Passive optical element with selective angular reflection

Passive optical element with selective angular reflection

Christine Tremblay, Fernand Rheault, Russell Boulay, and Real Tremblay

This work is related to the development of passive selective transmission materials that will contribute toregularize the solar thermal gain. We propose an original solution to the problem of seasonal control ofenergetic input into buildings through windows. A passive optical element with selective angular reflection isused to solve this problem. This optical element allows sunlight to enter windows during the fall and winter,whereas, owing to the different astronomical path of the sun, it stops and rejects direct sunlight by means ofthe optical effect called total internal reflection (TIR) during the central spring-summer period. Thepurpose of this paper is to describe the optical element in some detail, to develop the principal designequations, and give the results of the optimization of optical and geometrical parameters.

1. Introduction

The idea of controlling sunlight transmissionthrough transparent plates has been a subject of re-search for many years. Screens or blinds made ofplastic or metal or window curtains as well are used toprevent direct solar radiation from entering houses.Certainly these accessories are very efficient for block-ing solar rays, yet they also obstruct the view anddarken rooms. Verandas are used for the same reasonbut only in small houses. This is the reason the devel-opment of passive selective transmission materialsthat could control the solar thermal gain into buildingshas become more important year after year. In anarticle on the potential of passive solar strategies foroffice buildings, Jones' concluded that the use of largesouth-facing areas for fenestration could reduce ener-gy needs. However, the development of systems madein such a way to control the solar gain is necessary toexploit this potential.

Until now most research in the field of passive solarenergy has been devoted to the design of energy-effi-cient windows using spectrally selective materials.Most of the passive elements for radiation control useenergy-efficient windows made of a class of coatingswhich are transparent at short wavelengths and reflec-tive at long wavelengths.

Two types of selective coating, called transparentheat mirrors, are of interest in different applications.2The first class of coatings has high visible transmit-tance and high infrared reflectance. In a hot climate, awindow with such a coating placed on its outer surface

C. Tremblay and F. Rheault are with University of Quebec, INRS-Energy, C.P. 1020, Varennes, Quebec JOL 2P0; the other authors arewith Laval University, Physics Department LROL, Quebec GK7P4.

Received 16 July 1986.0003-6935/87/030570-08$02.00/0.© 1987 Optical Society of America.

will then provide natural lighting in the day while thenear-IR solar radiation is reflected so that the poten-tial need for energy-consuming air conditioning is di-minished.3 The most practical approach for obtainingcoatings for this application is to use very thin layers(<50 nm) of the coinage metals (copper, silver, andgold). Typical optical properties of such thin films arehigh transmittance (80%) in the visible part of thesolar spectrum (0.3 < X < 0.7 Mm) and a high reflec-tance (100%) in the infrared part of the solar radia-tion (0.7 < X < 3 m). The second class of transparentheat mirror transmits the solar radiation (0.3 < X < 3Am) even though thermal radiation (3 X 100 Am) isimpeded. Hence a coating deposited on a windowdiminishes its heat transfer coefficient and thereby thepotential need for space heating.3 Coatings made ofwide band gap semiconductors doped or dielectric/metal/dielectric coatings have such properties. In thebest films, the visible transmittance approaches 95%and the thermal infrared reflectance is very high(290%).

Such coatings are certainly of great value for energy-efficient windows. However, they have the funda-mental limitation that their properties are static, beingunable to adjust to the variable demands on heatingand lighting during the day or season. For example, itmay be that a coating which has low thermal emittanceand is adequate during the winter in a mid-latituderegion causes overheating during the summer.

There are also some insulating glazings made of twosheets or more of glass separated by an air gap that isfiltered and dehydrated (desiccated). The behavior ofsuch glazings is based on the insulating power of desic-cated air. Such systems allow insulation against coldand protection against heat but are not adapted to theseasonal variation of the energy needs in buildings,since 56-77% of the direct solar radiation enters theseglazings all the time. 4 This kind of glazing is alsosusceptible to breakage by thermal shock when some ofits parts are submitted to different temperatures.This has led.some scientists to consider optical switch-ing materials which show dynamic optical properties.

570 APPLIED OPTICS / Vol. 26, No. 3 / 1 February 1987

Different types of substance (organic or inorganic)exhibit such properties and could be used as smartwindows.2 The intended coatings can be photochro-mic, thermochromic, or electrochromic, as their prop-erties change with the irradiation, the temperature, orthe strength and direction of an applied electric field,respectively.

Presently, the electrochromic materials are the mostpromising. The advantages associated with their usecome from the fact that their optical properties can bechanged by a voltage pulse (<1 V) and that there is noneed for a continuous input of electrical energy tomaintain the desired properties of transparence. It isfound that the solar transmittance can be adjustedfrom 12% to 86%.5 However, the research on windowcoatings with variable optical properties is only in itsinfancy.

Another way to solve the problem of seasonal radia-tion control into buildings, particularly in the mid-latitude regions, is based on the design of a transparentoptical element made in such a way that it would allowonly the solar rays with angles of incidence in an appro-priate range to enter windows. Only a few systems ofthis kind have been proposed as solar reflectors.

Some are obliquely deposited films.6 7 These coat-ings exhibit both spectral and angular selectivity andcan be applied to visible transparent windows whereangular selectivity may be required. The behavior ofother systems8 9 is based on the phenomenon of TIR inconnection with the fact that the apparent height ofthe sun in the sky varies throughout the year and ishigher during the summer months than during thewinter months. Such elements are interesting be-cause they are entirely passive.

The original idea on which the present work is basedis the design of an optical element with selective angu-lar reflection that could control the incident solar ener-gy. The element is made in such a way that the directsolar radiation could be partially reflected for a greatpart of the day during summer, reducing needs forclimatization; inversely, it would allow the sun rays topenetrate during winter time, contributing to heatingbuildings. Diffused light at low angles would pene-trate without appreciable attenuation.

II. Optical Behavior of the Selective Reflector

The principle of operation of the selective reflectoris related to the fact that by using coupling prisms it ispossible to design a multidielectric guiding plate in amanner that would cause deviation and guiding be-tween its faces of light that impinge on one of its faces.

The optical behavior of this optical element is basedon the following:

a light coupling module by means of total internalreflection at the intersection of two dielectric transpar-ent media of different refractive indices;

a lightguiding plate made of many prismatic ele-ments distributed periodically along the plate; and

the fact that the light coupling element is an inte-grated element of the periodic structure.

2

3

Fig. 1. Transverse cross section of the selective reflector.

Figure 1 is a transverse cross section of the selectivereflector. Figure 2 is an enlargement of a part of Fig. 1.The element ABCDD' is a coupling module. Eachcoupling module is made up of two prisms of transpar-ent dielectric materials having different indices of re-fraction. The prism ABC has an index n2 > 1 and theprism ACDD' has an index of refraction n, > n2.

Let O be the angle of incidence of a ray striking theinlet face of a reflector placed in a vertical positionfacing south with a the azimuthal angle and h the solaraltitude (Fig. 3). We can write

cos0i = sinh sinOe + cosh cosa cosOe. (1)

All the rays striking the inlet face AD' of a couplingmodule with angles of incidence O greater than a mini-mum angle of incidence 0 i min are coupled by total innerreflection in the coupling module. Thereafter, therays are successively deviated by the other couplingmodules and thus are guided along the plate.

For angles of incidence that are smaller than Oi mim

only a portion of the light is reflected at points P2 andpi in Fig. 2. In fact, the light passes through the platewith almost all its energy. We can see in Fig. 1 that thepath of a ray striking the plate with Oi 00 is practical-

1 February 1987 / Vol. 26, No. 3 / APPLIED OPTICS 571

I

'I.- i B

noonno-I

D'P

C

I

-I,

I

Fig. 2. Geometry of the coupling module ABCDD'. Rays 1 and 2are typical paths of input rays. Rays 3 and 4 are for output rays.

ly not deviated. Nevertheless, depending on whetherthe ray follows a path similar to the path of ray 2 or 3(Fig. 1), its deviation will be different, causing splittingof images looked at perpendicular to the plate.

A. Cutoff Angle

The selective reflector is made in such a way that theray coupling is on the common surface AC of the twomedia (ray 2, Fig. 2). A light ray incident on the inletface AD' is refracted into the medium of index nj andthereafter strikes the common surface AC at point P2.The light ray is completely reflected at point P2, giventhat the angle of incidence 02 at that point is equal to orgreater than the critical angle 02, given by the law ofrefraction

02C = in t 1(n2/n1 ). (2)

The condition 02 02, implies that the angle ofincidence Os at the inlet face of the reflector is equal toor greater than 0

L min- In terms of a and h, this impliesthat, for a given azimuthal angle, there is a minimumsolar altitude hA for which the ray is completely re-flected on AC given by

Fig. 3. Position of the sun in relation to a reflector placed in avertical position facing south.

\A

h, (degrees)

c50-

40--Total Internal , ' -

Reflection on BC , / 30 Total InternalReflection on AC

20-

-90 -60 -30 0 30 60 90AZIMUTH (degrees)

Fig. 4. Minimum angular altitude of the sun as a function of theazimuthal angle of the ray for the coupling effect on the surface BC

(dashed line) or AC (solid line).

the interface AC and the transmitted ray is coupled byTIR on the interface BC between the medium of indexn2 and air. The ray partially transmitted at AC istotally reflected in p1 when the angle of incidence 01 onBC is greater than or equal to the critical angle Oi, givenby the law of refraction

°lc= sin-1(1/n2). (4)

The condition 01 2 Oic implies that the effective criticalsolar height satisfies the relation

2 - 2= Djn 2 = (3)

with

D = C + B cos(0a + Oe),

C = cosh cosa cosO,, - sinh sinO0a,

B = A - sinh sinOe - cosh cosa cosO,

A = [n2- 1 + (sinh sinOe + cosh cosa cosOe)21

1/2,

h = hA-

However the phenomenon of TIR on AC is not theonly cause of ray coupling. In fact, the critical solarheight is determined by another phenomenon, illus-trated by ray 1 (Fig. 2). When a ray strikes the surfaceAC with an angle of incidence slightly smaller than thecritical angle 0 2c, a portion of its energy is reflected at

coshB cOsOa + B cosOe + Vn2 -n2 + D2 cosOa

-D cosO = n-

B and D are defined above. We always have

hCB < hcA-

(5)

Figure 4 illustrates the dependence of hA and hcB onthe azimuthal angle of the ray. We can see that thecritical altitude hB or hA decreases as the azimuthincreases. However, the azimuthal dependence of hBis much more pronounced than that of hcA. The valueof hB, when a = 300, is only slightly smaller (50 or less)than hA. Thus we can say that the coupling on BCmay be neglected when the azimuth is small. Howev-er, for a > 300, the minimum solar altitude for whichthere is coupling on BC (hcB) gets smaller and smallerthan hA as a increases. It is then necessary to take


100into account the coupling on BC when we have tocalculate accurately the cutoff angle of the reflector.

B. Geometrical Parameters.

The maximum of Ob is selected according to thefollowing relation:

Ob < 90 - ii mini a=O

- 60

. 4Q 40

'Z(6)

where Oi mi is the minimum angle of refraction of a rayat the inlet surface in the plane a = 0 for which there iscoupling on AC. Expressed otherwise, the angle b iSselected to be greater than or equal to the angle ofrefraction at the inlet surface when the angle of inci-dence of the ray is Oi min. In this way, the number ofrays coupled on AC is maximized.

By tilting the inlet surface AD' with respect to avertical plane, we give the rays propagating along thefaces a way out via DD'.

The surface DD' is oriented perpendicular to ADinstead of AD' to impede too many rays having beentotally reflected on AD' (ray 3, Fig. 2) to be totallyreflected on DD' or to leave by AD' with an angle sothat they strike the inlet surface AD' of the next mod-ule.

Ill. Optimization of Optical and Geometrical Parameters

A. Ray Tracing Analysis

A computer simulation program has been developedto study the propagation of rays inside the reflector.

The lightwave (supposed plane) incident on the re-flector is divided into a large number of individualrays, and the laws of geometrical optics are used todetermine the path of every ray between its inlet pointand its outgoing points.

At each interface between the two different media,the portion reflected and the portion transmitted of itsenergy are calculated. We understand that a singleray can generate a number of secondary rays thatgrows exponentially as the distance traveled throughthe reflector increases. However, taking into accountthe quantities of energy involved, only the path of oneof the two rays generated at the interface (usually thepath of the transmitted ray, except for the case of TIR)is considered. The results obtained this way give theminimum limit to the percentage of energy reflectedoutside the reflector (a part of the energy neglected ateach interface can eventually come out by DD' or AD').

The coefficient of transmission, associated with awave passing from one medium to another, is given bythe Fresnel equations. The parallel and the perpen-dicular polarizations of the rays are considered.

Thus it is possible with this program to determinethe path of a given number of rays striking the inletsurface AD' of a module with a given angle of incidenceas a function of the geometrical parameters (a, 0 e, Ob)and the optical parameters (n1, n2 ) of the reflector.The intensity and the orientation of each ray are deter-mined at every point on its path. For a given angle ofincidence of the rays, the percentage of reflected ener-gy is obtained by adding intensities of rays leaving the

Hour of the Day

Fig. 5. Seasonal behavior of a reflector installed in a vertical posi-tion facing south in Montreal (latitude = 45.630).

reflector by AD' or DD' and dividing all by the totalintensity of the incident rays.

B. Evaluation of Performance

The quality of the performance of the selective an-gular reflector is directly related to the portion of theincident energy reflected by the optical element. Thisis the reason the evaluation of its performance is basedon the calculation of the percentage of incident energyreflected away by the optical element at every hour ona given day. We obtain the daily behavior of thereflector this way.

The method of doing this calculation lies in makingthe numerical integral of a plane wave incident on thereflector to determine the redistribution of the wave'senergy (portion transmitted and reflected). The ab-sorption and diffusion of the materials have been ne-glected. Once the angle of incidence of the rays fromthe hour of the day and the latitude is determined, thepath of 200 parallel rays, equally spaced, incident on amodule (ABCDD') is computed.

The accuracy of the result is related to the finitenumber of rays. With 200 rays the resulting percent-age of reflection differs by < 1% from the results ob-tained using 150 rays. Thus we used 200 rays.

The reflector's performance throughout a day is afunction of

external parameters: orientation of the reflectorand latitude of the site; and

internal parameters: the geometrical characteris-tics of the coupling system (a, b, Oe) and the opticalcharacteristics of the media (n1 , n2 ).

Three criteria have been selected to evaluate thereflector's performance:

an annual working period limited to the summer;a minimum duration of the daily working period of 6

h; the percentage of energy reflected must exceed 50between 09:00 and 15:00; and

the materials must be transparent in the visibleregion.

By looking at Fig. 5, which shows the seasonal behav-ior of a reflector installed in a vertical position facingsouth in Montreal (latitude = 45.63°), we can see thatit is possible to satisfy such conditions by adjusting the


80

70

60

50

40. _

a: 75

65-90 -60 -30 0 30 60 90

AZIMUTH (degrees)

Fig. 6. Angular altitude of the sun for typical days of the year (solidlines) and the critical solar height for the coupling effect as a func-

tion of the azimuth.

internal parameters of a reflector for given externalparameters. In Fig. 6 we can see the position of the sunduring these typical days of the year and the criticalsolar height as a function of the azimuth. Also, wenote that the good performance of the reflector duringsummer is associated with the fact that the position ofthe sun at this time of the year is above the cutoff anglehcA. By looking at the position of the sun on 21 Sept.and the corresponding percentage of the reflectioncomputed for this day, we can see that the coupling onBC is less effective than the coupling on AC.

In fact, it has been found that the percentage ofreflection is generally above 50 for h hA, between 20and 35 for hcB • h < hA, and below 10 for h < hcB-

We also note an increase of the percentage of reflec-tion at the beginning and the end of the day. Thisphenomenon is due to the fact that the portion ofenergy reflected on AD' increases with the angle ofincidence. It is not an effect of a particularly efficientguiding of rays through the output DD' or AD'.

C. Effect of the Geometrical and Optical Parameters onthe Reflector's Performance

To evaluate the effect of these parameters, we fix theexternal parameters as follows: we consider a south-facing reflector in a vertical position in Montreal.

1. Geometrical Characteristics of the CouplingSystem

The parameter a plays an important role in raycoupling. Once nj, n2, and Oe are determined, we canshow that the value of a is directly related to thelatitude of the site via hcAI a=O- On the other hand, weknow that the reflector has a cutoff angle, i.e., a mini-mum solar altitude for which it works. On the otherhand, the solar altitude reaches a maximum of 68 on21 June (when a = 0) and decreases throughout thesummer to reach 56° at the end of August. Therefore,by letting hcA a= = 550, the annual working period islimited to the summer months. In fact, the solar alti-tude in the plane a = 0 is also 560 at the end of April.

55

45

35

21 June 1984

6 8 10 12 14 16 IE

21 August 984

h.A'S V4.

X _-+ - to

l \ IM~ 'V 6 8 t0 12 14

Hour of the Day

16 18

Fig. 7. Fraction of the incident energy reflected as a function of Ob:

(a) in June; (b) in August.

The reflector, then, works between April and August (5months). The value of a is then obtained from thefollowing relation:

sin(hCA a= - Oe) = nj sin(02, - da - Oe) (7)

The maximum value of b is determined by Eq. (6).The computer simulation program has been used tooptimize b. Two typical summer days-21 June(when the position of the sun is far above the cutoffangle) and 21 Aug. (when the position of the sun is closeto the cutoff angle)-have been considered. On eachof these days, the portion of energy reflected has beencomputed as a function of AOb = b max - Ob with 0 < A0b• 10°. The results (Fig. 7) show that A0b 4 givesoptimum performance.

The acute angle orientation 0e of the front prism'ssurfaces with respect to the vertical plane allows therays to leave the optical element. We can expect thisphenomenon to become more important as 0 e in-creases.

Figure 8 shows the percentage of reflection on 21June and 21 Aug. as a function of Se, varying between50 and 200. No energy leaves the optical elements bythe inlet surface when 0 e = 0.9 We can see that theportion of energy reflected throughout these days in-creases with 0 e and shows an optimum for 0 e 15°.However, if we consider the fact that for 100 < 0, < 150the splitting of images becomes more pronounced as eincreases, 0 e = 100 seems to be the best choice.

2. Optical CharacteristicsTwo factors can play an important role in the reflec-

tor's performance: the absolute value of the refractiveindices (nj, n2) and the difference of indices (n - n2).


h.A

. 35

.0_

1

t

6 8 10 12 14 16 18Hour of the Doy

Fig. 8. Fraction of the incident energy reflected as a function of Ge:(a) in June; (b) in August.

The method used to evaluate the effect of thesefactors lies in computing the portion of energy reflect-ed at 09:00 on 21 Aug. as a function of the indices ofrefraction. The range of refractive indices selected(1.30 < n1,2 S 1.70) corresponds to transparent mass-produced materials.

We know that the duration of the daily workingperiod during summer is at a minimum when the posi-tion of the sun is just above the cutoff angle (at the endof April and August). So this calculation has allowedus to identify the relation between the combination ofindices and the duration of the daily working period.

Figure 9 shows the results. The only criterion usedto construct this diagram is the duration of the dailyworking period. The diagram is divided into severalzones corresponding to the percentage of reflection at09:00 on 21 Aug. (%Rmin), the minimum acceptablebeing 50%. We can see that it is possible to maintainthe duration of the daily working period above 6 hduring the summer months by selecting appropriateindices of refraction.

By looking at Fig. 9, we can also see that the maxi-mum possible value for n2 seems to be around 1.44 andthat there is no optimum difference of refractive indi-ces. In fact, we observe that lower differences of indi-ces can be used as n, decreases.

Computation of the percentage of reflection in Juneand July using n, and n2 such as %Rmin = 70 hasrevealed that the portion of energy reflected for a givenAn increases with n, and that this phenomenon is notonly due to the increase with n, of the portion of energyreflected by the inlet surface.

The effect of An on the performance of a reflector inJune and July for which %Rmin = 70 in August has also

1.601

(.50 ~ 0.=0'1

1.40

1.30 1.40 1.50 1.60 1.70n,

Fig. 9. Reflection incident energy as a function of the refractive-index combination. Bold lines indicate indices of transparent mass-

produced materials.

-e0.tIW1i

su6

Fig. 10.

8 l0 12 14Hour of the day

16 (8

Effect of the index difference on the behavior of the reflec-tor in June. (a) n = 1.55; (b) n = 1.50.

been calculated (Fig. 10). We have found that, with n,= 1.50 or 1.55, the best performance is achieved withAn 0.08, which corresponds to a daily working periodof < 3 h in August. Thus the increase of the durationof the working period in August is accompanied by apercentage of reflection smaller in June (-15% for An= 0.17) and July.

D. Effect of Absorption

Until now we have neglected absorption of energy inthe optical element. The effect of absorption in thematerials has been simulated by introducing a coeffi-cient of absorption per unit length a in the calcula-


h,,, - 55' o~

En I oe

n, 1.50

| . . . .

.t/ An .0.04V .*0.08a 0. 12a *0.17'

20

16

2 12o (a:0.

M] 8

4

00

21 June 1984

8*. t o*

8B 6

0.10 0.20 0.30

INDEX DIFFERENCE

Fig. 11. Variation of the percentage of the maximum absorptionduring a summer day as a function of the index difference.

tions. We have made the assumption that the intensi-ty of a wave which leaves the reflector, after havingbeen guided between its faces, is given by

Io = Ii exp(-al), (8)

where I is the intensity at the output obtained bytaking into account losses produced by partial reflec-tion at each interface, and 1 is the length of the straightline joining the input and output points. The fact thatthe curvature of the path of most of the rays is not verypronounced (Fig. 1) justifies the assumption of a recti-linear path. a is an average coefficient of absorptionper unit length for the two media.

The results are shown in Fig. 11. We can see that areflector having a given thickness absorbs a portion ofthe energy which decreases when An increases. Thisphenomenon can be explained as follows: when thedifference of indices between the two media is low, therays deviate less at each interface and are thus guided agreater distance between the faces before leaving. It isquite obvious that the absorption can be reduced byreducing the thickness of the reflector.

E. Effect of the External Parameters

The internal parameters of the reflector have beenoptimized as a function of given external parameters:a south-facing reflector placed vertically in Montreal.The effect of the external parameters on the reflector'sperformance has been evaluated.

1. Latitude of the SiteThe minimum solar altitude during summer in the

plane a = 0 is a function of the latitude of the site.Thus a change of latitude will affect the cutoff angle.For example, if we want the duration of the annualworking period of a reflector placed in New York or LosAngeles to be the same as in Montreal, we have toincrease its cutoff angle, as indicated in Table I.

2. OrientationTwo cases are considered: an inclination a of the

reflector with respect to a vertical plane [Fig. 12(a)]and an orientation of fi degrees offset from full south[Fig. 12(b)].

Table I. Influence of the Latitude on the Geometrical Factors: n = 1.50,n2 = 1.33, Ge = 10°

Latitude h, 0a Ob(degrees)

Montreal 45.63 55 24.33 47.87New York 40.70 59 22.25 45.79Los Angeles 33.93 65 19.36 42.90

In the first case, we can note that a reflector tiltedwith an angle a should have a lower cutoff angle thanthe cutoff angle of a reflector with a = 0 to work duringthe same months. As we can see in Fig. 13, whichshows the behavior in June and August of a reflectorwith hCA = 550 (a = 0), 45° (a = 100), and 350 (a = 200),an increase of .a is accompanied by a decrease of thepercentage of reflection, particularly in June.

In the second case, we can see by looking at Fig. 14that the advantage of the selective reflector holds whenit is oriented ,3 degrees offset from full south. As amatter of fact, by rotating the reflector in the senseindicated in Fig. 12(c), with an angle -y equal to A andby slightly reducing the value of the cutoff angle, wecan reestablish the relative positions of the sun and thereflector. For example, a rotation of a reflector =100 toward the east, for which hAI a0 = 550, can becompensated by a rotation of y = 100 of the reflector,in the sense indicated in Fig. 12(c), and a decrease of 20of the cutoff angle. It should be noted that it is notnecessary to change the cutoff angle; the duration ofthe annual working period would then be slightly re-duced.

a I

ide view

(a)

(c)

Fig. 12. Reflector as seen from (a) the side, (b) above, (c) the front.


Above view

west 5 eastsou\I \

south

(b)

Art- Foce view(I

west - - eastI

I I/ I/ I

j i

I I I I __ I I

100

80[

60

40

20-e

0.t;IW

-6 8 10 12 14 16 18

Hour of the day

Fig. 13. Effect of the inclination a of the reflector on its behavior:(a) in June; (b) in August.

18

Hour of the day

Fig. 14. Seasonal behavior of the reflector turned 100 east. Inter-nal parameters and orientation have been adjusted for optimal

performance in these conditions.

IV. Conclusion

From the theoretical considerations presentedabove, we believe that it is possible to design an opticalelement with selective angular reflection that couldreflect sunlight away for the whole length of the dayduring the summer period between the end of Apriland August and could admit it during the winter peri-od. Given the refractive indices of the two media, onecan obtain a convenient value for the critical height ofthe sun that will set the limit between the summerbehavior and the winter behavior by an appropriatechoice of the geometrical parameter Oa. The passagebetween the winter and the summer period is notabrupt, but there are two transition periods of aboutone month each (in April and in September at a lati-tude of 45.63° corresponding to Montreal). We have

also found that an appropriate selection of the combi-nation of refractive indices sets the duration of thedaily working period to 6 h or more.

In fact, many reasons seem to indicate that the opti-cal element with selective angular reflection could be asuitable solution to the problem of passive radiationcontrol:

it is an efficient static element that requires neitherdaily nor seasonal adjustment to accommodate solarmovements;

its performance-a high reflectance during the sum-mer months (56-77%) and relatively low reflectance(below 10%) during the winter months-is quite welladapted to satisfying energy needs of buildings in mid-latitude regions;

it can be easily adapted to various conditions(change of latitude, orientation and period of opera-tion, etc.); and

it enables diffused light to pass while deviating andguiding direct rays.

This is why it is possible to consider some potentialuses of the optical element:

windows for buildings, greenhouses (note that theuse of the reflector as a greenhouse coating supposes aninclination a of the reflector with respect to the verti-cal plane, which may not be as good if a is too high); and

light concentrator: computations have shown thatthe sun rays may be guided on a relatively long dis-tance along the plate if the internal parameters areproperly adjusted (e - 0, and small An).

Funding for this project was received from the Que-bec Government FCAR Centre Program.

References1. L. Jones, "Review of the Potential of Passive Solar Strategies for

Office Buildings," Conseil national de recherches Canada, con-tract 045X.31155-2-2702 (Aug. 1983).

2. C.-G. Granqvist, "Spectrally Selective Surface Coatings for Ener-gy Efficiency and Solar Applications," Phys. Teacher 22, 372(1984).

3. C.-G. Granqvist, "Radiative Heating and Cooling with SpectrallySelective Surfaces," Appl. Opt. 20, 2606 (1981).

4. Technical note, Glaverbel Co., 166 Chaussee de la Hulpe, Bru-xelles 1170 (Jan. 1979).

5. J. S. E. M. Svensson and C.-G. Granqvist, "Optical MaterialsTechnology for Energy Efficiency and Solar Energy ConversionIII," Proc. Soc. Photo-Opt. Instrum. Eng. 502, 30 (1984).

6. R. T. Kivaisi, "Spectral and Angular Selectivity of ObliquelyDeposited Films," Proc. Soc. Photo-Opt. Instrum. Eng. 428, 32(1983).

7. R. T. Kivaisi, "Optical Properties of Obliquely Evaporated Alu-minum Films," Thin Solid Films 97, 153 (1982).

8. U. Flisi, F. Scamoni, U. Monaco, and G. V. Nardini, "Solar EnergyApplications to Dwellings," Proceedings of the EC Contractors'Meeting held in Meersburg, F.R.G., 14-16 June 1982 Ser. A 2,195(1983).

9. R. Tremblay, "Electromagnetic Wave Concentrator," U.S. Pat-ent 4,505,264 (Mar. 1985).


a. I . . .21 June 1984

-a - (.50N 5n, =(.33 Aa = iol-8. = 10° h., z45°

8 = 86 - Va =201ho = 35-

I I I I | I I I IAI I

6 8 10 12 14 (6 (80 0

b I I I I I I l I

21 August 1984

80

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Passive optical element with selective angular reflection

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