Abstract:
A rotationally tunable time delay line device for providing a continually adjustable time delay between two orthogonally polarized laser pulses is described. The device is comprised of one or more rotational delay crystals, each made of a flat uniaxially birefringent crystal with a special orientation of its internal optical axis. The time delay generated between the two orthogonally polarized laser pulses that travel through the rotationally tunable delay line can be continually adjusted by rotating the constituent rotational delay crystals around their surface normals. An application is demonstrated in detail where the rotationally tunable time delay line device is used to form an optical autocorrelator for measuring femtosecond or picosecond duration laser pulses.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
     This application claims priority from Provisional Patent Application No. 60/998,374 filed Oct. 10, 2007 by the present inventors, which is incorporated by reference. 
    
    
     FEDERALLY SPONSORED RESEARCH 
     None 
     SEQUENCE LISTING 
     None 
     FIELD OF INVENTION 
     The present invention relates to tunable optical delay lines, specifically tunable optical delay lines that have applications in optical communications systems as well as in optical test and measurement devices, including a device known as an optical autocorrelator which is commonly used for measuring the duration of ultrashort optical pulses. 
     DISCUSSION OF PRIOR ART 
     Tunable optical delay lines are used to control the transit time of a light beam between two points. Conventionally a delay line device has been utilized in many applications including compensating time delay in pulsed laser devices, and scanning the delay of one pulse relative to another in ultrafast spectroscopy or optical coherence tomography. A typical delay line device utilizes several mirrors, and a movable stage which holds mirrors, to redirect a light path. It generally functions as follows: a first stationary mirror directs a light beam into the movable stage where it is redirected to a second stationary mirror. The total distance the light beam travels between the stationary mirrors is controlled by adjusting the movable stage. There are many ways to adjust the path length such as by a linear displacement of a stage[Kurobori T, Cho Y, Matsuo Y Opt. Commun. 40 156 (1981), Watanabe A, Tanaka S, Kobayashi H Rev. Sci. Instr. 56 2259 (1985), Watanabe A, Saito H, Ishida Y, Yajima T Opt. Commun. 69 405 (1989)], rotation of a corner reflector [Harde H, Burggraf H Opt. Commun. 38 211 (1981), Xinan G, Lambsdorff M, Kuhl J, Biachang W Rev. Sci. Instr. 59 2088 (1988)], rotation (swinging) of a two-mirror periscope [Yasa Z A, Amer N M Opt. Commun. 36 406 (1981), Baraulya V I, Kobtsev S M, Korablev A V, Kukarin S V, Yurkin, A M Techn. Progr. of IX Intern. Conf. Laser Optics&#39; (St.Petersburg, Russia, 1998), p. 79, Riffe D M, Sabbah A J Rev. Sci. Instr. 69 3099 (1998)], or rotation of a reflector of special multi-surfaced shape [C. L. Wang U.S. Pat. No. 5,907,423]. Most, if not all of these approaches require multiple mechanical components which take up significant space and require careful optical alignment that is difficult to maintain over time. 
     One common and critical application of a tunable optical delay line is in an optical autocorrelator. An optical autocorrelator is an instrument that is used to measure the temporal width of femtosecond or picosecond light pulses. In most autocorrelators a light beam of these temporally short pulses is split into two beams. One of the beams travels a fixed optical path to a detector and the other traverses a tunable optical delay line and is then recombined with the first light beam before entering the detector. By repeatedly scanning the optical delay line and recording the detector signal, the temporal width of the optical pulses can be measured. 
     The prior art most pertinent to the current invention are a patent published in 1998 by Wan [U.S. Pat. No. 5,852,620] and a publication covering the same material by Kobtsev [Kobtsev S M, Kukarin S V, Sorokin V B Digest CLEO/Europe-2000 (Nice, France, 2000, CTuK 103), p. 138] in 2000. Wan describes an optical autocorrelator that uses a specially cut birefringent crystal referred to in his patent as a “Tunable Time Plate”. The specially cut crystal explicitly removes the optical components conventionally used to split and recombine light beams in an autocorrelator by exploiting well-known optical properties of a birefringent crystal. A birefringent crystal, due to the fact that it has a unique internal axis often referred to as the optic axis or c-axis, can split a light pulse into two orthogonally polarized beams called an ordinary beam and an extraordinary beam. Referring to  FIG. 1  and  FIG. 2 , the Tunable Time Plate in the Wan patent (hereafter referred to as the Wan Time Plate) is a birefringent plate  10  that swings about the Z axis, so that the incident angle  13  of the light beam to both the plate&#39;s surface normal and the c-axis  11  is changed. Changing the angle of incidence  13  continuously varies the propagation time of the extraordinary beam  2  relative to the ordinary beam  1  through the Wan Time Plate  10  making it the act as a tunable time delay line. Note that the c-axis  11  always stays perpendicular to the rotation axis, that is the Z axis in  FIG. 1 . This is not the case in the present invention. 
     The time delay between the ordinary beam  1  and extraordinary beam  2  for the Wan Time Plate is plotted in  FIG. 3  for different cut angles  14  of the crystal c-axis relative to the surface normal  15 . A drawback of this approach is that large changes in the angle of incidence  13 , that is large swing angles, are necessary to achieve time delays commonly used in autocorrelators. For example a swing of the angle of incidence  13  of more than 50 degrees is required for a −0.2 ps delay per mm of crystal for the 0 degree case in  FIG. 3 . This is a drawback because changing the angle of incidence  13  also changes the intensity of transmitted light in both the ordinary ray  1  and extraordinary ray  2 , and an autocorrelator requires two beams of equal and constant intensity to work properly. Another drawback of this approach, as can be seen in  FIG. 3 , is that the delay of one beam relative to the other never crosses through zero. In other words the first beam is always delayed relative to the second beam by some delay time, so a second plate that acts as an constant offset delay, is needed by Wan to generate both positive and negative net delays. A further drawback of this approach is that the mechanical drive that repeatedly scans the Wan Time Plate must be of a reciprocating nature or at the very least an indirect drive mechanism which requires some complex coupling or control. 
     Therefore, it is desirable to have a new device for generating time delays in autocorrelators or pulsed laser devices, which can overcome the drawbacks of both conventional delay lines and existing tunable time plate delay line devices, as well as provide new features for time delay generation and compensation. 
     SUMMARY 
     Objects and Advantages 
     The present invention is a tunable rotational delay line, or RDL, for generation of time delays in pulsed laser devices, particularly femtosecond and picosecond pulsed laser devices. 
     It is an object of the present invention to provide a new optical delay line device for generating the time delay between two laser pulses. The new rotationally tunable delay device utilizes one or more specially manufactured crystals with a predetermined cutting angle. Each crystal is called a “rotational delay crystal” (abbreviated hereafter as RDC) and is generally round or rectangular shaped with two parallel surfaces. The RDC is positioned in the passage of one or more light beams that may be comprised of picosecond or femtosecond duration laser pulses. The optical property of the RDC causes a tim dispersion or time delay between two orthogonally polarized laser pulses. The adjustment of the time delay is achieved by rotating the RDC about its surface normal. The value of the time delay is determined by the rotation angle about the RDC surface normal, the cutting angle, the thickness, and the indices of refraction of the RDC. This time dispersion can be used to generate a time delay line in many laser apparatuses, such as a polarization mode dispersion (PMD) compensator in telecommunications, a “tripler” for second and third harmonic generation of laser light, and an autocorrelator for measuring femtosecond or picosecond duration laser pulses. 
     In one of the basic embodiments of the present invention, one RDC is used to split a light beam into orthogonally polarized components and delay one component relative to the other. The induced delay is either always negative or always positive. In an alternative embodiment two RDCs are juxtaposed and attached together to make a composite RDC, which when rotated can produce a positive or negative time delay, depending on the rotation angle of the composite RDC. 
     Either embodiment allows the rotationally tunable delay plate device to be utilized in femtosecond third harmonic generators (THG), an autocorrelator, or a PMD compensator. 
     Further novel features and other objects of the present invention will become apparent from the following detailed description, discussion and the appended claims, taken in conjunction with the drawings. 
    
    
     
       DRAWINGS  
       FIGS.  1 - 9   
         FIG. 1 . Prior art—Wan Time Plate, side view 
         FIG. 2 . Prior art—Wan Time Plate, top view 
         FIG. 3 . Prior art—Wan Time Plate, time delay versus rotation angle. 
         FIG. 4 . Rotational Delay Line showing a first orientation of a rotational delay crystal. 
         FIG. 5 . Rotational Delay Line showing a second orientation of the rotational delay crystal. 
         FIG. 6 . Rotational Delay Line with a composite rotational delay crystal. 
         FIG. 7 . Rotational Delay Line; Time Delay versus rotation angle. 
         FIG. 8   a . A first embodiment of an optical autocorrelator made from a Rotational Delay Line. 
         FIG. 8   b . A second embodiment of an optical autocorrelator made from a Rotational Delay Line. 
         FIG. 8   c . A third embodiment of an optical autocorrelator made from a Rotational Delay Line. 
         FIG. 9 . Autocorrelation trace from an autocorrelator made from an autocorrelator configured as in the autocorrelator of  FIG. 8   c.    
     
    
    
     DRAWINGS 
     References and Numerals 
     
         
           1  Prior Art: ordinary ray 
           2  Prior Art: extraordinary ray 
           10  Prior Art: Tunable Time Plate 
           11  Prior Art: crystal c-axis 
           13  Prior Art: Angle of Incidence 
           14  Prior Art: Cut angle of crystal c-axis 
           15  Prior Art: Surface normal 
           25  First embodiment of Rotational Delay Line or RDL 
           26  Uniaxial birefringent crystal or RDC 
           28  Length L of RDC 
           30  Surface normal of RDC 
           32  Internal optical axis or c-axis of first RDC  26   
           33  Angle φ between the RDC c-axis  32  and o-ray inside RDC  26   
           36  Angle of c-axis to the surface normal of RDC 
           38  Shaft or means of rotation of RDC 
           40  Second uniaxial birefringent crystal or second RDC 
           42  C-axis of second RDC 
           44  Angle of the c-axis of first RDC to the c-axis of second RDC 
           48  Rotation angle of Rotational Delay Line 
           50  Path P 1   
           50   a  o-ray inside RDC  26   
           50   b  e-ray inside RDC  26   
           52  Path P 2  of e-ray starting from point A  54  and ending at Surface S  70   
           54  Point A 
           60  incident light ray 
           62  incident ray angle θ 
           64  o-ray refraction angle, θ r    
           70  Surface S 
           100  Time Delay curve of RDL with RDC  26   
           110  Time Delay curve of RDL with RDC  40   
           120  Time Delay curve of RDL  27  with RDC  26  and RDC  40   
           124  Nearly linear region of RDL  27  Time Delay curve  120   
           140  Optical Autocorrelator 
           142  RDL in Autocorrelator  140   
           143  Circular Polarizer 
           144  Linear polarizer 
           146  Quarter Wave Plate 
           148  Incident beam into autocorrelator  140   
           149  Circularly polarized beam 
           150  One or two unit RDC of RDL  142   
           156  Focusing lens 
           158  Photodetector unit 
           160  Polarization beam splitter 
           170  Second embodiment of an autocorrelator 
           172  Quarter Wave Plate 
           174  Linear polarizer 
           180  Third embodiment of an autocorrelator 
           182  Reflector or retroreflector 
           200  Actual trace from an autocorrelator according to embodiment in  FIG. 8   c.    
       
    
     DETAILED DESCRIPTION 
     FIGS.  4 - 7   
     A. Theory of Propagation of Light in a Uniaxial Crystal 
     This section briefly summarizes some of the important optical properties of uniaxial crystals that are relevant to this invention. A uniaxial crystal has three principal crystallographic axes usually labeled as the a-, b-, and c-axis, with the c-axis being a unique axis. When a light ray enters a uniaxial crystal there are three cases of interest. 
     Case 1 
     The light ray enters traveling parallel to the c-axis. In this case the light ray is polarized perpendicular to the c-axis and is called an ordinary ray or “o-ray”. Its propagation velocity depends only on the value of the crystal&#39;s ordinary refractive index, n o . 
     Case 2 
     The light ray enters traveling perpendicular to the c-axis. In this case any component of the light ray that is polarized perpendicular to the c-axis is an o-ray, but any component of the light that is polarized parallel to the c-axis is called an extraordinary ray or “e-ray”. The propagation velocity of the e-ray is different from that of the o-ray and depends only on the value of the crystal&#39;s extra-ordinary refractive index, n e . 
     Case 3 
     The light ray enters the uniaxial crystal along a direction not parallel to the crystal c-axis. It separates into two orthogonally polarized rays: an ordinary ray or “o-ray”, and an extraordinary ray or “e-ray”. These two rays travel at slightly different velocities and in slightly different directions. The o-ray is polarized perpendicular to the c-axis and propagates at a speed dependent on the crystal&#39;s ordinary refractive index, n o . The e-ray is polarized in the plane defined by the o-ray and c-axis, and propagates at a speed that depends on n o , n e , and φ—the angle between the o-ray and the c-axis. For this general case the e-ray refractive index has an angular dependence
 
 n   e (φ)=[sin 2 (φ)/ n   e   2 +cos 2 (φ)/ n   o   2 ] −1/2   (1)
 
When φ=0 degrees, case 3 reduces to case 1. When φ=90 degrees, case 3 reduces to case 2. Since the e-ray propagation velocity depends on n e ,(φ), then equation (1) shows that the e-ray transit time through a uniaxial crystal can be changed by adjusting φ. This property is exploited in the present invention to make a tunable optical delay line.
 
     B. Rotational Delay Line Comprised of One or Two RDCs 
       FIGS. 4 and 5  show two views of a first embodiment  25  of the present invention, which is comprised of a uniaxial birefringent crystal  26  of length L  28 , having two parallel surfaces through which light will pass, and a means  38  to rotate the crystal about an axis parallel to its surface normal  30 . The crystal  26  is cut so that the internal optical axis  32  makes an angle  36  of magnitude β with surface normal  30 . Birefringent crystal  26  will hereafter be referred to as an RDC. 
     A second embodiment  27  of the present invention, shown in  FIG. 6 , has a second birefringent crystal or RDC  40  that is identical to RDC  26 . The second RDC  40  is fixed in space with respect to the first RDC  26  either by direct attachment or some other means. The second RDC  40  is rotated around the surface normal  30  by π radians with respect to first RDC  26  so that the second RDC optic axis  42  is coplanar with the first RDC optic axis  32  and surface normal  30 . The second optic axis  42  forms angle  44  of magnitude 2β with the first RDC optic axis  32 . 
     Examples of uniaxial birefringent crystals that may be used for the first RDC  26  or second RDC  40  include yttrium orthovanadate (YVO4), alpha-barium borate (alpha-BBO), quartz, and calcite. Examples of a means to rotate RDC  26  in  FIGS. 4 and 5 , or the RDC pair  26  and  40  in  FIG. 6 , include a rotation stage or a motor with a shaft attached to either the first RDC  26  or the second RDC  40 . In  FIGS. 4-6  a shaft  38  is shown as a means of rotation with the rotation angle denoted by γ  48 . 
     C Operation of Rotational Delay Line 
     An important quantity for understanding the operation of the RDL is “Time Delay”. Referring to  FIGS. 4-6 , Time Delay is defined as the difference in transit time between light that travels from point A  54  to Surface S  70  along path P 2   52  versus path P 1   50 . As will be further explained, in  FIG. 4  path P 1   50  and path P 2   52  are the same while in  FIG. 5  they are not. Correspondingly, in  FIG. 4  Time Delay is zero and in  FIG. 5  Time Delay is not zero. 
     The Rotational Delay Line  25  in  FIGS. 4 and 5 , and the Rotational Delay Line  27  in  FIG. 6 , is used by inclining the RDC  26  or RDC pair  26  and  40 , so that the surface normal  30  makes a predetermined angle θ  62  relative to incident light ray  60 . The angle of incidence θ  62  is set such that the ordinary ray refraction angle θ r    64  is equal in magnitude to the c-axis orientation angle β  36 . That is, θ  62  is set so that
 
|θ r |=|β|  (2)
 
or equivalently
 
sin (θ)= n   o  sin (β)  (3)
 
since by Snell&#39;s Law of Refraction
 
sin (θ)= n   o  sin (θ r ).  (4)
 
     In this case there is a unique rotational orientation of the RDC  26 , such as the one shown in  FIG. 4 , where a light ray enters the RDC  26  and the refracted ordinary ray  50   a  travels parallel to c-axis  32 . The propagation of a light ray inside the RDC  26  for this situation is described by Case 1 in section 6A. The propagation time from the point A  54  to the surface S  70 , which is normal to the light ray  60 , is polarization independent and the Time Delay is zero. 
       FIG. 5  shows another rotational orientation of RDC  26  in RDL  25 . The c-axis  32  makes a nonzero angle φ  33  with the o-ray  50   a . The propagation of a light ray inside the RDC  26  for this situation is described by Case 3 in section 6A and the propagation time from the point A  54  to the surface S  70  is polarization dependent. At point A  54  the incident ray  60  separates into an o-ray and an e-ray, both of which terminate at Surface S  70 . The o-ray travels along path P 1   50  and the e-ray travels along path P 2   52 . Path P 2   52  includes an e-ray segment  50   b  inside the RDC  26  that is different from the o-ray segment  50   a , which is part of path P 1   50 . The Time Delay for this orientation of the RDC  26 , is not zero. Note that path P 2   52  is different in  FIGS. 4 and 5 , while path P 1   50  is not. 
       FIG. 4  and  FIG. 5  taken together illustrate how the Rotational Delay Line  25  functions as a tunable optical delay line. Simply by rotating the RDC  26  the e-ray path P 2   52  and the corresponding Time Delay, can be varied in a smooth manner by an amount that depends only on the rotation angle γ  48 . Note that unlike the prior art of  FIG. 2 , the angle of incidence θ  62  does not change as the Time Delay line is adjusted. This is extremely important because optical alignment and reflection coefficients at surfaces change with angle of incidence  13  in the prior art, but not in this invention. 
     The plane of polarization of the e-ray rotates as RDC  26  rotates and therefore for RDL  25  in  FIGS. 4 and 5 , or for the RDL  27  in  FIG. 6  to function as a single polarization delay line there must be a means of maintaining the input polarization of incident ray  60  in the plane defined by the o-ray  50   a  and c-axis  32 . This can be done in many ways such as by rotating the input polarization plane with a half wave plate. If ray  60  is not polarized in the plane defined by the o-ray  50   a  and c-axis  32  it will separate in to two rays, an o-ray and e-ray, as described earlier. 
     In some situations, such as in an optical autocorrelator, it is necessary that the incident beam  60  is polarized such that it will split into two orthogonally polarized rays of equal intensity, regardless of the rotational orientation of the first RDL  25  or second RDL  27 . This can be guaranteed by placing a circular polarizer, comprised of a polarizer and quarter wave plate, in the incident beam path  60  in front of RDC  26 . 
       FIG. 7  shows a curve  100  which is the result of a calculation of the Time Delay as a function of rotation angle γ  48 . The curve  100  can be derived using formalism presented in optics textbooks which cover the topic of propagation of light in anisotropic media, such as “Principle of Optics” by M. Born and E. Wolf. For the exemplary calculated curve  100 , incidence angle θ  62  is 30 degrees, RDC  26  is made from a birefringent material YVO4 with refractive indices n o =1.9447 and n e =2.1486. Relative to surface normal  30 , the c-axis orientation angle β  36  is 14.9 degrees. When the rotation angle γ  48  is zero, the Time Delay is zero, but at all other values of γ  48  the Time Delay is positive. 
     Curve  110  in  FIG. 7  shows the Time Delay, in the absence of RDC  26 , in RDC  40  as a function of γ  48 . The curve  110  is the same as curve  100  except shifted by 180 degrees due to the 180 degree rotation of the second RDC  40  relative to the first RDC  26 . When both RDC  26  and RDC  40  are present as in  FIG. 6 , the Time Delay is curve  120 , which is the difference between curve  110  and curve  100   
     The maximum value of the time delay in curve  120  is ±175 femtoseconds per mm length of YVO4. A larger maximum time delay is achievable in three ways:
         1) use a larger crystal thickness L  28 ;   2) use a different material with refractive indices n o  and n e  that result in a larger maximum Time Delay per mm of crystal;   3) use a larger internal c-axis angle β  32 .       

     Curve  120  has some important advantages as compared to the prior art of  FIG. 3 . Unlike the prior art of  FIG. 3  curve  120  shows a Time Delay that
         1) can be tuned to a positive or negative amount.   2) is symmetric with respect to the zero delay value.   3) is nearly linear as a function of rotation angle γ over a large tuning range  124  including in the range where the curve crosses zero.       

     These features are important in certain applications such as the delay line in an optical autocorrelator. 
     REDUCTION TO PRACTICE OF ROTATIONAL DELAY LINE  
     FIGS.  8 - 9   
     Application of Rotational Delay Line in an Optical Autocorrelator 
     An optical autocorrelator is an instrument that is used to measure the temporal width of femtosecond or picosecond light pulses. In most autocorrelators a periodic light beam of these temporally short pulses is split into two beams. One of the beams travels a fixed optical path to a detector and the other traverses a tunable optical delay line and is then recombined with the first light beam before entering the detector. By repeatedly scanning the optical delay line and recording the detector signal the width of the optical pulses can be measured. 
       FIG. 8   a  shows an embodiment of an optical autocorrelator  140  using a Rotational Delay Line  142 . RDL  142  can be either the RDL  25  in  FIG. 4  or the RDL  27  in  FIG. 6 . The autocorrelator  140  has a circular polarizer  143  comprised of a linear polarizer  144  and quarter wave plate  146  that prepares an incident beam  148  to have circular polarization. If the incident beam  148  is linearly polarized then the linear polarizer  144  is not necessary. If a polarizer  144  is used it can be of the plate type or a cubic polarization beam splitter. The circularly polarized beam gets decomposed in to two orthogonally polarized components of equal intensity as it enters the RDL  142 . The incident beam  148  emerges after traveling through the RDL  142  and is focused with a lens  156  onto a photodetector unit  158  that is either a photodetector that detects two-photon absorption, or is a combination of a second harmonic crystal and photodetector fitted with an appropriate optical filter, that detects only the second harmonically generated light. The photodetector signal is recorded as the RDC unit  150  rotates, and an autocorrelation trace is obtained. 
     There are many variations of optical autocorrelator  140 .  FIG. 8   b  shows an embodiment of an autocorrelator  170  where a second quarter wave plate  172  and second polarizer  174  are used at the output of RDL  142  to insure that only one polarization of light is incident on photodetector unit  158 . Either polarizer  144  or polarizer  174  can be replaced by an equivalent function polarization beam splitter 
       FIG. 8   c  shows an embodiment of autocorrelator  180  where a reflector or retroreflector  182  is used to send the light back through RDL  142 . The second pass through the RDC unit  150  doubles the generated Time Delay Range of RDL  142 , and when a reflector is used this embodiment also has the advantage of removing the small spatial displacement between the two orthogonally polarized temporally displaced beams. A polarization beam splitter  160  is used in place of polarizer  144 . A lens  156  and photodetector unit  158  are positioned to receive the retroreflected beam. 
       FIG. 9  shows a repetitive interferometric autocorrelation trace  200  acquired from an autocorrelator constructed according to the embodiment  180  in  FIG. 8   c . In this case an RDL constructed according to the RDL embodiment  27  in  FIG. 6  was used and a motor was used as the means to rotate the RDC pair  150 . The repetitive autocorrelation trace  200  recorded from an oscilloscope attached to the photodetector output displays all the features expected of an interferometric autocorrelator and the measured laser pulses were found to have a pulse width of about 100 femtoseconds. 
     Although specific embodiments of the present invention have been described with reference to the drawings, it should be understood that such embodiments are a subset of the possible specific embodiments which can represent applications of the principles of the present invention. Various changes and modifications obvious to one skilled in the art to which the present invention pertains are deemed to be within the spirit, scope and contemplation of the present invention as further defined in the appended claims.