Definition: the frequency dependence of the group velocity in a medium, or (quantitatively) the derivative of the inverse group velocity with respect to angular frequency

See also: chromatic dispersion, group delay dispersion, group velocity mismatchand other articles in the categories general optics, fiber optics and waveguides, light pulses

For optical fibers (e.g. in the context of optical fiber communications), the group velocity dispersion is usually defined as a derivative with respect to wavelength (rather than angular frequency). This can be calculated from the above-mentioned GVD parameter:

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Of St. George, Ontario fell asleep in the Lord peacefully at Brantford General Hospital on December 8, 2023 at the age of 73. This came quickly and unexpectedly, but as a faithful believer in Jesus, Pat took great comfort in the hope of the resurrection. Loving husband of Susan, cherished father of Lisa (Bill) and Melanie (Tim) and beloved stepfather of Dennis (Abby) and Andrew (Carly). Adoring grandfather of Olivia, Aiden, Owen, Silas, Kylie, Wayde, Wesley, Lydia, Landen, and Vayda. Brother of Jennifer, Alexis, and Jeff (Lily). Predeceased by his father Alexander and mother Patricia, sister Marie, stepson Michael, and daughter-in-law Sarah. Born in Calcutta, India in 1950, Pat immigrated to Canada with his family at age 14. He began his career at the Texaco refinery in Port Credit in 1973, transferred to the Nanticoke refinery in 1978, and worked at that site until his retirement in 2005. Patrick was celebrated by his colleagues not only for his strong work ethic and high standards, but also for the mentorship he provided for so many. In “retirement” he continued to lend his expertise as a consultant on refinery projects in Canada for another 15 years. If Pat worked hard, he played harder. He loved water sports, backpacking, and more than anything, his children, grandchildren, and nieces and nephews. Together with Susan, they created their “happy place”, a property on Sparrow Lake, enjoyed by their family, right in the place they first met. Pat created incredible experiences and memories with his family and friends that will be treasured for a lifetime.

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Group velocity dispersion is the phenomenon that the group velocity of light in a transparent medium depends on the optical frequency or wavelength. The term can also be used as a precisely defined quantity, namely the derivative of the inverse group velocity with respect to the angular frequency (or sometimes the wavelength):

I am wondering about the example numbers you are giving here. Specifically the −26 fs2/mm at 1500 nm; by using the calculator, I get 2.25 · 103 fs2/m. Why is there a difference or am I missing something here?

The calculator is not calculating the chromatic dispersion of silica, but only converting chromatic dispersion values given with different units. The value which you obtain just resulted from the conversion of the original value of −1.88 ps/(nm km) to the other units.

The group velocity dispersion is the group delay dispersion per unit length. The basic units are s2/m. For example, the group velocity dispersion of silica is +35 fs2/mm at 800 nm and −26 fs2/mm at 1500 nm. Somewhere between these wavelengths (at about 1.3 μm), there is the zero-dispersion wavelength.

A celebration of Patrick’s life will be held at the Dwayne D. Budgell Funeral Home, 1105 Rest Acres Road, in Paris, Ontario on Saturday, December 16th, 2023 at 11 am with a reception to follow. The service will be live streamed and will be available online starting at 10:50 am. In lieu of flowers, a memorial donation to Agape in Action would honor Pat’s life and memory and would be gratefully appreciated by the family.

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It is important to realize the different signs of GVD and Dλ, resulting from the fact that a long wavelength corresponds to a smaller optical frequency. In order to avoid confusion, the terms normal and anomalous dispersion can be used instead of positive and negative dispersion. Normal dispersion implies that the group velocity decreases for increasing optical frequency; this occurs in most cases.

This quantity is usually specified with units of ps/(nm km) (picoseconds per nanometer wavelength change and kilometer propagation distance). For example, 20 ps/(nm km) at 1550 nm (a typical value for telecom fibers) corresponds to −25 509 fs2/m.

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