CN106841110B - Device and method for measuring complex refractive index of absorptive medium - Google Patents

Device and method for measuring complex refractive index of absorptive medium Download PDF

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CN106841110B
CN106841110B CN201710223714.2A CN201710223714A CN106841110B CN 106841110 B CN106841110 B CN 106841110B CN 201710223714 A CN201710223714 A CN 201710223714A CN 106841110 B CN106841110 B CN 106841110B
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refractive index
absorptive medium
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CN106841110A (en
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张秋长
罗天舒
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Xiamen University Tan Kah Kee College
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01—Arrangements or apparatus for facilitating the optical investigation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01—Arrangements or apparatus for facilitating the optical investigation
    • G01N2021/0106—General arrangement of respective parts
    • G01N2021/0112—Apparatus in one mechanical, optical or electronic block
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2201/00—Features of devices classified in G01N21/00
    • G01N2201/06—Illumination; Optics
    • G01N2201/061—Sources
    • G01N2201/06113—Coherent sources; lasers
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Abstract

The invention relates to an absorptive medium complex refractive index measuring device and a measuring method thereof, wherein the absorptive medium complex refractive index measuring device comprises a laser emitter, a wedge-shaped absorptive medium, a CCD detector, an oscilloscope and a rotating mechanism, wherein the rotating mechanism comprises a straight rod, a first platform fixedly connected with one end of the straight rod and a second platform hinged with the other end of the straight rod, the laser emitter is placed on the first platform, and the wedge-shaped absorptive medium is placed on the second platform; the CCD detector is arranged behind the second platform, receives the light beam directly emitted by the laser emitter or the light beam refracted by the wedge-shaped absorptive medium and transmits the light signal to the oscilloscope for real-time display. The invention has the advantages of easy understanding of the measuring principle, simple light path and low instrument cost.

Description

Device and method for measuring complex refractive index of absorptive medium
Technical Field
The invention relates to an absorptive medium complex refractive index measuring device and a measuring method thereof.
Background
For the refractive index of the absorptive medium, its value is characterized by the complex refractive index. This change in form also changes the properties of the wave, especially the imaginary part of the refractive index, not only the root of the absorption properties of the medium, but also the polarization state of the reflected light, transmitted light. The research of the complex refractive index not only has theoretical significance, but also has practical application value.
The existing complex refractive index measuring method mainly comprises a polarization technology, incident linearly polarized light is changed into elliptical polarized light after being reflected by an absorptive medium, the real part and the imaginary part of the complex refractive index are measured by measuring the phase and the amplitude of the reflected light, the principle is complex, more components are needed for completing the measurement, the light path is complex, and the price of an instrument is high; also, some measure the complex refractive index by using the surface plasmon resonance technology, calculate the complex refractive index of the sample by measuring the reflectivity, resonance angle, phase difference, etc., and the experimental principle is difficult to understand, and the instrument structure is complex.
Disclosure of Invention
In view of the above, the present invention aims to provide an apparatus and a method for measuring complex refractive index of an absorptive medium, which have the advantages of easy understanding of measurement principle, simple optical path and low instrument cost.
In order to achieve the above purpose, the invention adopts the following technical scheme: an absorptive medium complex refractive index measuring device, characterized in that: the device comprises a laser emitter, a wedge-shaped absorptive medium, a CCD detector, an oscilloscope and a rotating mechanism, wherein the rotating mechanism comprises a straight rod, a first platform fixedly connected with one end of the straight rod and a second platform hinged with the other end of the straight rod, the laser emitter is placed on the first platform, and the wedge-shaped absorptive medium is placed on the second platform; the CCD detector is arranged behind the second platform, receives the light beam directly emitted by the laser emitter or the light beam refracted by the wedge-shaped absorptive medium and transmits the light signal to the oscilloscope for real-time display.
Further, the upper end face of the second platform is provided with a baffle, an opening is formed in the middle of the baffle, and the hinge point of the straight rod and the second platform coincides with the opening in the vertical direction.
Further, a dial is arranged on the lower side face of the second platform, and a pointer which is tightly attached to the dial is arranged on the straight rod.
Further, a beam expander is further arranged between the laser emitter and the wedge-shaped absorptive medium to expand the laser.
A method of measuring a complex refractive index of an absorptive medium, comprising the steps of:
step S1: placing a laser emitter on a first platform, adjusting the angle of the laser emitter to enable emitted laser to directly pass through an opening in the middle of a baffle, taking the direction of the laser as the initial direction of the laser, and transmitting a corresponding optical signal to an oscilloscope for display after a CCD detector receives the laser;
step S2: recording the corresponding angle of the pointer on the dial at the moment as a reference angle;
step S3: the wedge-shaped absorptive medium is tightly attached to the baffle, the first platform and the straight rod are rotated to a first angle, laser emitted by the laser emitter is refracted through the wedge-shaped absorptive medium, and the CCD detector receives the refracted laser and then transmits a corresponding optical signal to the oscilloscope for display;
step S4: calculating the distance Y of the light beam moving on an acquisition window of the CCD detector perpendicular to the initial direction of the laser through the position movement of the peak on the oscilloscope, and further calculating the deflection angle beta of the laser passing through the emergent surface of the wedge-shaped absorptive medium relative to the initial direction of the laser and the first real refraction angle of the laser
Figure GDA0004043059100000025
Figure GDA0004043059100000021
Figure GDA0004043059100000022
Wherein L is the distance from the exit point on the exit surface to the acquisition window of the CCD detector, and alpha is the apex angle of the wedge-shaped absorbent medium;
step S5: rotating the first platform communicated with the straight rod to a second angle, and performing operations from step S3 to step S4 to obtain a second real refraction angle of the laser
Figure GDA0004043059100000023
Step S6: the relationship between the real part and the imaginary part of the complex refractive index is obtained by combining the relationship between the real refractive index and the complex refractive index of the wedge-shaped absorptive medium as follows:
Figure GDA0004043059100000024
Figure GDA0004043059100000031
wherein ,θ1 For the incident angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium, i.e. the difference between the first angle and the reference angle, theta 2 Is the refraction angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium; θ'. 1 For the incident angle at the right-angle side when the laser light is obliquely incident on the wedge-shaped absorbent medium for the second time, i.e. the difference between the first angle and the reference angle, θ' 2 Is the refraction angle at the right-angle side when the laser is obliquely incident to the wedge-shaped absorptive medium for the second time; n is n i Is the refractive index, k of air 0 N and k are the real part and the imaginary part of the wedge-shaped absorptive medium respectively.
Further, the specific calculation process in the step S6 is as follows:
let light wave E (r, t) =e (r) E -iωt ，H(r,t)＝H(r)e -iωt Instead of maxwell's equations, it is possible to obtain light waves in an absorptive medium satisfying the following equation:
Figure GDA0004043059100000032
Figure GDA0004043059100000033
/>
wherein ,
Figure GDA0004043059100000034
is equivalent complex permittivity, epsilon is permittivity, mu is permeability, sigma is conductivity,
Figure GDA0004043059100000035
is the complex refractive index of the absorptive medium, n, k are the real part, the imaginary part, k of the absorptive medium respectively 0 Is wave vector in vacuum, +.>
Figure GDA0004043059100000036
The unit vectors of the equal-breadth and the equal-phase surfaces are q and s respectively, and the included angle between the two unit vectors is xi=cos -1 (q.s)，k s and kq The phase constant and the attenuation constant of the wave respectively;
the phase constant, the decay constant in the absorptive medium are related to the real and imaginary parts of the complex refractive index as follows:
Figure GDA0004043059100000041
since neither n nor κ is zero, it is known from equation (5) that ζ+.pi/2, i.e. the two unit vectors are not perpendicular:
Figure GDA0004043059100000042
parameter N s ，N q Is the effective refractive index for light propagation and attenuation in an absorptive medium, and their magnitude is related not only to the complex refractive index but also to the angle between the equal-phase and equal-amplitude surfaces;
when the light is at an angle theta 1 The right-angle side of the incident wedge, at which, according to the boundary conditions,
n i k 0 sinθ 1 ＝k s sinθ 2 (7)
the relationship between the phase constant and attenuation constant of the light wave after entering the absorptive medium through the right-angle side refraction and the real part and the imaginary part of the complex refractive index is as follows
Figure GDA0004043059100000043
From formulae (7), (8)
Figure GDA0004043059100000044
In the same way, the absorption medium is refracted into the air at the bevel edge, and the real refraction angle of the refraction into the air is
Figure GDA0004043059100000045
Since the phase wave vector and the attenuation wave vector of the wave in the absorptive medium have tangential components at the interface, the phase constant k 'of the refracted wave' s Attenuation constant k' q The relationship between them is as follows:
Figure GDA0004043059100000046
at the same time according to boundary conditions
Figure GDA0004043059100000051
The correlation of the real and imaginary parts of complex refractive index and refraction angle can be obtained by the combination of (7), (8), (10), (11):
Figure GDA0004043059100000052
similarly, it can be obtained at an angle of θ' 1 At the time of incidence, it is assumed that the real refraction angle at the right-angle side is θ' 2 Angle of refraction is real at the hypotenuse
Figure GDA0004043059100000053
The relationship between the real and imaginary parts of the complex refractive index and the refraction angle is as follows
Figure GDA0004043059100000054
The relationship between the real and imaginary parts of the complex refractive index, i.e., equation (12) and equation (13), is obtained by combining the real refraction angle and the complex refractive index of the absorptive medium as follows:
Figure GDA0004043059100000055
wherein ：
Figure GDA0004043059100000056
the real part n and the imaginary part κ of the complex refractive index in the above equation can be solved by using the function solve () in matlab software.
Compared with the prior art, the invention has the following beneficial effects: the invention only needs to use laser to make incidence of different angles to a single sample twice, and respectively measures the real refraction angle of the laser passing through the single medium twice, thus the complex refraction index of the absorptive medium can be calculated. The measuring principle is easy to understand, the light path is simple, and the measurement is simpler; on the other hand, the device ensures that the laser transmitter can still pass through the same incidence point of the absorptive medium after rotating at different angles, reduces unstable factors such as different thicknesses of incidence points at different positions caused by different incidence points, and conveniently reads the rotated angle of the laser transmitter by arranging the dial arranged on the lower side surface on the second platform.
Drawings
FIG. 1 is a schematic view of an apparatus according to an embodiment of the present invention.
Fig. 2 is a top view of a rotary mechanism according to an embodiment of the present invention.
Fig. 3 is a side view of a rotating structure according to an embodiment of the present invention.
Fig. 4 is a schematic view of the present invention after rotation of the laser transmitter.
Fig. 5 is a refractive schematic of a wedge-shaped absorbent medium.
In the figure: 1-a laser emitter; 11-a beam expander; 2-wedge-shaped absorbent media; a 3-CCD detector; 4-oscilloscopes; 5-a straight rod; 51-a first platform; 52-a second platform; 53-baffle; 54-opening; 55-dial; 56-pointer.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the invention provides an apparatus for measuring complex refractive index of an absorptive medium, which comprises a laser emitter 1, a wedge-shaped absorptive medium 2, a CCD detector 3, an oscilloscope 4 and a rotating mechanism, wherein the rotating mechanism comprises a straight rod 5, a first platform 51 fixedly connected with one end of the straight rod 5 and a second platform 52 hinged with the other end of the straight rod 5, the laser emitter 1 is placed on the first platform 51, and the wedge-shaped absorptive medium 2 is placed on the second platform 52; the straight bar 5 together with the first platform 51 can be rotated about the hinge point such that the laser light emitted by the laser transmitter 1 is incident on the wedge-shaped absorbent medium 2 at different angles. The CCD detector 3 is arranged behind the second platform 51, receives the light beam directly emitted by the laser emitter 1 or the light beam refracted by the wedge-shaped absorptive medium 2, and transmits the light signal to the oscilloscope 4 for real-time display.
Referring to fig. 2 and 3, a baffle 53 is disposed on an upper end surface of the second platform 52, an opening 54 is disposed in the middle of the baffle 53, and a hinge point of the straight rod and the second platform 52 coincides with the opening 54 in a vertical direction; the laser transmitter can still be incident on the same incident point of the absorptive medium through the opening after rotating at different angles. The lower side of the second platform 52 is provided with a dial 55, the straight rod 5 is provided with a pointer 56 which is clung to the dial, and the pointer rotates along with the rotation of the straight rod 5 and is used for reading the scale marks on the dial 55.
Referring to fig. 1, a beam expander 11 is further disposed between the laser emitter 1 and the wedge-shaped absorbent medium 2 to expand the laser beam.
The embodiment also provides a measuring method of the absorptive medium complex refractive index measuring device, which comprises the following steps:
step S1: referring to fig. 1, a laser emitter 1 is placed on a first platform 51, the angle of the laser emitter is adjusted to enable emitted laser to directly pass through an opening 54 in the middle of a baffle 53, the direction of the laser is used as the initial direction of the laser, and a CCD detector 3 receives the laser and then transmits a corresponding optical signal to an oscilloscope 4 for display;
step S2: the angle of the pointer 56 corresponding to this time on the dial 55 is recorded as a reference angle;
step S3: referring to fig. 4, the wedge-shaped absorbent medium 2 is tightly attached to the baffle, the first platform 51 and the straight rod 5 are rotated to a first angle, the laser emitted by the laser emitter 1 is refracted at the wedge-shaped absorbent medium 2, and the CCD detector 3 receives the refracted laser and then transmits a corresponding optical signal to the oscilloscope 4 for display;
step S4: the distance Y of the beam moving on the acquisition window of the CCD detector perpendicular to the initial direction of the laser is calculated by the position movement of the wave crest on the oscilloscope 4. Taking an LM601 type CCD light intensity distribution measuring apparatus as an example, its photosensor has 2592 pixels, the center distance of the photosensor is 11 μm, if one period of the waveform corresponds to m big cells on the oscilloscope, the actual space distance corresponding to each big cell on the oscilloscope is 2592×11/m, the distance corresponding to each small cell is 2592×11/m/5, and assuming that the number of cells moved by the two light spots on the oscilloscope is p small cells, the distance corresponding to the movement on the CCD is y=2592×11/m/5×p.
Then, the deflection angle beta of the laser passing through the emergent surface of the wedge-shaped absorptive medium relative to the initial direction of the laser and the first real refraction angle of the laser are calculated according to the distance Y
Figure GDA0004043059100000071
/>
Figure GDA0004043059100000072
Figure GDA0004043059100000073
Wherein L is the distance from the exit point on the exit surface to the acquisition window of the CCD detector, and alpha is the apex angle of the wedge-shaped absorbent medium;
step S5: rotating the first platform 51 to a second angle with the straight rod 5, and performing the operations from step S3 to step S4 to obtain a second refraction angle of the laser
Figure GDA0004043059100000081
Step S6: the relationship between the real part and the imaginary part of the complex refractive index is obtained by combining the relationship between the real refractive index and the complex refractive index of the wedge-shaped absorptive medium as follows:
Figure GDA0004043059100000082
Figure GDA0004043059100000083
wherein ,θ1 For the incident angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium, i.e. the difference between the first angle and the reference angle, theta 2 Is the refraction angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium; θ'. 1 For the incident angle at the right-angle side when the laser light is obliquely incident on the wedge-shaped absorbent medium for the second time, i.e. the difference between the first angle and the reference angle, θ' 2 Is the refraction angle at the right-angle side when the laser is obliquely incident to the wedge-shaped absorptive medium for the second time; n is n i Is the refractive index, k of air 0 N and k are the real part and the imaginary part of the wedge-shaped absorptive medium respectively.
Further, the specific calculation process in the step S6 is as follows:
let light wave E (r, t) =e (r) E -iωt ，H(r,t)＝H(r)e -iωt Instead of maxwell's equations, it is possible to obtain light waves in an absorptive medium satisfying the following equation:
Figure GDA0004043059100000084
Figure GDA0004043059100000091
wherein ,
Figure GDA0004043059100000092
is equivalent complex permittivity, epsilon is permittivity, mu is permeability, sigma is conductivity,
Figure GDA0004043059100000093
is the complex refractive index of the absorptive medium, n, k are the real part, the imaginary part, k of the absorptive medium respectively 0 Is wave vector in vacuum, +.>
Figure GDA0004043059100000094
The unit vectors of the equal-breadth and the equal-phase surfaces are q and s respectively, and the included angle between the two unit vectors is xi=cos -1 (q.s)，k s and kq The phase constant and the attenuation constant of the wave respectively;
the phase constant, the decay constant in the absorptive medium are related to the real and imaginary parts of the complex refractive index as follows:
Figure GDA0004043059100000095
since neither n nor κ is zero, it is known from equation (5) that ζ+.pi/2, i.e. the two unit vectors are not perpendicular:
Figure GDA0004043059100000096
parameter N s ，N q Is the effective refractive index for light propagation and attenuation in an absorptive medium, and their magnitude is related not only to the complex refractive index but also to the angle between the equal-phase and equal-amplitude surfaces;
referring to FIG. 5, when the light is at an angle θ 1 The right-angle edge of the incident wedge is known from the boundary conditions，
n i k 0 sinθ 1 ＝k s sinθ 2 (7)
The relationship between the phase constant and attenuation constant of the light wave after entering the absorptive medium through the right-angle side refraction and the real part and the imaginary part of the complex refractive index is as follows
Figure GDA0004043059100000101
From formulae (7), (8)
Figure GDA0004043059100000102
In the same way, the absorption medium is refracted into the air at the bevel edge, and the real refraction angle of the refraction into the air is
Figure GDA0004043059100000103
Since the phase wave vector and the attenuation wave vector of the wave in the absorptive medium have tangential components at the interface, the phase constant k 'of the refracted wave' s Attenuation constant k' q The relationship between them is as follows:
Figure GDA0004043059100000104
at the same time according to boundary conditions
Figure GDA0004043059100000105
The correlation of the real and imaginary parts of complex refractive index and refraction angle can be obtained by the combination of (7), (8), (10), (11):
Figure GDA0004043059100000106
similarly, it can be obtained at an angle of θ' 1 At the time of incidence, it is assumed thatThe real refraction angle at the corner edge is theta' 2 Angle of refraction is real at the hypotenuse
Figure GDA0004043059100000107
The relationship between the real and imaginary parts of the complex refractive index and the refraction angle is as follows
Figure GDA0004043059100000108
The relationship between the real and imaginary parts of the complex refractive index, i.e., equation (12) and equation (13), is obtained by combining the real refraction angle and the complex refractive index of the absorptive medium as follows:
Figure GDA0004043059100000111
wherein ：
Figure GDA0004043059100000112
the real part n and the imaginary part κ of the complex refractive index in the above equation can be solved by using the function solve () in matlab software.
The foregoing description is only of the preferred embodiments of the invention, and all changes and modifications that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (2)

1. A measuring method of an absorptive medium complex refractive index measuring device is characterized in that: the measuring device comprises a laser emitter, a wedge-shaped absorptive medium, a CCD detector, an oscilloscope and a rotating mechanism, wherein the rotating mechanism comprises a straight rod, a first platform fixedly connected with one end of the straight rod and a second platform hinged with the other end of the straight rod, the laser emitter is placed on the first platform, and the wedge-shaped absorptive medium is placed on the second platform; the CCD detector is arranged behind the second platform, receives the light beam directly emitted by the laser emitter or the light beam refracted by the wedge-shaped absorptive medium and transmits the light signal to the oscilloscope for real-time display;
the upper end face of the second platform is provided with a baffle, the middle of the baffle is provided with an opening, and the hinge point of the straight rod and the second platform is overlapped with the opening in the vertical direction;
a dial is arranged on the lower side surface of the second platform, and a pointer which is tightly attached to the dial is arranged on the straight rod;
a beam expander is also arranged between the laser emitter and the wedge-shaped absorptive medium to expand the laser;
the measuring method comprises the following steps:
step S1: placing a laser emitter on a first platform, adjusting the angle of the laser emitter to enable emitted laser to directly pass through an opening in the middle of a baffle, taking the direction of the laser as the initial direction of the laser, and transmitting a corresponding optical signal to an oscilloscope for display after a CCD detector receives the laser;
step S2: recording the corresponding angle of the pointer on the dial at the moment as a reference angle;
step S3: the wedge-shaped absorptive medium is tightly attached to the baffle, the first platform and the straight rod are rotated to a first angle, laser emitted by the laser emitter is refracted through the wedge-shaped absorptive medium, and the CCD detector receives the refracted laser and then transmits a corresponding optical signal to the oscilloscope for display;
step S4: calculating the distance Y of the light beam moving on an acquisition window of the CCD detector perpendicular to the initial direction of the laser through the position movement of the peak on the oscilloscope, and further calculating the deflection angle beta of the laser passing through the emergent surface of the wedge-shaped absorptive medium relative to the initial direction of the laser and the first real refraction angle of the laser
Figure FDA0004047226420000014
Figure FDA0004047226420000011
Figure FDA0004047226420000012
Wherein L is the distance from the exit point on the exit surface to the acquisition window of the CCD detector, and alpha is the apex angle of the wedge-shaped absorbent medium;
step S5: rotating the first platform communicated with the straight rod to a second angle, and performing operations from step S3 to step S5 to obtain a second real refraction angle of the laser
Figure FDA0004047226420000013
Step S6: the relationship between the real part and the imaginary part of the complex refractive index is obtained by combining the relationship between the real refractive index and the complex refractive index of the wedge-shaped absorptive medium as follows:
Figure FDA0004047226420000021
/>
Figure FDA0004047226420000022
wherein ,θ1 For the incident angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium, i.e. the difference between the first angle and the reference angle, theta 2 Is the refraction angle at the right-angle side when the laser first obliquely enters the wedge-shaped absorptive medium; θ'. 1 For the incident angle at the right-angle side when the laser light is obliquely incident on the wedge-shaped absorbent medium for the second time, i.e. the difference between the first angle and the reference angle, θ' 2 Is the refraction angle at the right-angle side when the laser is obliquely incident to the wedge-shaped absorptive medium for the second time; n is n i Is the refractive index, k of air 0 N and k are the real part and the imaginary part of the wedge-shaped absorptive medium respectively.
2. The method for measuring the complex refractive index of an absorptive medium according to claim 1, wherein: the specific calculation process in the step S6 is as follows:
let light wave E (r, t) =e (r) E -iωt ，H(r,t)＝H(r)e -iωt Substituting maxwell's equations, one can get the light wave in the absorptive medium to satisfy the following equation:
Figure FDA0004047226420000023
Figure FDA0004047226420000024
wherein ,
Figure FDA0004047226420000031
is equivalent complex permittivity, epsilon is permittivity, mu is permeability, sigma is conductivity,
Figure FDA0004047226420000032
is the complex refractive index of the absorptive medium, n, k are the real part, the imaginary part, k of the absorptive medium respectively 0 Is wave vector in vacuum, +.>
Figure FDA0004047226420000033
The unit vectors of the equal-breadth and the equal-phase surfaces are q and s respectively, and the included angle between the two unit vectors is xi=cos -1 (q.s)，k s and kq The phase constant and the attenuation constant of the wave respectively;
the phase constant, the decay constant in the absorptive medium are related to the real and imaginary parts of the complex refractive index as follows:
Figure FDA0004047226420000034
since neither n nor κ is zero, it is known from equation (5) that ζ+.pi/2, i.e. the two unit vectors are not perpendicular:
Figure FDA0004047226420000035
parameter N s ，N q Is the effective refractive index for light propagation and attenuation in an absorptive medium, and their magnitude is related not only to the complex refractive index but also to the angle between the equal-phase and equal-amplitude surfaces;
when the light is at an angle theta 1 The right-angle side of the incident wedge, at which, according to the boundary conditions,
n i k 0 sinθ 1 ＝k s sinθ 2 (7)
the relationship between the phase constant and attenuation constant of the light wave after entering the absorptive medium through the right-angle side refraction and the real part and the imaginary part of the complex refractive index is as follows
Figure FDA0004047226420000036
From formulae (7), (8)
Figure FDA0004047226420000041
In the same way, the absorption medium is refracted into the air at the bevel edge, and the real refraction angle of the refraction into the air is
Figure FDA0004047226420000048
Since the phase wave vector and the attenuation wave vector of the wave in the absorptive medium have tangential components at the interface, the phase constant k of the refracted wave s ' decay constant k q The relationship between' is as follows:
Figure FDA0004047226420000042
at the same time according to boundary conditions
Figure FDA0004047226420000043
The correlation of the real and imaginary parts of complex refractive index and refraction angle can be obtained by the combination of (7), (8), (10), (11):
Figure FDA0004047226420000044
similarly, it can be obtained at an angle of 1 At the time of 'incidence', assume that the real refraction angle at the right-angle side is θ 2 ' real refraction angle at hypotenuse
Figure FDA0004047226420000045
The relationship between the real and imaginary parts of the complex refractive index and the refraction angle is as follows>
Figure FDA0004047226420000046
The relationship between the real and imaginary parts of the complex refractive index, i.e., equation (12) and equation (13), is obtained by combining the real refraction angle and the complex refractive index of the absorptive medium as follows:
Figure FDA0004047226420000047
wherein ：
Figure FDA0004047226420000051
the real part n and the imaginary part κ of the complex refractive index in the above equation can be solved by using the function solve () in matlab software.
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