**How Nature Produces Blue Color**

Priscilla Simonis and Serge Berthier

*Institut des Nanosciences de Paris (INSP), University Pierre et Marie Curie, Paris, France*

## **1. Introduction**

Today, blue is a very fashionable color in European countries. This has not always been the case (Pastoureau, 2000), as cultural perceptions have slowly evolved since prehistoric times. In cave paintings, white, red and black have been the only available tones and these colors remained basic for Greek and Latin cultures, where blue was neglected or even strongly devalued. The word *caeruleus*, which is often used for brightly blue species, in naming plants and insects, is etymologically related to the word *cera*, which designates wax (not to the world *caelum* – sky – as often believed): it meant first white, brown or yellow (André, 1949), before being applied to green and black, and much lately, to a range of blues. Latin and Greek philosophers were so diverted from blue that they even did not notice its presence in the rainbow: for *Anaximenes* (585-528 BC) and later for *Lucretius* (98-55 BC), the rainbow only displayed red, yellow and violet; *Aristotle* (384-322 BC) and *Epicurus* (341-270 BC) described it as red, yellow, green and violet. *Seneca* (ca. 4 BC - 65 AD) only mentioned red, orange, green, violet but, strangely, also added purple, a metameric color not found in the decomposition of white light. Later in the Middle-Ages, *Robert Grosseteste* (ca. 1175-1253) revisited the rainbow phenomenon in its book "*De Iride*" and still did not find there any blue color (Boyer, 1954). Blue emerged slowly in minds and art, only after the advent of technological breakthroughs in stained glass fabrication (as introduced in the 12th century rebuild of St Denis Basilica) and after the progressive use of blue dyes, which followed the extension of woad cultivation, all after the 13th century.

Another slow emergence of blue has been observed in the development of an efficient blue light-emitting diode. Red, yellow and green solid-state diodes appeared early after the development of the first device by Nick Holonyak Jr and S. Bevacqua in 1962, but the blue diode did not become practical until the work of Shuji Nakamura, in 1993. Since then, the blue and ultraviolet diodes have gained maturity and give rise to the emergence of powerful white sources that appear to be the future of all lightening devices.

If the blue color has been slow to emerge in human culture and technology, it was not so in nature. Blue flowers, birds, fishes, reptiles, insects, spiders, shrimps… have been observed very frequently. Blue colored structures have even been found on fossil beetles. The objective of this chapter is to discover how blue colorations are achieved in living organisms.

A classification of *natural* photonic structures is not straightforward: these structures are complex, with multiscale effects and disorder. A useful classification requires some mathematical idealization of the structures. Our scheme is based on the number of dimensions

How Nature Produces Blue Color 5

distance from the particle's center, *n* is the refractive index of the particle and *d* its diameter. Typically, for visible light, the diameter of the scatterer should be smaller than about 50 nm to warrant a good quantitative accuracy of the scattering. This expression was probably first derived by John William Strutt (third Baron Rayleigh), based on dimensional ("similitude") arguments (Hoeppe, 1969). Assuming that the scattering is proportional to the number of atoms in the particle – which is the atom concentration times the volume *V* , and inversely proportional to the distance *R* between the particle center and the detector used for measurement, the ratio between the scattered amplitude *A* and the incident amplitude

0

which should be a dimensionless quantity. The light speed *c* and the wavelength

*A V <sup>x</sup> <sup>y</sup> <sup>c</sup> A R*

also enter the formula because this is an optical phenomenon, but we do not yet know the exponents *x* and *y* . The right-hand side of the equation, in terms of time [ ] *T* and length[ ] *L* , has dimensions <sup>2</sup> [] [] *<sup>x</sup> y y L T* . For this to become dimensionless, we must have *y* 0 and *x* 2 . This means (as the volume *V* is proportional to the cube of the particle

> 2 4 0 0 *IA d I A R*

Much of the physics of the Rayleigh scattering is already present in this result, based on this simple reasoning. In particular, the essential point is the so-called "inverse fourth power law", stating that the scattered intensity is inversely proportional to the fourth power of the wavelength. This means that the short wavelengths in the visible white light (violet-blue) are scattered much more efficiently than the long wavelengths (orange-red). The sunlight scattered by small particles appears essentially blue because the solar spectrum contains less

The Irish physicist John Tyndall contributed to this question as early as in 1860. He noticed the appearance of blue scattering by a vapor of hydrochloric acid, as the particles condensed into larger size droplets and its desaturation, reaching white color, when the particles became too large. Indeed the blue Rayleigh scattering is reinforced as the volume of the scattering center is increased, and continues to do so until the particle becomes larger than the illuminating wavelength. Then, standing waves and resonances start affecting the wavelength dependence of the scattering, giving rise to a much more complex scatter color. Typically, the range of particle sizes that produce a strong blue scattering is between 50 nm to 900 nm and, for this range, where the characteristics of Rayleigh scattering are still qualitatively useful, the scattering is usually called "Tyndall scattering". For spherical particles of small, medium or large sizes, a general treatment

This is not quite the end, as Rayleigh, Tyndall and Mie scattering only describe the scattered intensity by a single isolated particle. When considering aggregated particles,

 

violet than blue and because we are less sensitive to violet than to blue.

<sup>2</sup> <sup>6</sup>

from the incident direction, *R* is the

, (2)

. (3)

should

where *I* is the intensity scattered at an angle

*<sup>A</sup>*0 can be expressed as

exists: Mie scattering (Mie, 1908).

diameter *d* )

in which we can assume a total translational invariance. One-dimensional structures are only inhomogeneous in one dimension, with, perpendicularly, complete invariance for two independent translations. These one-dimensional structures are then described as "layered". Thin films, thin film stacks and Bragg mirrors (with the repetition of identical layers) are examples of one-dimensional structures. Two-dimensional structures are totally invariant under a single direction. A straight optic fiber is a two-dimensional structure. A periodic array of parallel fibers, such as the bunch of cilia in ctenophores or the aligned melanin rods in peacock or other bird's feathers, is also a two-dimensional, as well as gratings engraved on flat surfaces. In three-dimensional structures, no direction shows total invariance under translations. This is the most general geometry for a photonic structure.

When inhomogeneous, the refractive index can be periodic, in which case the propagation acquires special features that will be examined later. A one-dimensional periodic structure is the basis for a Bragg mirror that produces well-defined reflection bands around specific frequencies. Obtaining blue colors with such a system is relatively tricky and, as will be discussed in this chapter, requires particularly thin layers in order to avoid producing a metameric purple color. Blue two-dimensional photonic crystal also requires special scatterer's spacing and specific conditions: the blue coloration of the wing feathers in the magpies is a very instructive example. Somewhat more complex, when neglecting cross-ribs, microribs and lamellae slant, the *Morpho rhetenor* ribs structure is another example of a twodimensional photonic structure that produces a vivid blue under most directions. Gratings, as found in butterflies can also produce blue iridescence for specific grating periods. Finally, blue three-dimensional photonic crystals are observed in weevils and longhorns.
