splitting element 110, a first optical collimating element 120, a first quarter-wave plate 130, a phase adjusting element 140, a second quarter-wave plate 150, a second optical collimating element 160, and a second light splitting element 170, which are arranged in sequence, wherein a distance from the first optical collimating element 120 to the first light splitting element 110 is equal to a distance from the phase adjusting element 140, and is equal to a focal length of the first optical collimating element 120; the distance between the second optical collimating element 160 and the second beam splitting element 170 is equal to the distance between the second optical collimating element 160 and the phase modulating element 140, and is equal to the focal length of the second optical collimating element 160, and the focal lengths of the first optical collimating element 120 and the second optical collimating element 160 are the same; the second quarter wave plate 150 and the first quarter wave plate 130 are mirror symmetric with respect to the phase adjustment element 140. The first light splitting element 110 and the second light splitting element 170 are reflective gratings, transmissive gratings, or prisms. The first optical collimating element 120 and the second optical collimating element 160 are cylindrical lenses or cylindrical mirrors. The phase modulating element 140 is a spatial light modulator or a custom phase panel. When the phase adjusting element 140 is a reflective device, the first quarter-wave plate 130 and the phase adjusting element 140 form a vector light field adjuster; when the phase adjusting element 140 is a transmissive device, the first quarter-wave plate 130, the phase adjusting element 140 and the second quarter-wave plate 150 form a vector light field adjuster.
In addition, a space-time vector light field generation method is also provided, and the space-time vector light field generation device is combined to generate the space-time vector light field.
As shown in fig. 2, in one embodiment, a method of generating a spatio-temporal vector light field includes the steps of:
step S110, the collimated space-time light field is transmitted to the space-time vector light field generating device and passes through the first light splitting element, the first optical collimating element, the first quarter wave plate and the phase regulating element in sequence.
Step S120, making the fast axis of the first quarter-wave plate and the y axis form an angle of +45 degrees.
And S130, selecting the phase adjusting and controlling element as a reflective device, adjusting the phase adjusting and controlling element to apply phase adjustment and control on the light field in the y direction in the polarization direction, returning the light field after the light field is reflected by the phase adjusting and controlling element according to the original path, and reconstructing the light field into a collimated space-time vector light field through the first quarter-wave plate, the first optical collimating element and the first light splitting element. At the moment, the first quarter-wave plate and the phase regulating element form a vector light field regulator, and after passing through the vector light field regulator, the light field returns to the first optical collimating element and the first light splitting element according to the original path to be reconstructed into a collimated space-time vector light field.
After passing through the space-time vector light field generating device, the light field obtains polarization rotation in a space-time domain and obtains an additional phase, and the angle and the phase of the polarization rotation are half of the applied phase of the phase regulating element.
In this embodiment, the method further includes the following steps:
And 150, making the fast axis of the second quarter-wave plate and the y axis form an included angle of-45 degrees.
In the present embodiment, the polarization rotation and the resulting phase of the light field in the space-time domain are obtained by the relationship between the magnitude and the applied phase of the phase modulating element:
thereby obtaining:
in the formula: einThe method is a Jones matrix form of a spatial frequency domain light field obtained after an incident light field passes through a first light splitting element and a first optical collimation element, wherein the light field is assumed to be linearly polarized light along the y direction, after the light field enters a vector light field regulator, the light field respectively passes through a first quarter wave plate with a + 45-degree included angle between a fast axis and the y axis, a phase regulating element for regulating the phase of the light field along the y direction along the polarization direction, and a second quarter wave plate with a-45-degree included angle between the fast axis and the y axis, R (theta) is a rotation matrix, M (theta) is a rotation matrixQWPRepresenting the phase retardation imposed by the quarter-wave plate, MpRepresenting the phase applied by the phase-regulating element, thetapSpatial phase applied to phase-regulating elements, EoutIs an emergent space-time vector light field.
After passing through the vector light field regulator, the light field E is emittedoutWill obtain a magnitude of thetapA polarization rotation of 2 and additionally a magnitude of thetapPhase of/2. When the incident light field has a certain chirp state, the spatial phase theta applied by the phase control elementpWill be mapped to the light field in the spatio-temporal domain, yielding a spatio-temporal vector light field.
The regulation applied by the vector light field regulator can be expressed by the following jones matrix:
thus, the method can obtain the product,
the above formula shows that the vector light field regulator can implement polarization rotation regulation and control on any incident light field, so that the polarization state of the incident light field can be rotated by thetap2 and additionally obtains a magnitude of thetapPhase of/2.
Vector light field regulation applied by space-time vector light field generator by varying thetapRealization of thetapIs a function of two dimensions and can be written as thetap(x ', y'). By the light splitting element in the generator, the vector light field regulation can be mapped to a space-time domain to generate a space-time vector light field, and the mapping relation can be obtained by the following formula:
Ein(x′，y′)＝Ein(x，a·Ω). (9)
Ω＝kGDD·t. (10)
equation (9) shows that the light field E is in the plane of the phase control elementp(x ', y') is the incident light field EinA represents a spectral coefficient of the generator with respect to an incident light field, and is determined by the first light splitting element and the first optical collimating element, and Ω - ω0Representing the relative transient frequency, k, of the light fieldGDDThe chirp state of the optical field is determined for the chirp coefficient. By combining the formulas (9) and (10), the compound can be obtained
Ein(x′，y′)＝Ein(x，a·kGDD·t)。 (11)
When k isGDD>0, the light field is in a positive chirp state, and the applied vector light field regulation and control map the mode of positive mapping to a space-time light field to generate the space-time vector light field;
when k isGDD<0, the light field is in a negative chirp state, and the applied vector light field regulation and control map the space-time light field in a reverse mapping mode to generate the space-time vector light field;
when k isGDDThe light field is in a zero chirp state, and the applied vector light field modulation maps the mapping mode of one-dimensional Fourier transform to a space-time light field to generateA spatio-temporal vector light field.
The following description will be given by taking an example in which the first light splitting element and the second light splitting element select reflective gratings, the first optical collimating element and the second optical collimating element select cylindrical lenses, and the phase adjusting element selects a spatial light modulator.
First, a collimated gaussian-gaussian, linearly polarized spatio-temporal light field along the y-direction is input into a spatio-temporal vector light field generating device (refer to fig. 1), and after a wave packet passes through a reflective grating (at point a 0), different optical frequency components of the incident wave packet pass through a cylindrical lens at different angles and are collimated to a plane where a Spatial Light Modulator (SLM) is located. When the distance between the reflective grating, the cylindrical lens and the SLM is the focal length f of the cylindrical lens, the space-frequency domain light field of the incident space-time light field wave packet is projected to the SLM plane.
Secondly, the light field is modulated by the vector light field, passes through the second group of cylindrical lenses and the reflective grating, and is reconstructed into a collimated emergent space-time vector light field at the grating (point A1).
Then, when the SLM is loaded with a spatial phase (e.g., a spatial vortex phase), the polarization state of the outgoing spatio-temporal light field in its spatio-temporal domain at the departure point a1 (defined herein as z ═ 0) will obtain a polarization rotation that is one-half of the loaded phase. The distribution is some mapping of the spatial phase loaded by the generator, the specific mapping mode depending on the chirp state in which the light field is.
Finally, when the space-time light field is positively chirped, the polarization rotation of the space-time light field in the space-time domain is a direct mapping of the spatial phase applied by the generator.
Compared with the traditional space-time light field, the traditional space-time light field regulation and control are limited to the regulation and control of the phase and the intensity of the space-time light field, the means for regulating and controlling the polarization state of the space-time light field is lacked, and the space-time vector light field with complex polarization distribution in the space-time domain cannot be generated. The invention realizes the vector light field regulation and control in the time-space domain of the time-space light field and can be used for generating the complex time-space vector light field.
In addition, the traditional regulation and control method of the space-time light field is based on one-dimensional Fourier transform, and direct polarization state mapping regulation and control cannot be performed on the space-time domain polarization state distribution of the light field. The invention realizes the mapping of any polarization state to the space-time domain of the space-time light field in different modes by utilizing the chirp state of the incident light field, wherein the method comprises the step of directly mapping the space vector light field regulation and control to the space-time domain polarization state distribution of the space-time light field to generate the space-time vector light field.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A space-time vector light field generating device is characterized by comprising a first light splitting element, a first optical collimating element, a first quarter wave plate, a phase regulating element, a second quarter wave plate, a second optical collimating element and a second light splitting element which are sequentially arranged, wherein the distance from the first optical collimating element to the first light splitting element is equal to the distance from the first optical collimating element to the phase regulating element and is equal to the focal length of the first optical collimating element;
the distance between the second optical collimating element and the second light splitting element is equal to the distance between the second optical collimating element and the phase regulating element and equal to the focal length of the second optical collimating element;
the second quarter wave plate and the first quarter wave plate are mirror symmetric with respect to the phase adjustment element.
2. The space-time vector light field generating device according to claim 1, wherein the first and second light splitting elements are reflective gratings, transmissive gratings, or prisms.
3. The spatio-temporal vector light field generation apparatus according to claim 1, wherein the first and second optical collimating elements are cylindrical lenses or cylindrical mirrors.
4. The spatio-temporal vector light field generation apparatus according to claim 1, wherein the phase modulation element is a spatial light modulator or a customized phase panel.
5. A method of spatio-temporal vector light field generation, the method comprising:
the collimated space-time light field is transmitted to a space-time vector light field generating device and sequentially passes through a first light splitting element, a first optical collimating element, a first quarter wave plate and a phase regulating element;
making the fast axis of the first quarter-wave plate and the y axis form an included angle of +45 degrees;
and selecting the phase regulating element as a reflective device, regulating the phase regulating element to apply phase regulation on the light field in the y direction in the polarization direction, returning the light field after the light field is reflected by the phase regulating element according to the original path, and reconstructing the light field into a collimated space-time vector light field through the first quarter-wave plate, the first optical collimating element and the first light splitting element.
6. The method of claim 5, wherein after passing through the space-time vector light field generating device, the light field obtains a polarization rotation in the space-time domain and obtains an additional phase, and the angle of the polarization rotation and the phase are half of the applied phase of the phase modulating element.
7. The method of generating a spatio-temporal vector light field according to claim 6, further comprising:
selecting the phase regulating element as a transmission type device, adjusting the phase regulating element to perform phase regulation on an optical field in the y direction along the polarization direction, and enabling the optical field to transmit through the phase regulating element;
making the fast axis of the second quarter-wave plate and the y axis form an angle of-45 degrees;
the light field is reconstructed into a collimated space-time vector light field through the second quarter-wave plate, the second optical collimation element and the second light splitting element.
8. The method of generating a spatio-temporal vector light field according to claim 7, wherein the obtained polarization rotation and the obtained phase of the light field in the spatio-temporal domain are obtained in a way that the magnitude thereof is related to the applied phase of the phase modulating element:
thereby obtaining:
in the formula: einThe light field is assumed to be linearly polarized light along the y direction in the Jones matrix form of the spatial frequency domain light field obtained after the incident light field passes through the first light splitting element and the first optical collimating element, and the light field can be split after entering the vector light field regulatorA first quarter-wave plate with an angle of +45 degrees between the fast axis and the y axis, a phase control element for controlling the phase of the light field in the y direction along the polarization direction, and a second quarter-wave plate with an angle of-45 degrees between the fast axis and the y axis, wherein R (theta) is a rotation matrix, M (theta) is a linear matrix, andQWPrepresenting the phase retardation imposed by the quarter-wave plate, MpRepresenting the phase applied by the phase-regulating element, thetapSpatial phase applied to phase-regulating elements, EoutIs an emergent space-time vector light field;
the first quarter-wave plate, the phase regulating element and the second quarter-wave plate form a vector light field regulator, and a light field E is emitted after passing through the vector light field regulatoroutWill obtain a magnitude of thetapA polarization rotation of 2 and additionally a magnitude of thetapA phase of/2; when the incident light field has a certain chirp state, the spatial phase theta applied by the phase control elementpWill be mapped to the light field in the spatio-temporal domain, yielding a spatio-temporal vector light field.
9. The method of generating a spatio-temporal vector light field according to claim 8, wherein the modulation applied by the vector light field modulator is expressed by the following jones matrix:
thus, the method can obtain the product,
the above formula shows that the vector light field regulator can implement polarization rotation regulation and control on any incident light field, so that the polarization state of the incident light field can be rotated by thetap2 and additionally obtains a magnitude of thetapPhase of/2.
10. The method of generating a space-time vector light field according to claim 9, wherein the vector light field modulation applied by the vector light field modulator is mapped to a space-time domain by the first beam splitting element to generate the space-time vector light field, and the mapping relationship is:
Ein(x′,y′)＝Ein(x,a·kGDD·t)；
where a denotes the spectral coefficient of the generator with respect to the incident light field, determined by the first light-splitting element and the first optical collimating element, kGDDDetermining the chirp state of the optical field for the chirp coefficient;
when k isGDD>0, the light field is in a positive chirp state, and the applied vector light field regulation and control map the mode of positive mapping to a space-time light field to generate the space-time vector light field;
when k isGDD<0, the light field is in a negative chirp state, and the applied vector light field regulation and control map the space-time light field in a reverse mapping mode to generate the space-time vector light field;
when k isGDDAnd (2) the light field is in a zero chirp state, and the applied vector light field regulation and control is mapped to a space-time light field in a mapping mode of one-dimensional Fourier transform to generate the space-time vector light field.
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| WO2009066755A1 (en) * | 2007-11-22 | 2009-05-28 | National University Corporation Tokyo University Of Agriculture And Technology | Vortex producing device, body controller, and vortex producing method |
| CN113805347A (en) * | 2021-09-18 | 2021-12-17 | 上海理工大学 | Method for mapping space phase to space-time light field time-space domain phase |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2009066755A1 (en) * | 2007-11-22 | 2009-05-28 | National University Corporation Tokyo University Of Agriculture And Technology | Vortex producing device, body controller, and vortex producing method |
| CN113805347A (en) * | 2021-09-18 | 2021-12-17 | 上海理工大学 | Method for mapping space phase to space-time light field time-space domain phase |
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| H.ESAT KONDAKCI ET AL: ""Diffraction-free space–time light sheets"", 《NATURE PHOTONICS》 * |
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