a The necessary refractive index and b extinction coefficient of the anti-reflection layer as a function of light wavelength and thickness for achieving perfect absorption. The wavelength is varied from 300 to 800nm. The thickness of the anti-reflection layer is increased from 10 to 30nm in steps of 2nm. The thickness of the α-Si:H layer = 15nm. c, d The same as with a and b , but for thickness increased from 10 to 30nm, and = 15nm. The in a and c indicate the boundaries at which the refractive index is equal to zero
Here, we discuss the physical mechanism that underlined the perfect absorber of light waves. In order to obtain perfect absorption or zero reflection, the two terms (
\( {r}_{01} \)
and
\( {r}_{123}{e}^{2 i{\beta}_1} \)
) in Eq. (
1
) should have the same amplitude but opposite phase, from which one can deduce two equations to define the condition for perfect absorption [
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]:
\( 4\pi {k}_1{d}_1/\lambda = In\left({R}_{123}/{R}_{01}\right) \)
,
\( 4\pi {n}_1{d}_1/\lambda =\pi +{\varphi}_{01}-{\varphi}_{123} \)
, where
\( {R}_{01} \)
(
\( {R}_{123} \)
) and
\( {\varphi}_{01} \)
(
\( {\varphi}_{123} \)
) denote the amplitude and the phase of
\( {r}_{01} \)
(
\( {r}_{123} \)
), respectively. When both equations are satisfied, completely destructive interference will happen. As a result, reflection is reduced to zero, and perfect absorption is achieved.
The relative permittivity and permeability of the metamaterial anti-reflection layer for achieving perfect absorption, with the thickness of the anti-reflection layer = 15nm and the thickness of the α-Si:H layer = 30nm. The give the numerically calculated values of the real and imaginary parts ( , , , ) of and , and the give the corresponding results ( , , , ) fitted through the Lorentz model
Here,
i
is the imaginary unit,
\( {\omega}_p \)
is the plasma frequency,
\( {\omega}_{a1},{\omega}_{a2} \)
are the center frequencies of the oscillators,
\( {\omega}_{c1},{\omega}_{c2} \)
are the damping frequencies, and
\( {\varepsilon}_1,{\mu}_1 \)
are the static permittivity and permeability at infinite frequency, respectively. The solid lines in Fig.
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show the fitted results by Eq. (
3
), with the corresponding parameters
\( {\varepsilon}_1=-3.9,{\mu}_1=-1.5,{\omega}_p=4.6*{10}^{15} Hz,{\omega}_{a1}=3.32*{10}^{15} Hz,{\omega}_{a2}=3.62*{10}^{15} Hz,{\omega}_{c1}=1.3*{10}^{15} Hz,{\omega}_{c2}=1.26*{10}^{15} Hz \)
. It is clearly seen in Fig.
4
that the metamaterial anti-reflection layer should have both electric and magnetic resonances.
In other states, the enhancement for firearm possession tends to range from 1 to 5 years, before even accounting for the fact that many states do not criminalize firearm possession or allow judges discretion to withhold the enhancement.
Outside Illinois, only four other states have mandatory possession minimums that come close. Firearm possession during a felony carries a 10-year minimum in both Florida and California, though California recently made all of its various firearm enhancements fully discretionary . Rhode Island also requires an additional 10 years for a first firearm offense, but this only applies in cases of “use,” not necessarily for possession alone.
though California recently made all of its various firearm enhancements fully discretionaryWhat about discharge, brandishing, and other forms of use? For the purposes of sentencing, few states outside Illinois distinguish between possession, discharge, and “use” (which may or may not encompass all, both, or some of the above).
Still, if we compare Illinois to the many states that distinguish between the various states that penalize felony use, we find again a general range of 1 to 5 years, compared to the 20 or 25-year enhancement for firearm discharge in Illinois.
As before, only Florida and California come close (both at 25 years), and only Florida is the enhancement also mandatory in nature. Alaska also stands out for requiring a mandatory enhancement of 25 to 35 years for firearm use during the commission of a limited set of crimes involving the sexual exploitation, abuse, or assault of minors. Outside of these offenses, however, Alaska’s minimum enhancement for a first firearm-assisted crime is 5 years.
Beyond length, Illinois enhancements are also rigidly mandatory.Until a policy change 2015, Illinois judges had no choice but to indiscriminately apply our state’s extreme firearm enhancements (judges can now depart from the enhancement in cases involving juvenile defendants).
But not every state applies enhancements in such a rigid way. Many grant some degree of discretion to judges and sentencing courts in terms of how they implement enhancements. These states permit, as follows:
Full to near-full discretion to apply or not apply an enhancement . Arkansas gives judges the discretion to add anywhere from 0 to 15 years to a first offense sentence if firearms are employed during a felony. California, Idaho, Oregon, Vermont, West Virginia, Wisconsin, and Wyoming also grant judges a similar level of discretion for a first firearm offense. Among these states, Arkansas and Oregon require a mandatory enhancement for second and subsequent offenses (10 years for Arkansas, 5 for Oregon).
Full to near-full discretion to apply or not apply an enhancementDiscretion to depart with on-the-record rationale . New York gives sentencing courts the choice to depart from applying a 5-year enhancement for criminal firearm use, provided that the court state on record that the enhancement would be “unduly harsh and that not imposing [the enhancement] would be consistent with the public safety.” Louisiana also gives judges to depart from the firearm enhancement provided they “state for the records the reasons” a sentence is “excess,” as does Kansas for its own version of a firearm enhancement.
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