CN111999918B - All-optical switch device and method - Google Patents

All-optical switch device and method Download PDF

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Publication number
CN111999918B
CN111999918B CN202010823976.4A CN202010823976A CN111999918B CN 111999918 B CN111999918 B CN 111999918B CN 202010823976 A CN202010823976 A CN 202010823976A CN 111999918 B CN111999918 B CN 111999918B
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light
beam splitter
light beam
reflector
path
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CN111999918A (en
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夏可宇
阮亚平
葛士军
吴浩东
唐磊
陆延青
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Nanjing University
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Nanjing University
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    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/10Beam splitting or combining systems
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/28Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
    • G02B27/283Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising used for beam splitting or combining
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/28Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
    • G02B27/286Optical 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
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333Constructional arrangements; Manufacturing methods
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333Constructional arrangements; Manufacturing methods
    • G02F1/1337Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/133711Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by organic films, e.g. polymeric films
    • G02F1/133723Polyimide, polyamide-imide
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333Constructional arrangements; Manufacturing methods
    • G02F1/1343Electrodes
    • G02F1/13439Electrodes characterised by their electrical, optical, physical properties; materials therefor; method of making
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering

Abstract

The invention discloses an all-optical switch device and a method, the device comprises a first beam splitter, a liquid crystal box, a second beam splitter, a third beam splitter, a chiral substance, a fourth beam splitter, a first reflector, a second reflector, a phase regulator, a fifth beam splitter, a first photoelectric detector and a second photoelectric detector, wherein narrow-linewidth laser is split into control light and reference light by the first beam splitter, the reference light is detected by the first photoelectric detector, the control light and incident signal light passing through the liquid crystal box are combined by the second beam splitter, the narrow-linewidth laser is split into a first light beam and a second light beam by the third beam splitter, the first light beam reaches the fourth beam splitter through the chiral substance and the first reflector, the second light beam reaches the fourth beam splitter through the second reflector and the phase regulator, the two light beams are interfered to generate a path 1 light beam and a path 2 light beam, the path 1 light beam is divided into a transmission light beam and a reflection light beam, the transmitted beam is detected by a second photodetector. The invention can realize the rapid, stable and low-energy consumption all-optical switch control.

Description

All-optical switch device and method
Technical Field
The present invention relates to optical switches, and more particularly, to an all-optical switch apparatus and method.
Background
Under the background of the high-speed development of the current big data market, a huge amount of information needs to be sent and received every day, the performance and reliability of a transmission network are very important, an all-optical switching technology needs to be developed vigorously, signal transmission and switching of all-optical communication are carried out in an optical domain, the transmission rate of data breaks through the limit of an electronic technology, the process of electric signal processing is omitted, and the stability, the information capacity and the energy consumption are greatly improved. The optical communication device is the basis for constructing an all-optical network, and the all-optical switch is an important component of the optical device and influences the performance of the device to a certain extent. Most of the conventional optical switches are based on active materials, optical characteristics are changed remarkably by utilizing a nonlinear effect, high optical power is often needed, the high switching power can bring strong thermal effect and other losses, the performance of an optical device is unstable in practical application, the response time of the nonlinear process is greatly increased, and the response of the switches cannot keep pace with the speed of information processing.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides an all-optical switch device and a method with low energy consumption, stable performance and short response time.
The technical scheme is as follows: the all-optical switch device comprises a first beam splitter, a liquid crystal box, a second beam splitter, a third beam splitter, a chiral substance, a fourth beam splitter, a first reflector, a second reflector, a phase regulator, a fifth beam splitter, a first photoelectric detector and a second photoelectric detector, wherein the first beam splitter splits incident narrow-linewidth laser into control light and reference light, the first photoelectric detector receives and detects the reference light, the liquid crystal box modulates the phase of the passing control light, the second beam splitter combines the incident signal light and the control light after phase modulation, the third beam splitter splits the combined laser into a first light beam and a second light beam again, the chiral substance and the first reflector are sequentially positioned on the light path of the first light beam, the second reflector and the phase regulator are sequentially positioned on the light path of the second light beam, the fourth beam splitter combines and interferes the first light beam reflected by the first reflector and the second light beam adjusted by the phase adjuster, a path 1 light beam parallel to the incident first light beam path and a path 2 light beam perpendicular to the incident first light beam path are generated after interference, the fifth beam splitter splits the path 1 light beam into a transmitted light beam and a reflected light beam, and the second photoelectric detector receives and detects the transmitted light beam.
Further, the all-optical switch device further includes a first beam terminator that terminates the path 2 beam and a second beam terminator that terminates the reflected beam split by the fifth beam splitter.
Further, the first beam splitter, the third beam splitter and the fourth beam splitter are polarization independent beam splitters, and the second beam splitter and the fifth beam splitter are polarization beam splitters.
Furthermore, a first glass sheet and a second glass sheet which are arranged in parallel are arranged on the inner side of the liquid crystal box, the first glass sheet and the second glass sheet are both plated with an indium tin oxide conducting layer and a polyimide orientation layer, and nematic liquid crystal molecules are filled in the liquid crystal box, wherein the direction of the orientation layer is the same as the polarization direction of control light. The voltage of the liquid crystal box is adjusted when in use, so that the phase of the control light and the phase of the signal light passing through the liquid crystal box when the signal light reaches the second beam splitter are different by 90 degrees.
Further, the chiral substance is specifically a chiral substance which enables the polarization state of the first light beam to be rotated by 90 degrees after the first light beam passes through the chiral substance. The signal light is horizontally polarized signal light.
The full switching method comprises the following steps:
(1) the method comprises the steps that narrow-line-width laser is turned on, the narrow-line-width laser is divided into control light and reference light on a first beam splitter, the control light and signal light are combined into circularly polarized light on a second beam splitter, the circularly polarized light is divided into a first light beam and a second light beam through a third beam splitter, the first light beam is reflected to a fourth beam splitter through a first reflector after passing through a chiral substance, the second light beam is reflected to a fourth beam splitter through a second reflector after passing through a phase adjuster, the phase adjuster is adjusted, the phase difference between the first light beam and the second light beam is 180 degrees, the light beams are combined and interfered on the fourth beam splitter, the interference of the light beams in a path 1 is cancelled, the light intensity is extremely low, and the off state of the signal light of the all-optical switch;
(2) the narrow-line-width laser is turned off, signal light is divided into a first light beam and a second light beam through the third beam splitter, the polarization state of the first light beam is rotated by 90 degrees after passing through the chiral substances, the first light beam is reflected to the fourth beam splitter through the first reflector, the second light beam is reflected to the fourth beam splitter through the second reflector after passing through the phase adjuster, the polarization states of the first light beam and the second light beam on the fourth beam splitter are orthogonal, and the first light beam and the second light beam are directly emitted to the fifth beam splitter without interference after being combined, so that the signal light of the all-optical switch is in an 'on' state.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention achieves the function of the optical switch by combining the control light and the signal light to change the property of the light incident into the linear optical system, keeps the property of the output switch signal consistent with that of the input signal light, and greatly reduces the energy consumption of the all-optical switch and has more stable performance because the control light is weak and the intensity is equal to the signal light; meanwhile, because no optical microcavity is adopted, the speed of the optical switch is extremely high.
Drawings
Fig. 1 is a block diagram of one embodiment of an all-optical switching device provided by the present invention;
FIG. 2 is a graph showing the results of the present invention.
Detailed Description
Example 1
The embodiment provides an all-optical switching device, as shown in fig. 1, including a first beam splitter 1-1, a second beam splitter 1-2, a third beam splitter 1-3, a fourth beam splitter 1-4, a fifth beam splitter 1-5, a first photodetector 2, a liquid crystal cell 3, a first mirror 4-1, a second mirror 4-2, a chiral substance 5, a phase adjuster 6, a second photodetector 7, a first beam terminator 8-1, and a second beam terminator 8-2. Wherein, the first beam splitter 1-1 splits the incident narrow linewidth laser into control light and reference light, the first photoelectric detector 2 receives and detects the reference light, the liquid crystal box 3 modulates the phase of the passed control light, the second beam splitter 1-2 combines the incident horizontal line polarization signal light with the phase-modulated control light, the third beam splitter 1-3 divides the combined laser into a first beam and a second beam again, the chiral substance 5 and the first reflector 4-1 are sequentially positioned on the light path of the first beam, the second reflector 4-2 and the phase adjuster 6 are sequentially positioned on the light path of the second beam, the fourth beam splitter 1-4 combines and interferes the first beam reflected by the first reflector 4-1 and the second beam adjusted by the phase adjuster 6 to generate a path 1 beam parallel to the incident first beam path and a path 2 beam perpendicular to the incident first beam path after interference, the first beam terminator 8-1 terminates the path 2 beam, the fifth beam splitter 1-5 splits the path 1 beam into a transmitted beam and a reflected beam, the second photodetector receives and detects the transmitted beam, and the second beam terminator 8-2 terminates the reflected beam. The first beam splitter, the third beam splitter and the fourth beam splitter are polarization independent beam splitters, the splitting ratios are all 50:50, and the second beam splitter and the fifth beam splitter are polarization beam splitters. The signal of the control light and the output signal of the all-optical switch device are detected by the first photodetector 2 and the second photodetector 7 respectively and input to an oscilloscope (not shown in the figure) for displaying.
The liquid crystal box 3 is used for changing the phase by adding alternating currents with different voltages, and when the polarization axis of linearly polarized incident light is aligned with the optical axis of the liquid crystal box, the liquid crystal box only influences the phase of the incident light beam without changing the polarization. The chiral substance may be a crystal, a solution, a film, or the like, and is specifically a chiral substance that enables the polarization state of the first light beam to rotate by 90 degrees after passing through the chiral substance, that is, the light is changed from horizontal linear polarization to vertical linear polarization.
The embodiment also provides a full switching method based on the all-optical switching device, which comprises the following steps:
(1) the method comprises the steps that narrow-line-width laser is turned on, the narrow-line-width laser is divided into control light and reference light on a first beam splitter, the control light and signal light are combined into circularly polarized light on a second beam splitter, the circularly polarized light is divided into a first light beam and a second light beam through a third beam splitter, the first light beam is reflected to a fourth beam splitter through a first reflector after passing through a chiral substance, the second light beam is reflected to a fourth beam splitter through a second reflector after passing through a phase adjuster, the phase adjuster is adjusted, the phase difference between the first light beam and the second light beam is 180 degrees, the light beams are combined and interfered on the fourth beam splitter, the interference of the light beams in a path 1 is cancelled, the light intensity is extremely low, and the off state of the signal light of the all-optical switch;
(2) the narrow-line-width laser is turned off, signal light is divided into a first light beam and a second light beam through the third beam splitter, the polarization state of the first light beam is rotated by 90 degrees after passing through the chiral substances, the first light beam is reflected to the fourth beam splitter through the first reflector, the second light beam is reflected to the fourth beam splitter through the second reflector after passing through the phase adjuster, the polarization states of the first light beam and the second light beam on the fourth beam splitter are orthogonal, and the first light beam and the second light beam are directly emitted to the fifth beam splitter without interference after being combined, so that the signal light of the all-optical switch is in an 'on' state.
Example 2
The all-optical switching device of this embodiment is the same as embodiment 1, and the all-optical switching method is based on the all-optical switching device of this embodiment, and the specific implementation method is as follows:
(1) selecting a light source of signal light and control light as a narrow linewidth light source with the central wavelength of 780nm, wherein the linewidth is less than 100KHz, and the emergent light is linearly polarized light;
(2) when the narrow-linewidth light source is turned on, adjusting the voltage on the liquid crystal box, and when the peak value is 2.32V, combining the vertical linear polarization control light and the horizontal linear polarization signal light into circularly polarized light through the first polarization beam splitter;
(3) the chiral substance is selected from quartz crystal, the length of the chiral substance is 7.5mm, the optical rotation angle of 780nm light is just equal to 90 degrees, horizontal line polarized light is changed into vertical linear polarized light after passing through the horizontal line polarized light, and the polarization of the circular polarized light is kept unchanged after passing through the quartz crystal;
(4) selecting the first photoelectric detector 2 and the second photoelectric detector 7 as silicon-based amplification photoelectric detectors with response ranges of 400 and 1000nm, and detecting control light and output signals of the all-optical switch device;
(5) the power of the signal light and the control light is adjusted to be 1 muW, the narrow linewidth light source of the control light is alternately turned on and off, and the signal of the control light and the switch signal are respectively detected by the first photoelectric detector and the second photoelectric detector and input into the oscilloscope.
The oscilloscope results are shown in fig. 2. The open square represents the signal of the control light, the solid round dot represents the signal of the switch, and it can be seen that when the control light is on, the electric signal output by the switch is at low level, the switch is in off state, when the control light is off, the electric signal output by the switch is at high level, the switch is in on state, the extinction ratio of the off state to the on state can be calculated to reach 18.8dB, the on and off states are effectively realized, and the performance is stable.

Claims (8)

1. An all-optical switching device, characterized by: the device comprises a first beam splitter, a liquid crystal box, a second beam splitter, a third beam splitter, a chiral substance, a fourth beam splitter, a first reflector, a second reflector, a phase adjuster, a fifth beam splitter, a first photoelectric detector and a second photoelectric detector, wherein the first beam splitter splits incident narrow-linewidth laser into control light and reference light, the first photoelectric detector receives and detects the reference light, the liquid crystal box modulates the phase of the passing control light, the second beam splitter combines the incident signal light and the control light after phase modulation, the third beam splitter divides the combined laser into a first light beam and a second light beam again, the chiral substance and the first reflector are sequentially positioned on the light path of the first light beam, the second reflector and the phase adjuster are sequentially positioned on the light path of the second light beam, and the fourth beam splitter combines and interferes the first light beam reflected by the first reflector and the second light beam adjusted by the phase adjuster, after interference, a path 1 light beam parallel to the incident first light beam path and a path 2 light beam perpendicular to the incident first light beam path are generated, the fifth beam splitter splits the path 1 light beam into a transmitted light beam and a reflected light beam, and the second photoelectric detector receives and detects the transmitted light beam.
2. The all-optical switching device of claim 1, wherein: the all-optical switching device further comprises a first beam terminator which terminates the path 2 beam and a second beam terminator which terminates the reflected beam split by the fifth beam splitter.
3. The all-optical switching device of claim 1, wherein: the first beam splitter, the third beam splitter and the fourth beam splitter are polarization independent beam splitters, and the second beam splitter and the fifth beam splitter are polarization beam splitters.
4. The all-optical switching device of claim 1, wherein: the liquid crystal display panel comprises a liquid crystal box and is characterized in that a first glass sheet and a second glass sheet are arranged on the inner side of the liquid crystal box in parallel, the first glass sheet and the second glass sheet are plated with an indium tin oxide conducting layer and a polyimide orientation layer, and nematic liquid crystal molecules are filled in the liquid crystal box, wherein the direction of the orientation layer is the same as the polarization direction of control light.
5. The all-optical switching device of claim 1, wherein: the voltage of the liquid crystal box is adjusted when in use, so that the phase of the control light and the phase of the signal light passing through the liquid crystal box when the signal light reaches the second beam splitter are different by 90 degrees.
6. The all-optical switching device of claim 1, wherein: the chiral substance is specifically a chiral substance which enables the polarization state of the first light beam to rotate by 90 degrees after the first light beam passes through the chiral substance.
7. The all-optical switching device of claim 1, wherein: the signal light is horizontally polarized signal light.
8. An all-optical switching method based on the all-optical switching device according to claim 1, comprising:
(1) the method comprises the steps that narrow-line-width laser is turned on, the narrow-line-width laser is divided into control light and reference light on a first beam splitter, the control light and signal light are combined into circularly polarized light on a second beam splitter, the circularly polarized light is divided into a first light beam and a second light beam through a third beam splitter, the first light beam is reflected to a fourth beam splitter through a first reflector after passing through a chiral substance, the second light beam is reflected to a fourth beam splitter through a second reflector after passing through a phase adjuster, the phase adjuster is adjusted, the phase difference between the first light beam and the second light beam is 180 degrees, the light beams are combined and interfered on the fourth beam splitter, the interference of the light beams in a path 1 is cancelled, the light intensity is extremely low, and the off state of the signal light of the all-optical switch;
(2) the narrow-line-width laser is turned off, signal light is divided into a first light beam and a second light beam through the third beam splitter, the polarization state of the first light beam is rotated by 90 degrees after passing through the chiral substances, the first light beam is reflected to the fourth beam splitter through the first reflector, the second light beam is reflected to the fourth beam splitter through the second reflector after passing through the phase adjuster, the polarization states of the first light beam and the second light beam on the fourth beam splitter are orthogonal, and the first light beam and the second light beam are directly emitted to the fifth beam splitter without interference after being combined, so that the signal light of the all-optical switch is in an 'on' state.
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