Photonic bandgap apparatus and method for delaying photonic signals

Apparatus for delaying photonic signals of predetermined frequency and predetermined bandwidth by a predetermined delay, comprising:

• a predetermined plurality of first and second alternating layers which exhibit a series of photonic bandgaps, said first and second alternating layers having predetermined thicknesses and having predetermined indices of refraction, wherein said predetermined plurality, said predetermined thicknesses and said predetermined indices of refraction cooperate to produce a photonic band edge transmission resonance in said plurality of first and second alternating layers, having a photonic band edge transmission resonance center frequency corresponding to said predetermined frequency, and a corresponding photonic band edge transmission resonance bandwidth which is at least as wide as said predetermined bandwidth, to thereby impart said predetermined delay to said photonic signals which pass therethrough,
• wherein said predetermined thicknesses and said predetermined plurality are described by a solution of the following two simultaneous equations:
• 1/T.sub.12 =›1+cos .pi./N cos .pi./(2N)!/›1- cos (.pi..DELTA..omega./.omega..sub.0) cos (.pi..omega./.omega..sub.0)!
• 1/T.sub.12 =›sin .pi./N sin .pi./(2N)!/›sin (.pi..DELTA..omega./.omega..sub.0) sin (.pi..omega./.omega..sub.0)!,
• where T.sub.12 =4n.sub.1 n.sub.2 /(n.sub.1 +N.sub.2).sup.2, n.sub.1 is the index of refraction of said first alternating layers, n.sub.2 is the index of refraction of said second alternating layers, N is said predetermined plurality, .omega..sub.0 is the mid-gap frequency of said photonic bandgap structure, and a=.pi.c/(2.omega..sub.0 n.sub.1) and b=.pi.c/(2.omega..sub.0 n.sub.2), where a is said predetermined thickness of said first alternating layers, b is said predetermined thickness of said second alternating layers and c is the free space speed of light.

A method of delaying photonic signals of predetermined frequency and predetermined bandwidth by a predetermined delay, comprising the steps of:

• directing the photonic signals into a predetermined plurality of first and second alternating layers which are generally parallel and which exhibit a series of photonic bandgaps, said first and second alternating layers having predetermined thicknesses and having predetermined indices of refraction, wherein said predetermined plurality, said predetermined thicknesses and said predetermined indices of refraction cooperate to produce a photonic band edge transmission resonance in said plurality of first and second alternating layers, having a photonic band edge transmission resonance center frequency corresponding to said predetermined frequency, and a corresponding photonic band edge transmission resonance bandwidth which is at least as wide as said predetermined bandwidth, to thereby impart said predetermined delay to said photonic signals which pass therethrough;
• wherein said directing step comprises directing the photonic signals into the plurality of first and second alternating layers such that the photonic signals propagate in a direction generally perpendicular to the plurality of first and second alternating layers;
• and
• receiving the delayed electromagnetic pulses which emerge from said predetermined plurality of first and second alternating layers.

A method of delaying photonic signals of predetermined frequency and predetermined bandwidth by a predetermined delay, comprising the steps of:

• directing the photonic signals into a predetermined plurality of first and second alternating layers which exhibit a series of photonic bandgaps, said first and second alternating layers having predetermined thicknesses and having predetermined indices of refraction, wherein said predetermined plurality, said predetermined thicknesses and said predetermined indices of refraction cooperate to produce a photonic band edge transmission resonance in said plurality of first and second alternating layers, having a photonic band edge transmission resonance center frequency corresponding to said predetermined frequency, and a corresponding photonic band edge transmission resonance bandwidth which is at least as wide as said predetermined bandwidth, to thereby impart said predetermined delay to said photonic signals which pass therethrough, wherein said predetermined thicknesses and said predetermined plurality are described by a solution of the following two simultaneous equations:
• 1/T.sub.12 =›1+cos .pi./N cos .pi./(2N)!/›1- cos (.pi..DELTA..omega./.omega..sub.0) cos (.pi..omega./.omega..sub.0)!
• 1/T.sub.12 =›sin .pi./N sin .pi./(2N!/›sin (.pi..DELTA..omega./.omega..sub.0) sin (.pi..omega./.omega..sub.0 !,
• where T.sub.12 =4n.sub.1 n.sub.2 /(n.sub.1 +n.sub.2).sup.2, n.sub.1 is the index of refraction of said first alternating layers, n.sub.2 is the index of refraction of said second alternating layers, N is said predetermined plurality, .omega..sub.0 is the mid-gap frequency of said photonic bandgap structure, and a=.pi.c/(2.omega..sub.0 n.sub.1) and b=.pi.c/(2.omega..sub.0 n.sub.2), where a is said predetermined thickness of said first alternating layers, b is aid predetermined thickness of said second alternating layers and c is the free space speed of light;
• and
• receiving the delayed electromagnetic pulses which emerge from said predetermined plurality of first and second alternating layers.

Apparatus for delaying photonic signals of predetermined frequency and predetermined bandwidth by a predetermined delay, comprising:

• a predetermined plurality of unit cells which exhibit a series of photonic bandgaps, said plurality of unit cells being generally parallel and including a first unit cell and a last unit cell, said predetermined plurality of unit cells each having a predetermined thickness and having variable index of refraction which varies across said predetermined thickness, wherein said predetermined plurality and said predetermined thickness cooperate to produce a photonic band edge transmission resonance in said plurality of unit cells, having a photonic band edge transmission resonance center frequency corresponding to said predetermined frequency, and a corresponding photonic band edge transmission resonance bandwidth which is at least as wide as said predetermined bandwidth, to thereby impart said predetermined delay to said photonic signals which pass therethrough
• means for directing said photonic signals into said first unit cell such that said photonic signals propagate in a direction generally perpendicular to said plurality of unit cells;
• and
• means for receiving the delayed photonic signals which emerge from said last unit cell.

A method of delaying photonic signals of predetermined frequency and predetermined bandwidth by a predetermined delay, comprising the steps of:

• directing the photonic signals into a predetermined plurality of unit cells which are generally parallel and which exhibit a series of photonic bandgaps, said predetermined plurality of unit cells each having a predetermined thickness and having variable index of refraction which varies across said predetermined thickness, wherein said predetermined plurality and said predetermined thickness cooperate to produce a photonic band edge transmission resonance in said plurality of unit cells, having a photonic band edge transmission resonance center frequency corresponding to said predetermined frequency, and a corresponding photonic band edge transmission resonance bandwidth which is at least as wide as said predetermined bandwidth, to thereby impart said predetermined delay to said photonic signals which pass therethrough,
• wherein said directing step comprises directing the photonic signals into the plurality of unit cells such that the photonic signals propagate in a direction generally perpendicular to the plurality of unit cells;
• and
• receiving the delayed electromagnetic pulses which emerge from said predetermined plurality of unit cells.