CN102749189B - Double-linear track detecting method of refraction effect of two-dimensional photonic quasi-crystal wedge lens - Google Patents
Double-linear track detecting method of refraction effect of two-dimensional photonic quasi-crystal wedge lens Download PDFInfo
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- CN102749189B CN102749189B CN201210254546.0A CN201210254546A CN102749189B CN 102749189 B CN102749189 B CN 102749189B CN 201210254546 A CN201210254546 A CN 201210254546A CN 102749189 B CN102749189 B CN 102749189B
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- refraction
- hypotenuse
- prism wedge
- prism
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Abstract
The invention provides a double-linear track detecting method of a refraction effect of a two-dimensional photonic quasi-crystal wedge lens, which relates to a double-linear track detecting method. According to the invention, the double-linear track detecting method comprises the following steps of: arranging two linear tracks parallel to a bevel edge of the two-dimensional photonic quasi-crystal wedge lens; and according to opposite positions of the two tracks and the bevel edge as well as maximum strength positions detected on the two tracks, determining a refraction angle and effective index of a refracted beam as well as an emission position and emission position offset of the refracted beam through a geometrical relationship and a refraction law, so as to determine the refraction effect of the two-dimensional photonic quasi-crystal wedge lens. The double-linear track detecting method provided by the invention can be applied to any electromagnetic wave and any two-dimensional N-fold quasi-crystal wedge lens. The double-linear track detecting method provided by the invention is suitable for the field of photonic crystals, in particular photonic quasi-crystals. Meanwhile, according to the invention, a problem that the refraction angle and the effective index cannot be accurately detected or calculated by the traditional single circular arc track detecting method is also solved.
Description
Technical field
The present invention relates to a kind of bilinear track detection method, be specifically related to a kind of bilinear track detection method that is applicable to survey or calculate the accurate brilliant prism wedge refraction effect of random two-dimensional photon.
Background technology
Refraction effect, is the deviation effect (comprising positive refraction and negative refraction) that electromagnetic material or device produce incident electromagnetic wave (or light wave).In the accurate brilliant device of two-dimensional photon (as: lens, prism), as the important parameter that determines the behavior of incident wave beam deviation, equivalent refractive index (comprising positive refracting power and negative index) has determined the concrete direction of wave beam transmission and outgoing, the particular location of wave beam focusing and imaging.Therefore, the calculating of equivalent refractive index is an important topic of refraction effect research in the accurate brilliant device of two-dimensional photon.Feng etc. (Z. F. Feng,
et al. Phys. Rev. Lett. 2005,94 (24): 247402) numerical evaluation experimental verification the equivalent negative refractive index of the accurate brilliant prism wedges of two dimension ten double Stampfli type photons.Neve-Oz etc. (Y. Neve-Oz,
et al. J. Appl. Phys. 2010,107 (6): 063105) numerical evaluation has obtained the equivalent positive refracting power of the accurate brilliant prism wedge of the heavy Penrose type photon of two dimension ten.But the two does not consider the impact on equivalent refractive index of heterogeneity that in the accurate crystalline substance of two-dimensional photon, scattering is arranged, the result of study only drawing for single incoming position.Although Gennaro etc. (E. Di Gennaro,
et al. Phys. Rev. B 2008,77 (19): 193104) consider the impact that scattering is arranged and obtained different outgoing field distribution, but quantitative result not.Therefore, for the accurate brilliant prism wedge of certain specific two-dimensional photon, if change the incoming position of incident wave beam, whether the exit direction of maximum intensity outgoing beam (or refraction angle) or equivalent refractive index change, whether outgoing position is offset, and needs further to be studied.If the outgoing position of outgoing beam is offset, the sniffer of traditional single arc-shaped rail or computation model all cannot accurately obtain its refraction angle, equivalent refractive index and outgoing position offset.
For whether the outgoing position of investigating outgoing beam is offset, taking the accurate crystalline substance of germanium base for post two dimension ten heavy Penrose type photon as example, appoint and get a prism wedge below, calculate its outgoing field distribution.The heavy Penrose accurate crystalline substance of type photon of two dimension ten and prism wedge thereof, be shown in Fig. 1 and Fig. 2.
As Fig. 1, establish the heavy Penrose type photon of two dimension ten accurate brilliant Rotational Symmetry central point and two dimensional surface
initial point
overlap; Germanium post refractive index
, air refraction
; The sub-radius of scattering
,
for grating constant.As Fig. 2, for making border Section Effect low as far as possible, establish prism wedge drift angle value and be
, and three boundary values are respectively
,
,
.
For making the deviation of wave beam in prism wedge succinct as far as possible and directly perceived, establish a right-angle side of incident wave beam vertical incidence prism.Find as calculated, the eye point position of maximum intensity outgoing beam is or not the intersection point place of beams incident direction and prism wedge hypotenuse, but departs from this intersection point, sees Fig. 3.
This problem has been ignored in research in the past, the semicircle sniffer of the employings such as Feng (being made up of semicircle chamber and the probe that moves along semicircular track) direct detection obtains refraction angle, peak value eye point is thought by mistake in the center of circle of semicircular track, and its refraction angle is not actual value.Therefore, detector is along single semicircle or the only peak of detectable outgoing beam on semicircle or rectilinear orbit of linear path, but can not obtain its accurate refraction angle.
Summary of the invention
In order to solve better the problem that detector can not accurate detection refraction angle along single semicircle or linear path, the invention provides a kind of for surveying the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon.
The present invention is achieved through the following technical solutions:
Two rectilinear orbits that are parallel to the accurate brilliant prism wedge hypotenuse of two-dimensional photon are set, according to the relative position of two tracks and hypotenuse (
,
for the wavelength of incident electromagnetic wave) and the maximum of intensity position that detects on two tracks, can be determined refraction angle and the equivalent refractive index of refracted beam by geometric relationship and refraction law, and outgoing position and outgoing position offset, the i.e. refraction effect of the accurate brilliant prism wedge of definite two-dimensional photon.
Bilinear track detection method of the present invention can be applicable to any electromagnetism and involves the heavy accurate brilliant prism wedge of random two-dimensional N.The present invention is applicable to photonic crystal, especially the accurate brilliant field of photon.
Prior art is single arc-shaped rail detection method.Because of from the actual outgoing position deviation incident direction of prism wedge hypotenuse maximum intensity outgoing beam and the intersection point of prism wedge hypotenuse, make prior art cannot accurately obtain its refraction angle, equivalent refractive index and outgoing position offset.And this method adopts bilinear track, for the electromagnetic wave of vertical incidence, no matter whether the outgoing position of outgoing beam is offset, can accurately obtain according to geometric relationship and refraction law refraction angle, outgoing position and the outgoing position offset of prism wedge hypotenuse outgoing beam, and corresponding equivalent refractive index.
Brief description of the drawings
Fig. 1 is that the heavy Penrose type photon of two dimension ten is accurate brilliant;
Fig. 2 is the accurate brilliant prism wedge model of two-dimensional photon;
Fig. 3 is that the actual eye point of maximum intensity outgoing beam departs from beams incident direction and prism hypotenuse intersection point certain distance;
Fig. 4 is the schematic diagram of the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon;
Fig. 5 is the transmission spectrum of the accurate brilliant prism wedge of the heavy Penrose type photon of germanium base for post two dimension ten;
Fig. 6 be given electromagnetic wave (
,
) at incoming position be
,
time, the field distribution of TE pattern;
Fig. 7 be given electromagnetic wave (
,
) at incoming position be
,
time, the TE mould intensity that detector 1 and detector 2 are surveyed;
Fig. 8 be given electromagnetic wave (
,
) under different incoming positions, the TE mould intensity that detector 1 is surveyed;
Fig. 9 be given electromagnetic wave (
,
) under different incoming positions, the TE mould intensity that detector 2 is surveyed;
Figure 10 be given electromagnetic wave (
,
) under different incoming positions, the TM mould intensity that detector 1 is surveyed;
Figure 11 be given electromagnetic wave (
,
) under different incoming positions, the TM mould intensity that detector 2 is surveyed.
Embodiment
Embodiment one: the concrete detection principle of the bilinear track detection method of present embodiment is shown in Fig. 4.
As shown in Figure 4, the mid point of establishing prism wedge hypotenuse and two rectilinear orbits is respectively
,
,
, and be made as the initial point of coordinate system separately, and three point on a straight line.Detector diverse location on rectilinear orbit is surveyed, and each position can detected intensity value, the intensity curve that all intensity levels form, and its peak value is maximum of intensity.If the maximum of intensity position that two detectors are surveyed on two tracks is respectively
,
, the spacing of two tracks and prism hypotenuse is respectively
,
, can try to achieve the direction of outgoing beam, refraction angle is:
(1)；
In the time being negative refraction,
,
; When for positive refraction,
,
.By refraction law (M. Notomi, Phys. Rev. B 2000,62 (16): 10696 – 10705), get final product to such an extent that corresponding equivalent refractive index is again:
(2)；
In addition, according to
,
,
or
,
,
, can know the eye point coordinate of its maximum intensity wave beam at hypotenuse by inference
for:
(3)；
According to geometric relationship, Yi Zhi
plane edge
the coordinate figure of axle is
(
value determined by concrete prism wedge), and eye point coordinate
projection coordinate at prism right-angle side (left surface) is:
(4)；
If incident wave beam at the incoming position of prism right-angle side is
, the difference of eye point projection coordinate and incoming position coordinate is:
(5)；
In formula (5)
be defined as outgoing position offset.When
time, eye point is upwards offset along hypotenuse with respect to incident wave beam direction and hypotenuse intersection point; When
time, eye point offsets downward along hypotenuse with respect to incident wave beam direction and hypotenuse intersection point.
It is pointed out that complicated near-field scattering effect and shot-range interaction make the light field of the accurate brilliant device near-field region of photon unstable (E. Di Gennaro,
et al. Phys. Rev. B 2008,77 (19): 193104),
,
actual value should be at near-field region, must make detector in far-field region, should be greater than with the distance of prism wedge
(N. Fabre,
et al. Phys. Rev. Lett. 2008,101 (7): 073901).If only, for analyzing the direction of outgoing beam, consider two parallel track hypotenuses, can know
,
with
relative position.For solving the eye point position of maximum intensity wave beam at hypotenuse, need to know three's relative position.In addition, for theoretical research, the position of rectilinear orbit and the scope of detection, need compromise to consider, both can Correct Analysis refraction effect, should save computing time again.For oblique incidence, although the calculating of equivalent refractive index is comparatively complicated, can obtain refraction angle corresponding to maximum intensity outgoing beam and outgoing position according to bilinear track detection method.
Embodiment two: in order to verify invention effect of the present invention, present embodiment is calculated electromagnetic transmission and field distribution thereof in conjunction with Finite-Difference Time-Domain Method, specifically investigates the refraction effect of the accurate brilliant prism wedge of two-dimensional photon.According to the prism wedge size relating in Fig. 1 and Fig. 2, establish the width (being rectilinear orbit length) that detector 1 and detector 2 survey and be
.For the conclusion that makes refraction effect has more universality, consider electromagnetic two kinds of polarization modes, i.e. TE mould, TM mould.Be located at
,
the lattice dimensions of direction
, time step
(
for the light velocity in vacuum), under TE, two kinds of patterns of TM, light transmission time is
(from simulating area border).
For the refraction effect in research prism wedge, must investigate its transmission spectrum, find out respectively its TE, TM band gap and transmission wave band, then calculate the equivalent refractive index that certain transmission peak wavelength is corresponding.Can obtain as calculated the transmission spectrum of the accurate brilliant prism wedge of the heavy Penrose type photon of germanium base for post two dimension ten, see Fig. 5.
As shown in Figure 5, there is TE, TM and complete band gap in prism wedge (Fig. 2), and TM band gap is preponderated.Under TM pattern
the corresponding normalized frequency of peak-peak
, i.e. corresponding angles frequency
, and this frequency for TE pattern also in passband.Taking this frequency as research object, adopt bilinear track detection method and Finite-Difference Time-Domain Method, the refraction effect of numerical evaluation prism below.It should be noted that, though frequency is selected arbitrarily, its TE mould and TM mould should be simultaneously in passbands.
If
,
.For avoid narrow beam cause its in the accurate crystalline substance of photon, produce multiple edge effect (L. A. Mel'nikov,
et al. J. Commun. Tech. EL+ 2005,50 (10): 1147
–1152), concentrate a branch of relatively wide incident wave beam of research at this, and establish width and be
.Below taking TE pattern and incoming position as
,
for example, calculate corresponding refraction angle, equivalent refractive index and outgoing position offset, as Fig. 6 and Fig. 7.
By two peak of curve positions in Fig. 7
,
, and formula (1), (2), be easy to get:
,
.By formula (3) ~ (5), can obtain the center eye point of maximum intensity outgoing beam
, this point is along right-angle side projection coordinate and incoming position coordinate difference
, eye point is upwards offset (as Fig. 3) with respect to incident wave beam direction and prism hypotenuse intersection point along hypotenuse.
Adopt same method, can calculate TM pattern, and under two kinds of patterns, incoming position is respectively
,
,
corresponding field distribution.Under each incoming position, two detectors, to the strength investigation value along two tracks under TE, TM pattern, are shown in Fig. 8～11.
According to Fig. 8～11, can reach a conclusion: (1), along with the monotone variation of incoming position, intensity peak position and size are not monotone variation; (2) intensity level under TE pattern is much larger than the intensity level under TM pattern (known by Fig. 5, TM pattern more easily produces band gap, and the intensity level of its transmission should more may be little); (3) with respect to TE pattern, the center of the more close detection track of maximum of intensity under TM pattern.
According to each curve maximum intensity correspondence position in Fig. 8～11
,
and formula (1) ~ (5), can calculate refraction angle, equivalent refractive index and outgoing position offset that under TE, TM pattern, different incoming positions are corresponding, in table 1.
Refraction angle, equivalent refractive index and outgoing position offset that under table 1 TE, TM pattern, different incoming positions are corresponding
| –2 | –1 | 0 | ＋1 | ＋2 | |
| 9.314 | 13.062 | 26.012 | 27.294 | 26.381 | |
| 4.574 | 9.537 | 5.711 | 13.712 | 17.952 | |
| 0.275 | 0.384 | 0.746 | 0.780 | 0.756 | |
| 0.136 | 0.282 | 0.169 | 0.403 | 0.524 | |
| 2.617 | 2.572 | 2.074 | 1.365 | –0.040 | |
| 4.300 | 4.142 | 1.523 | 2.611 | 2.404 |
According to table 1, can reach a conclusion: (1) determines refraction angle, equivalent refractive index and the outgoing position offset that incoming positions different under polarization mode is corresponding different, and in prism, wave beam exists non-rule or random refraction effect; (2), for any incoming position, two kinds of deviation patterns meet
, i.e. the easier deviation of TM pattern.In other words,, with respect to TE pattern, TM pattern more easily produces photon band gap, near the light wave its band gap more may show class refraction effect, report as institute in document (M. Notomi, Phys. Rev. B 2000,62 (16): 10696 – 10705).
The accurate crystalline substance of two-dimensional photon has rotational symmetry, arranging of its scattering do not there is translational symmetry (D. Shechtman,
et al. Phys. Rev. Lett. 1984,53 (20): 1951 – 1953).In the accurate brilliant prism wedge of two-dimensional photon, scattering with quasi-periodicity mode arrange, the local resonance state in accurate crystalline substance are also and arrange quasi-periodicity, and the local resonance state of diverse location are different, make electromagnetic wave transmission at random to act hurriedly in a messy situation in accurate crystalline substance of incident.Therefore, change incoming position will change transmission path, and its class Bragg diffraction (and diffraction) behavior and transmission mode different, its electric field is also coupled in local state, finally changes transmission beam width and the field distribution from prism surface outgoing.In other words, the heterogeneity that scattering is arranged causes the non-regularity of class Bragg diffraction effect, and finally causes the non-regularity of refraction effect.Therefore the result of calculation and the theoretical analysis that, utilize bilinear track detection method to obtain match.
For oblique incidence, know by inference according to the non-regularity of class Bragg diffraction effect, can obtain being similar to the conclusion in vertical incidence situation: beam diffraction exists non-regularity.Equally, this conclusion can be applicable to air pass, and the accurate brilliant prism wedge of other random two-dimensional N heavy photon, no longer introduces at this.
Therefore, be of the present inventionly a kind ofly applicable to survey or calculate the accurate brilliant prism wedge refraction effect of random two-dimensional photon for surveying the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon.Meanwhile, the present invention has also solved single arc-shaped rail detection method in the past and has failed accurate detection or calculate the problem of refraction angle and equivalent refractive index.
Claims (7)
1. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon, it is characterized in that described bilinear track detection method is: two rectilinear orbits that are parallel to the accurate brilliant prism wedge hypotenuse of two-dimensional photon are set, the maximum of intensity position detecting according to the relative position of two tracks and hypotenuse and on two tracks, can be determined refraction angle, equivalent refractive index, outgoing position and the outgoing position offset of refracted beam by geometric relationship and refraction law, determine the refraction effect of the accurate brilliant prism wedge of two-dimensional photon, wherein:
Refraction angle is: θ=arctan[(x
2'-x
1')/(d
2-d
1)], o
s', o
1', o
2' represent respectively the mid point of prism wedge hypotenuse and two rectilinear orbits, x
1', x
2' represent respectively the maximum of intensity position that detector is surveyed on two tracks, d
1, d
2represent respectively the spacing of two tracks and prism hypotenuse;
Equivalent refractive index is: n
eff=n
airsin θ/sin θ
0, n
airrepresent air refraction, θ
0represent prism wedge drift angle value;
Outgoing position is: x
s'=x
1'-d
itan θ (i=1,2);
Outgoing position offset is: Δ z=z
s-z, z represents the incoming position of incident wave beam at prism right-angle side, z
srepresent eye point coordinate x
s' in the projection coordinate of prism right-angle side, and x
s' be the eye point coordinate figure in hypotenuse coordinate system, z
sfor the coordinate figure in xoz coordinate system.
2. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon according to claim 1, is characterized in that when for negative refraction x
2' < x
1', θ < 0; When for positive refraction, x
2' > x
1', θ > 0.
3. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon according to claim 1, is characterized in that the mid point three point on a straight line of prism wedge hypotenuse and two rectilinear orbits.
4. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon according to claim 1, is characterized in that eye point is upwards offset along hypotenuse with respect to incident wave beam direction and hypotenuse intersection point in the time of Δ z > 0; In the time of Δ z < 0, eye point offsets downward along hypotenuse with respect to incident wave beam direction and hypotenuse intersection point.
5. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon according to claim 1, is characterized in that z
s=o
sz'-x
s' cos θ
0, x
s' represent the eye point coordinate figure of maximum intensity wave beam in hypotenuse coordinate system, o
sz' represent o
s' coordinate figure in xoz plane along z axle.
6. the bilinear track detection method of the accurate brilliant prism wedge refraction effect of two-dimensional photon according to claim 1, is characterized in that complicated near-field scattering effect and shot-range interaction make the light field of the accurate brilliant device near-field region of photon unstable, i.e. d
1, d
2actual value should be at near-field region, must make detector in far-field region, should be greater than 3 λ, the wavelength that λ is incident electromagnetic wave with the distance of prism wedge.
7. according to the bilinear track detection method of the accurate brilliant prism wedge refraction effect of the two-dimensional photon described in claim 1 or 6, it is characterized in that d
2> d
1> 3 λ, the wavelength that λ is incident electromagnetic wave.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1388894A (en) * | 2000-08-11 | 2003-01-01 | 株式会社拓普康 | Apparatus for measuring refractive power |
| JP3538281B2 (en) * | 1995-12-14 | 2004-06-14 | ペンタックス株式会社 | Optical member inspection device |
| JP2005257508A (en) * | 2004-03-12 | 2005-09-22 | Nokodai Tlo Kk | Double refraction characteristic measuring device and double refraction characteristic measuring method |
| CN101493376A (en) * | 2009-03-06 | 2009-07-29 | 北京理工大学 | Pentaprism combination ultralong focal-length measurement method and apparatus |
-
2012
- 2012-07-23 CN CN201210254546.0A patent/CN102749189B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP3538281B2 (en) * | 1995-12-14 | 2004-06-14 | ペンタックス株式会社 | Optical member inspection device |
| CN1388894A (en) * | 2000-08-11 | 2003-01-01 | 株式会社拓普康 | Apparatus for measuring refractive power |
| JP2005257508A (en) * | 2004-03-12 | 2005-09-22 | Nokodai Tlo Kk | Double refraction characteristic measuring device and double refraction characteristic measuring method |
| CN101493376A (en) * | 2009-03-06 | 2009-07-29 | 北京理工大学 | Pentaprism combination ultralong focal-length measurement method and apparatus |
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