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CHAPTER 2
INTERACTION OF LIGHT
WITH MATTER
2.1 INTRODUCTION
When light enters matter, its elecromagnetic field interacts with the localized elec- tromagnetic field of atoms. The result is that if and when light emerges from matter, its characteristics and properties may not be the same. How light is affected by mat- ter depends on the strength of the field of the light, its wavelength, and the matter it- self. In addition, external influences on matter, such as temperature, pressure, and other external fields (electrical, magnetic), influence the interaction of light with matter. The interaction of light with matter may be undesirable, but it may also be taken advantage of to construct optical devices. In this chapter, we examine the interaction of light with matter.
2.2 TRANSPARENT VERSUS OPAQUE MATTER
Some matter allows all light energy (all photons) to propagate through it and it is called optically transparent. In contrast, opaque matter does not.
Example
Clear glass is transparent; a sheet of iron is not.
Semitransparent matter passes a portion of light energy through it and absorbs the remainder. Such matter attenuates the optical power of light, and it may be used to make an optical device known as _optical attenuator. __
Example
Most transparent matter, semitransparent mirrors. An optical filter allows selected frequencies to be propagated through it. _
11
12 Part I Fundamentals of Light
Example Red, green, yellow, or blue glass (each allows a selected range of frequencies to be propagated through it). Some matter in the ionized state absorbs selected frequencies and passes all others. _
Example The sun's ionized surface.
2.3 PROPERTIES OF OPTICALLY
TRANSPARENT MATTER
When light enters matter, its electromagnetic field reacts with the near fields of its atoms. In dense matter, light is quickly absorbed within the first few atomic layers and, because it does not emerge from it, that matter is termed nonoptically trans- parent. In contrast to this, some types of matter do not completely absorb light. Such matter, termed optically transparent matter, allows light to propagate through it and emerge from it. Examples of optically transparent matter include water and clear glass. We are more interested in optically transparent matter; thus, we examine the interaction of light with it. In particular, we examine the following:
- Reflection and refraction
- Diffraction
- Interference
- Holography
- Polarization
- Birefringence
- Dispersion
- Nonlinear phenomena
- Optical isotropy and anisotropy
- Optical homogeneity and nonhomogeneity
- Effects of impurities and microcracks Absorption Scattering
2.3.1 Reflection and Refraction: Index of Refraction
The index of refraction of a transparent medium (nrned) is defined as the ratio of the speed of light in vacuum (c) to the speed of light in a medium (Vrned)' C
nrned = Vrned
14 Part I Fundamentals of Light
and is totally reflected (Figure 2.2). The critical angle depends on the refractive in- dex and the wavelength of light. We write
for _n _ = I (air) and then
sin ®c ritic at = lIn2 '
Refraction; (0 2 < 90°) No refraction; (0 2 = 90°) Figure 2.2 Definition of critical angle.
In certain cases, a continuous change of the refractive index may take place. When light rays enter from one side, the rays are refracted and may emerge from the same side (Figure 2.3).
Where: n1 > n2> n3> n4> ns> na> n-, > na Figure 2.3 Refraction through variable refractive index.
Chapter 2 Interaction of Light with Matter
2.3.4 Optical Prisms
15
Consider two planes of a plate that intersect to form a prism at an angle ®2' When a polychromatic narrow beam of light impinges one of the prism surfaces, each fre- quency component is refracted differently. When each frequency reaches the other surface, it is refracted again. The output light from the second surface of the prism consists of the frequency components separated by a small angle. The angle of each frequency component with the original compo site beam is known as the angle of de- flection , E. That is, the angle of deflection varies with frequency (Figure 2.4).
Composite beam A1 + A2 +. .. + AN
E = angle of deflection
Figure 2.4 The angle of deflection is different for each frequency component.
In Figure 2.4, when n l = 1, Snell's law yields:
sin[(®2 + 10)12]
nz = sin(®2/2)
The following prism laws hold:
- The angle ®A increases as the index of refraction increases.
- The angle ®A increases as the prism angle ®2 increases.
- The angle ®A increases as the angle of incidence ® 1 increases.
- The angle ®A increases as the frequency of light increases (or the wavelength decreases).
The angular variability of each frequency component of the prism is known as angular dispersion and it is given by dfJ/dA = [(dfJ/dn)(dn/dA)] , where n is the index of refraction and A the wavelength. The first term depends on the geometry of the prism, whereas the second term depends on the material.
Chapter 2 Interaction of Light with Matter
Collimator
Figure 2.6 Diffraction at infinity.
2.3.7 Gaussian Beams
~~ -- x
17
In our descriptions, we have assumed so far that the monochromatic beam of light has a uniform cross-sectional distribution of intensity. In reality, this is not true. Most beams have a radial intensity distribution that is most intense in the center of the beam and it reduces radially away from the center, closely matching a Gaussian dis- tribution. Such beams are known as Gaussian beams. Because of the Gaussian distribution of intensity, even if the beam is initially parallel, it does not remain so owing to spatial diffraction within the beam. Spatial diffraction causes the beam to first narrow and then diverge at an angle e. The narrowest point in the beam is known as the waist of the beam. Even laser beams with a Gaussian distribution exhibit such behavior.
2.3.8 Diffraction Gratings
A diffraction grating is a passive optical device that diffracts incident parallel light in specific directions according to the angle of incidence on the grating, the optical wavelength of the incident light, and the design characteristics of the grating, line spacing d, and blaze angle eB (Figure 2.7). A common form of a diffraction grating consists of a glass substrate with adja- cent epoxy strips that have been blazed. The number of strips per unit length is a pa- rameter known as the grating constant. The blaze angle eB , the wavelength A, and the line spacing d are related by
e (^) B = sin- I (A/2d ).
18 Part I Fundamentals of Light
Incident (collimated) parallel beam ,.-- ---, .. Diffracted beam
•••• Blaze angle 0 (^8) .'
Figure 2.7 When collimated light falIs on a grating, each frequency is diffracted differently.
2.3.9 The Huygens-Fresnel Principle
Let the light from a monochromatic point source impinge on a screen having a small round hole in the order of the wavelength. The hole then behaves like a source of light of the same wavelength (Figure 2.8). This is known as the Huygens-Fresnel principle, a key principle in the study of interferen ce of light.
Screen with a pinhole of a diameter = wavelength Wave
Monochromatic light point source Figure 2.8 The Huygens-Fresnel principle.
2.3.10 Interference of Light
Direction of propagation
Consider a monochromatic light source, a screen with two pinholes equidistant from the axis of symmetry, and a second screen behind the first and parallel to it (Figure 2.9). Based on the Huygens-Fresnel principle, the two pinholes become two sources of coherent light, and alternating bright and dark zones are seen on the second screen. Bright zones (constructive interference) are formed when the travel differ- ence between two rays d = Irz-rt' or d = Ir4-r31 is an integer multiple of A, and
20 Part I Fundamentals of Light
2.3.12 Holography
Holography is a method by which coherent light (laser light) is used to capture the phase and amplitude characteristics of a three-dimensional (3-D) object on a 2-D pho- tographic plate. Both diffraction and interference of light are employed in holography. Consider a monochromatic coherent light source split into two beams A and B. Beam A impinges the 3-D object and is diffracted on a photographic film (Figure 2.11). Beam B is reflected by a prism and it, too, impinges the photographic plate. At the plate, beams A and B interfere and, depending on the travel difference of rays in the two beams, because of the three-dimensionality of the object, the amplitude and the phase difference from each point of the object are recorded on the photo- graphic plate. The end result is an incomprehensible image of dense stripes and whorls on the plate. This is known as a hologram.
Beam splitter
Photographic plate (hologram)
Figure 2.11 Principles of holography: generating a hologram.
According to "diffraction at infinity," the information relating to the phase and the amplitude of a 3-D object has been recorded in a myriad of places on the holo- gram. Thu s, even a small segment of the hologram contains all information (phase and amplitude) for the 3-D object. To recreate an image of the 3-D object, the proce ss of holography is reversed. That is, the hologram is illuminated with coherent light (Figure 2.12). The dense stripes and whorls in the plate act as a diffraction grating that interacts with the in-
Chapter 2 Interaction of Light with Malter
Hologram
Coherent light
3-D object virtual image
3-D object image
21
Figure 2.12 Principles of holograph y: creating a holographic image.
cident coherent beam, which decodes the phase and amplitude information to recre- ate an image replica of the original 3-D object. One of the salient features of holography is its image recognition. When coher- ent light passes through a transparent plate with a set of image s, then through a holo- gram, an image is seen on a screen, one that matches an image previously recorded, in the hologram. It turns out that two conjugate inverted images appear about the axis of symmetry. If there is no match, a blurred dot is seen (Figure 2.13). Holograms are so small that many thousands may be contained in a square mil- limeter of a holographic plate. Thus, if each hologram contain s an individual image, thousands of different images may be stored in few square millimeters of a holo - graphic plate. If these images correspond to the frames of a movie, or the pages of an encyclopedia, and if they are selectable in a specified order, then clearly the ap- plicability of holograms in storage is enormou s. Hence, holography is a promising technology in very large capacity optical storage as well as in communications. In optical storage , Fe-doped LiNb0 3 and organic photopolymers have been used to construct WORM (write once, read many) devices. The write capability in WORMs is accomplished with high-power, low-cost semiconductor lasers (see Section 6.2),
Chapter 2 Interaction of Light with Matter 23
No polarization Elliptical TE polarization TM polarization (circular) polarization (linear) (linear) Figure 2.14 Example of polarization modes (direction of light is perpendicular to page).
Impinging circularly or elliptically polarized light
Impinging circularly or elliptically polarized light
Refracted circularly or elliptically polarized light (^) polarized lightRefracted linearly
Impinging linearly polarized light
Impinging linearly polarized light
No reflected .,~ light •••••••
Refracted linearly Refracted linearly polarized light polarized light Figure 2.15 Four examples of polarization by reflection and refraction.
24 Part I Fundamentals of Light
polarization depends on the angle of incidence and the refractive index of the material, given by Brewster's law: tan(Ip) = n, where n is the refractive index and lp the polar- izing angle. Figure 2.15 offers some examples of reflected and refracted polarization.
2.3.16 Extinction Ratio
Consider polarized light traveling through a polarizer. When transmittance is maxi- mum, Tb it is termed major principal transmittance, and when minimum, T (^) z, it is termed minor principal transmittance. The ratio major to minor principal transmit- tance is known as the principal transmittance. The inverse, minimum to maximum, is known as the extinction ratio. Consider two polarizers in tandem, one behind the other with parallel surfaces.
If their polarization axes are parallel, the transmittance is T J^ zI2. If their axes are
crossed (perpendicular), the transmittance is 2Tz1Tj • This is also (but incorrectly) termed the extinction ratio.
2.3.17 Polarization Mode Shift: The Faraday Effect
When a material shifts the direction of polarization of transmitted light through it- self, the shift is also known as the Faraday effect (Figure 2.16). Devices based on the Faraday effect are known as rotators. Such materials are a-quartz, crystalized sodium chlorate, as well as cane sugar solution (liquid) and camphor (gas).
Rotator
Impinging (A) TE polarized light
PJ-....llp--. Transmitte d through
rotator of angle e
Figure 2.16 Principle of polarization rotator : Faraday effect.
The amount of the rotation angle or mode shift, e, depends on the thickness of material d (em), the magnetic field H [oersted (Oe)], and a constant V, known as the Verdet constant (measured in min/em. Oe). The mode shift is expressed by
e = VHd.
Devices with strong Verdet constant, magnetic field, and length may also shift the TE (transverse electric) polarization mode to TM (transverse magnetic) polar- ization mode (Figure 2.17).
26 Part I Fundamentals of Light
n 1
n
Isotropic Anisotropic n1 < n2 < n Figure 2.19 Principles of isotropic and anisotropic materials.
2.3.20 Birefringence
Anisotropic materials have a different index of refraction in specific directions. As such , when a beam of monochromatic unpolarized light travels through it in a spe- cific direction, it is refracted differently along the directions of different indices (Figure 2.20). That is, when an unpolarized ray enters the material, it is separated into two rays, each with a different polarization, different direction, and different propagation constant, called the ordinary ray (0) and the extraordinary ray (E). This property of anisotropic crystals is known as birefringence. Such crystals are calcite (CaC0 3 ) , mica, quartz, and magnesium fluoride (MgF 2 ).
Birefringent \ crystal
Unpolarized ray
","",~- -;; E- -+-. Extraordinary
Ordinary
Figure 2.20 Birefringent materials split the incident beam in the ordinary and extraordinary rays, which differ in polarization.
Some optically transparent isotropic materials, when they are under stress, be- come anisotropic. Mechanical forces (pulling, bending, twisting), thermal forces (ambient temperature variations) , and electrical fields may exert stress. Under such conditions, the index of refraction, polarization, and propagation characteristics be- come different in certain directions within the material. Birefringence in fiber transmission is undesirable. Birefringence alters the po- larization and the propagating characteristics of the transmitted signal and while the receiver expects one polarization, it receives another. To minimize birefringence in fibers, several techniques have been devised. One technique monitors and controls the received polarization by changing the polariza- tion of the receiver or by using polarization-maintaining fibers. Another technique uses transmitting and receiving strategies to "immunize" the system from fiber po-
Chapter 2 Interaction of Light with Matter 27
larization variations, such as polarization spreading (polarization scrambling, data- induced polarization), or polarization diversity. However, engineers have also taken advantage of birefringence to construct fil- ters that may also be used as wavelength multiplexers and demultiplexers (see Section 4.12). Figure 2.21 gives an example of a circularly polarized light ray tra- versing a birefringent plate.
Impinging circularly or elliptically polarized ray
Birefringent medium
Two refracted linearly polarized' rays
Figure 2.21 Example of birefringence on a nonpolarized beam before and after.
2.3.21 The Quarter-Wavelength Plate
A birefringent plate of one-quarter wavelength (>J4) thickness and with the surfaces parallel to the optical axis has some important propertiesin the realm of polarized light. If the linearly-polarized light is at 45° to the fast optical axis, the polarization is transformed into circularly polarized light, and vice versa. If the linearly-polarized light is parallel to the fast or slow axis, the polarization remains unchanged. If the linearly-polarized light is at any other angle with the optical axis, linear polarization is transformed into elliptical, and vice versa. If the plate consists of quartz or mica, the thickness d is related to wavelength by the relationship:
d = R>JAn,
Chapter 2 Interaction of Light with Matter
2.3.25 Homogeneity and Heterogeneity
29
A homogeneous optically transparent medium has the same consistency (chemical, me- chanical, electrical, magnetic, or crystallographic) throughout its volume (Figure 2.22). A heterogeneous optically transparent medium does not have the same consistency (chemical, mechanical, electrical, magnetic, or crystallographic) throughout its volume.
/
'------_------"1/ Homogeneous Heterogeneous Figure 2.22 Schematic illustrations of homogeneous and nonhomogeneous (heterogeneous) matter.
2.3.26 Effects of Impurities in Matter
An impurity is the presence of unwanted elements or compounds in matter. During the purification process of matter (e.g., silica), certain elements cannot be removed in their entirety and some traces will remain. These undesired elements or com- pounds alter the optical characteristics of the transparent material (e.g., fiber) and ei- ther have an absorptive effect or result in optical throughput loss by scattering pho- tons in other directions. Figure 2.23 captures the absorptive and scattering effect of photons as they transverse matter.
Absorption
G> "", e G> 0 ~G>^0 0 ~ u (^0) n 0 0 0 G> (^0) G> 0 0 0
- Impurities ----+ Rays of light Figure 2.23 Matter with absorption center and with scattering centers.
Examples of impurities that affect optical transmission are the elements iron, copper, and cobalt, and their oxides. The result is selective optical wavelength ab- sorption. For instance, blue glass is the result of cobalt or copper in glass, (which
30 Part I Fundamentals of Light
looks blue because it absorbs all wavelengths but the blue. One of the most difficult "impurities" to remove from glass fiber is the hydroxyl radical (OH). Hydroxyl radicals in fiber cable are responsible for increased absorption in the range below 1400 nm (Figure 2.24).
Attenuation due to -QH
Transmitted optical loss (dB)
1.2 1.4 1. Figure 2.24 Optical loss (or attenuation) by impurities in transparent matter.
2.3.27 Effects of Microcracks
Cracks may be viewed as discontinuities in the index of refraction of the material with planes that are not necessarily flat (Figure 2.25). Microcracks in the crystallized matrix of matter, or in amorphous solid matter, are generated by stresses (mechanical or ther- mal) or material aging. Microcracks are invisible to the naked eye and become visible only under a strong microscope or with specialized interferometric techniques. As light travels through matter in which there are cracks, its propagation is disrupted or distorted.
I Microcrack
Figure 2.25 Matter with microcracks.
2.3.28 Effects of Mechanical Pressure
When mechanical pressure is applied , the internal microstructure of the material is disturbed (Figure 2.26). As a result, there is a variation of the refractive index deter- mined by the pressure distribution in the material. Mechanical pressure is also ex- erted on the fibers as they are pulled or bent. Thus, assuming a circular bend, the outer periphery experiences stretching points while the inner experiences compres- sion points. Pressure and stretching points are clearly points of optical disturbances that are generally undesirable in optical communications. The safe bend radius recommended by ITU-T is the widely accepted radius of 37.5 mm (ITU-T G.652, para. 5.5, note 2).
