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Polaroid Corporation

Polaroid Corporation

The Polaroid Corporation was founded in 1937 by Edwin H. Land. It is most famous for its instant film cameras, which reached the market in 1948, and continue to be the company's flagship product line. The company's original dominant market was in polarized sunglasses, an outgrowth of Land's self-guided research in polarization after leaving Harvard at the age of 17 (he later returned to Harvard to continue his research). After Polaroid defeated Kodak in a patent battle, Kodak left the instant camera business on January 9, 1986. Polaroid managed to develop an instant movie system, Polavision, based on the Dufay color process. The product was too late to market and had to compete with the upcoming video based systems. As a result most of the manufactured product was sold off as a job lot. The company entered the digital photography market late in the game, and as a result has neither a significant market share nor significant innovation in this area. The company filed for federal bankruptcy protection in October 11, 2001, but most of the business was thereafter carried on by the Polaroid Holding Company (PHC), managed by Bank One. Criticism has been raised over the way this process was undertaken, because the process left the executives of the company with large bonuses, while stockholders, as well as current and retired employees, were left with nothing. On April 27, 2005, Petters Group Worldwide announced its acquisition of PHC. Petters has in the past bought up failed companies with well-known names for the value of those names.

See also


- List of Polaroid instant cameras
- List of United States companies
- instant camera

External link


- [http://www.polaroid.com/ Company home page]
- [http://www.polaroid.com/global/movie_2.jsp?PRODUCT%3C%3Eprd_id=845524441761320&FOLDER%3C%3Efolder_id=282574488338441&bmUID=1134326632680&bmLocale=en_US Company history]
- [http://www.cfo.com/Article?article=8524 On the Polaroid bankruptcy]
- [http://www.house.gov/delahunt/polaroid.htm Polaroid & Corporate Bankruptcy] Category:Manufacturing companies of the United StatesCategory:Photography companies

1937

1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar).

Events

January


- January 1 - Anastasio Somoza becomes President of Nicaragua
- January 11 - The first issue of Look magazine goes on sale in the United States.
- January 19 - Howard Hughes sets a new air record by flying from Los Angeles to New York City in 7 hours, 28 minutes and 25 seconds.
- January 23 - In Moscow, 17 leading Communists go on trial accused of participating in a plot led by Leon Trotsky to overthrow Joseph Stalin's regime and assassinate its leaders.
- January 31 - Ohio river floods
- January 31 - 31 people executed in the Soviet Union for "Trotskyism"

February


- February 5 - President Franklin D. Roosevelt proposes a plan to enlarge the Supreme Court of the United States.
- February 8 - Falangist troops take Málaga
- February 11 - A sit-down strike ends when General Motors recognises the United Automobile Workers Union
- February 16 - Wallace H. Carothers receives a patent for nylon.
- February 19 - During a public ceremony at the Viceregal Palace (the former Imperial residence) in Addis Ababa Ahmed, Ethiopia, two Eritrean nationalists attempt to kill viceroy Rodolfo Graziani with a number of grenades. The Italian security guard fire into the crowd of Ethiopian onlookers, and over the passing weeks indiscriminately slaughter native Ethiopians in reprisal.
- February 21 - Initial flight of the first successful flying car, Waldo Waterman's Arrowbile; the League of Nations Non-Intervention Committee ban on foreign national "volunteers" in the Spanish Civil War.

March


- March - The first issue of the comic book Detective Comics is published in the United States. Twenty-seven issues later, Detective Comics would introduce Batman. The comic would go on to become the longest continually-published comic magazine in American history; it is still published as of 2005.
- March 10 - The Encyclical Mit Brennender Sorge of pope Pius XI is published in Nazi Germany
- March 18 - The New London School explosion kills three hundred.
- March 26 - In Crystal City, Texas spinach growers erect a statue of the cartoon character Popeye.
- March 26 - William Henry Hastie becomes the first African-American appointed to federal judgeship.

April


- April 1 - Aden becomes a British crown colony.
- April 17 - Release of the animated short Porky's Duck Hunt, directed by Tex Avery for the Merrie Melodies series, featuring the debut of Daffy Duck.
- April 26 - Spanish Civil War: Guernica, Spain is bombed by German Luftwaffe.
- April 26 - In his report of the Falangist attack on Guernica, British journalist George Steer reports that he had found German bomb casing; that means that Luftwaffe planes were connected with the attack

May

Luftwaffe, with their daughters Princesses Elizabeth and Margaret.]]
- May 1 - General strike in Paris, France
- May 6 - In United States, the German airship Hindenburg bursts into flame when mooring to a mast in Lakehurst.
- May 7 - Spanish Civil War: The German Condor Legion Fighter Group, equipped with Heinkel He 51 biplanes arrive in Spain to assist Francisco Franco's forces.
- May 12 - Coronation of King George VI and Queen Elizabeth takes place at Westminster Abbey, London.
- May 21 - As one of the reprisals for the attempted assassination of Italian viceroy Rodolfo Graziani, a detachment of Italian troops massacre the entire community of Debre Libanos. 297 monks and 23 laymen are killed.
- May 27 - In California, the Golden Gate Bridge opens to pedestrian traffic creating a vital link between San Francisco and Marin County. The next day, President Franklin D. Roosevelt pushes a button in Washington, DC signaling the start of vehicle traffic over the Golden Gate Bridge.
- May - Dáil Éireann passes the Executive Authority (Consequential Provisions) Act, 1937 which retrospectively abolishes the office of Governor-General of the Irish Free State. The abolition is retrospectively dated to December 1936.

June


- June 8 - First total solar eclipse to exceed 7 minutes of totality in over 800 years; visible in the Pacific and Peru.
- June 14 - Pennsylvania becomes the first (and only) of the United States to celebrate Flag Day officially as a state holiday.
- June 21 - Coalition government of Leon Blum resigns in France.
- June/July - Dáil Éireann debates and passes the draft new constitution of Éire, to be called Bunreacht na hÉireann. The new constitution is then submitted for public approval by plebiscite.

July


- July 1 - Gestapo arrests priest Martin Niemöller.
- July 1 - In a referendum the people of the Irish Free State accept the new Constitution by 685,105 votes to 527,945.
- July 2 - Amelia Earhart disappears
- July 5 - Highest recorded temperature in Canada, at Yellow Grass, Saskatchewan: 45 °C.
- July 7 - Sino-Japanese War: Battle of Lugou Bridge - Japanese forces invade China.
- July 21 - Eamon de Valera elected president of Eire
- July 22 - New Deal: The United States Senate votes down President Franklin D. Roosevelt's proposal to add more justices to the Supreme Court of the United States.
- July 24 - Alabama drops rape charges against the so-called "Scottsboro Boys."
- July 28 - IRA attempts bombing assassination against King George VI in Belfast.

August


- August 6 - Falangist artillery bombards Madrid.

September


- September 5 - Spanish Civil War: The fall of Llanes.
- September 16 - birth of Keith Bosley, broadcaster (retired), poet and translator.
- September 21 - George Allen & Unwin, Ltd. of London published the first edition of J. R. R. Tolkien's The Hobbit.
- September 25 - Sino-Japanese War: Battle of Pingxingguan.

October


- October 1 - Marijuana Tax Act in USA.
- October 3 - Japanese troops advance toward Nanking.
- October 5 - Roosevelt "Quarantine the Aggressors" speech at Chicago
- October 21 - The whole Spanish northern seaboard in the Falangists' hands.
- October 21 - Roberto Ortiz elected president of Argentina.
- October 27 - Spanish Civil War - Republican forces in Gijon, Spain, set fire to petrol reserves before they retreat before the advancing Falangists.

November


- November 5 Spanish Civil War - Massacre of Republican supporters in Piedrafita de Babia, near León. Possibly 35,000 executed.
- November 5 - World War II: In the Reich Chancellery, Adolf Hitler holds a secret meeting and states his plans for acquiring "living space" for the German people.
- November 9 - Japanese troops take Shanghai.

December


- December 3 - The Dandy, the world's longest running comic, was first published.
- December 12 - Panay incident
- December 13 - Battle of Nanjing ends and the Nanjing Massacre begins. Japanese troops would slaughter over 250,000 civilians and prisoners over three months.
- December 27 - Mae West performance gets her banned from NBC Radio
- December 29 - New Irish Constitution, Bunreacht na hÉireann comes into force. The Irish Free State becomes Éire. Eamon de Valera becomes the first Taoiseach (prime minister) of the new state. A Presidential Commission (made up the Irish Chief Justice, the Speaker of Dáil Éireann and the President of the High Court) assumes the powers of the new presidency of Ireland pending the election of the first president in June 1938.
- December - The Marijuana Tax Act is signed, ending the US hemp industry just as it was about to benefit from a mechanised brake and compete with cotton and wood pulp.

Unknown dates


- Japan invades Manchuria. (Some consider this the start of World War II. Most historians disagree).
- New Irish constitution bans divorce.
- First science fiction convention in Leeds, United Kingdom.
- Italy joins Antikomintern Pact.
- The National House Builders Registration Council (now the NHBC) was formed in the United Kingdom.
- Donald Goines (1937 - 1973)
- Jimmie Angel lands his plane on top of Devil's Mountain however the plane gets damaged and he has to trek through the rainforest for help.

Ongoing events


- Spanish Civil War (1936-1939)
- Sino-Japanese War (1937-1945)
- Harlem Renaissance (1920-1940) [http://en.wikipedia.org/wiki/Harlem_Renaissance]

Births

January


- January 1 - Anne Aubrey, British actor
- January 4 - Dyan Cannon, Ameircan actress
- January 6 - Underwood Dudley, American mathematician
- January 8 - Shirley Bassey, Welsh singer
- January 14 - Ken Higgs, English cricketer
- January 15 - Margaret O'Brien, American actress
- January 18 - John Hume, Irish politician, recipient of the Nobel Peace Prize
- January 27 - John Ogdon, English pianist (d. 1989)
- January 30 - Vanessa Redgrave, English actress
- January 30 - Boris Spassky, Russian chess player
- January 31 - Suzanne Pleshette, Amrican actress
- January 31 - Philip Glass, American composer

February


- February 1 - Garrett Morris, American comedian
- February 1 - Don Everly, American musician
- February 2 - Tom Smothers, American musician and comedian
- February 2 - Magic Sam, American musician (d. 1969)
- February 8 - Manfred Krug, German actor and singer
- February 11 - Bill Lawry, Australian cricketer
- February 12 - Charles Dumas, American athlete
- February 20 - Robert Huber, German chemist, Nobel Prize laureate
- February 20 - Roger Penske, American race car driver
- February 20 - Nancy Wilson, American singer and actress
- February 21 - King Harald V of Norway
- February 25 - Tom Courtenay, English actor

March


- March 2 - Abdelaziz Bouteflika, Algerian president
- March 4 - Graham Dowling, New Zealand cricket captains
- March 6 - Valentina Tereshkova, cosmonaut
- March 9 - Mickey Gilly, American musician
- March 17 - Rudy Ray Moore, American comedian
- March 20 - Jerry Reed, American musician
- March 22 - Armin Hary, German athlete
- March 23 - Craig Breedlove, American race car driver
- March 30 - Warren Beatty, American actor and director

April


- April 5 - Colin Powell, U.S. Secretary of State
- April 6 - Merle Haggard, American musician
- April 6 - Billy Dee Williams, American actor
- April 10 - Bella Akhmadulina, Russian poet
- April 16 - Joseph Whipp, American actor
- April 22 - Jack Nicholson, American actor
- April 29 - Jill Paton Walsh, English novelist

May


- May 1 - Una Stubbs, British actor
- May 8 - Thomas Pynchon, American writer
- May 6 - Rubin 'Hurricane' Carter, American boxer
- May 12 - George Carlin, American comedian
- May 13 - Roch Carrier, Canadian writer
- May 13 - Roger Zelazny, American writer (d. 1995)
- May 15 - Madeleine Albright, U.S. Secretary of State
- May 15 - Trini López, American musician
- May 17 - Hazel R. O'Leary, U.S. Secretary of Energy
- May 18 - Brooks Robinson, baseball player
- May 18 - Jacques Santer, Luxembourg politician, President of the European Council

June


- June 1 - Morgan Freeman, American actor
- June 3 - Solomon P. Ortiz, U.S. Congressman from Texas
- June 7 - Neemi Järvi, Estonian conductor
- June 9 - Harald Rosenthal, German biologist
- June 11 - Robin Warren, Australian pathologist, recipient of the Nobel Prize in Physiology or Medicine
- June 18 - Wray Carlton, American football player
- June 18 - Vitali Zholobov, cosmonaut
- June 23 - Martti Ahtisaari, President of Finland
- June 25 - Keizo Obuchi, Prime Minister of Japan (d. 2000)
- June 26 - Robert Coleman Richardson, American physicist, Nobel Prize laureate
- June 28 - Ron Luciano, baseball umpire and writer (d. 1995)

July


- July 6 - Vladimir Ashkenazy, Russian pianist
- July 6 - Ned Beatty, American actor
- July 7 - Tung Chee-Hwa, Hong Kong administrator
- July 9 - David Hockney, English-born artist
- July 12 - Lionel Jospin, Prime Minister of France
- July 12 - Bill Cosby, American actor and comedian
- July 14 - Yoshiro Mori, Japanese politician
- July 18 - Roald Hoffmann, Polish-born chemist, Nobel Prize laureate
- July 29 - Daniel McFadden, American economist, Nobel Prize laureate

August


- August 4 - David Bedford, American musician
- August 5 - Herb Brooks, American hockey coach (d. 2003)
- August 8 - Dustin Hoffman, American actor
- August 18 - Robert Redford, American actor
- August 18 - Willie Rushton, English comedian and cartoonist (d. 1996)
- August 21 - Donald Dewar, First Minister of Scotland (d. 2000)
- August 29 - James Florio, Governor of New Jersey

September


- September 4 - Dawn Fraser, Australian swimmer
- September 15 - Robert Lucas, Jr., American economist, Nobel Prize laureate
- September 15 - Fernando de la Rúa, President of Argentina
- September 19 - Abner Haynes, American football player
- September 28 - Rod Roddy, American television announcer (d. 2003)

October


- October 2 - Johnnie Cochran, American attorney (d. 2005)
- October 5 - Barry Switzer, American football coach
- October 10 - Bobby Charlton, English footballer

November


- November 8 - Paul Mackintosh Foot, British journalist
- November 15 - Yaphet Kotto, American actor
- November 17 - Peter Cook, English comedian and writer
- November 26 - Boris Yegorov, cosmonaut

December


- December 3 - Bobby Allison, American race car driver
- December 8 - Arne Næss Jr., Norwegian mountaineer and businessman (d. 2004)
- December 21 - Jane Fonda, American actress and social activist
- December 26 - Gnassingbe Eyadema, President of Togo (d. 2005)
- December 29 - Maumoon Abdul Gayoom, President of the Maldives
- December 30 - John Hartford, American musician and composer (d. 2001)
- December 30 - Jim Marshall, American football player
- December 31 - Avram Hershko, Israeli biologist, recipient of the Nobel Prize in Chemistry
- December 31 - Sir Anthony Hopkins, Welsh actor

Deaths


- January 6 - Brother Andre, Canadian religious leader (b. 1845)
- January 23 - Marie Prevost, Canadian actress (b. 1898)
- February 5 - Lou Andreas-Salome, Russian-born writer (b. 1861)
- February 7 - Elihu Root, American statesman and diplomat, recipient of the Nobel Peace Prize (b. 1845)
- February 11 - Walter Burley Griffin, American architect and town planner (b. 1876)
- March 9 - Paul Elmer More, American critic and essayist (b. 1864)
- March 12 - Charles-Marie Widor, French organist and composer (b. 1840)
- March 15 - H. P. Lovecraft, American writer (b. 1890)
- March 17 - Austen Chamberlain, English statesman, recipient of the Nobel Peace Prize (b. 1863)
- March 29 - Karol Szymanowski, Polish composer (b. 1882)
- April 19 - William Martin Conway, British art critic and mountaineer (b. 1856)
- April 21 - Saima Harmaja, Finnish poet (b. 1913)
- April 25 - Michał Drzymała, Polish rebel (b.1857)
- May 23 - John D. Rockefeller, American industrialist and philanthropist (b. 1839)
- May 28 - Alfred Adler, Austrian psychologist (b. 1870)
- June 19 - J. M. Barrie, Scottish novelist and dramatist (b. 1860)
- July 9 - Oliver Law, American labor organizer and Army officer (killed in battle) (b. 1899)
- July 11 - George Gershwin, American composer (b. 1898)
- July 20 - Guglielmo Marconi, Italian inventor (b. 1874)
- July 21 - Louis Vierne, French composer (b. 1870)
- August 11 - Edith Wharton, American writer (b. 1862)
- September 2 - Pierre de Coubertin, French founder of the modern Olympic Games (b. 1863)
- September 26 - Bessie Smith, American singer (b. 1894)
- September 29 - Ray Ewry, American athlete (b. 1873)
- October 16 - Jean de Brunhoff, French writer (b. 1899)
- October 19 - Ernest Rutherford, 1st Baron Rutherford of Nelson, New Zealand physicist, recipient of the Nobel Prize in Chemistry (b. 1871)
- October 26 - Józef Dowbór-Muśnicki, Polish general (b. 1867)
- November 17 - Jack Worrall, Australian cricketer and coach (b. 1860)
- November 23 - Jagdish Chandra Bose, Indian Physicist (b. 1858)
- December 9 - Gustaf Dalén, Swedish physicist, Nobel Prize laureate (b. 1869)
- December 20 - Erich Ludendorff, German general (b. 1865)
- December 21 - Frank B. Kellogg, United States Secretary of State, recipient of the Nobel Peace Prize (b. 1856)
- December 28 - Maurice Ravel, French composer (b. 1875)

Nobel Prizes


- Physics - Clinton Joseph Davisson, George Paget Thomson
- Chemistry - Walter Haworth, Paul Karrer
- Medicine - Albert von Szent-Györgyi Nagyrapolt
- Literature - Roger Martin du Gard
- Peace - Robert Cecil Category:1937 ko:1937년 ms:1937 ja:1937年 simple:1937 th:พ.ศ. 2480

1948

1948 (MCMXLVIII) is a leap year starting on Thursday (link will take you to calendar).

Events

January-February


- January 1 - Nationalisation of UK railways to form British Railways. Arab militants lay siege to the Jewish Quarter of the Old City of Jerusalem. First day of the Italian republican constitution.
- January 4 - Burma gains its independence from the United Kingdom.
- January 5 - Warner Brothers shows the first color newsreel (Tournament of Roses Parade and the Rose Bowl).
- January 17 - Truce between nationalist Indonesian and Dutch troops in Java
- January 26 - Teigin poison case - Man masquerading as a doctor poisons 12 out of 15 bank employees of the Tokyo branch of Imperial Bank and takes the money; artist Sadamichi Hirasawa is later sentenced for the crime.
- January 30 - Indian pacifist and leader Mahatma Gandhi is murdered by a Hindu extremist.
- January 30 - 1948 Winter Olympics open in St. Moritz, Switzerland.
- February 1 - Soviet Union begins to jam Voice of America broadcasts.
- February 4 - Ceylon (later renamed Sri Lanka) becomes independent within the British Commonwealth. King George VI becomes King of Ceylon.
- February 18 - Eamon de Valera, head of government since 1932, loses power to an opposition coalition. John A. Costello is appointed Taoiseach of Éire (formerly called the Irish Free State) by President O'Kelly.
- February 24 - The Communist Party seizes control of Czechoslovakia.

March-April


- March 8 - The United States Supreme Court rules that religious instruction in public schools violated the Constitution.
- March 10 - Czech foreign minister Jan Masaryk killed in fall from a window of his apartment in Prague. Later communist government rules it "suicide".
- March 17 - Hell's Angels founded in California
- March 20 - First elections in Singapore
- April 1 - Faroe Islands receive autonomy from Denmark
- April 3 - President Harry Truman signs the Marshall Plan which authorizes $5 billion in aid for 16 countries.
- April 7 - The World Health Organization is established by the United Nations.
- April 7 - Buddhist monastery burns in Shanghai - 20 monks dead
- April 9 - Jorge Eliécer Gaitán's assassination provokes a violent riot in Bogotá (the Bogotazo), and a further ten years of violence in all of Colombia (La violencia).
- April 9 - The Deir Yassin massacre takes place in Palestine.

May

Palestine
- May 1 - 213 communists executed in Greece.
- May 2 - Hour of Charm's last broadcast.
- May 11 - Luigi Einaudi becomes President of the Italian Republic.
- May 14 - Israel is declared as an independent state.
- May 14 - The murder of a three-year-old girl in Blackburn, England leads to the fingerprinting of more than 40,000 men in the city in an attempt to find the murderer.
- May 15 - 1948 Arab-Israeli War: Egypt, Transjordan, Lebanon, Syria, Iraq and Saudi Arabia attack Israel.
- May 16 - Chaim Weizmann is elected as the first President of Israel.
- May 18 - The First Legislative Yuan of the Republic of China officially convenes in Nanking.
- May 26 - The U.S. Congress passes Public Law 557 which permanently establishes the Civil Air Patrol as the auxiliary of the United States Air Force.
- May 30 - A dike along the Columbia River breaks, obliterating Vanport, Oregon within minutes. 15 people die and tens of thousands are left homeless.

June-July


- June 3 - Palomar Observatory telescope finished in California.
- June 16 - Communist guerillas kill three rubber planters in Malaya.
- June 16 - Three armed men hijack Cathay Pacific passenger plane Miss Macao and shoot the pilot. The plane crashes - one of 27 survives
- June 17 - A Douglas DC-6 carrying United Air Lines Flight 624 crashes near Mount Carmel, Pennsylvania, killing all 43 people on board.
- June 18 - State of Emergency declared in Malaysia for communist insurgency - Malayan Emergency begins.
- June 21 - The Deutsche Mark becomes official currency of the Federal Republic of Germany.
- June 24 - Cold War: The Berlin Blockade begins.
- June 28 - Cominform Resolution marks the beginning of the Informbiro period in Yugoslavia and Soviet/Yugoslav split.
- July 5 - British National Health Service Act enacted.
- July 13 - The Coptic and Ethiopian Churches reach an agreement leading to the promotion of the Ethiopian church to the rank of an autocephalous Patriarchate. Five bishops are immediately consecrated by the Patriarch of Alexandria, and the successor to Abuna Qerellos IV is granted the power to consecrate new bishops, who are empowered to elect a new Patriarch for their church.
- July 15 - Attempted assassination of Palmiro Togliatti, general secretary of the Italian Communist Party, incites number of strikes all over the country.
- July 15 - First London, England chapter of Alcoholics Anonymous
- July 20 - Cold War: President Harry S. Truman issues the second peacetime military draft in the United States amid increasing tensions with the Soviet Union (the first peacetime draft occurred in 1940 under President Roosevelt).
- July 24 - Great oil fire in the harbor of Naantali, Finland
- July 26 - U.S. President signs Executive Order 9981, ending racial segregation in the United States Armed Forces.
- July 29 - 1948 Summer Olympics begin in London.
- July 31 - At Idlewild Field in New York, New York International Airport (later renamed John F. Kennedy International Airport) is dedicated.

August-December


- August 1 - The U.S. Air Force Office of Special Investigations is founded.
- August 12 - USA recognizes the government of South Korea.
- August 19 - Soviet troops fire at German demonstrators that protest against the Berlin Blockade.
- August 23 - World Council of Churches established.
- September 4 - Queen Wilhelmina of the Netherlands abdicates for health reasons.
- September 5 - Robert Schuman becomes Prime Minister of France.
- September 6 - Juliana becomes Queen of the Netherlands.
- September 17 - Stern Gang assassinates count Folke Bernadotte.
- October 11 - Cleveland Indians defeat the Boston Braves to win the World Series, four games to two.
- November 2 - U.S. presidential election, 1948: Harry S. Truman defeats Thomas E. Dewey for the US presidency.
- November 12 - In Tokyo, an international war crimes tribunal sentences seven Japanese military and government officials to death, including General Hideki Tojo, for their roles in World War II.
- November 15 - Louis Stephen St. Laurent becomes Canada's twelfth prime minister.
- November 16 - Operation Magic Carpet to transport Jews from Yemen to Israel begins.
- November 17 - Mohammad Reza Shah Pahlavi divorces his second wife, the former Princess Fawzia of Egypt.
- November 24 - In Venezuela, president Rómulo Betancourt is outsed by a military coup. A military junta takes over the government.
- December 7 - Gary Morris, singer and actor
- December 7 - Mads Vinding, Danish bassist
- December 10 - United Nations General Assembly adopts Universal Declaration of Human Rights.
- December 26 - Last Soviet troops withdraw from North Korea.
- December 28 - Member of Muslim Brotherhood assassinates Egyptian Prime Minister Mahmud Fahmi Nokrashi.
- December 30 - The play Kiss Me, Kate opens for the first of 1,077 performances.
- December 31 - 1948 Arab-Israeli War: Israeli troops drive Egyptians from Negev.

Undated


- Empire Windrush immigrant ship arrives in Britain
- Civil war in Costa Rica
- Civil war in Colombia
- Rope (film) released

Unknown date


- Porsche is founded.
- Miranda, the innermost moon of Uranus, is discovered by Gerard Kuiper.
- Casimir effect discovered by Dutch physicist Hendrik Casimir.
- Tunnel of Vielha is opened in Val d'Aran, Spanish Pyrenees.
- Fresh Kills, world's largest landfill, opens in Staten Island, New York.
- The law firm of Skadden, Arps, Slate, Meagher & Flom is founded.
- Brandeis University is founded.
- Oakridge Transit Centre opened in Vancouver, British Columbia.

Births

January-February


- January 2 - Mary Archer, British scientist
- January 2 - Deborah Watling, British actress
- January 7 - Kenny Loggins, American singer
- January 10 - Donald Fagen, American keyboardist
- January 10 - Mischa Maisky, Latvian cellist
- January 14 - Carl Weathers, American football player and actor
- January 14 - T-Bone Burnett, American record producer and musician
- January 15 - Ronnie Van Zant, American musician (d. 1977)
- January 16 - John Carpenter, American film director and composer
- January 17 - Davíð Oddsson, Prime Minister of Iceland
- January 19 - Frank McKenna, Premier of New Brunswick and Canadian Ambassador
- January 27 - Mikhail Baryshnikov, Russian-born dancer
- January 28 - Charles Taylor, Liberian president
- January 29 - Marc Singer, Canadian actor
- January 31 - Muneo Suzuki, Japanese politician
- February 1 - Elisabeth Sladen, British actress
- February 3 - Carlos Felipe Ximenes Belo, East Timorean Catholic bishop, recipient of the Nobel Peace Prize
- February 4 - Alice Cooper, American musician
- February 5 - Christopher Guest, American actor, writer, director, and composer
- February 5 - V. Alexander Stefan, American physicist, educator, and writer
- February 14 - Teller, American magician
- February 24 - J. Jayalalithaa, Indian politician
- February 25 - Danny Denzongpa, Indian actor
- February 28 - Steven Chu, American physicist, Nobel Prize laureate
- February 28 - Mike Figgis, American director, writer, and composer
- February 28 - Bernadette Peters, American actress and singer
- February 28 - Mercedes Ruehl, American actress

March-April


- March 1 - Burning Spear, Jamaican singer and musician
- March 2 - Jeff Kennett, Australian politician
- March 2 - R. T. Crowley, pioneer of electronic commerce
- March 9 - Jeffrey Osborne, American singer
- March 12 - James Taylor, American musician
- March 15 - Sérgio Vieira de Mello, Brazilian diplomat (d. 2003)
- March 17 - William Gibson, Canadian writer
- March 20 - John de Lancie, American actor
- March 20 - Bobby Orr, Canadian hockey player
- March 22 - Andrew Lloyd Webber, English composer
- March 22 - Wolf Blitzer, American television journalist
- March 26 - Steven Tyler, American singer (Aerosmith)
- March 28 - Dianne Wiest, American actress
- March 31 - Al Gore, former Vice President of the United States
- March 31 - Rhea Perlman, American actress
- April 1 - Jimmy Cliff, Jamaican musician
- April 15 - Michael Kamen, American composer (d. 2003)
- (April 23)-
- April 29 - Michael Karoli, German musician (d. 2001)

May-July


- May 8 - Felicity Lott, English soprano
- May 11 - Shigeru Izumiya, Japanese musician
- May 12 - Steve Winwood, English singer
- May 14 - Bob Woolmer, British cricket coach
- May 15 - Brian Eno, English musician and record producer
- May 19 - Grace Jones, Jamaican singer and actress
- May 21 - Leo Sayer, English musician
- May 26 - Stevie Nicks, American singer and songwriter (Fleetwood Mac)
- May 29 - Michael Berkeley, British composer
- May 31 - John Bonham, British drummer (Led Zeppelin) (d. 1980)
- June 2 - Todd Rundgren, American singer and record producer
- June 13 - Garnet Bailey, Canadian hockey player and scout
- June 17 - Dave Concepcion, Venezuelan baseball player
- June 19 - Phylicia Rashad, American actress
- June 20 - Ludwig Scotty, President of Nauru
- June 21 - Lionel Rose, Australian boxer
- June 21 - Andrzej Sapkowski, Polish writer
- July 8 - Raffi Cavoukian, Egyptian-born singer
- July 16 - Pinchas Zukerman, Israeli violinist
- July 18 - Hartmut Michel, German chemist, Nobel Prize laureate
- July 21 - Ed Hinton, American sportswriter
- July 21 - Cat Stevens, English musician
- July 21 - Garry Trudeau, American cartoonist
- July 25 - Peggy Fleming, American figure skater
- July 28 - Sally Struthers, American actress
- July 30 - Jean Reno, French actor

August-December


- August 2 - Dennis Prager, American radio talk show host and author
- August 3 - Jean-Pierre Raffarin, Prime Minister of France
- August 13 - Kathleen Battle, American soprano
- August 15 - Uschi Digard, American erotic actress and figure model
- August 20 - Robert Plant, English singer (Led Zeppelin)
- August 30 - Lewis Black, American comedian
- September 4 - Samuel Hui, Hong Kong singer
- September 5 - Benita Ferrero-Waldner, Austrian diplomat and politician
- September 10 - Bob Lanier, American basketball player
- September 10 - Margaret Trudeau, First Lady of Canada
- September 13 - Nell Carter, American singer and actress (d. 2003)
- September 17 - John Ritter, American actor (d. 2003)
- September 22 - Denis Burke, Australian politician
- September 24 - Heinz Chur, German composer
- September 27 - Michele Dotrice, English actor
- September 29 - Bryant Gumbel, American television broadcaster
- October 1 - Sir Sir Peter Blake New Zealand yachtsman (d. 2001)
- October 2 - Avery Brooks, American television actor
- October 2 - Chris LeDoux, American singer and rodeo star (d. 2005)
- October 8 - Johnny Ramone, American guitarist (The Ramones) (d. 2004)
- October 9 - Jackson Browne, American musician
- October 13 - Ted Poe, American politician
- October 17 - George Wendt, American television actor
- November 1 - Jim Steinman, American songwriter and producer
- November 5 - William Daniel Phillips, American physicist, Nobel Prize laureate
- November 10 - Vincent Schiavelli, American actor
- November 14 - Charles, Prince of Wales
- November 16 - Mutt Lange, Rhodesian-born record producer
- November 17 - Howard Dean, American politician
- November 20 - John R. Bolton, U.S. Ambassador to the UN
- November 20 - Barbara Hendricks, American-born soprano
- December 3 - Ozzy Osbourne, British singer
- December 6 - JoBeth Williams, American actress
- December 10 - Abu Abbas, founder of the Palestine Liberation Front (d. 2004)
- December 21 - Willi Resetarits, Austrian musician and cabaret artist
- December 27 - Gérard Depardieu, French actor

Unknown date


- Maurizio Gucci Italian business man and murder victim (d. 1995)
- Edward Rutherfurd, British novelist

Deaths


- January 21 - Ermanno Wolf-Ferrari, Italian composer (b. 1876)
- January 30 - Mohandas Gandhi, Indian independence movement leader (assassinated) (b. 1869)
- January 30 - Orville Wright, American co-inventor of the airplane (b. 1871)
- February 2 - Bevil Rudd, South African athlete (b. 1894)
- February 11 - Sergy Eisenstein, Russian film director (b. 1898)
- February 23 - John Robert Gregg, Irish-born inventor of shorthand (b. 1866)
- March 6 - Ross Lockridge, Jr., American novelist (suicide) (b. 1914)
- March 10 - Jan Masaryk, Foreign Minister of Czechoslovakia (b. 1886)
- March 31 - Egon Erwin Kisch, Austrian journalist and author (b. 1885)
- April 9 - Jorge Eliécer Gaitán, Colombian politician (b. 1903)
- April 17 - Suzuki Kantaro, Prime Minister of Japan (b. 1867)
- May 15 - Father Edward J. Flanagan, Irish-born priest and founder of Boys Town (b. 1886)
- May 28 - Unity Mitford, British friend of Hitler (b. 1914)
- June 25 - William C. Lee, American general (b. 1895)
- July 5 - Georges Bernanos, French writer (b. 1888)
- July 15 - John J. Pershing, American general (b. 1860)
- July 23 - David Wark Griffith, American film director (b. 1875)
- August 12 - Harry Brearley, English inventor of stainless steel (b. 1871)
- August 16 - Babe Ruth, baseball player (b. 1895)
- September 2 - Sylvanus G. Morley, American scholar and World War I spy (b. 1883)
- September 11 - Muhammed Ali Jinnah, first Governor-General of Pakistan (b. 1876)
- October 24 - Franz Lehár, Hungarian composer (b. 1870)
- November 28 - D.D. Sheehan, Irish politician (b. 1873)
- December 23 - Japanese war leaders (hanged):
  - Kenji Doihara, spy (b. 1883)
  - Koki Hirota, Prime Minister of Japan (b. 1878)
  - Iwane Matsui, general (b. 1878)
  - Itagaki Seishiro, military officer (b. 1885)
  - Hideki Tojo, general (b. 1884)
- December 31 - Sir Malcolm Campbell, English land and water racer (b. 1885)

Nobel Prizes


- Physics - Patrick Maynard Stuart Blackett
- Chemistry - Arne Wilhelm Kaurin Tiselius
- Medicine - Paul Hermann Müller
- Literature - T. S. Eliot
- Peace - not awarded Category:1948 als:1948 ko:1948년 ms:1948 ja:1948年 simple:1948 th:พ.ศ. 2491

Polarized

In electrodynamics, polarization (also spelled polarisation) is a property of waves, such as light and other electromagnetic radiation. Unlike more familiar wave phenomena such as waves on water or sound waves, electromagnetic waves are three-dimensional, and it is their vector nature that gives rise to the phenomenon of polarization.

Theory

Basics - plane waves

The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves. A plane wave is one where the direction of the magnetic and electric fields are confined to a plane perpendicular to the propagation direction. Simply because the plane is two-dimensional, the electric vector in the plane at a point in space can be decomposed into two orthogonal components. Call these the x and y components (following the conventions of analytic geometry). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time in the fixed plane we are talking about. By considering the shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure), we obtain a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue) with time, along with its x and y components (red/left and green/right) and the path made by the vector in the plane (purple):
Lissajous figure
Circular
Lissajous figure
Elliptical

Consider first the special case (left) where the two orthogonal components are in phase. In this case the strength of the two components are always equal or related by a constant ratio, so the direction of the electric vector (the vector sum of these two components) will always fall on a single line in the plane. We call this special case linear polarization. The direction of this line will depend on the relative amplitude of the two components. This direction can be in any angle in the plane, but the direction never varies. Now consider another special case (center), where the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. Notice that there are two possible phase relationships that satisfy this requirement. The x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector in the plane formed by summing the two components will rotate in a circle. We call this special case circular polarization. The direction of rotation will depend on which of the two phase relationships exists. We call these cases right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates. All the other cases, that is where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase (e.g. right) are called elliptical polarization because the sum electric vector in the plane will trace out an ellipse (the "polarization ellipse"). ellipse The use of plane polarized waves as a basis to decompose light waves is not essential; waves of opposite circular polarization can similarly be combined to yield any kind of polarization. The plane polarization decomposition is natural when dealing with reflection from surfaces, birefringent materials, or synchrotron radiation. The circularly polarized modes are a most useful basis set for the study of light propagation in stereoisomers - see, e.g. [http://bio.classes.ucsc.edu/bio100/LECTNOTES/CHIRAL/chirality.PDF].

Incoherent radiation

In nature, electromagnetic radiation is often produced by a large ensemble of individual radiators, producing waves independently of each other. This type of light is termed incoherent. In general there is no single frequency but rather a spectrum of different frequencies present, and even if filtered to an arbitrarily narrow frequency range, there may not be a consistent state of polarization. However, this does not mean that polarization is only a feature of coherent radiation. Incoherent radiation may show statistical correlation between the components of the electric field, which can be interpreted as partial polarization. In general it is possible to describe an observed wave field as the sum of a completely incoherent part (no correlations) and a completely polarized part. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.

Parameterizing polarization

correlation For ease of visualization, polarization states are often specified in terms of the polarization ellipse, specifically its orientation and elongation. A common parameterization uses the azimuth angle, ψ (the angle between the major semi-axis of the ellipse and the x-axis) and the ellipticity, ε (the ratio of the two semi-axes). Ellipticity is used in preference to the more common geometrical concept of eccentricity, which is of limited physical meaning in the case of polarization. An ellipticity of zero corresponds to linear polarization and an ellipticity of 1 corresponds to circular polarization. The arctangent of the ellipticity, χ = tan−1 ε (the "ellipticity angle"), is also commonly used. An example is shown in the diagram to the right. Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector): : \mathbf = \begin a_1 e^ \\ a_2 e^ \end . Notice that the product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. The physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase. Note also that the basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product. A common choice is left and right circular polarizations, for example to model the different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization.
inner product Reflection of a plane wave from a surface perpendicular to the page. The p-components of the waves are in the page, while the s components are perpendicular to it.
Regardless of whether polarization ellipses are represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about the propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle. On the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the horizontal coordinate system) corresponding to due north. Another coordinate system frequently used relates to the plane made by the propagation direction and a vector normal to the plane of a reflecting surface. This is illustrated in the diagram to the right. The components of the electric field parallel and perpendicular to this plane are termed "p-like" (parallel) and "s-like" (senkrecht, i.e. perpendicular in German). Alternative terms are pi-polarized, tangential plane polarized, vertically polarized, or a transverse-magnetic (TM) wave for the p-component; and sigma-polarized, sagittal plane polarized, horizontally polarized, or a transverse-electric (TE) wave for the s-component. In the case of partially polarized radiation, the Jones vector varies in time and space in a way that differs from the constant rate of phase rotation of monochromatic, purely polarized waves. In this case, the wave field is likely stochastic, and only statistical information can be gathered about the variations and correlations between components of the electric field. This information is embodied in the coherency matrix: :\mathbf = \left\langle\mathbf \mathbf^\dagger \right\rangle\, ::=\left\langle\begin e_1 e_1 & e_1 e_2^
- \\ e_2 e_1^
- & e_2 e_2 \end \right\rangle ::=\left\langle\begin a_1^2 & a_1 a_2 e^ \\ a_1 a_2 e^& a_2^2 \end \right\rangle where angular brackets denote averaging over many wave cycles. Several variants of the coherency matrix have been proposed: the Wiener coherency matrix and the spectral coherency matrix of Richard Barakat measure the coherence of a spectral decomposition of the signal, while the Wolf coherency matrix averages over all time/frequencies. The coherency matrix contains all of the information on polarization that is obtainable using second order statistics. It can be decomposed into the sum of two idempotent matrices, corresponding to the eigenvectors of the coherency matrix, each representing a polarization state that is orthogonal to the other. An alternative decomposition is into completely polarized (zero determinant) and unpolarized (scaled identity matrix) components. In either case, the operation of summing the components corresponds to the incoherent superposition of waves from the two components. The latter case gives rise to the concept of the "degree of polarization", i.e. the fraction of the total intensity contributed by the completely polarized component. The coherency matrix is not easy to visualize, and it is therefore common to describe incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. An alternative and mathematically convenient description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852. The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations and figure below. 1852 :S_0 = I \, :S_1 = I p \cos 2\psi \cos 2\chi\, :S_2 = I p \sin 2\psi \cos 2\chi\, :S_3 = I p \sin 2\chi\, Here Ip, 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters. Note the factors of two before ψ and χ corresponding respectively to the facts that any polarization ellipse is indistinguishable from one rotated by 180°, or one with the semi-axis lengths swapped accompanied by a 90° rotation. The Stokes parameters are sometimes denoted I, Q, U and V. The Stokes parameters contain all of the information of the coherency matrix, and are related to it linearly by means of the identity matrix plus the three Pauli matrices: : \mathbf = \frac\sum_^3 S_j \mathbf,\;\mbox : \begin \mathbf &=& \begin 1 & 0 \\ 0 & 1 \end & \mathbf &=& \begin 1 & 0 \\ 0 & -1 \end \\ \\ \mathbf &=& \begin 0 & 1 \\ 1 & 0 \end & \mathbf &=& \begin 0 & -i \\ i & 0 \end \end Mathematically, the factor of two relating physical angles to their counterparts in Stokes space derives from the use of second-order moments and correlations, and incorporates the loss of information due to absolute phase invariance. The figure above makes use of a convenient representation of the last three Stokes parameters as components in a three-dimensional vector space. This space is closely related to the Poincaré sphere, which is the spherical surface occupied by completely polarized states in the space of the vector : \mathbf = \frac\begin S_1\\S_2\\S_3\end. All four Stokes parameters can also be combined into the four-dimensional Stokes vector, which can be interpreted as four-vectors of Minkowski space. In this case, all physically realizable polarization states correspond to time-like, future-directed vectors.

Propagation, reflection and scattering

In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space in time while the polarization state does not. That is: : \mathbf(z+\Delta z,t+\Delta t) = \mathbf(z, t) e^, where k is the wavenumber and positive z is the direction of propagation. As noted above, the physical electric vector is the real part of the Jones vector. When electromagnetic waves interact with matter, their propagation is altered. If this depends on the polarization states of the waves, then their polarization may also be altered. In many types of media, electromagnetic waves are decomposed into two orthogonal components that encounter different propagation effects. A similar situation occurs in the signal processing paths of detection systems that record the electric field directly. Such effects are most easily characterized in the form of a complex 2×2 transformation matrix called the Jones matrix: :\mathbf = \mathbf\mathbf. In general the Jones matrix of a medium depends on the frequency of the waves. For propagation effects in two orthogonal modes, the Jones matrix can be written as: :\mathbf = \mathbf \begin g_1 & 0 \\ 0 & g_2 \end \mathbf^, where g1 and g2 are complex numbers representing the change in amplitude and phase caused in each of the two propagation modes, and T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors. For those media in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is unitary, while those affecting amplitude without phase have Hermitian Jones matrices. In fact, since any matrix may be written as the product of unitary and positive Hermitian matrices, any sequence of linear propagation effects, no matter how complex, can be written as the a product of these two basic types of transformations.
Hermitian Paths taken by vectors in the Poincaré sphere under birefringence. The propagation modes (=rotation axes) are shown with red, blue and yellow lines, the initial vectors by thick black lines, and the paths they take by colored ellipses (which represent circles in three dimensions).
Media in which the two modes accrue a differential delay are called birefringent. Well known manifestations of this effect appear in optical wave plates/retarders (linear modes) and in Faraday rotation/optical rotation (circular modes). An easily visualized example is one where the propagation modes are linear, and the incoming radiation is linearly polarized at a 45° angle to the modes. As the phase difference starts to appear, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) with an azimuth angle perpendicular to the original direction, then through circular again (270° phase), then elliptical with the original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes (this is a consequence of the isomorphism of SU(2) with SO(3)). Examples for linear (blue), circular (red) and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. For example, this is the case with macroscopic crystals of calcite, which present the viewer with two offset, orthogonally polarized images of whatever is viewed through them. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism, often gives rise to bright colors and rainbow-like effects. Media in which the amplitude of waves propagating in one of the modes is reduced are called dichroic. Devices that block nearly all of the radiation in one mode are known as polarizing filters or simply "polarizers". In terms of the Stokes parameters, the total intensity is reduced while vectors in the Poincaré sphere are "dragged" towards the direction of the favored mode. Mathematically, under the treatment of the Stokes parameters as a Minkowski 4-vector, the transformation is a scaled Lorentz boost (due to the isomorphism of SL(2,C) and the restricted Lorentz group, SO(3,1)). Just as the Lorentz transformation preserves the proper time, the quantity det Ψ = S02-S12-S22-S32 is invariant within a multiplicative scalar constant under Jones matrix transformations (dichroic and/or birefringent). In birefringent and dichroic media, in addition to writing a Jones matrix for the net effect of passing through a particular path in a given medium, the evolution of the polarization state along that path can be characterized as the (matrix) product of an infinite series of infinitesimal steps, each operating on the state produced by all earlier matrices. In a uniform medium each step is the same, and one may write :\mathbf = Je^, where J is an overall (real) gain/loss factor. Here D is a traceless matrix such that αDe gives the derivative of e with respect to z. If D is Hermitian the effect is dichroism, while a unitary matrix models birefringence. The matrix D can be expressed as a linear combination of the Pauli matrices, where real coefficients give Hermitian matrices and imaginary coefficients give unitary matrices. The Jones matrix in each case may therefore be written with the convenient construction: :\begin \mathbf &=& J_be^ \\ \\ \mathbf &=& J_re^, \end where σ is a 3-vector composed of the Pauli matrices (used here as generators for the Lie group SL(2,C)) and n and m are real 3-vectors on the Poincaré sphere corresponding to one of the propagation modes of the medium. The effects in that space correspond to a Lorentz boost of velocity parameter 2β along the given direction, or a rotation of angle 2φ about the given axis. These transformations may also be written as biquaternions (quaternions with complex elements), where the elements are related to the Jones matrix in the same way that the Stokes parameters are related to the coherency matrix. They may then be applied in pre- and post-multiplication to the quaternion representation of the coherency matrix, with the usual exploitation of the quaternion exponential for performing rotations and boosts taking a form equivalent to the matrix exponential equations above (See: Quaternion rotation). In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In addition, if th