Abstract:
Improved optical alignment precision to a passive optical cavity is provided by including a combination of a weak focusing element and a translation plate in the input coupling optics. Adjustment of positions and angles of these optical elements, preferably after all other input optical elements are fixed in place, advantageously provides for high-precision optical alignment to the cavity, without requiring excessively tight fabrication tolerances. Fabrication tolerances are relaxed by making the optical power of the weak focusing element significantly less than the optical power of a strong focusing element in the input optics. The position and angles of the beam with respect to the cavity can be adjusted, as can the size of the beam at the cavity. Differential adjustment of the beam size in two orthogonal directions (e.g., tangential plane and sagittal plane) at the cavity can also be provided.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of US provisional patent application 60/776,396, filed on Feb. 23, 2006, entitled “Methods and Apparatus for Improved Cavity Ring-down Spectroscopy”, and hereby incorporated by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This invention relates to optical alignment in connection with cavity-enhanced spectroscopy. 
       BACKGROUND 
       [0003]    Optical spectroscopy entails passing optical radiation through a sample, often referred to an analyte, and inferring properties of the analyte from measurements performed on the optical radiation. For example, trace gas detection can be spectroscopically performed by performing measurements to detect the presence or absence of spectral absorption lines corresponding to the gas species of interest. Spectroscopy has been intensively developed over a period of many decades, and various ideas have been developed to improve performance. 
         [0004]    One such idea can be referred to as cavity-enhanced spectroscopy, in which the analyte is disposed within an optical cavity (i.e., an optical resonator). The cavity can enhance the interaction between the analyte and the optical radiation, thereby improving spectroscopic performance. For example, in cavity ring-down spectroscopy (CRDS), the absorption is measured by way of its effect on the energy decay time of an optical cavity. Increased absorption decreases the decay time, and vice versa. As another example, cavity enhanced absorption spectroscopy (CEAS) entails the use of an optical cavity to increase the sensitivity of absorption spectroscopy, in connection with direct absorption measurements. 
         [0005]    One of the noteworthy features of cavity-enhanced spectroscopy is that issues of optical alignment can arise which differ in important respects from alignment issues in other branches of optics. More specifically, a key alignment issue faced in many implementations of cavity enhanced spectroscopy is selectively exciting the lowest order mode of a passive optical cavity with an external optical source while minimizing excitation of the higher order modes of the cavity. The theoretical condition for providing such selective mode excitation is well known in the art, and is often referred to as “mode matching”. For example, suppose radiation in the lowest order mode of an optical cavity would be emitted from the cavity as a Gaussian beam having certain parameters (e.g., waist size w 0 , waist position z 0 ) along a beam axis L. In this example, radiation provided to the cavity as a Gaussian beam with waist size w 0  and waist position z 0  along beam axis L is mode matched to the lowest order mode of the resonator, and will selectively excite the lowest order mode of the cavity. 
         [0006]    Although the theoretical condition for mode matching is well known, practical issues such as assembly tolerances and optical component tolerances can cause substantial difficulties. In this context, it is important to note that the passive cavity alignment problem is a much less forgiving single-mode alignment problem than the extensively explored problem of coupling to a single mode optical fiber or waveguide. The reason for this difference can be appreciated with a simple example where practical imperfections are assumed to cause a 1% loss of power coupled to the desired mode. 
         [0007]    In the case of fiber or waveguide coupling, this 1% of the incident light that does not couple to the desired mode is lost from the system. There is typically no degradation of performance other than the 1% loss. In the case of coupling to a passive spectroscopic cavity, the 1% of the incident light that does not couple to the desired lowest order mode can couple to one or more of the higher order modes of the cavity. Such excitation of undesired cavity modes can seriously degrade spectroscopic performance, by effectively raising the noise floor. Such an effective increase in noise is typically a much more significant performance degradation than the 1% signal loss entailed by the above assumption. 
         [0008]    Although the importance of achieving the mode matching condition is well known (e.g., as indicated in U.S. Pat. No. 5,912,790), specific methods for providing mode matching to a passive cavity in practice do not appear to have been explicitly considered in the art. US 2005/0168826 is an example where a somewhat related alignment problem is considered. In this work, an alignment system including a weak lens provides coupling of a source to a single mode waveguide. Coupling efficiency to the waveguide is enhanced by adjusting the position and angles of the weak lens during assembly. Another somewhat related problem of alignment has been considered in U.S. Pat. No. 6,563,583, where alignment is required to a multi-pass cell as opposed to an optical cavity. In this work, active feedback control is employed to measure and correct beam position and angle errors. 
         [0009]    However, it is preferable to provide the level of alignment precision needed for cavity enhanced spectroscopy with an optical system having no moving parts, to reduce cost and simplify the resulting system. Accordingly, it would be an advance in the art to provide improved mode matching to a passive optical cavity while allowing for fabrication and assembly tolerances. 
       SUMMARY 
       [0010]    Improved optical alignment precision to a passive optical cavity is provided by including a combination of a weak focusing element and a translation plate in the input coupling optics. Adjustment of positions and angles of these optical elements, preferably after all other input optical elements are fixed in place, advantageously provides for high-precision optical alignment to the cavity, without requiring excessively tight fabrication tolerances. Fabrication tolerances are relaxed by making the optical power of the weak focusing element significantly less than the optical power of a strong focusing element in the input optics. The position and angles of the beam with respect to the cavity can be adjusted, as can the size of the beam at the cavity. Differential adjustment of the beam size in two orthogonal directions (e.g., tangential plane and sagittal plane) at the cavity can also be provided. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  shows a cavity enhanced spectroscopy system according to an embodiment of the invention. 
           [0012]      FIGS. 2   a - c  show adjustment of beam position by tilting a beam translation plate. 
           [0013]      FIGS. 3   a - f  show adjustment of beam angle by laterally translating a weak lens. 
           [0014]      FIGS. 4   a - c  show adjustment of beam size by longitudinally translating a weak lens. 
           [0015]      FIGS. 5   a - c  show another example of adjustment of beam size by longitudinally translating a weak lens. 
           [0016]      FIGS. 6   a - c  show differential adjustment of beam size in the tangential and sagittal planes by tilting a weak lens. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]      FIG. 1  shows a cavity enhanced spectroscopy system  100  according to an embodiment of the invention. In this example, various optical components are affixed to a bench  102 . Bench  102  can be made of any sufficiently stable and strong material, and preferably has a low coefficient of thermal expansion (CTE). Accordingly, bench  102  preferably includes FeNi36, which is a generic designation for the steel alloy known in trade as Invar®. A first beam of optical radiation  130  is emitted from a fiber pigtail  106  coupled to an optical fiber  104  which receives radiation from a laser diode  103 . In this example, fiber  104  is preferably polarization-maintaining (PM) fiber, since it is desirable to fix the polarization of the first light beam. More specifically, it is preferable for the polarization to be TE at the cavity (i.e., electric field parallel to the surfaces of mirrors  116  and  118 ) because cavity loss can be made lower for TE polarization than for TM polarization, and for the polarization emitted from fiber  104  to be set accordingly. Isolator  112 , if present, may change the state of polarization, and any such change should be accounted for. It is also preferred for the end face of fiber pigtail  106  to be angled, to reduce back-reflection into source  103  along fiber  104 . 
         [0018]    However, practice of the invention does not depend critically on details of the optical source configuration, and any source of spatially coherent single-mode optical radiation having a temporal coherence suitable for the kind of spectroscopy being employed (e.g., narrow linewidth for continuous-wave (CW) CRDS, wide linewidth for pulsed CRDS) can be employed. Suitable sources include, but are not limited to: lasers, diode lasers, standard single mode fiber (SMF) coupled lasers, SMF coupled diode lasers, PM fiber coupled lasers, and PM fiber coupled diode lasers. 
         [0019]    First beam  130  is received by a strong focusing element  108  which provides a second beam  140 . Second beam  140  passes in succession through a weak focusing element  110 , an optional isolator  112 , and a translation plate  114  before impinging on resonator mirror  116 . Mirrors  116 ,  118  and  120  form an optical resonator (also referred to as an optical cavity). In this example, the cavity is a ring resonator, as indicated by the cavity round trip path having segments  152 ,  154 , and  156 . The resonator mirrors are affixed to a mechanical cavity housing  124 , which provides stable mechanical support to the resonator mirrors. Mechanical housing  124  can be made of any sufficiently stable and strong material, and preferably has a low CTE which is preferably matched to the CTE of bench  102 . Accordingly, mechanical housing  124  also preferably includes FeNi36 (Invar®). Radiation is emitted from the cavity as an output beam  160 , which is received by a detector  122 . The system of  FIG. 1  is suitable for performing various kinds of cavity enhanced spectroscopy, such as cavity ring-down spectroscopy (CRDS) and cavity enhanced absorption spectroscopy (CEAS). It is also suitable for performing multi-pass absorption spectroscopy where the optical cavity is replaced by a multi-pass cell, since multi-pass cells often require precise input beam alignment. Multi-pass cells can often be treated as optical cavities for purposes of analysis 
         [0020]    The example of  FIG. 1  shows a specific cavity configuration for illustrative purposes, and practice of the invention does not depend critically on the resonator configuration. In particular, the invention is applicable to both ring cavities having three or more mirrors and to standing wave cavities having two or more mirrors. 
         [0021]    The example of  FIG. 1  also show an optional isolator  112 . The purpose of isolator  112  is to prevent optical feedback from the cavity from propagating back into fiber  104  and to source  103 , since such feedback can impair performance. 
         [0022]    The cavity formed by mirrors  116 ,  118 , and  120  has a lowest order mode and also supports one or more higher order modes. It is important for second beam  140  to selectively excite the lowest order mode while minimizing excitation of the higher order modes as much as possible. Accordingly, the combination of strong focusing element  108  and weak focusing element  110  should provide an exact or approximate mode match of second beam  140  to the lowest order mode of the optical resonator. In practice, achieving an exact mode match is typically not possible, so the approximate mode match is preferably made as close to exact as possible, given assembly and fabrication tolerances. 
         [0023]    A key aspect of the present invention can be better appreciated by noting that it is possible, in principle, to mode match second beam  140  to the lowest order cavity mode using strong focusing element  108  alone, and omitting translation plate  114  and weak focusing element  110 . However, the resulting positioning tolerances on strong focusing element  108  tend to be unattainable in practice. Accordingly, a key idea of the present invention is that by introducing “extra” elements (i.e., weak focusing element  110  and translation plate  114 ), the assembly tolerances on the strong focusing element (and throughout the mode matching subsystem) can be relaxed, while still providing a very precise mode match of second beam  140  to the lowest order cavity mode. In particular, positions and angles of weak focusing element  110  and of translation plate  114  can be adjusted during assembly to minimize excitation of higher order modes (while coupling to the lowest order mode), preferably after the positions of the cavity, strong focusing element  108 , and fiber pigtail  106  have all been fixed. 
         [0024]    To accomplish this purpose, it is important that weak focusing element  110  be weak relative to strong focusing element  108 . The optical power of an optical element (in diopters) is 1/f, where f is the focal length in meters. The focal length and power are positive quantities for positive focusing elements, and are negative quantities for negative focusing elements. Typically, strong focusing element  108  is a positive lens or mirror (e.g., a collimator) since it is typically preferable to approximately collimate the diverging beam provided by most optical sources prior to any other operations on the beam. In unusual situations, a negative strong focusing element  108  can be employed. Weak focusing element  110  can be either positive or negative. Let the optical powers of the weak and strong focusing elements respectively be denoted as d w  and d s . Then |d w | is substantially less than |d s |, and preferably 0.01|d s |&lt;|d w |&lt;0.2|d s |. 
         [0025]    The limits of the preferred range can be better appreciated by considering the following two cases. If the weak focusing element is too weak, its effect on the optical beam may be too small to provide the adjustment range required to compensate for assembly and fabrication tolerances, which is undesirable. However, if the weak focusing element is too strong, its alignment tolerances will be comparable to those of the strong focusing element, which is also undesirable. The alignment precision required for a focusing element to provide a given level of beam positioning precision at the cavity scales roughly as the focal length of the focusing element. Thus a weak focusing element having a focal length 10× the focal length of a strong focusing element will have roughly a 10× larger alignment tolerance than the strong focusing element. 
         [0026]    Similarly, the translation plate  114  must be thick enough to provide adequate displacement of beam  140  through angular adjustment of the plate, but not so thick that the displacement is too sensitive to the angular adjustment. Usually, the surfaces of the translation plate will be parallel or nearly parallel, in which case rotation of the plate displaces the beam  140  but does not (significantly) change its direction. If the translation plate has a substantial wedge angle between the input and output surfaces, then rotation will change both the displacement and angle of beam  140 . 
         [0027]    Translation of the weak focusing element  110  changes both the angle of beam  140  and its displacement at the cavity mirror. A pure change in angle at the cavity mirror is accomplished by simultaneous adjustment of the weak focusing element and the translation plate. Since the translation plate will usually have (nearly) parallel surfaces, a pure change in position of the beam at the cavity mirror is, in that case, accomplished by adjustment of only the translation plate. 
         [0028]    Strong focusing element  108  can be a single optical element, or can be a combination of any number of optical elements (e.g., lenses and/or mirrors) having a “strong” optical power as described above. Similarly, weak focusing element  110  can be a single optical element, or can be a combination of any number of optical elements (e.g., lenses and/or mirrors) having a “weak” optical power as described above. It is preferable for strong focusing element  108  to be CTE matched to bench  102 . In one design, strong focusing element  108  includes two fused silica lenses in series and in close proximity, having a combined focal length of about  8  mm and acting as a collimator. In this design, the weak focusing element is a single lens which can have a focal length from about 20 mm to about 200 mm (or from about −200 mm to about −20 mm). 
         [0029]    Translation plate  114  is a transparent plate having planar and parallel or nearly parallel input and output faces. The main purpose of translation plate  114  is to provide adjustment of the position of second beam  140  at the input to the optical cavity (i.e., at mirror  116 ). Translation plate  114  can be made of any optical material. Suitable materials include glass and fused silica. 
         [0030]    In practice, the positions of fiber pigtail  106 , strong focusing element  108  and the cavity (i.e., mirrors  116 ,  118  and  120 ) are preferably fixed during a first assembly phase. If isolator  112  is present, its position is preferably also fixed during the first assembly phase. The positions and angles of weak focusing element  110  and translation plate  114  are adjusted to minimize excitation of higher-order cavity modes in a second assembly phase. Such adjustment is preferably performed by lighting up fiber  104  to excite the cavity and directly measuring the excitation of the higher-order modes. Positions and angles of weak focusing element  110  and translation plate  114  can then be adjusted to minimize the measured excitation of higher-order cavity modes. Once a minimum level of higher order mode excitation is achieved, the positions and angles of elements  110  and  114  are fixed. 
         [0031]    The combination of weak focusing element  110  and translation plate  114  advantageously provides a large number of degrees of freedom to employ in optimizing coupling to the lowest order cavity mode. We have found that such extra degrees of freedom are sufficiently helpful for optimizing cavity coupling to warrant the use of two elements for beam adjustment, even though the total number of optical elements could be reduced by employing only a single beam adjustment element. 
         [0032]    Relevant degrees of freedom (DOF) include the following: a) angular pitch and yaw of adjustment plate  114  with respect to beam  140 , primarily for adjusting the lateral position of second beam  140  with respect to the cavity (2 DOF); b) lateral translation of weak focusing element  110  with respect to beam  140 , primarily for adjusting the pitch and yaw angles of second beam  140  with respect to the cavity (2 DOF); c) longitudinal translation of weak focusing element  110  with respect to beam  140 , primarily for adjusting the waist position of beam  140  with respect to the cavity (1 DOF); and d) angular pitch and yaw of weak focusing element  110  with respect to beam  140 , primarily for providing a differential adjustment of beam waist position relative to the cavity in the tangential and sagittal planes (1 DOF).  FIGS. 2   a - 6   c  show simplified examples of how these degrees of freedom can provide the adjustments indicated above. 
         [0033]      FIGS. 2   a - c  show adjustment of beam position by tilting a beam translation plate. In each of these examples, an input beam  204  passes through a translation plate  202 . Tilting of plate  202  displaces beam  204  by refraction at the input and output surfaces, by a distance equal to, 
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         [0000]    where T is the thickness of plate  202 , n is its refractive index, and θ is the angle of incidence on plate  202 , assuming the surrounding medium has refractive index of 1 (e.g. air or vacuum). The displacement of beam  204  is in the same plane as the angle of incidence. A wedge between the input and output surfaces, if present, only introduces an angular deviation of beam  204  in the plane of the wedge angle, approximately independent of the angle of incidence.  FIG. 2   a  shows an untilted translation plate  202 , so output beam  206  is undeviated with respect to input beam  204 .  FIG. 2   b  shows translation plate  202  having a clockwise tilt, so output beam  208  is shifted to the right with respect to input beam  204 . Similarly,  FIG. 2   c  shows translation plate  202  having a counter-clockwise tilt, so output beam  210  is shifted to the left with respect to input beam  204 . Such adjustment of the beam position can be done in both lateral directions (e.g., x and y directions for a z-propagating beam), thereby providing two degrees of freedom. 
         [0034]      FIGS. 3   a - c  show adjustment of beam angle by translating a weak focusing element. In each of these examples, an input beam  304  passes through a positive weak focusing element  302 . Translation of weak focusing element  302  changes the angle of beam  304  by an amount equal to, r×d w , where d w =1/f w  is the power and r is the lateral displacement of weak focusing element  302 . The change in the angle of beam  304  is in the same plane as the translation of weak focusing element  302 .  FIG. 3   a  shows a centered weak focusing element  302 , so output beam  306  is undeviated with respect to input beam  304 .  FIG. 3   b  shows weak focusing element  302  shifted to the right with respect to beam  304 , so output beam  308  is tilted to the right with respect to input beam  304 . Similarly,  FIG. 3   c  shows weak focusing element  302  shifted to the left with respect to beam  304 , so output beam  310  is tilted to the left with respect to input beam  304 . Such adjustment of the beam angle can be done in both lateral directions (e.g., x and y directions for a z-propagating beam), thereby providing two degrees of freedom. 
         [0035]      FIGS. 3   d - f  also show adjustment of beam angle by translating a weak focusing element. In each of these examples, an input beam  304  passes through a negative weak focusing element  312 .  FIG. 3   d  shows a centered weak focusing element  312 , so output beam  306  is undeviated with respect to input beam  304 .  FIG. 3   e  shows weak focusing element  312  shifted to the left with respect to beam  304 , so output beam  308  is tilted to the right with respect to input beam  304 . Similarly,  FIG. 3   f  shows weak focusing element  312  shifted to the right with respect to beam  304 , so output beam  310  is tilted to the left with respect to input beam  304 . Thus the weak focusing element (e.g.,  110  on  FIG. 1 ) can be either positive or negative in practicing the invention. 
         [0036]      FIGS. 4   a - c  show adjustment of beam size by longitudinally translating a weak positive lens. In each of these examples, an input beam  408  is emitted from a strong focusing element  402  and passes through a weak focusing element  404  to provide an output beam.  FIG. 4   a  shows a weak lens  404  in a nominal position, and output beam  410  incident on cavity input coupler  406  (e.g., a mirror).  FIG. 4   b  shows weak lens  404  shifted toward strong focusing element  402 , thereby moving the waist of output beam  412  in the same direction. In this example, the beam size at input coupler  406  decreases. Similarly,  FIG. 4   c  shows weak lens  404  shifted away from strong focusing element  402 , thereby moving the waist of beam  414  in the same direction. Here the beam size at input coupler  406  increases. 
         [0037]    It is also possible for the relation between the change of longitudinal position of lens  404  and the increase or decrease of beam size at input coupler  406  to be opposite to that shown on  FIGS. 4   a - c.  For example,  FIGS. 5   a - c  also show adjustment of beam size by longitudinally translating a weak positive lens. In each of these examples, an input beam  508  is emitted from a strong focusing element  402  and passes through a weak focusing element  404  to provide an output beam.  FIG. 5   a  shows a weak lens  404  in a nominal position, and output beam  510  incident on cavity input coupler  406  (e.g., a mirror).  FIG. 5   b  shows weak lens  404  shifted toward strong focusing element  402 , thereby moving the waist of output beam  512  in the opposite direction. In this example, the beam size at input coupler  406  increases. Similarly,  FIG. 5   c  shows weak lens  404  shifted away from strong focusing element  402 , thereby moving the waist of beam  514  in the opposite direction. Here the beam size at input coupler  406  decreases. 
         [0038]    The principles of such beam shaping are well known to art workers, as are methods for detailed design for any particular case. In practicing the present invention, it is preferred for the longitudinal adjustment range of the weak focusing element to provide a range of beam waist positions that is sufficiently large to enable a match of beam waist size and location between the lowest order cavity mode and the beam incident on the cavity. 
         [0039]    In some cases, the lowest order cavity mode may not have the same beam profile in the two transverse directions, e.g. as a result of fabrication tolerances and/or off-axis incidence on an optical surface inside the cavity. Such a cavity mode is astigmatic, so mode matching to such a cavity can be improved by providing an input beam that at least approximately has the same kind and amount of astigmatism. Astigmatism of second beam  140  can be provided in the embodiment of  FIG. 1  by tilting weak focusing element  110  with respect to the beam. The astigmatism introduced by tilting a curved surface with respect to an optical beam is known in the art (e.g., as described in “Lasers” by Siegman on page 586). The need for such an astigmatic adjustment may also arise from an imperfect fiber facet or imperfect alignment of the strong lens  108 , causing beam  140  in  FIG. 1  to have an elliptical cross-section and/or astigmatic focusing. 
         [0040]    Such tilting of the weak focusing element can be regarded as providing a differential adjustment of beam size in the tangential and sagittal planes at the resonator input, as shown in the example of  FIGS. 6   a - c.    FIG. 6   a  shows an untilted configuration, where beam  608  is emitted from strong focusing element  402  and passes through weak lens  404  to impinge on cavity input coupler  406  as beam  610 .  FIGS. 6   b - c  show tangential and sagittal views, respectively, of a configuration in which the weak lens  404  is tilted with respect to the beam. The profiles of the beam in the tangential plane ( 612 ) and the sagittal plane ( 614 ) differ (e.g., as shown), thereby providing a differential adjustment of beam size at cavity input coupler  406 . Alternatively, this can also be regarded as providing a differential adjustment of beam waist position relative to the cavity. 
         [0041]    In this example, the tangential and sagittal planes are defined with respect to lens tilt as follows: the sagittal plane includes the axis of lens rotation, while the tangential plane is perpendicular to the axis of lens rotation. Thus for a z-propagating beam and a lens tilt that is a rotation about the y axis, the tangential plane ( FIG. 6   b ) is the x-z plane, and the sagittal plane ( FIG. 6   c ) is the y-z plane. 
         [0042]    Methods for adjusting the positions and angles of elements  110  and  114  of  FIG. 1  during assembly are well known in the art. Methods of fixing the positions of these elements once a configuration minimizing excitation of higher order cavity modes has been identified are also well known in the art.