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Tuesday, November 8, 2022

Constructivism (philosophy of science)

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_science)

Constructivism is a view in the philosophy of science that maintains that scientific knowledge is constructed by the scientific community, which seeks to measure and construct models of the natural world. According to the constructivist, natural science, therefore, consists of mental constructs that aim to explain sensory experience and measurements.

According to constructivists, the world is independent of human minds, but knowledge of the world is always a human and social construction. Constructivism opposes the philosophy of objectivism, embracing the belief that a human can come to know the truth about the natural world not mediated by scientific approximations with different degrees of validity and accuracy.

According to constructivists, there is no single valid methodology in science but rather a diversity of useful methods.

Etymology

The term originates from psychology, education, and social constructivism. The expression "constructivist epistemology" was first used by Jean Piaget, 1967, with plural form in the famous article from the "Encyclopédie de la Pléiade" Logique et connaissance scientifique or "Logic and Scientific knowledge", an important text for epistemology. He refers directly to the mathematician Brouwer and his radical constructivism.

The terms Constructionism and constructivism are often, but should not be, used interchangeably. Constructionism is an approach to learning that was developed by Papert; the approach was greatly influenced by his work with Piaget, but it is very different. Constructionism involves the creation of a product to show learning. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender, as well as tables, chairs, and atoms, are socially constructed. Marx was among the first to suggest such an ambitious expansion of the power of ideas to inform the material realities of people's lives.

History

Constructivism stems from a number of philosophies. For instance, early development can be attributed to the thought of Greek philosophers such as Heraclitus (Everything flows, nothing stands still), Protagoras (Man is the measure of all things). Protagoras is clearly represented by Plato and hence the tradition as a relativist. The Pyrrhonist skeptics have also been so interpreted. (Although this is more contentious.)

Following the Renaissance and the Enlightenment, with the phenomenology and the event, Kant gives a decisive contradiction to Cartesians' epistemology that has grown since Descartes despite Giambattista Vico calling in Scienza nuova ("New Science") in 1725 that "the norm of the truth is to have made it". The Enlightenment's claim of the universality of Reason as the only true source of knowledge generated a Romantic reaction involving an emphasis on the separate natures of races, species, sexes, and types of human.

  • Gaston Bachelard, who is known for his physics psychoanalysis and the definition of an "epistemologic obstacle" that can disturb a changing of scientific paradigm as the one that occurred between classical mechanics and Einstein's relativism, opens the teleological way with "The meditation on the object takes the form of the project". In the following famous saying, he insists that the ways in which questions are posed determine the trajectory of scientific movement, before summarizing "nothing is given, all is constructed": "And, irrespective of what one might assume, in the life of a science, problems do not arise by themselves. It is precisely this that marks out a problem as being of the true scientific spirit: all knowledge is in response to a question. If there were no questions, there would be no scientific knowledge. Nothing proceeds from itself. Nothing is given. All is constructed.", Gaston Bachelard (La formation de l'esprit scientifique, 1934). While quantum mechanics is starting to grow, Gaston Bachelard makes a call for new science in Le nouvel esprit scientifique (The New Scientific Spirit).
  • Paul Valéry, a French poet (20th century) reminds us of the importance of representations and action: "We have always sought explanations when it was only representations that we could seek to invent", "My hand feels touched as well as it touches; reality says this, and nothing more".
  • This link with action, which could be called a "philosophy of action", was well represented by Spanish poet Antonio Machado: Caminante, no hay camino, se hace camino al andar. ("Traveler, there is no road; you make your own path as you walk.")
  • Ludwik Fleck establishes scientific constructivism by introducing the notions of thought collective (Denkkollektiv), and thought style (Denkstil), through which the evolution of science is much more understandable because the research objects can be described in terms of the assumptions (thought style) that are shared for practical but also inherently social reasons, or just because any thought collective tends to preserve itself. These notions have been drawn upon by Thomas Kuhn.
  • Norbert Wiener gives another defense of teleology in 1943 Behavior, Intention and Teleology and is one of the creators of cybernetics.
  • Jean Piaget, after the creation in 1955 of the International Centre for Genetic Epistemology in Geneva, first uses the expression "constructivist epistemologies" (see above). According to Ernst von Glasersfeld, Jean Piaget is "the great pioneer of the constructivist theory of knowing" (in An Exposition of Constructivism: Why Some Like it Radical, 1990) and "the most prolific constructivist in our century" (in Aspects of Radical Constructivism, 1996).
  • J. L. Austin is associated with the view that speech is not only passively describing a given reality, but it can change the (social) reality to which it is applied through speech acts.
  • Herbert A. Simon called "the sciences of the artificial" these new sciences (cybernetics, cognitive sciences, decision and organization sciences) that, because of the abstraction of their object (information, communication, decision), cannot match with the classical epistemology and its experimental method and refutability.
  • Gregory Bateson and his book Steps to an Ecology of Mind (1972).
  • George Kelly (psychologist) and his book The Psychology of Personal Constructs (1955).
  • Heinz von Foerster, invited by Jean Piaget, presented "Objects: tokens for (Eigen-)behaviors" in 1976 in Geneva at a genetic epistemology symposium, a text that would become a reference for constructivist epistemology. His epistemological arguments were summarized in the book The Dream of Reality by Lynn Segal.
  • Paul Watzlawick, who supervised in 1984 the publication of The Invented Reality: How Do We Know What We Believe We Know? (Contributions to Constructivism).
  • Ernst von Glasersfeld, has promoted since the end of the 70s radical constructivism (see below).
  • Edgar Morin and his book La méthode (1977–2004, six volumes).
  • Mioara Mugur-Schächter is also a quantum mechanics specialist.
  • Jean-Louis Le Moigne for his encyclopedic work on constructivist epistemology and his General Systems theory (see "Le Moigne's Defense of Constructivism" by Ernst von Glasersfeld).
  • Niklas Luhmann who developed "operative constructivism" in the course of developing his theory of autopoietic social systems, drawing on the works of (among others) Bachelard, Valéry, Bateson, von Foerster, von Glasersfeld, and Morin.

Constructivism and sciences

Social constructivism in sociology

One version of social constructivism contends that categories of knowledge and reality are actively created by social relationships and interactions. These interactions also alter the way in which scientific episteme is organized.

Social activity presupposes human interaction, and in the case of social construction, utilizing semiotic resources (meaning-making and signifying) with reference to social structures and institutions. Several traditions use the term Social Constructivism: psychology (after Lev Vygotsky), sociology (after Peter Berger and Thomas Luckmann, themselves influenced by Alfred Schütz), sociology of knowledge (David Bloor), sociology of mathematics (Sal Restivo), philosophy of mathematics (Paul Ernest). Ludwig Wittgenstein's later philosophy can be seen as a foundation for social constructivism, with its key theoretical concepts of language games embedded in forms of life.

Constructivism in philosophy of science

Thomas Kuhn argued that changes in scientists' views of reality not only contain subjective elements but result from group dynamics, "revolutions" in scientific practice, and changes in "paradigms". As an example, Kuhn suggested that the Sun-centric Copernican "revolution" replaced the Earth-centric views of Ptolemy not because of empirical failures but because of a new "paradigm" that exerted control over what scientists felt to be the more fruitful way to pursue their goals.

But paradigm debates are not really about relative problem-solving ability, though for good reasons they are usually couched in those terms. Instead, the issue is which paradigm should in future guide research on problems many of which neither competitor can yet claim to resolve completely. A decision between alternate ways of practicing science is called for, and in the circumstances that decision must be based less on past achievement than on future promise. ... A decision of that kind can only be made on faith.

— Thomas Kuhn, The Structure of Scientific Revolutions, pp 157-8

The view of reality as accessible only through models was called model-dependent realism by Stephen Hawking and Leonard Mlodinow. While not rejecting an independent reality, model-dependent realism says that we can know only an approximation of it provided by the intermediary of models. These models evolve over time as guided by scientific inspiration and experiments.

In the field of the social sciences, constructivism as an epistemology urges that researchers reflect upon the paradigms that may be underpinning their research, and in the light of this that they become more open to considering other ways of interpreting any results of the research. Furthermore, the focus is on presenting results as negotiable constructs rather than as models that aim to "represent" social realities more or less accurately. Norma Romm, in her book Accountability in Social Research (2001), argues that social researchers can earn trust from participants and wider audiences insofar as they adopt this orientation and invite inputs from others regarding their inquiry practices and the results thereof.

Constructivism and psychology

In psychology, constructivism refers to many schools of thought that, though extraordinarily different in their techniques (applied in fields such as education and psychotherapy), are all connected by a common critique of previous standard objectivist approaches. Constructivist psychology schools share assumptions about the active constructive nature of human knowledge. In particular, the critique is aimed at the "associationist" postulate of empiricism, "by which the mind is conceived as a passive system that gathers its contents from its environment and, through the act of knowing, produces a copy of the order of reality."

In contrast, "constructivism is an epistemological premise grounded on the assertion that, in the act of knowing, it is the human mind that actively gives meaning and order to that reality to which it is responding". The constructivist psychologies theorize about and investigate how human beings create systems for meaningfully understanding their worlds and experiences.

Constructivism and education

Joe L. Kincheloe has published numerous social and educational books on critical constructivism (2001, 2005, 2008), a version of constructivist epistemology that places emphasis on the exaggerated influence of political and cultural power in the construction of knowledge, consciousness, and views of reality. In the contemporary mediated electronic era, Kincheloe argues, dominant modes of power have never exerted such influence on human affairs. Coming from a critical pedagogical perspective, Kincheloe argues that understanding a critical constructivist epistemology is central to becoming an educated person and to the institution of just social change.

Kincheloe's characteristics of critical constructivism:

  • Knowledge is socially constructed: World and information co-construct one another
  • Consciousness is a social construction
  • Political struggles: Power plays an exaggerated role in the production of knowledge and consciousness
  • The necessity of understanding consciousness—even though it does not lend itself to traditional reductionistic modes of measurability
  • The importance of uniting logic and emotion in the process of knowledge and producing knowledge
  • The inseparability of the knower and the known
  • The centrality of the perspectives of oppressed peoples—the value of the insights of those who have suffered as the result of existing social arrangements
  • The existence of multiple realities: Making sense of a world far more complex than we originally imagined
  • Becoming humble knowledge workers: Understanding our location in the tangled web of reality
  • Standpoint epistemology: Locating ourselves in the web of reality, we are better equipped to produce our own knowledge
  • Constructing practical knowledge for critical social action
  • Complexity: Overcoming reductionism
  • Knowledge is always entrenched in a larger process
  • The centrality of interpretation: Critical hermeneutics
  • The new frontier of classroom knowledge: Personal experiences intersecting with pluriversal information
  • Constructing new ways of being human: Critical ontology

Constructivist approaches

Critical constructivism

A series of articles published in the journal Critical Inquiry (1991) served as a manifesto for the movement of critical constructivism in various disciplines, including the natural sciences. Not only truth and reality, but also "evidence", "document", "experience", "fact", "proof", and other central categories of empirical research (in physics, biology, statistics, history, law, etc.) reveal their contingent character as a social and ideological construction. Thus, a "realist" or "rationalist" interpretation is subjected to criticism. Kincheloe's political and pedagogical notion (above) has emerged as a central articulation of the concept.

Cultural constructivism

Cultural constructivism asserts that knowledge and reality are a product of their cultural context, meaning that two independent cultures will likely form different observational methodologies.

Genetic epistemology

James Mark Baldwin invented this expression, which was later popularized by Jean Piaget. From 1955 to 1980, Piaget was Director of the International Centre for Genetic Epistemology in Geneva.

Radical constructivism

Ernst von Glasersfeld was a prominent proponent of radical constructivism. This claims that knowledge is not a commodity that is transported from one mind into another. Rather, it is up to the individual to "link up" specific interpretations of experiences and ideas with their own reference of what is possible and viable. That is, the process of constructing knowledge, of understanding, is dependent on the individual's subjective interpretation of their active experience, not what "actually" occurs. Understanding and acting are seen by radical constructivists not as dualistic processes but "circularly conjoined".

Radical constructivism is closely related to second-order cybernetics.

Constructivist Foundations is a free online journal publishing peer-reviewed articles on radical constructivism by researchers from multiple domains.

Relational constructivism

Relational constructivism can be perceived as a relational consequence of radical constructivism. In contrary to social constructivism, it picks up the epistemological threads. It maintains the radical constructivist idea that humans cannot overcome their limited conditions of reception (i.e., self-referentially operating cognition). Therefore, humans are not able to come to objective conclusions about the world.

In spite of the subjectivity of human constructions of reality, relational constructivism focuses on the relational conditions applying to human perceptional processes. Björn Kraus puts it in a nutshell:

It is substantial for relational constructivism that it basically originates from an epistemological point of view, thus from the subject and its construction processes. Coming from this perspective it then focusses on the (not only social, but also material) relations under which these cognitive construction processes are performed. Consequently, it's not only about social construction processes, but about cognitive construction processes performed under certain relational conditions.

Social Constructivism

Criticisms

Numerous criticisms have been levelled at Constructivism. The most common one is that it either explicitly advocates or implicitly reduces to relativism.

Another criticism of constructivism is that it holds that the concepts of two different social formations be entirely different and incommensurate. This being the case, it is impossible to make comparative judgments about statements made according to each worldview. This is because the criteria of judgment will themselves have to be based on some worldview or other. If this is the case, then it brings into question how communication between them about the truth or falsity of any given statement could be established.

The Wittgensteinian philosopher Gavin Kitching argues that constructivists usually implicitly presuppose a deterministic view of language, which severely constrains the minds and use of words by members of societies: they are not just "constructed" by language on this view but are literally "determined" by it. Kitching notes the contradiction here: somehow, the advocate of constructivism is not similarly constrained. While other individuals are controlled by the dominant concepts of society, the advocate of constructivism can transcend these concepts and see through them.

Anti-realism

From Wikipedia, the free encyclopedia

In analytic philosophy, anti-realism is a position which encompasses many varieties such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument against a form of realism Dummett saw as 'colorless reductionism'.

In anti-realism, the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality. In anti-realism, this external reality is hypothetical and is not assumed.

Anti-realism in its most general sense can be understood as being in contrast to a generic realism, which holds that distinctive objects of a subject-matter exist and have properties independent of one's beliefs and conceptual schemes. The ways in which anti-realism rejects these type of claims can vary dramatically. Because this encompasses statements containing abstract ideal objects (i.e. mathematical objects), anti-realism may apply to a wide range of philosophical topics, from material objects to the theoretical entities of science, mathematical statement, mental states, events and processes, the past and the future.

Varieties

Metaphysical anti-realism

One kind of metaphysical anti-realism maintains a skepticism about the physical world, arguing either: 1) that nothing exists outside the mind, or 2) that we would have no access to a mind-independent reality, even if it exists. The latter case often takes the form of a denial of the idea that we can have 'unconceptualised' experiences (see Myth of the Given). Conversely, most realists (specifically, indirect realists) hold that perceptions or sense data are caused by mind-independent objects. But this introduces the possibility of another kind of skepticism: since our understanding of causality is that the same effect can be produced by multiple causes, there is a lack of determinacy about what one is really perceiving, as in the brain in a vat scenario. The main alternative to this sort of metaphysical anti-realism is metaphysical realism.

On a more abstract level, model-theoretic anti-realist arguments hold that a given set of symbols in a theory can be mapped onto any number of sets of real-world objects—each set being a "model" of the theory—provided the relationship between the objects is the same (compare with symbol grounding.)

In ancient Greek philosophy, nominalist (anti-realist) doctrines about universals were proposed by the Stoics, especially Chrysippus. In early modern philosophy, conceptualist anti-realist doctrines about universals were proposed by thinkers like René Descartes, John Locke, Baruch Spinoza, Gottfried Wilhelm Leibniz, George Berkeley, and David Hume. In late modern philosophy, anti-realist doctrines about knowledge were proposed by the German idealist Georg Wilhelm Friedrich Hegel. Hegel was a proponent of what is now called inferentialism: he believed that the ground for the axioms and the foundation for the validity of the inferences are the right consequences and that the axioms do not explain the consequence. Kant and Hegel held conceptualist views about universals. In contemporary philosophy, anti-realism was revived in the form of empirio-criticism, logical positivism, semantic anti-realism and scientific instrumentalism (see below).

Mathematical anti-realism

In the philosophy of mathematics, realism is the claim that mathematical entities such as 'number' have an observer-independent existence. Empiricism, which associates numbers with concrete physical objects, and Platonism, in which numbers are abstract, non-physical entities, are the preeminent forms of mathematical realism.

The "epistemic argument" against Platonism has been made by Paul Benacerraf and Hartry Field. Platonism posits that mathematical objects are abstract entities. By general agreement, abstract entities cannot interact causally with physical entities ("the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time") Whilst our knowledge of physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Field developed his views into fictionalism. Benacerraf also developed the philosophy of mathematical structuralism, according to which there are no mathematical objects. Nonetheless, some versions of structuralism are compatible with some versions of realism.

Counterarguments

Anti-realist arguments hinge on the idea that a satisfactory, naturalistic account of thought processes can be given for mathematical reasoning. One line of defense is to maintain that this is false, so that mathematical reasoning uses some special intuition that involves contact with the Platonic realm, as in the argument given by Sir Roger Penrose.

Another line of defense is to maintain that abstract objects are relevant to mathematical reasoning in a way that is non causal, and not analogous to perception. This argument is developed by Jerrold Katz in his 2000 book Realistic Rationalism. In this book, he put forward a position called realistic rationalism, which combines metaphysical realism and rationalism.

A more radical defense is to deny the separation of physical world and the platonic world, i.e. the mathematical universe hypothesis (a variety of mathematicism). In that case, a mathematician's knowledge of mathematics is one mathematical object making contact with another.

Semantic anti-realism

The term "anti-realism" was introduced by Michael Dummett in his 1982 paper "Realism" in order to re-examine a number of classical philosophical disputes, involving such doctrines as nominalism, Platonic realism, idealism and phenomenalism. The novelty of Dummett's approach consisted in portraying these disputes as analogous to the dispute between intuitionism and Platonism in the philosophy of mathematics.

According to intuitionists (anti-realists with respect to mathematical objects), the truth of a mathematical statement consists in our ability to prove it. According to Platonic realists, the truth of a statement is proven in its correspondence to objective reality. Thus, intuitionists are ready to accept a statement of the form "P or Q" as true only if we can prove P or if we can prove Q. In particular, we cannot in general claim that "P or not P" is true (the law of excluded middle), since in some cases we may not be able to prove the statement "P" nor prove the statement "not P". Similarly, intuitionists object to the existence property for classical logic, where one can prove , without being able to produce any term of which holds.

Dummett argues that this notion of truth lies at the bottom of various classical forms of anti-realism, and uses it to re-interpret phenomenalism, claiming that it need not take the form of reductionism.

Dummett's writings on anti-realism draw heavily on the later writings of Ludwig Wittgenstein, concerning meaning and rule following, and can be seen as an attempt to integrate central ideas from the Philosophical Investigations into the constructive tradition of analytic philosophy deriving from Gottlob Frege.

Scientific anti-realism

In philosophy of science, anti-realism applies chiefly to claims about the non-reality of "unobservable" entities such as electrons or genes, which are not detectable with human senses.

One prominent variety of scientific anti-realism is instrumentalism, which takes a purely agnostic view towards the existence of unobservable entities, in which the unobservable entity X serves as an instrument to aid in the success of theory Y and does not require proof for the existence or non-existence of X.

Moral anti-realism

In the philosophy of ethics, moral anti-realism (or moral irrealism) is a meta-ethical doctrine that there are no objective moral values or normative facts. It is usually defined in opposition to moral realism, which holds that there are objective moral values, such that a moral claim may be either true or false. Specifically the moral anti-realist is committed to denying one of the following three statements: 

  1. The Semantic Thesis: Moral statements have meaning, they express propositions, or are the kind of things that can be true or false.
  2. The Alethic Thesis: Some moral propositions are true.
  3. The Metaphysical Thesis: The metaphysical status of moral facts is robust and ordinary, not importantly different from other facts about the world.

Different version of moral anti-realism deny different statements: specifically, non-cognitivism denies the first claim, arguing that moral statements have no meaning or truth content, error theory denies the second claim, arguing that all moral statements are false, and ethical subjectivism denies the third claim, arguing that the truth of moral statements is mind dependent.

Examples of anti-realist moral theories might be:

There is a debate as to whether moral relativism is actually an anti-realist position. While many versions deny the metaphysical thesis, some do not, as one could imagine a system of morality which requires you to obey the written laws in your country. Such a system would be a version of moral relativism, as different individuals would be required to follow different laws, but the moral facts are physical facts about the world, not mental facts, so they are metaphysically ordinary. Thus, different versions of moral relativism might be considered anti-realist or realist.

Epistemic anti-realism

Just as moral anti-realism asserts the nonexistence of normative facts, epistemic anti-realism asserts the nonexistence of facts in the domain of epistemology. Thus, the two are now sometimes grouped together as "metanormative anti-realism". Prominent defenders of epistemic anti-realism include Hartry Field, Simon Blackburn, Matthew Chrisman, and Allan Gibbard, among others.

Monday, November 7, 2022

Laser diode

From Wikipedia, the free encyclopedia
 
Laser diode
Diode laser.jpg
A packaged laser diode shown with a penny for scale*488 nm: InGaN green-blue laser; became widely available in mid-2018.
Typesemiconductor, light-emitting diode
Working principlesemiconductor, Carrier generation and recombination
InventedRobert N. Hall, 1962; Nick Holonyak, Jr., 1962
Pin configuration Anode and cathode
The laser diode chip removed and placed on the eye of a needle for scale
 
A laser diode with the case cut away. The laser diode chip is the small black chip at the front; a photodiode at the back is used to control output power.
 
SEM (scanning electron microscope) image of a commercial laser diode with its case and window cut away. The anode connection on the right has been accidentally broken by the case cut process.

A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a diode pumped directly with electrical current can create lasing conditions at the diode's junction.

Driven by voltage, the doped p–n-transition allows for recombination of an electron with a hole. Due to the drop of the electron from a higher energy level to a lower one, radiation, in the form of an emitted photon is generated. This is spontaneous emission. Stimulated emission can be produced when the process is continued and further generates light with the same phase, coherence and wavelength.

The choice of the semiconductor material determines the wavelength of the emitted beam, which in today's laser diodes range from infra-red to the UV spectrum. Laser diodes are the most common type of lasers produced, with a wide range of uses that include fiber optic communications, barcode readers, laser pointers, CD/DVD/Blu-ray disc reading/recording, laser printing, laser scanning and light beam illumination. With the use of a phosphor like that found on white LEDs, Laser diodes can be used for general illumination.

Theory

Semi-conductor lasers (Top to bottom: 660 nm, 635 nm, 532 nm, 520 nm, 445 nm, 405 nm)

A laser diode is electrically a PIN diode. The active region of the laser diode is in the intrinsic (I) region, and the carriers (electrons and holes) are pumped into that region from the N and P regions respectively. While initial diode laser research was conducted on simple P–N diodes, all modern lasers use the double-hetero-structure implementation, where the carriers and the photons are confined in order to maximize their chances for recombination and light generation. Unlike a regular diode, the goal for a laser diode is to recombine all carriers in the I region, and produce light. Thus, laser diodes are fabricated using direct band-gap semiconductors. The laser diode epitaxial structure is grown using one of the crystal growth techniques, usually starting from an N doped substrate, and growing the I doped active layer, followed by the P doped cladding, and a contact layer. The active layer most often consists of quantum wells, which provide lower threshold current and higher efficiency.

Electrical and optical pumping

Laser diodes form a subset of the larger classification of semiconductor pn junction diodes. Forward electrical bias across the laser diode causes the two species of charge carrierholes and electrons – to be "injected" from opposite sides of the pn junction into the depletion region. Holes are injected from the p-doped into the n-doped, and electrons vice versa, semiconductor. (A depletion region, devoid of any charge carriers, forms as a result of the difference in electrical potential between n- and p-type semiconductors wherever they are in physical contact.) Due to the use of charge injection in powering most diode lasers, this class of lasers is sometimes termed "injection lasers," or "injection laser diode" (ILD). As diode lasers are semiconductor devices, they may also be classified as semiconductor lasers. Either designation distinguishes diode lasers from solid-state lasers.

Another method of powering some diode lasers is the use of optical pumping. Optically pumped semiconductor lasers (OPSL) use a III-V semiconductor chip as the gain medium, and another laser (often another diode laser) as the pump source. OPSL offer several advantages over ILDs, particularly in wavelength selection and lack of interference from internal electrode structures. A further advantage of OPSLs is invariance of the beam parameters – divergence, shape, and pointing – as pump power (and hence output power) is varied, even over a 10:1 output power ratio.

Generation of spontaneous emission

When an electron and a hole are present in the same region, they may recombine or "annihilate" producing a spontaneous emission — i.e., the electron may re-occupy the energy state of the hole, emitting a photon with energy equal to the difference between the electron's original state and hole's state. (In a conventional semiconductor junction diode, the energy released from the recombination of electrons and holes is carried away as phonons, i.e., lattice vibrations, rather than as photons.) Spontaneous emission below the lasing threshold produces similar properties to an LED. Spontaneous emission is necessary to initiate laser oscillation, but it is one among several sources of inefficiency once the laser is oscillating.

Direct and indirect bandgap semiconductors

The difference between the photon-emitting semiconductor laser and a conventional phonon-emitting (non-light-emitting) semiconductor junction diode lies in the type of semiconductor used, one whose physical and atomic structure confers the possibility for photon emission. These photon-emitting semiconductors are the so-called "direct bandgap" semiconductors. The properties of silicon and germanium, which are single-element semiconductors, have bandgaps that do not align in the way needed to allow photon emission and are not considered "direct." Other materials, the so-called compound semiconductors, have virtually identical crystalline structures as silicon or germanium but use alternating arrangements of two different atomic species in a checkerboard-like pattern to break the symmetry. The transition between the materials in the alternating pattern creates the critical "direct bandgap" property. Gallium arsenide, indium phosphide, gallium antimonide, and gallium nitride are all examples of compound semiconductor materials that can be used to create junction diodes that emit
light.

Diagram of a simple laser diode, such as shown above; not to scale
 
A simple and low power metal enclosed laser diode

Generation of stimulated emission

In the absence of stimulated emission (e.g., lasing) conditions, electrons and holes may coexist in proximity to one another, without recombining, for a certain time, termed the "upper-state lifetime" or "recombination time" (about a nanosecond for typical diode laser materials), before they recombine. A nearby photon with energy equal to the recombination energy can cause recombination by stimulated emission. This generates another photon of the same frequency, polarization, and phase, travelling in the same direction as the first photon. This means that stimulated emission will cause gain in an optical wave (of the correct wavelength) in the injection region, and the gain increases as the number of electrons and holes injected across the junction increases. The spontaneous and stimulated emission processes are vastly more efficient in direct bandgap semiconductors than in indirect bandgap semiconductors; therefore silicon is not a common material for laser diodes.

Optical cavity and laser modes

As in other lasers, the gain region is surrounded with an optical cavity to form a laser. In the simplest form of laser diode, an optical waveguide is made on that crystal's surface, such that the light is confined to a relatively narrow line. The two ends of the crystal are cleaved to form perfectly smooth, parallel edges, forming a Fabry–Pérot resonator. Photons emitted into a mode of the waveguide will travel along the waveguide and be reflected several times from each end face before they exit. As a light wave passes through the cavity, it is amplified by stimulated emission, but light is also lost due to absorption and by incomplete reflection from the end facets. Finally, if there is more amplification than loss, the diode begins to "lase".

Some important properties of laser diodes are determined by the geometry of the optical cavity. Generally, the light is contained within a very thin layer, and the structure supports only a single optical mode in the direction perpendicular to the layers. In the transverse direction, if the waveguide is wide compared to the wavelength of light, then the waveguide can support multiple transverse optical modes, and the laser is known as "multi-mode". These transversely multi-mode lasers are adequate in cases where one needs a very large amount of power, but not a small diffraction-limited TEM00 beam; for example in printing, activating chemicals, microscopy, or pumping other types of lasers.

In applications where a small focused beam is needed, the waveguide must be made narrow, on the order of the optical wavelength. This way, only a single transverse mode is supported and one ends up with a diffraction-limited beam. Such single spatial mode devices are used for optical storage, laser pointers, and fiber optics. Note that these lasers may still support multiple longitudinal modes, and thus can lase at multiple wavelengths simultaneously. The wavelength emitted is a function of the band-gap of the semiconductor material and the modes of the optical cavity. In general, the maximum gain will occur for photons with energy slightly above the band-gap energy, and the modes nearest the peak of the gain curve will lase most strongly. The width of the gain curve will determine the number of additional "side modes" that may also lase, depending on the operating conditions. Single spatial mode lasers that can support multiple longitudinal modes are called Fabry Perot (FP) lasers. An FP laser will lase at multiple cavity modes within the gain bandwidth of the lasing medium. The number of lasing modes in an FP laser is usually unstable, and can fluctuate due to changes in current or temperature.

Single spatial mode diode lasers can be designed so as to operate on a single longitudinal mode. These single frequency diode lasers exhibit a high degree of stability, and are used in spectroscopy and metrology, and as frequency references. Single frequency diode lasers are classed as either distributed feedback (DFB) lasers or distributed Bragg reflector (DBR) lasers.

Formation of laser beam

Due to diffraction, the beam diverges (expands) rapidly after leaving the chip, typically at 30 degrees vertically by 10 degrees laterally. A lens must be used in order to form a collimated beam like that produced by a laser pointer. If a circular beam is required, cylindrical lenses and other optics are used. For single spatial mode lasers, using symmetrical lenses, the collimated beam ends up being elliptical in shape, due to the difference in the vertical and lateral divergences. This is easily observable with a red laser pointer.

The simple diode described above has been heavily modified in recent years to accommodate modern technology, resulting in a variety of types of laser diodes, as described below.

History

Nick Holonyak

As early as 1953 John von Neumann described the concept of semiconductor laser in an unpublished manuscript.

Following theoretical treatments of M.G. Bernard, G. Duraffourg and William P. Dumke in the early 1960s coherent light emission from a gallium arsenide (GaAs) semiconductor diode (a laser diode) was demonstrated in 1962 by two US groups led by Robert N. Hall at the General Electric research center and by Marshall Nathan at the IBM T.J. Watson Research Center. There has been ongoing debate as to whether IBM or GE invented the first laser diode which was largely based on theoretical work by William P. Dumke at IBM's Kitchawan Lab (currently known as the Thomas J. Watson Research Center) in Yorktown Heights, NY. The priority is given to General Electric group who have obtained and submitted their results earlier; they also went further and made a resonant cavity for their diode. It was initially speculated, by MIT's Ben Lax among other leading physicists, that silicon or germanium could be used to create a lasing effect, but theoretical analyses convinced William P. Dumke that these materials would not work. Instead, he suggested Gallium Arsenide as a good candidate. The first visible wavelength GaAs laser diode was demonstrated by Nick Holonyak, Jr. later in 1962.

Other teams at MIT Lincoln Laboratory, Texas Instruments, and RCA Laboratories were also involved in and received credit for their historic initial demonstrations of efficient light emission and lasing in semiconductor diodes in 1962 and thereafter. GaAs lasers were also produced in early 1963 in the Soviet Union by the team led by Nikolay Basov.

In the early 1960s liquid phase epitaxy (LPE) was invented by Herbert Nelson of RCA Laboratories. By layering the highest quality crystals of varying compositions, it enabled the demonstration of the highest quality heterojunction semiconductor laser materials for many years. LPE was adopted by all the leading laboratories, worldwide and used for many years. It was finally supplanted in the 1970s by molecular beam epitaxy and organometallic chemical vapor deposition.

Diode lasers of that era operated with threshold current densities of 1000 A/cm2 at 77 K temperatures. Such performance enabled continuous-lasing to be demonstrated in the earliest days. However, when operated at room temperature, about 300 K, threshold current densities were two orders of magnitude greater, or 100,000 A/cm2 in the best devices. The dominant challenge for the remainder of the 1960s was to obtain low threshold current density at 300 K and thereby to demonstrate continuous-wave lasing at room temperature from a diode laser.

The first diode lasers were homojunction diodes. That is, the material (and thus the bandgap) of the waveguide core layer and that of the surrounding clad layers, were identical. It was recognized that there was an opportunity, particularly afforded by the use of liquid phase epitaxy using aluminum gallium arsenide, to introduce heterojunctions. Heterostructures consist of layers of semiconductor crystal having varying bandgap and refractive index. Heterojunctions (formed from heterostructures) had been recognized by Herbert Kroemer, while working at RCA Laboratories in the mid-1950s, as having unique advantages for several types of electronic and optoelectronic devices including diode lasers. LPE afforded the technology of making heterojunction diode lasers. In 1963 he proposed the double heterostructure laser.

The first heterojunction diode lasers were single-heterojunction lasers. These lasers utilized aluminum gallium arsenide p-type injectors situated over n-type gallium arsenide layers grown on the substrate by LPE. An admixture of aluminum replaced gallium in the semiconductor crystal and raised the bandgap of the p-type injector over that of the n-type layers beneath. It worked; the 300 K threshold currents went down by 10× to 10,000 amperes per square centimeter. Unfortunately, this was still not in the needed range and these single-heterostructure diode lasers did not function in continuous wave operation at room temperature.

The innovation that met the room temperature challenge was the double heterostructure laser. The trick was to quickly move the wafer in the LPE apparatus between different "melts" of aluminum gallium arsenide (p- and n-type) and a third melt of gallium arsenide. It had to be done rapidly since the gallium arsenide core region needed to be significantly under 1 µm in thickness. The first laser diode to achieve continuous wave operation was a double heterostructure demonstrated in 1970 essentially simultaneously by Zhores Alferov and collaborators (including Dmitri Z. Garbuzov) of the Soviet Union, and Morton Panish and Izuo Hayashi working in the United States. However, it is widely accepted that Zhores I. Alferov and team reached the milestone first.

For their accomplishment and that of their co-workers, Alferov and Kroemer shared the 2000 Nobel Prize in Physics.

Types

The simple laser diode structure, described above, is inefficient. Such devices require so much power that they can only achieve pulsed operation without damage. Although historically important and easy to explain, such devices are not practical.

Double heterostructure lasers

Diagram of front view of a double heterostructure laser diode; not to scale

In these devices, a layer of low bandgap material is sandwiched between two high bandgap layers. One commonly-used pair of materials is gallium arsenide (GaAs) with aluminium gallium arsenide (AlxGa(1-x)As). Each of the junctions between different bandgap materials is called a heterostructure, hence the name "double heterostructure laser" or DH laser. The kind of laser diode described in the first part of the article may be referred to as a homojunction laser, for contrast with these more popular devices.

The advantage of a DH laser is that the region where free electrons and holes exist simultaneously—the active region—is confined to the thin middle layer. This means that many more of the electron-hole pairs can contribute to amplification—not so many are left out in the poorly amplifying periphery. In addition, light is reflected within the heterojunction; hence, the light is confined to the region where the amplification takes place.

Quantum well lasers

Diagram of front view of a simple quantum well laser diode; not to scale

If the middle layer is made thin enough, it acts as a quantum well. This means that the vertical variation of the electron's wavefunction, and thus a component of its energy, is quantized. The efficiency of a quantum well laser is greater than that of a bulk laser because the density of states function of electrons in the quantum well system has an abrupt edge that concentrates electrons in energy states that contribute to laser action.

Lasers containing more than one quantum well layer are known as multiple quantum well lasers. Multiple quantum wells improve the overlap of the gain region with the optical waveguide mode.

Further improvements in the laser efficiency have also been demonstrated by reducing the quantum well layer to a quantum wire or to a "sea" of quantum dots.

Quantum cascade lasers

In a quantum cascade laser, the difference between quantum well energy levels is used for the laser transition instead of the bandgap. This enables laser action at relatively long wavelengths, which can be tuned simply by altering the thickness of the layer. They are heterojunction lasers.

Interband cascade lasers

An Interband cascade laser (ICL) is a type of laser diode that can produce coherent radiation over a large part of the mid-infrared region of the electromagnetic spectrum.

Separate confinement heterostructure lasers

Diagram of front view of a separate confinement heterostructure quantum well laser diode; not to scale

The problem with the simple quantum well diode described above is that the thin layer is simply too small to effectively confine the light. To compensate, another two layers are added on, outside the first three. These layers have a lower refractive index than the centre layers, and hence confine the light effectively. Such a design is called a separate confinement heterostructure (SCH) laser diode.

Almost all commercial laser diodes since the 1990s have been SCH quantum well diodes.

Distributed Bragg reflector lasers

A distributed Bragg reflector laser (DBR) is a type of single frequency laser diode. It is characterized by an optical cavity consisting of an electrically or optically pumped gain region between two mirrors to provide feedback. One of the mirrors is a broadband reflector and the other mirror is wavelength selective so that gain is favored on a single longitudinal mode, resulting in lasing at a single resonant frequency. The broadband mirror is usually coated with a low reflectivity coating to allow emission. The wavelength selective mirror is a periodically structured diffraction grating with high reflectivity. The diffraction grating is within a non-pumped, or passive region of the cavity . A DBR laser is a monolithic single chip device with the grating etched into the semiconductor. DBR lasers can be edge emitting lasers or VCSELs. Alternative hybrid architectures that share the same topology include extended cavity diode lasers and volume Bragg grating lasers, but these are not properly called DBR lasers.

Distributed feedback lasers

A distributed feedback laser (DFB) is a type of single frequency laser diode. DFBs are the most common transmitter type in DWDM-systems. To stabilize the lasing wavelength, a diffraction grating is etched close to the p–n junction of the diode. This grating acts like an optical filter, causing a single wavelength to be fed back to the gain region and lase. Since the grating provides the feedback that is required for lasing, reflection from the facets is not required. Thus, at least one facet of a DFB is anti-reflection coated. The DFB laser has a stable wavelength that is set during manufacturing by the pitch of the grating, and can only be tuned slightly with temperature. DFB lasers are widely used in optical communication applications where a precise and stable wavelength is critical.

The threshold current of this DFB laser, based on its static characteristic, is around 11 mA. The appropriate bias current in a linear regime could be taken in the middle of the static characteristic (50 mA).Several techniques have been proposed in order to enhance the single-mode operation in these kinds of lasers by inserting a onephase-shift (1PS) or multiple-phase-shift (MPS) in the uniform Bragg grating. However, multiple-phase-shift DFB lasers represent the optimal solution because they have the combination of higher side-mode suppression ratio and reduced spatial hole-burning.

Vertical-cavity surface-emitting laser

Diagram of a simple VCSEL structure; not to scale

Vertical-cavity surface-emitting lasers (VCSELs) have the optical cavity axis along the direction of current flow rather than perpendicular to the current flow as in conventional laser diodes. The active region length is very short compared with the lateral dimensions so that the radiation emerges from the surface of the cavity rather than from its edge as shown in the figure. The reflectors at the ends of the cavity are dielectric mirrors made from alternating high and low refractive index quarter-wave thick multilayer.

Such dielectric mirrors provide a high degree of wavelength-selective reflectance at the required free surface wavelength λ if the thicknesses of alternating layers d1 and d2 with refractive indices n1 and n2 are such that n1d1 + n2d2 = λ/2 which then leads to the constructive interference of all partially reflected waves at the interfaces. But there is a disadvantage: because of the high mirror reflectivities, VCSELs have lower output powers when compared to edge-emitting lasers.

There are several advantages to producing VCSELs when compared with the production process of edge-emitting lasers. Edge-emitters cannot be tested until the end of the production process. If the edge-emitter does not work, whether due to bad contacts or poor material growth quality, the production time and the processing materials have been wasted.

Additionally, because VCSELs emit the beam perpendicular to the active region of the laser as opposed to parallel as with an edge emitter, tens of thousands of VCSELs can be processed simultaneously on a three-inch gallium arsenide wafer. Furthermore, even though the VCSEL production process is more labor- and material-intensive, the yield can be controlled to a more predictable outcome. However, they normally show a lower power output level.

Vertical-external-cavity surface-emitting-laser

Vertical external-cavity surface-emitting lasers, or VECSELs, are similar to VCSELs. In VCSELs, the mirrors are typically grown epitaxially as part of the diode structure, or grown separately and bonded directly to the semiconductor containing the active region. VECSELs are distinguished by a construction in which one of the two mirrors is external to the diode structure. As a result, the cavity includes a free-space region. A typical distance from the diode to the external mirror would be 1 cm.

One of the most interesting features of any VECSEL is the small thickness of the semiconductor gain region in the direction of propagation, less than 100 nm. In contrast, a conventional in-plane semiconductor laser entails light propagation over distances of from 250 µm upward to 2 mm or longer. The significance of the short propagation distance is that it causes the effect of "antiguiding" nonlinearities in the diode laser gain region to be minimized. The result is a large-cross-section single-mode optical beam which is not attainable from in-plane ("edge-emitting") diode lasers.

Several workers demonstrated optically pumped VECSELs, and they continue to be developed for many applications including high power sources for use in industrial machining (cutting, punching, etc.) because of their unusually high power and efficiency when pumped by multi-mode diode laser bars. However, because of their lack of p–n junction, optically pumped VECSELs are not considered "diode lasers", and are classified as semiconductor lasers.

Electrically pumped VECSELs have also been demonstrated. Applications for electrically pumped VECSELs include projection displays, served by frequency doubling of near-IR VECSEL emitters to produce blue and green light.

External-cavity diode lasers

External-cavity diode lasers are tunable lasers which use mainly double heterostructures diodes of the AlxGa(1-x)As type. The first external-cavity diode lasers used intracavity etalons and simple tuning Littrow gratings. Other designs include gratings in grazing-incidence configuration and multiple-prism grating configurations.

Reliability

Laser diodes have the same reliability and failure issues as light emitting diodes. In addition they are subject to catastrophic optical damage (COD) when operated at higher power.

Many of the advances in reliability of diode lasers in the last 20 years remain proprietary to their developers. Reverse engineering is not always able to reveal the differences between more-reliable and less-reliable diode laser products.

Semiconductor lasers can be surface-emitting lasers such as VCSELs, or in-plane edge-emitting lasers. For edge-emitting lasers, the edge facet mirror is often formed by cleaving the semiconductor wafer to form a specularly reflecting plane. This approach is facilitated by the weakness of the [110] crystallographic plane in III-V semiconductor crystals (such as GaAs, InP, GaSb, etc.) compared to other planes.

The atomic states at the cleavage plane are altered compared to their bulk properties within the crystal by the termination of the perfectly periodic lattice at that plane. Surface states at the cleaved plane have energy levels within the (otherwise forbidden) bandgap of the semiconductor.

As a result, when light propagates through the cleavage plane and transits to free space from within the semiconductor crystal, a fraction of the light energy is absorbed by the surface states where it is converted to heat by phonon-electron interactions. This heats the cleaved mirror. In addition, the mirror may heat simply because the edge of the diode laser—which is electrically pumped—is in less-than-perfect contact with the mount that provides a path for heat removal. The heating of the mirror causes the bandgap of the semiconductor to shrink in the warmer areas. The bandgap shrinkage brings more electronic band-to-band transitions into alignment with the photon energy causing yet more absorption. This is thermal runaway, a form of positive feedback, and the result can be melting of the facet, known as catastrophic optical damage, or COD.

In the 1970s, this problem, which is particularly nettlesome for GaAs-based lasers emitting between 0.630 µm and 1 µm wavelengths (less so for InP-based lasers used for long-haul telecommunications which emit between 1.3 µm and 2 µm), was identified. Michael Ettenberg, a researcher and later Vice President at RCA Laboratories' David Sarnoff Research Center in Princeton, New Jersey, devised a solution. A thin layer of aluminum oxide was deposited on the facet. If the aluminum oxide thickness is chosen correctly, it functions as an anti-reflective coating, reducing reflection at the surface. This alleviated the heating and COD at the facet.

Since then, various other refinements have been employed. One approach is to create a so-called non-absorbing mirror (NAM) such that the final 10 µm or so before the light emits from the cleaved facet are rendered non-absorbing at the wavelength of interest.

In the very early 1990s, SDL, Inc. began supplying high power diode lasers with good reliability characteristics. CEO Donald Scifres and CTO David Welch presented new reliability performance data at, e.g., SPIE Photonics West conferences of the era. The methods used by SDL to defeat COD were considered to be highly proprietary and were still undisclosed publicly as of June 2006.

In the mid-1990s, IBM Research (Ruschlikon, Switzerland) announced that it had devised its so-called "E2 process" which conferred extraordinary resistance to COD in GaAs-based lasers. This process, too, was undisclosed as of June 2006.

Reliability of high-power diode laser pump bars (used to pump solid-state lasers) remains a difficult problem in a variety of applications, in spite of these proprietary advances. Indeed, the physics of diode laser failure is still being worked out and research on this subject remains active, if proprietary.

Extension of the lifetime of laser diodes is critical to their continued adaptation to a wide variety of applications.

Applications

Laser diodes can be arrayed to produce very high power outputs, continuous wave or pulsed. Such arrays may be used to efficiently pump solid-state lasers for high average power drilling, burning or for inertial confinement fusion

Laser diodes are numerically the most common laser type, with 2004 sales of approximately 733 million units, as compared to 131,000 of other types of lasers.

Telecommunications, scanning and spectrometry

Laser diodes find wide use in telecommunication as easily modulated and easily coupled light sources for fiber optics communication. They are used in various measuring instruments, such as rangefinders. Another common use is in barcode readers. Visible lasers, typically red but later also green, are common as laser pointers. Both low and high-power diodes are used extensively in the printing industry both as light sources for scanning (input) of images and for very high-speed and high-resolution printing plate (output) manufacturing. Infrared and red laser diodes are common in CD players, CD-ROMs and DVD technology. Violet lasers are used in HD DVD and Blu-ray technology. Diode lasers have also found many applications in laser absorption spectrometry (LAS) for high-speed, low-cost assessment or monitoring of the concentration of various species in gas phase. High-power laser diodes are used in industrial applications such as heat treating, cladding, seam welding and for pumping other lasers, such as diode-pumped solid-state lasers.

Uses of laser diodes can be categorized in various ways. Most applications could be served by larger solid-state lasers or optical parametric oscillators, but the low cost of mass-produced diode lasers makes them essential for mass-market applications. Diode lasers can be used in a great many fields; since light has many different properties (power, wavelength, spectral and beam quality, polarization, etc.) it is useful to classify applications by these basic properties.

Many applications of diode lasers primarily make use of the "directed energy" property of an optical beam. In this category, one might include the laser printers, barcode readers, image scanning, illuminators, designators, optical data recording, combustion ignition, laser surgery, industrial sorting, industrial machining, wireless power transfer (as power beaming), and directed energy weaponry. Some of these applications are well-established while others are emerging.

Medical uses

Laser medicine: medicine and especially dentistry have found many new uses for diode lasers. The shrinking size and cost of the units and their increasing user friendliness makes them very attractive to clinicians for minor soft tissue procedures. Diode wavelengths range from 810 to 1,100 nm, are poorly absorbed by soft tissue, and are not used for cutting or ablation. Soft tissue is not cut by the laser's beam, but is instead cut by contact with a hot charred glass tip. The laser's irradiation is highly absorbed at the distal end of the tip and heats it up to 500 °C to 900 °C. Because the tip is so hot, it can be used to cut soft-tissue and can cause hemostasis through cauterization and carbonization. Diode lasers when used on soft tissue can cause extensive collateral thermal damage to surrounding tissue.

As laser beam light is inherently coherent, certain applications utilize the coherence of laser diodes. These include interferometric distance measurement, holography, coherent communications, and coherent control of chemical reactions.

Laser diodes are used for their "narrow spectral" properties in the areas of range-finding, telecommunications, infra-red countermeasures, spectroscopic sensing, generation of radio-frequency or terahertz waves, atomic clock state preparation, quantum key cryptography, frequency doubling and conversion, water purification (in the UV), and photodynamic therapy (where a particular wavelength of light would cause a substance such as porphyrin to become chemically active as an anti-cancer agent only where the tissue is illuminated by light).

Laser diodes are used for their ability to generate ultra-short pulses of light by the technique known as "mode-locking." Areas of use include clock distribution for high-performance integrated circuits, high-peak-power sources for laser-induced breakdown spectroscopy sensing, arbitrary waveform generation for radio-frequency waves, photonic sampling for analog-to-digital conversion, and optical code-division-multiple-access systems for secure communication.

Maskless photolithography

laser diodes are used in maskless photolithography.

Common wavelengths

Visible light

  • 405 nm: InGaN blue-violet laser, in Blu-ray Disc and HD DVD drives
  • 445–465 nm: InGaN blue laser multimode diode recently introduced (2010) for use in mercury-free high-brightness data projectors
  • 488 nm: InGaN green-blue laser; became widely available in mid-2018.
  • 505 nm: InGaN bluish-green laser; also became widely available in mid-2018.
  • 510–525 nm: InGaN Green diodes recently (2010) developed by Nichia and OSRAM for laser projectors.
  • 635 nm: AlGaInP better red laser pointers, same power subjectively twice as bright as 650 nm
  • 650–660 nm: GaInP/AlGaInP CD and DVD drives, cheap red laser pointers
  • 670 nm: AlGaInP bar code readers, first diode laser pointers (now obsolete, replaced by brighter 650 nm and 671 nm DPSS)

Infrared

Inequality (mathematics)

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