Abstract:
An optical system and associated method are provided. Included is a first branch capable of allowing light to pass therethrough in a forward direction and a reverse direction. The first branch includes a first medium with a first refractive index (n 1 ), and a first end and a second end. Also included is a second branch capable of allowing light to pass therethrough in the forward direction. The second branch includes a second medium with a second refractive index (n 2 , with n 2 &lt;n 1 ), and a first end and a second end. The second end of the second branch is further coupled to the first branch to form an angle (θ 2 ). In use, θ 1 ≦sin −1 (n 2 /n 1 ) in order to prevent the light passing through the first branch in the reverse direction from passing into the second branch, where θ 1  is the incident angle of the light passing in the reverse direction from the first branch to the second branch.

Description:
FIELD AND BACKGROUND OF THE INVENTION 
   The present invention relates to optics, and more particularly to optical isolators. 
   BACKGROUND OF THE INVENTION 
   An optical isolator is a 1×1 unidirectional connector. It allows light to travel along a path in one direction only but not in the reverse direction within an optical system. 
   Optical isolators are typically employed in bulk optical systems to eliminate one of two counter-propagating electro-magnetic light waves. An optical isolator is comparable with a diode having a low electrical resistance for the forward current from its input to its output and a very high resistance for the reverse current from its output to its input. Analogous, a forward light wave, fed via the optical input port of an optical isolator to its output port, is guided with low loss, and a reverse light wave, i.e. a light wave being fed to the isolator&#39;s optical output port, is attenuated such that only a very small amount thereof leaves the isolator via its input port. Such an optical isolator has a unidirectional transmittance property, and cuts off most of the light fed back into its output port. 
   The “non-reciprocity principle” may be applied to such optical devices to achieve the required isolation. The non-reciprocity principle refers to the fact that an optical signal transmits only in the forward direction but not in reverse. An ideal optical isolator is based on this non-reciprocity principle. 
   A Faraday rotator is one prior art optical isolator, which employs a magnetic-optic element as a non-reciprocal component. Unfortunately, such prior art optical isolator exhibits many difficulties. Not only is its function polarization dependent, but it is also difficult to be integrated with other optical devices. 
   DISCLOSURE OF THE INVENTION 
   An optical system and associated method are provided. Included is a first branch capable of allowing light to pass therethrough in a forward direction and a reverse direction. The first branch includes a first medium with a first refractive index (n 1 ), and a first end and a second end. Also included is a second branch capable of allowing light to pass therethrough in the forward direction. The second branch includes a second medium with a second refractive index (n 2 , with n 2 &lt;n 1 ), and a first end and a second end. The second end of the second branch is further coupled to the first branch to form an angle (θ 2 ). In use, θ 1 ≧sin −1 (n 2 /n 1 ) to utilize the total reflection principle to prevent the light passing through the first branch in the reverse direction from passing into the second branch, where θ 1  is the incident angle of the light passing in the reverse direction from the first branch to the second branch. 
   In some embodiments, the first branch and the second branch may be components of a Y-junction, a K-junction, and/or an X-junction. 
   As an option, the first branch may include an optical absorber for absorbing the reverse light that is prevented from passing into the second branch by the total reflection. In another embodiment, an optical choker may be positioned at one of the ends of one of the branches for increasing isolation. 
   In use, the isolation provided between the first branch and the second branch is polarization independent. As an option, a numerical aperture of one of the ends of one of the branches may be lowered for increasing the isolation. Moreover, a transmitting area of one of the branches may be decreased for increasing the isolation. Still yet, an optical choker may be positioned at one of the ends of one of the branches for increasing the isolation. 
   In various embodiments, the optical system may function as an optical isolator and/or an optical attenuator. Optionally, both the first branch and the second branch may have a substantially rectangular cross-section. 
   Still yet, the first branch and the second branch may be components of a first optical isolator. Optionally, a wavelength selector may be coupled to the optical isolator to form a de-multiplexer. 
   Further, a second optical isolator may be integrated with the first optical isolator. Thus, an optical coupler may be formed. When the optical coupler is formed, such may optionally function as an add-multiplexer, an optical inserter or a polarization beam combiner. Moreover, the optical coupler may include a Y-splitter. 
   In another embodiment, the first optical isolator and the second optical isolator may be integrated with a third optical isolator to form an optical circulator with 3 ports. In the same manner, an N-port optical circulator can be built. An optional wavelength selector may also be coupled to the circulator to form a de-multiplexer. 
   Each of the foregoing embodiments may be made of a very simple structure and have numerous optional features: ruggedness, superb thermal and environmental properties, premium stability and reliability, and excellent optical performance that are independent of polarization. Moreover, they may be easily integrated with other optical and opto-electronic devices. Each of them may be built with one or a combination of the waveguide, optical fiber, micro-optic, and photonic crystal technologies. 
   Moreover, the optical system may be designed to function as a polarizer. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1   a ,  1   b ,  1   c ,  1   d ,  1   e ,  1   f ,  1   g  and  1   h  each show an optical isolator/attenuator of one embodiment. 
       FIGS. 1   i  and  1   j  show a modified output port of  FIGS. 1   a  and  1   b.    
       FIGS. 2   a  and  2   b  show the optical coupler/inserter/add-multiplexer/polarization beam combiner of one embodiment. 
       FIG. 3  represents an optical circulator of one embodiment. 
       FIG. 4  exhibits a 2×2 optical coupler with isolation among its inputs and outputs. 
       FIG. 5  depicts an optical polarizer of one embodiment. 
       FIGS. 6   a  and  6   b  illustrate an optical de-multiplexer of one embodiment. 
       FIG. 7  displays the magnified Y-junction of branches  14  and  15  in  FIG. 1   a.    
       FIG. 8  illustrates an optical choker of one embodiment. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIGS. 1   a ,  1   b ,  1   c ,  1   d ,  1   e ,  1   f ,  1   g  and  1   h  each show an optical isolator/attenuator of one embodiment. Specially, each optical isolator/attenuator represents an optical device with a pair of ends. In the context of the present description, such ends may be any termination or intermediate reference points. For example, such ends may include an input port  18  and an output port  19 . 
   Optical isolators  301   a ,  301   c  and  301   e  of  FIGS. 1   a ,  1   c  and  1   e , respectively, comprise a Y-junction coupler made from two branches  14  and  15  of different refraction indices. In the context of the present description, a branch may refer to any medium capable of allowing light to pass therethrough. Referring to  FIG. 1   a , branch  15  extends in a horizontal (first) direction, and includes a first end  15   1 , a second end  15   2 , and a side edge  15   3  extending between first end  15   1  and second end  15   2  in the horizontal (first) direction. Similarly, branch  14  includes a first end  14   1 , a second end  14   2 , and a side edge  14   3  extending between first end  14   1  and second end  14   2  in a diagonal (second) direction. The second end  14   2  of branch  14  abuts the side edge  15   3  of branch  15  such that the interface is parallel to the branch  15  (i.e., horizontal), and forms an incidence angle θ 1  relative to the side edge, and the side edge  14   3  of the second branch  14  forms an angle (θ 2 ) with the first side edge  15   3  of the first branch  15 . 
   Optical isolators  301   b ,  301   d ,  301   f  of  FIGS. 1   b ,  1   d  and  1   f , respectively, comprise a K-junction. Moreover, optical isolators  301   g ,  301   h  of  FIGS. 1   g  and  1   h , respectively, comprise an X-Junction. Then an extra port (i.e. port  21 ) is available for monitoring output (i.e. port  19 ) as well as for feedback control of these optical isolators. 
   At the Y-junction of the optical isolators  301   a ,  301   c ,  301   e  (or K- or X-Junction in the other figures), the refraction index (n 1 ) of the branch  15  is greater than that (n 2 ) of the branch  14 . An optical unidirectional Y-junction (K- or X-Junction) coupler may then be constructed using the total reflection principle. This ensures that light travels only in the forward direction. Incoming light from port  18  travels through branch  14 , reaches branch  15  and through it to exit port  19 . And for the reverse direction, light entering from port  19  passes through branch  15 , meets the interface between the second end  14   2  of branch  14  and the side edge  15   3  of branch  15  with incident angle θ 1  (cf.  FIG. 7 ), but is blocked by the total reflection phenomenon because the condition of θ 1 ≧sin −1 (n 2 /n 1 ) is met. Thus, light cannot get into branch  14  but stays in branch  15 . In the end, it either exits from port  22  or is consumed by an optional absorber  17 . The following examples are estimations made based on the plane wave approximation: 
   EXAMPLE 1 
   Case 1) 
   For  FIGS. 1   a  and  1   b : given the refraction indexes n 1 =1.465, n 2 =1.460, n 3 =1.455 and θ 2 =85.30°, then the calculated insertion loss is ˜0.13 dB with ILp=0.129 dB and ILs=0.133 dB. The polarization dependent loss (i.e. ILs−ILp) is ˜0.004 dB and the isolation is ˜9 dB. 
   Case 2) 
   For  FIGS. 1   c  and  1   d : given the refractive indexes n 1 =1.465, n 1c =1.460, n 2 =1.4625, n 2c =1.4575 and θ 2 =86.70°, then the calculated insertion loss is ˜0.13 dB with ILp=0.133 dB and ILs=0.136 dB. The polarization dependent loss is ˜0.003 dB while the isolation is also ˜9 dB. 
   Thus, the isolation is polarization independent (ILp≈ILs). However, the isolation of ˜9 dB is below expectation. In Case 1 of Example 1 above, although with ideally parallel incident light, the numerical aperture of the output light NA(n 1 , n 3 ) is 0.171 at the output port  19  while the other numerical apertures are: NA(n 2 , n 3 )=0.121, NA(n 1 , n 2 )=0.121. Since NA (n 1 , n 3 ) is greater than NA (n 1 , n 2 ), a portion of the reverse light from Port  19  is able to get into port  18 . This is because the incident angle of some reverse light θ 1 (as in  FIG. 7 ) is smaller than the total reflection critical angle θ 1c , causing the isolation to be low. The resultant isolation is dependent on the effectiveness of the total reflection for the reverse light. The better the effectiveness of the total reflection for the reverse light, the higher the isolation. 
   One optional way to achieve higher isolation is to lower the numerical aperture of the output port  19 . Additional optical output ports  301   i  and  301   j  are illustrated by  FIGS. 1   i  and  1   j  respectively. For the optical output port  301   i , calculations indicate that for 97% of the output light, the numerical aperture has dropped to 0.121 (NA(n 2 , n 3 )). For the other 3%, the numerical aperture is still 0.171 (NA(n 1 , n 3 )). Removing this 3% of output light decreases the NA to 0.121, but it increases the insertion loss by 0.13 dB while the area of the output light is enlarged. For the optical output port  301   j , the optimal calculations generated essentially the same results but with an output area that is larger than that of  301   i . Although the output numerical aperture has been lowered, the isolation is not improved since the extra reverse light due to the enlarged area of port  19  is getting into port  18 . 
   One can use an X-Junction to lower the numerical aperture of the output port  19  (see, for example,  FIG. 1   g ). The following examples are pertinent to the embodiment of  FIG. 1   g.    
   EXAMPLE 2 
   For  FIG. 1   g : given the refraction indexes n 1 =1.500, n 1c =1.4958, n 2 =1.450 n 2c =1.4457, θ 2 =85° and θ 1 =76°, the calculated insertion loss are ILp=1.24 dB and ILs=1.39 dB. The polarization dependent loss is ˜0.15 dB, the numerical aperture of the output port  19  is low and thus the isolation greatly increases to ˜12 dB. 
   Another way of improving isolation for  301   a ,  301   b ,  301   c ,  301   d ,  301   e  and  301   f  is to decrease the transmitting area of the reverse light from branch  15  to branch  14 . If it is reduced to one half, the isolation increases by 3 dB, and by 6 dB if it is reduced to one fourth. And if all the reverse light were reflected at the junction of branches  15  and  14 , then the isolation becomes perfect. Therefore, one may add an optical choker  1  to port  18 ,  19 , as shown in  FIGS. 1   e ,  1   f  and  1   h . The optical choker  1  serves two purposes: (1) it lowers the numerical aperture NA, for example from 0.171 to 0.1 or even 0.01 (2) it converges the light to the center part of branches  14  and  15 . The resultant optical isolators  301   e ,  301   f  and  301   h  of  FIGS. 1   e ,  1   f  and  1   h  have much better optical performance and still can be easily cascaded and integrated. 
   Optical isolators  301   a ,  301   b ,  301   c ,  301   d ,  301   e ,  301   f ,  301   g  and  301   h  may also function as an optical attenuator. Light coming in from port  18  exits from port  19  with a fixed amount of attenuation. See Example 3: 
   EXAMPLE 3 
   In the context of Example 1, if the input light numerical aperture NA was 0.12 and θ 2 =85°, the attenuation of both the p- and s-polarization are ≈4.3 dB and their difference is almost zero (0.009 dB). 
   Therefore, the attenuation is polarization independent. Calculations indicate that the smaller the angle θ 2 , the larger the attenuation. The attenuation can be varied with the changing incident angle θ 2 . Thus, a variable optical attenuator is also feasible. 
   Optical isolator  301   a ,  301   b ,  301   c ,  301   d ,  301   e ,  301   f ,  301   g  and  301   h , based on the total reflection principle, have a very simple structure and result in numerous improvements: its ruggedness, its superior thermal and environmental properties, its exceptional stability and reliability, and its excellent polarization independent optical performance. Moreover, it is easily integrated with other optical and opto-electronic devices. These qualities make it suitable to construct other optical devices such as a coupler, inserter, polarization beam combiner, circulator, add-multiplexer, and de-multiplexer. 
   To optimize the optical isolators  301   a ,  301   b ,  301   c ,  301   d ,  301   e ,  301   f ,  301   g  and  301   h , the shape of the Y-, K- or X-Junction may be changed. Different refractive index n 1  and n 2  of branches  15  and  14  may be obtained (from different dielectric materials or the same dielectric material with different effective refractive index from tapered shape). The refractive index may not necessarily be constant, but rather be a function of position x, y, and z. The cross section of branches (waveguide or optical fibers, etc.) may, in one embodiment, be square or rectangular. 
   Thus, one embodiment is based on the non-reciprocal phenomenon of total reflection and can be polarization independent and ideally suited for integration. According to Snell&#39;s law of optical refraction, total reflection occurs when light propagates from an optically denser medium (with a higher refractive index n 1 ) into another less dense medium (with a lower refractive index n 2 ), and the incident angle θ 1  exceeds the critical value θ 1C , that is θ 1 ≧θ 1C =sin −1  (n 2 /n 1 ). 
   As a result, all the incident light is reflected back into the first medium, and the transmitted light is totally blocked. Since n 1  is greater than n 2 , n 2  must not be greater than n 1 . Thus, the total reflection is non-reciprocal and it occurs only when light travels from n 1  medium into n 2  medium, but never occurs for the reverse direction from n 2  medium into n 1  medium. Utilizing total reflection, one may build optical isolators  301   a ,  301   b ,  301   c ,  301   d ,  301   e ,  301   f ,  301   g  and  301   h . Any combination of suitable branches could constitute as the optical transmission path and can be easily integrated with other opto-electronic devices (e.g. semiconductor devices). 
     FIGS. 2   a  and  2   b  represent an optical coupler  302   a  and  302   b  built by cascading a series of optical isolators  301   e ,  301   f  and  301   h  together (for simplification, the K- and X-Junction type and the optical chokers  1  are not shown). Lights from input ports  18 ,  20  travel to output port  19 . Shown are 2×1 couplers with isolation function. Optical coupler  302   a  and  302   b  may also be used as polarization beam combiner with isolation because of their polarization independent performance. Optical couplers  302   a  and  302   b  also work as add-multiplexer to add an extra channel of signal (λ j ) from port  20  to an existing channel of signals (λ 1 ,λ 2  . . . ) from input port  18  without interfering each other, and outputs all signals (λ 1 ,λ 2  . . . λ j ) from port  19 . An N×1 add-multiplexer may be built using the same approach. Moreover, optical couplers  302   a  and  302   b  also work as an optical inserter (with isolation) for an optical fiber amplifier device with the optical signal connected to port  18 , the pump laser connected to port  20 , and the output port  19  connected to a fiber amplifier (not shown). 
     FIG. 3  depicts an optical circulator  303  built with three optical isolators  301   e ,  301   f , and  301   h  without absorbers (again for simplification, the K- and X-Junction type and the optical chokers  1  are not shown). Light entering at port  28  travels along and leaves at the next port  29 . In a similar manner, light from port  29  may exit port  30 , and so on. The circulator  303  is also polarization independent. Optical circulators with 4 or more ports can be built in the same way. 
     FIG. 4  shows a 2×2 optical coupler  304 . It comprises a 2×1 optical coupler  302   a  (or  302   b ) and a Y-splitter. Light coming from ports  18  and  20  travels to the output ports  19  and  21 . Shown is a 2×2 optical coupler with isolation among the input ports and output ports. In principle, an N×M optical coupler with isolation may even be built. 
     FIG. 5  illustrates a polarizer  305  with an input port  18 , an output port  19  and an optional absorber  17 . See Example 4: 
   EXAMPLE 4 
   Given n 1 =4.25, n 1c =4.248, n 2 =1.460, n 2c =1.455, θ 2 =71.04°, and θ 1 =19°, the resulting attenuation of the p-polarization light is A p =2.2×10 −9  dB whereas attenuation of the s-polarization is A s =4.2 dB at port  21 . 
   The attenuation is therefore very much polarization dependent. Input light from port  18  with intensity (p, s), where p is the intensity of p-polarization and s is the intensity of s-polarization respectively, travels through the branch  14  to reach the junction. On one hand, it refracts into branch  15  and continues on to exit port  21  with intensity (p, 0.38s). On the other hand, it reflects into branch  13  and continues on to output port  19  with intensity (0, 0.62s). Port  19  is the output port of the polarized light. 
   The insertion loss of the polarizer  305  is low at 2.07 dB. Consequently, it does not have good isolation. But, an optical isolator  301   a ,  301   b ,  301   c ,  301   d ,  301   e ,  301   f ,  301   g  and  301   h  can be integrated to build a polarizer  305  with good isolation. 
     FIG. 6   a  exhibits a de-multiplexer  306   a . It consists of an isolator  301   e  ( 301   f  or  301   h ) but without the absorber  17 , and a wavelength selector  61 . The wavelength selector  61  may be a band pass filter or a Bragg Gratings (with fiber or waveguide technology). Light signals with wavelength (λ 1 , λ 2 , λ 3  . . . ) coming from input port  18  travel through the output port  19  to reach the wavelength selector  61 . Then, the selected wavelength (e.g. λ 1 ) is reflected and exits from port  22 . The other signals with wavelength (λ 2 , λ 3  . . . ) are transmitted through the selector  61  without loss. 
   Similarly,  FIG. 6   b  displays a de-multiplexer  306   b . It includes a circulator  303  and a wavelength selector  61 . Optionally, the add-multiplexers  302   a  and  302   b  and de-multiplexers  306   a  and  306   b  can be cascaded together to construct an add-/drop-multiplexer (not shown). 
     FIG. 7  is a magnified Y-junction of branches  14  and  15  of the optical isolator  301   a . The incident ray of light  34  passes through the isolator  301   a . On its way, it is reflected r 21  and refracted t 21  at B 0 , again reflected r 13  and refracted t 13  at C 1 , and then again at B 1 , C 2 , B 2 , . . . and so on according to the Fresnel&#39;s formulae. For the most intensity of the incident light  34  to pass from the branch  14  into the branch  15 , 2h tan θ 1 &gt;d may be satisfied, where d and h are the width of branches  14  and  15  respectively. The transmission coefficient is t ij =2p i /(p i +p j ), the reflection coefficient is r ij =(p i −p j )/(p i +p j ) where p i =n i /cosθ i  for the TM wave, p i =n i  cosθ i  for the TE wave and i, j=1, 2, 3 for medium n 1 , n 2 , n 3 . Then, the transmissivity of region I is T=p 3 |t| 2 /p 1  where t=t 21 t 13 /(1−r 13   2 e i2β ). The phase difference of the adjacent transmitted lights E 1  and E 2  is 2β=(4πhn 1  cosθ 1 )/λ 0  where λ 0  is the light wavelength in vacuum. If θ 2 ≧θ 2c =sin −1 (n 3 /n 2 ), internal total reflections occur at C 1 , C 2  . . . B 1 , B 2  . . . and p 3  becomes a pure imaginary number. Hence the time average of the transmissivity T is zero. Similarly, the time average of the reflectivity R (R 1 , R 2 , . . . ) is also zero with the exception of R 0 =r 21   2 . Since the energy flux of R 0  can be very small and it almost always escapes into n 3  medium, it does not add to the reflection loss of the optical isolator. 
     FIG. 8  illustrates an optical choker  800  of one embodiment. 
   In another embodiment, a computer program operates on a set of input parameters and desired output parameters associated with an optical system under design. Given such inputs, the computer program calculates and simulates the optical system, optimizes it so the resultant outputs meet the desired conditions such as the power, isolation, insertion loss, polarization, polarization dependent loss, return loss, etc. Optionally, the various concepts and equations set forth hereinabove may be incorporated into the computer program for being calculated accordingly. 
   While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of a preferred embodiment should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.