Abstract:
An optical modulator that performs wide bandwidth optical modulation by using multiple Fabry-Perot resonant modes, and an apparatus for capturing a three-dimensional image including the optical modulator are provided. The optical modulator may include: a substrate; a first contact layer disposed on the substrate; a bottom distributed Bragg reflective (DBR) layer disposed on the first contact layer; an active layer disposed on the bottom DBR layer and includes a multiple quantum well layer; a top DBR layer disposed on the active layer; a cavity layer disposed in the top DBR layer; and a second contact layer disposed on the top DBR layer. Since the optical modulator achieves both a high contrast ratio and a wide bandwidth by using two or more Fabry-Perot resonant modes, the optical modulator may show a stable performance even when a resonant wavelength is changed during manufacture or due to an external environment such as temperature.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority from Korean Patent Application No. 10-2010-0137229, filed on Dec. 28, 2010 in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference. 
       BACKGROUND 
       [0002]    1. Field 
         [0003]    Apparatuses and methods consistent with exemplary embodiments relate to optical modulators and apparatuses for capturing three-dimensional (3D) images, and more particularly, to optical modulators which may perform wide bandwidth optical modulation by using multiple Fabry-Perot resonant modes, and apparatuses for capturing 3D images including the optical modulators. 
         [0004]    2. Description of the Related Art 
         [0005]    An image captured by a general camera does not include information about distance. In order to realize an apparatus for capturing a three-dimensional (3D) image such as a 3D camera, an additional unit for measuring a distance from a plurality of points on a surface of an object is required. 
         [0006]    Distance information about an object is generally obtained by using a binocular stereovision method using two cameras or a triangulation method using structured light and a camera. However, according to the two methods, the accuracy of the distance information is sharply reduced when a distance between an object and a camera increases. Also, these methods are dependent on a surface state of the object and, thus, precise distance information may not be obtained. 
         [0007]    In order to obtain more precise distance information, a time-of-flight (TOF) method has been introduced. The TOF method irradiates a laser beam on an object and measures a TOF of a light until the light is received by a light receiver after being reflected off the object. According to the TOF method, light having a certain wavelength, such as near infrared rays of 850 nm, is projected to the object by using a light-emitting diode (LED) or a laser diode (LD), such that the light receiver receives a light having the same wavelength and reflected from the object, and then special processes are performed to extract distance information. Various TOF methods based on such a series of processes have been suggested. For example, a TOF method using direct time measurement involves measuring a time taken for a pulse light to be projected to an object and reflected from the object by using a timer. Also, a TOF method using correlation involves projecting a pulse light to an object and measuring a distance by using information about brightness of a light that is reflected from the object. A TOF method using phase delay measurement involves projecting a light having a continuous sinusoidal wave to an object and detecting a phase difference of a light reflected from the object to calculate a distance. 
         [0008]    Also, there are many examples of the phase delay measurement. From among them, for example, external modulation involves performing amplitude modulation on a reflected light by using an optical modulator, capturing the modulated reflected light by using an image sensor, and measuring a phase delay. It is easy to obtain a high resolution distance image by using the external modulation. The external modulation method, however, requires an optical modulator capable of modulating a light at a high speed of several tens to several hundreds of MHz in order to obtain a precise phase delay. Accordingly, various types of optical modulators, such as an image intensifier including a multi-channel plate (MCP), a thin modulator device using an electro-optic (EO) material, and a gallium arsenide (GaAs)-based solid modulator device have been suggested. 
         [0009]    For example, the image intensifier includes a photocathode for converting a light into electrons, an MCP for amplifying the number of electrons, and a phosphor for converting the electrons back to light. However, the image intensifier occupies a large volume, uses a high voltage of several kV, and is expensive. Also, the thin modulator device using the EO material uses a refractive index change of a nonlinear crystalline material according to a voltage as an operating principle. Such a thin modulator device using the EO material is thick and also requires a high voltage. 
         [0010]    Recently, a GaAs semiconductor-based modulator that is easily manufactured, small, and operable with a low voltage has been suggested. The GaAs semiconductor-based modulator includes a multiple quantum well (MQW) layer disposed between a P-electrode and an N-electrode, and uses a phenomenon of the MQW layer absorbing a light when a reverse bias voltage is applied to each end of the P- and N-electrodes. The GaAs-based modulator has advantages in that it may operate at high speed, has a relatively low driving voltage, and has a high reflectivity difference (i.e., contrast ratio) during on/off cycles. However, a bandwidth of a modulator of the GaAs semiconductor-based optical modulator is about 4 nm to about 5 nm, which is very narrow. A 3D camera uses several light sources, and there are differences between center wavelengths of the light sources. Also, a center wavelength of a light source may change according to temperature. Similarly, a center absorption wavelength of an optical modulator changes according to a process variable during manufacture and temperature. Accordingly, in order to apply the optical modulator to the 3D camera, the optical modulator needs to be capable of performing wide bandwidth optical modulation. However, since there is a trade-off between a reflectivity difference during on/off cycles and a bandwidth, it is difficult to increase both the reflectivity difference during on/off cycles and the bandwidth. 
       SUMMARY 
       [0011]    Aspects of one or more exemplary embodiments provide optical modulators having a high contrast ratio and a wide bandwidth by using multiple Fabry-Perot resonant modes. 
         [0012]    Moreover, aspects of one or more exemplary embodiments provide apparatuses for capturing three-dimensional (3D) images including the optical modulators. 
         [0013]    Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the presented embodiments. 
         [0014]    According to an aspect of an exemplary embodiment, there is provided an optical modulator including: a bottom reflective layer; an active layer that is disposed on the bottom reflective layer and including a multiple quantum well layer; a top reflective layer that is disposed on the active layer; and at least one cavity layer that is disposed in the top reflective layer, wherein, when a center wavelength of an incident light to be modulated is λ, each of the active layer and the at least one cavity layer has an optical thickness that is an integer multiple of λ/2 in order to form an individual resonant cavity. 
         [0015]    The optical thickness of the active layer may be 2λ, and the optical thickness of the at least one cavity layer may be λ/2. 
         [0016]    One cavity layer may be disposed in the top reflective layer, wherein the top reflective layer includes a first top reflective layer that is disposed on the active layer, the one cavity layer that is disposed on the first top reflective layer, and a second top reflective layer that is disposed on the one cavity layer. 
         [0017]    A phase of a light directly reflected from the second top reflective layer may be π, and a phase of each of a light resonated in the one cavity layer and then reflected from the first top reflective layer and a light resonated in the active layer and then reflected from the bottom reflective layer may be 0. 
         [0018]    Each of the bottom reflective layer, the first top reflective layer, and the second top reflective layer may be a distributed Bragg reflective (DBR) layer that is formed by repeatedly alternately stacking a first refractive index layer and a second refractive index layer with different refractive indices, each of the first and second refractive index layers having an optical thickness of λ/4. 
         [0019]    The one cavity layer may be formed of a material of the first refractive index layer or a material of the second refractive index layer. 
         [0020]    If the one cavity layer is formed of the material of the first refractive index layer, the second refractive index layer of the first top reflective layer may be disposed under the one cavity layer to contact the one cavity layer, and the second refractive index layer of the second top reflective layer may be disposed above the one cavity layer to contact the one cavity layer. 
         [0021]    If the one cavity layer is formed of the material of the second refractive index layer, the first refractive index layer of the first top reflective layer may be disposed under the one cavity layer to contact the one cavity layer and the first refractive index layer of the second top reflective layer may be disposed above the one cavity layer to contact the one cavity layer. 
         [0022]    The first refractive index layer may include Al x Ga 1-x As, the second refractive index layer may include Al y Ga 1-y As, and 0&lt;x&lt;1, 0&lt;y&lt;1, and x&lt;y. 
         [0023]    A reflectivity of the bottom reflective layer may be about 98% to 99%, a reflectivity of the first top reflective layer may be about 90%, and a reflectivity of the second top reflective layer may be about 60% to 70%. 
         [0024]    Two Fabry-Perot resonant modes may occur due to the active layer and the one cavity layer, and center values of two resonant wavelengths may be equal to the center wavelength λ of the incident light to be modulated. 
         [0025]    Two cavity layers may be disposed in the top reflective layer, wherein the top reflective layer includes a first top reflective layer that is disposed on the active layer, a first cavity layer that is disposed on the first top reflective layer, a second top reflective layer that is disposed on the first cavity layer, a second cavity layer that is disposed on the second top reflective layer, and a third top reflective layer that is disposed on the second cavity layer. 
         [0026]    A phase of a light directly reflected from the third top reflective layer may be π, a phase of a light resonated in the second cavity layer and then reflected from the second reflective layer may be 0, a phase of a light resonated in the first cavity layer and reflected from the first top reflective layer may be π, and a phase of a light resonated in the active layer and then reflected from the bottom reflective layer may be 0. 
         [0027]    Each of the bottom reflective layer and the first through third top reflective layers may be a DBR layer that is formed by repeatedly alternately stacking a first refractive index layer and a second refractive index layer with different refractive indices, each of the first and second refractive index layers having an optical thickness of λ/4. 
         [0028]    The first cavity layer may be formed of a material of the first refractive index layer or a material of the second refractive index layer, and the second cavity layer may be formed of the material of the first refractive index layer or the material of the second refractive index layer. 
         [0029]    If the first cavity layer is formed of the material of the first refractive index layer, the second refractive index layer of the first top reflective layer may be disposed under the first cavity layer to contact the first cavity layer and the second refractive index layer of the second top reflective layer may be disposed above the first cavity layer to contact the first cavity layer. 
         [0030]    If the first cavity layer is formed of the material of the second refractive index layer, the first refractive index layer of the first top reflective layer may be disposed under the first cavity layer to contact the first cavity layer and the first refractive index layer of the second top reflective layer may be disposed above the first cavity layer to contact the first cavity layer. 
         [0031]    If the second cavity layer is formed of the material of the first refractive index layer, the second refractive index layer of the second top reflective layer may be disposed under the second cavity layer to contact the second cavity layer and the second refractive index layer of the third top reflective layer may be disposed above the second cavity layer to contact the second cavity layer. 
         [0032]    If the second cavity layer is formed of the material of the second refractive index layer, the first refractive index layer of the second top reflective layer may be disposed under the second cavity layer to contact the second cavity layer and the first refractive index layer of the third top reflective layer may be disposed above the second cavity layer to contact the second cavity layer. 
         [0033]    A reflectivity of the bottom reflective layer may be about 98% to 99%, a reflectivity of the first top reflective layer may be about 91%, a reflectivity of the second top reflective layer may be about 93%, and a reflectivity of the third top reflective layer may be about 46%. 
         [0034]    Three Fabry-Perot resonant modes may occur due to the active layer and the first and second cavity layers, and center values of three resonant wavelengths may be equal to the center wavelength λ of the incident light to be modulated. 
         [0035]    When an exciton absorption wavelength due to the active layer is λ EX  and a shortest resonant wavelength from among resonant wavelengths of Fabry-Perot resonant modes generated due to the at least one cavity layer is λ FP1 , λ EX +10 nm&lt;λ FP1 . 
         [0036]    The active layer may include a plurality of barrier layers and a plurality of quantum well layers which are alternately disposed. 
         [0037]    When an incident angle of the incident light on a surface of the top reflective layer is θ t0 , a refraction angle of the incident light on the top reflective layer is θ t1 , and a refraction angle of the incident light on the active layer is θ t2 , thicknesses of the first and second refractive index layers and a thickness of the cavity layer may be increased by a multiple of a reciprocal of cos(θ t1 ) and a thickness of the active layer may be increased by a multiple of a reciprocal of cos(θ t1 ). 
         [0038]    The optical modulator may further include: a first contact layer that is disposed under the bottom reflective layer; a substrate that is disposed under the first contact layer; and a second contact layer that is disposed above the top reflective layer. 
         [0039]    According to an aspect of another exemplary embodiment, there is provided an optical modulator array including: an insulating frame; a plurality of the optical modulators within the insulating frame; a trench surrounding each of the optical modulators; a first electrode that is disposed on a bottom surface of the trench; a second electrode that is disposed on a top surface of each of the optical modulators; a first electrode pad that is disposed on a top surface of the insulating frame and is electrically connected to the first electrode; and a second electrode pad that is disposed on the top surface of the insulating frame and is electrically connected to the second electrode. 
         [0040]    The optical modulator array may further include an insulating film that surrounds a sidewall of the optical modulators. 
         [0041]    The optical modulator array may further include an adhesive layer that is disposed between the first electrode pad and the insulating frame and between the second electrode pad and the insulating frame. 
         [0042]    A first contact layer, which is disposed under the bottom reflective layer of the optical modulator, may be disposed on the bottom surface of the trench, and the first electrode may be disposed on the first contact layer. 
         [0043]    The first electrode may extend along a sidewall of the trench to be electrically connected to the first electrode pad. 
         [0044]    The second electrode may have a lattice shape. 
         [0045]    The second electrode may have a fishbone shape or a matrix shape. 
         [0046]    According to an aspect of another exemplary embodiment, there is provided an apparatus for capturing a 3D image, the apparatus including: a light source that projects a light to an object; the optical modulator that modulates a light reflected from the object; an imager that captures a light modulated by the optical modulator and generates an image; and a calculator that calculates a distance to the object by using the image generated by the imager. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0047]    These and/or other aspects will become apparent and more readily appreciated from the following description of exemplary embodiments, taken in conjunction with the accompanying drawings of which: 
           [0048]      FIG. 1  is a cross-sectional view illustrating an optical modulator according to an exemplary embodiment; 
           [0049]      FIG. 2  is a cross-sectional view for explaining an operation of the optical modulator of  FIG. 1 ; 
           [0050]      FIG. 3  is a graph illustrating a reflectivity of the optical modulator of  FIG. 1  and a total phase of a reflected light according to a wavelength of an incident light when no voltage is applied to the optical modulator; 
           [0051]      FIG. 4  is a table showing optimal materials and thicknesses of layers of the optical modulator of  FIG. 1 , according to an exemplary embodiment; 
           [0052]      FIG. 5  is a table showing optimal materials and thicknesses of layers of the optical modulator of  FIG. 1 , according to another exemplary embodiment; 
           [0053]      FIG. 6  is a graph illustrating a reflectivity when no voltage is applied to the optical modulator and a reflectivity when a voltage is applied to the optical modulator according to an exemplary embodiment; 
           [0054]      FIG. 7  is a graph illustrating a reflectivity difference when no voltage is applied and a voltage is applied to the optical modulator of  FIG. 4  or  5 ; 
           [0055]      FIG. 8  is a cross-sectional view for explaining an operation of an optical modulator including two cavity layers in a top distributed Bragg reflective (DBR) layer, according to another exemplary embodiment; 
           [0056]      FIG. 9  is a table showing optimal materials and thicknesses of the optical modulator of  FIG. 8 ; 
           [0057]      FIG. 10  is a graph illustrating a reflectivity when no voltage is applied to the optical modulator of  FIG. 9  and a reflectivity when a voltage is applied to the optical modulator; 
           [0058]      FIG. 11  is a graph illustrating a reflectivity difference when no voltage is applied and when a voltage is applied to the optical modulator of  FIG. 9 ; 
           [0059]      FIG. 12  is a cross-sectional view illustrating an optical path according to an incident angle of an obliquely incident light incident on the optical modulator of  FIG. 4 ,  5 , or  9 ; 
           [0060]      FIG. 13  is a table showing optimal materials and thicknesses of a modified optical modulator of the optical modulator of  FIG. 4 , which considers an obliquely incident light according to an exemplary embodiment; 
           [0061]      FIGS. 14 and 15  are graphs illustrating operation characteristics of the modified optical modulator of  FIG. 13 ; 
           [0062]      FIG. 16  is a cross-sectional view illustrating an example where a light is focused by a lens on a surface of an optical modulator according to an exemplary embodiment; 
           [0063]      FIG. 17  is a plan view illustrating an optical modulator array including an array of optical modulators according to an exemplary embodiment; 
           [0064]      FIG. 18  is a cross-sectional view taken along line A-A′ of  FIG. 17 ; 
           [0065]      FIG. 19  is a cross-sectional view taken along line B-B′ of  FIGS. 17 ; and 
           [0066]      FIG. 20  is a view illustrating an apparatus for capturing a three-dimensional (3D) image including the optical modulator array of  FIG. 17  according to an exemplary embodiment. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0067]    Exemplary embodiments will now be described more fully with reference to the accompanying drawings. In the drawings, like reference numerals denote like elements, and sizes of elements may be exaggerated for clarity. 
         [0068]      FIG. 1  is a cross-sectional view illustrating an optical modulator  100  according to an exemplary embodiment. Referring to  FIG. 1 , the optical modulator  100  may include a substrate  101 , a first contact layer  102  disposed on the substrate  101 , a bottom distributed Bragg reflective (DBR) layer  110  disposed on the first contact layer  102 , an active layer  120  disposed on the bottom DBR layer  110  and having a multiple quantum well layer structure, a top DBR layer  130  disposed on the active layer  120 , a cavity layer  132  disposed in the top DBR layer  130 , and a second contact layer  140  disposed on the top DBR layer  130 . 
         [0069]    The substrate  101  may be formed of, for example, undoped gallium arsenide (GaAs). The first contact layer  102 , which is a layer for connecting to an electrode (not shown) for applying a voltage to the active layer  120 , may be formed of, for example, silicon-doped n-GaAs. Also, the second contact layer  140 , which is a layer for connecting to another electrode (not shown) for applying a voltage to the active layer  120 , may be formed of, for example, a beryllium (Be)-doped p-GaAs. 
         [0070]    Each of the bottom DBR layer  110  and the top DBR layer  130  has a structure in which a low refractive index layer with a relatively low refractive index and a high refractive index layer with a relatively high refractive index are repeatedly alternately stacked. For example, each of the bottom and top DBR layers  110  and  130  may include pairs of the high refractive index layer and the low refractive index layer respectively including Al x Ga 1-x As and Al y Ga 1-y As, where 0&lt;x&lt;1, 0&lt;y&lt;1, and x&lt;y. For example, each of the bottom and top DBR layers  110  and  130  may have a structure in which Al 0.31 Ga 0.69 As and Al 0.84 Ga 0.16 As are repeatedly stacked, or Al 0.5 Ga 0.5 As and AlAs are repeatedly stacked. 
         [0071]    If a light having a specific wavelength is incident on the bottom and top DBR layers  110  and  130  constructed as described above, reflection occurs on an interface between two layers with different refractive indices (that is, the high refractive index layer and the low refractive index layer) in the bottom and top DBR layers  110  and  130 . In this case, a high reflectivity is achieved by enabling phase differences of all reflected lights to be the same. To this end, an optical thickness, which is obtained by multiplying a physical thickness by a refractive index of a corresponding layer, of each layer in the bottom and top DBR layers  110  and  130  is adjusted to be an odd multiple of λ/4 (where λ is a wavelength of an incident light to be modulated). A reflectivity of each of the bottom and top DBR layers  110  and  130  increases as the number of times pairs of the high refractive index layer and the low refractive index layer increases. Also, each of the bottom and top DBR layers  110  and  130  acts as a path through which current flows to be transmitted to the active layer  120 . To this end, the bottom DBR layer  110  may be, for example, a Si-doped n-DBR layer, and the top DBR layer  130  may be, for example, a Be-doped p-DBR layer. 
         [0072]    The active layer  120 , which is a layer for absorbing a light, has a multiple quantum well layer structure in which a plurality of quantum well layers and a plurality of barrier layers are repeatedly stacked. For example, the active layer  120  may include barrier layers each formed of Al 0.31 Ga 0.69 As and quantum well layers each formed of GaAs. The active layer  120  may also act as a cavity for Fabry-Perot resonance. To this end, an optical thickness of the active layer  120  may be adjusted to be equal to an integer multiple of λ/2. Accordingly, a light having a wavelength λ may be sufficiently absorbed in the active layer  120  while being resonated between the bottom DBR layer  110  and the top DBR layer  130 . For example, an optical thickness of the active layer  120  may be 2.0*λ. In general, as a thickness of the active layer  120  increases, an absorptivity increases and a driving voltage increases, and as a thickness of the active layer  120  decreases, an absorptivity decreases and a driving voltage decreases. 
         [0073]    The cavity layer  132  is further disposed in the top DBR layer  130 . The cavity layer  132  acts as an additional micro cavity for Fabry-Perot resonance. To this end, an optical thickness of the cavity layer  132  may be adjusted to be equal to an integer multiple of λ/2. For example, an optical thickness of the cavity layer  132  may be λ/2. The cavity layer  132  may be formed of a single material. For example, a material of the cavity layer  132  may be the same as that of the high refractive index layer (e.g., Al 0.31 Ga 0.69 As or Al 0.5 Ga 0.5 As) of the top DBR layer  130  or that of the low refractive index layer (e.g., Al 0.84 Ga 0.16 As or AlAs) of the top DBR layer  130 . Also, the cavity layer  132  is p-type doped to transmit current to the active layer  120 , like the top DBR layer  130 . 
         [0074]    The top DBR layer  130  is divided into two parts by the cavity layer  132 . That is, a first top DBR layer  131  is disposed under the cavity layer  132  and a second top DBR layer  133  is disposed above the cavity layer  132 . In this case, in the entire structure including the first top DBR layer  131 , the cavity layer  132 , and the second top DBR layer  133 , an order in which the high refractive index layer and the low refractive index layer are repeatedly stacked is maintained. For example, if the cavity layer  132  is formed of a material of the high refractive index layer, a layer disposed under the cavity layer  132  to contact the cavity layer  132  is the low refractive index layer of the first top DBR layer  131 , and a layer disposed above the cavity layer  132  to contact the cavity layer  132  is the low refractive index layer of the second top DBR layer  133 . If the cavity layer  132  is formed of a material of the low refractive index layer, a layer disposed under the cavity layer  132  to contact the cavity layer  132  is the high refractive index layer of the first top DBR layer  131 , and a layer disposed above the cavity layer  132  to contact the cavity layer  132  is the high refractive index layer of the second top DBR layer  133 . In this regard, the cavity layer  132  can be considered such that any one of a plurality of the high refractive index layers and the low refractive index layers in the top DBR layer  130  is formed to have an optical thickness of λ/2, not λ/4. 
         [0075]      FIG. 2  is a cross-sectional view for explaining an operation of the optical modulator  100  of  FIG. 1 . Referring to  FIG. 2 , the optical modulator  100  includes three reflective layers, that is, the bottom DBR layer  110 , the first top DBR layer  131 , and the second top DBR layer  133 . Furthermore, the optical modulator  100  includes two resonant cavities, that is, the active layer  120  and the cavity layer  132 . The active layer  120  acts as a main resonant cavity, and the bottom DBR layer  110  and the first top DBR layer  131  are respectively disposed under and above the active layer  120  for Fabry-Perot resonance. Also, the cavity layer  132  acts as an additional micro-resonant cavity, and the first top DBR layer  131  and the second top DBR layer  133  are respectively disposed under and above the cavity layer  132  for Fabry-Perot resonance. Although both the active layer  120  and the cavity layer  132  act as resonant cavities, light absorption occurs only in the active layer  120  having a multiple quantum well layer structure and the cavity layer  132  only causes Fabry-Perot resonance. 
         [0076]    In this structure, when a light is incident on a top surface of the optical modulator  100 , three reflective lights with different phases are generated. That is, a light directly reflected from the second top DBR layer  133  has a phase of π, a light resonated in the cavity layer  132  and then reflected from the first top DBR layer  131  and a light resonated in the active layer  120  and then reflected from the bottom DBR layer  110  have a phase of 0. Accordingly, the light reflected from the second top DBR layer  133  is offset by the lights reflected from the first top DBR layer  131  and the bottom DBR layer  110 . To this end, a position of the cavity layer  132  in the top DBR layer  130  and reflectivities of the reflective layers, the bottom, first, and second DBR layers  110 ,  131 , and  133 , may vary by design. For example, the bottom DBR layer  110  may have a reflectivity of 98% to 99% for a light having a wavelength of about 850 nm in order to maximize light absorption in the active layer  120 , and a reflectivity of the second top DBR layer  133  may be about 60% to 70% and a reflectivity of the first top DBR layer  131  may be about 90% in order for part of a light to reach the active layer  120 . Also, a reflected light may have a desired phase by adjusting the number of pairs of the high refractive index layer and the low refractive index layer in the first top DBR layer  131  and the number of pairs of the high refractive index layer and the low refractive index layer in the second top DBR layer  133 . 
         [0077]    As described above, since the optical modulator  100  according to the present exemplary embodiment has two resonant cavities, there are two Fabry-Perot resonant modes.  FIG. 3  is a graph illustrating a reflectivity of the optical modulator  100  of  FIG. 1  and a total phase of a reflected light according to a wavelength of an incident light when no voltage is applied to the optical modulator  100 . As shown in  FIG. 3 , two Fabry-Perot resonant modes occur around about 850 nm. That is, center values of two Fabry-Perot resonant wavelengths λ FP1  and λ FP2  are equal to 850 nm, which is a wavelength of an incident light to be modulated. Also, a total phase of reflected lights is 0 at around the two Fabry-Perot resonant wavelengths λ FP1  and λ FP2 , and a large phase shift of about 360 degrees occurs in a narrow section of about 10 nm between the two resonant wavelengths λ FP1  and λ FP2 . Also, exciton absorption by the quantum well layers in the active layer  120  occurs at a wavelength λ EX  of about 837 nm. 
         [0078]      FIG. 4  is a table showing optimal materials and thicknesses of layers of the optical modulator  100  of  FIG. 1 , according to an exemplary embodiment. The optical modulator  100  illustrated in  FIG. 4  is designed to have a center absorption wavelength of about 850 nm by using a GaAs compound semiconductor. Referring to  FIG. 4 , the second contact layer  140 , which acts as a p-contact layer, is formed of p-GaAs. Since a GaAs material has a low surface oxidation rate and a small band gap, it is easy to form an Ohmic contact to form an electrode by using the GaAs material. A thickness of the second contact layer  140  may be about 100 Å in consideration of light absorption. 
         [0079]    The second top DBR layer  133  disposed under the second contact layer  140  has a structure in which a high refractive index layer  130   a  and a low refractive index layer  130   b  are sequentially stacked downward. The high refractive index layer  130   a  may be formed of, for example, Al 0.31 Ga 0.69 As with a refractive index of about 3.413. In this case, a thickness of the high refractive index layer  130   a  may be about 623 Å. Thus, an optical thickness of the high refractive index layer  130   a  may be λ/4 (=850 nm/4=physical thickness×refractive index (=623 Å×3.413)). Also, the low refractive index layer  130   b  may be formed of, for example, Al 0.84 Ga 0.16 As with a refractive index of about 3.102. In this case, a thickness of the low refractive index layer  130   b  may be about 682 Å. Thus, an optical thickness of the low refractive index layer  130   b  may be λ/4 (=850 nm/4=physical thickness x refractive index (=682 Å×3.102)). In  FIG. 4 , the second top DBR layer  133  has 3.5 pairs of the high refractive index layer  130   a  and the low refractive index layer  130   b.  That is, the high refractive index layer  130   a  and the low refractive index layer  130   b  are sequentially repeatedly stacked 3 times downward and the high refractive index layer  130   a  is further disposed. 
         [0080]    The cavity layer  132  is disposed under the second top DBR layer  133 . Since the high refractive index layer  130   a  is a lowermost layer of the second top DBR layer  133 , the cavity layer  132  may be formed of Al 0.84 Ga 0.16 As, as the low refractive index layer  130   b.  In this case, in order to have an optical thickness of λ/2, a thickness of the cavity layer  132  may be about 1364 Å. 
         [0081]    Also, the first top DBR layer  131  is disposed under the cavity layer  132 . Like the second top DBR layer  133 , the first top DBR layer  131  also has a structure in which the high refractive index layer  130   a  and the low refractive index layer  130   b  are repeatedly stacked. Since the cavity layer  132  is formed of the same material as that of the low refractive index layer  130   b , the high refractive index layer  130   a  is a first layer disposed under the cavity layer  132 . The first top DBR layer  131  may have 17 pairs of the high refractive index layer  130   a  and the low refractive index layers  130   b,  though it is understood that another exemplary embodiment is not limited thereto. 
         [0082]    As described above, the first top DBR layer  131 , the cavity layer  132 , and the second top DBR layer  133  act as paths through which current flows. Accordingly, materials of the first top DBR layer  131 , the cavity layer  132 , and the second top DBR layer  133  may be p-doped by using Be as a dopant. A doping density may be about 8.0×10 18 /cm 3  to 1.2×10 19 /cm 3 . 
         [0083]    The active layer  120 , which absorbs a light and acts as a main resonant cavity, is disposed under the first top DBR layer  131 . The active layer  120  may include, for example, a plurality of quantum well layers  120   a  each formed of GaAs, and a plurality of barrier layers  120   b  each formed of Al 0.31 Ga 0.69 As and disposed between the plurality of quantum well layers  120   a.  For example, the active layer  120  may have a multiple quantum well layer structure including 38 quantum well layers  120   a.  A total thickness of the active layer  120  is determined such that the active layer  120  has an optical thickness of 2λ. For example, if the active layer  120  includes 38 quantum well layers  120   a,  a thickness of the quantum well layer  120   a  may be about 80 Å, and a thickness of the barrier layer  120   b  may be about 40 Å. 
         [0084]    Also, since a refractive index of GaAs, which is a material of the quantum well layer  120   a,  is about 3.702, which is high, an incident light may be reflected between the low refractive index layer  130   b  of the first top DBR layer  131  and the quantum well layer  120   a,  thereby leading to light loss. Accordingly, in order to minimize light loss and correct a thickness error of the active layer  120 , a spacer layer  121  with an intermediate refractive index may be further disposed between the low refractive index layer  130   b  of the first top DBR layer  131  and the quantum well layer  120   a  of the active layer  120 . For example, the spacer layer  121  may be formed of Al 0.31 Ga 0.69 As with a refractive index of about 3.413. For the same reason, the spacer layer  121  may be further disposed between the bottom DBR layer  110  and the active layer  120 . A thickness of the spacer layer  121  may be about 61 Å. 
         [0085]    The bottom DBR layer  110  is disposed under the active layer  120 . The bottom DBR layer  110  has a structure in which a low refractive index layer  110   b  and a high refractive index layer  110   a  are sequentially repeatedly stacked downward. The low refractive index layer  110   b  may be formed of, for example, Al 0.84 Ga 0.16 As and a thickness of the low refractive index layer  110   b  may be about 682 Å (that is, an optical thickness of the low refractive index layer  110  may be λ/4). The high refractive index layer  110   a  may be formed of, for example, Al 0.31 Ga 0.69 As, and a thickness of the high refractive index layer  110   a  may be about 623 Å. The bottom DBR layer  110  has a high reflectivity of higher than 98% in order to maximize light absorption in the active layer  120 . To this end, the bottom DBR layer  110  may include many pairs of the low refractive index layer  110   b  and the high refractive index layer  110   a.  In  FIG. 4 , the bottom DBR layer  110  has 30.5 pairs of the low refractive index layer  110   b  and the high refractive index layer  11   a . That is, after the low refractive index layer  110   b  and the high refractive index layer  110   a  are sequentially repeatedly stacked downward 30 times, the low refractive index layer  110   b  is further disposed. The bottom DBR layer  110  also acts as a path through which current flows. Accordingly, the bottom DBR layer  110  may be n-doped by using, for example, Si as a dopant. For example, a doping density may be 2.0 to 2.6×10 18 /cm 3 . 
         [0086]    Also, the first contact layer  102  formed of n-GaAs with a thickness of about 5000 Å is disposed under the bottom DBR layer  110 . The first contact layer  102  may be directly formed (i.e., disposed)on the substrate  101  formed of GaAs, or a buffer layer  102   a  formed of GaAs may be disposed between the first contact layer  102  and the substrate  101 . 
         [0087]    In  FIG. 4 , the cavity layer  132  is formed of the same material as that of the low refractive index layer  130   b  of the top DBR layer  130 . However, the cavity layer  132  may be formed of the same material as that of the high refractive index layer  130   a  of the top DBR layer  130 .  FIG. 5  is a table showing optimal materials and thicknesses of layers of the optical modulator  100  of  FIG. 1 , in which the cavity layer  132  is formed of the same material as that of the high refractive index layer  130   a,  according to another exemplary embodiment. As compared to the optical modulator  100  of  FIG. 4 , only structures of the top DBR layer  130  and the cavity layer  132  are slightly different and structures of the other layers including the active layer  120  and the bottom DBR layer  110  are the same. Accordingly, the following explanation will focus on the differences between  FIG. 4  and  FIG. 5 . 
         [0088]    Referring to  FIG. 5 , the second top DBR layer  133  has a structure in which the high refractive index layer  130   a  and the low refractive index layer  130   b  are repeatedly stacked downward. As described above, the high refractive index layer  130   a  may be formed of Al 0.31 Ga 0.69 As and may have a thickness of about 623 Å. Also, the low refractive index layer  130   b  may be formed of Al 0.84 Ga 0.16 As and may have a thickness of about 682 Å. In  FIG. 5 , the second top DBR layer  133  has 4 pairs of the high refractive index layer  130   a  and the low refractive index layer  130   b.  That is, the high refractive index layer  130   a  and the low refractive index layer  130   b  are repeatedly stacked 4 times downward. Accordingly, a lowermost layer of the second top DBR layer  133  is the low refractive index layer  130   b.    
         [0089]    The cavity layer  132  disposed under the second top DBR layer  133  may be formed of Al 0.31 Ga 0.69 As, as the high refractive index layer  130   a . In this case, in order to have an optical thickness of λ/2, a thickness of the cavity layer  132  may be about 1246 Å. The first top DBR layer  131  having a structure in which the low refractive index layer  130   b  and the high refractive index layer  130   a  are repeatedly stacked is disposed under the cavity layer  132 . Since the cavity layer  132  is formed of the same material as that of the high refractive index layer  130   a,  the low refractive index layer  130   b  is a first layer disposed under the cavity layer  132 . The high refractive index layer  130   a  and the low refractive index layer  130   b  may be repeatedly stacked, for example, 16 times, under the low refractive index layer  130   b  contacting the cavity layer  132 . Accordingly, the second top DBR layer  133  may have 16.5 pairs of the high refractive index layer  130   a  and the low refractive index layer  130   b.  A lowermost layer of the second top DBR layer  133  is the low refractive index layer  130   b.    
         [0090]    The optical modulators  100  of  FIGS. 4 and 5  have the same operation characteristics.  FIG. 6  is a graph illustrating operation characteristics of the optical modulator  100 , particularly illustrating a reflectivity when no voltage is applied to the optical modulator  100  and a reflectivity when a voltage is applied to the optical modulators  100 . Here, a voltage is a reverse bias voltage applied to the optical modulator  100 . For example, a negative voltage is applied to a p-electrode of the optical modulator  100 , and a positive voltage is applied to an n-electrode of the optical modulator  100 . According to the graph illustrating the reflectivity when no voltage is applied to the optical modulator  100 , absorption peaks occur at two resonant wavelengths λ FP1  and λ FP2  around 850 nm due to Fabry-Perot resonance by the active layer  120  and the cavity layer  132 . Also, aside from the Fabry-Perot resonance, an absorption peak occurs at a wavelength λ EX  of about 837 nm due to exciton absorption in the quantum well layers in the active layer  120 . 
         [0091]    If a reverse voltage of about 5.7 V is applied to the optical modulator  100 , an absorption wavelength of the active layer  120  is shifted to a longer wavelength due to a quantum confined stark effect. In the optical modulator  100  of  FIG. 4  or  5 , if a reverse voltage is applied, the wavelength λ EX  of about 837 nm at which the absorption peak occurs may be shifted to about 850 nm. Then, due to the Fabry-Perot resonance, light absorption in the active layer  120  may be maximized. According to the graph illustrating the reflectivity when a voltage is applied to the optical modulator  100 , very large absorption peaks occur at the two resonant wavelengths λ FP1  and λ FP2  around 850 nm. 
         [0092]    An optical modulation performance of the optical modulator  100  may be determined by using a difference between a reflectivity when no voltage is applied and a reflectivity when a voltage is applied, which is hereinafter referred to as a reflectivity difference. As a reflectivity difference increases, an optical modulation performance of the optical modulator  100  may increase. Also, as described above, considering various error factors, a high reflectivity difference may be maintained over as wide a wavelength band as possible. In this case, the wider bandwidth is advantageous to the optical modulator  100 .  FIG. 7  is a graph illustrating a reflectivity difference of the optical modulator  100  and a reflectivity difference of an optical modulator including only one Fabry-Perot resonant mode. Referring to  FIG. 7 , the optical modulator  100  according to the present exemplary embodiment has a high reflectivity difference ΔR of about 60% to 70% at two resonant wavelengths λ FP1  and λ FP2 . Also, a bandwidth with a reflectivity difference of higher than 50% is about 10.1 nm. Also, in the optical modulator including only one Fabry-Perot resonant mode, a bandwidth with a reflectivity difference of higher than 50% is about 5.1 nm. Accordingly, it is found that a bandwidth of the optical modulator  100  according to the present exemplary embodiment is about 2 times greater than that of the optical modulator including only one Fabry-Perot resonant mode. 
         [0093]    In the present exemplary embodiment, one cavity layer  132  is disposed in the top DBR layer  130 . However, according to one or more other exemplary embodiments, more cavity layers  132  may be disposed in the top DBR layer  130 .  FIG. 8  is a cross-sectional view for explaining an operation of an optical modulator  100   a  including two cavity layers in the top DBR layer  130 , according to another exemplary embodiment. Referring to  FIG. 8 , the optical modulator  100   a  includes 4 reflective layers, that is, the bottom DBR layer  110 , the first top DBR layer  131 , the second top DBR layer  133 , and a third top DBR layer  135 . Furthermore, the optical modulator  100   a  includes 3 resonant cavities, that is, the active layer  120 , the first cavity layer  132 , and a second cavity layer  134 . The active layer  120  acts as a main resonant cavity, and the bottom DBR layer  110  and the first top DBR layer  131  are respectively disposed under and above the active layer  120  for Fabry-Perot resonance. Also, the first and second cavity layers  132  and  134  act as additional micro-resonant cavities. The first top DBR layer  131  and the second top DBR layer  133  are respectively disposed under and above the first cavity layer  132  for Fabry-Perot resonance, and the second top DBR layer  133  and the third top DBR layer  135  are respectively disposed under and above the second cavity layer  134 . In order to act as a resonant cavity, each of the active layer  120  and the first and second cavity layers  132  and  134  has an optical thickness that is an integer multiple of λ/2. For example, the active layer  120  may have an optical thickness of 2λ and each of the first and second cavity layers  132  and  134  may have an optical thickness of λ/2. Although both the active layer  120  and the first and second cavity layers  132  and  134  act as resonant cavities, light absorption occurs only in the active layer  120  having a multiple quantum well layer structure and the first and second cavity layers  132  and  134  only cause Fabry-Perot resonance. 
         [0094]    In this structure, if a light is incident on a top surface of the optical modulator  100   a,  4 reflected lights with difference phases are generated. For example, a light directly reflected from the third top DBR layer  135  has a phase of π. Also, a light resonated in the second cavity layer  134  and then reflected from the second top DBR layer  133  has a phase of 0. A light resonated in the first cavity layer  132  and then reflected from the first top DBR layer  131  has a phase of π. A light resonated in the active layer  120  and then reflected from the bottom DBR layer  110  has a phase of 0. As a result, when a light travels downward, lights reflected from the four reflective layers, that is, the bottom DBR layer  110 , the first top DBR layer  131 , the second top DBR layer  133 , and the third top DBR layer  135 , have phases of π, 0, π, and 0, respectively. Then, the four reflected lights with different phases are offset from one another. 
         [0095]    For the above operation, positions of the first and second cavity layers  132  and  134  in the top DBR layer  130  and reflectivities of the bottom DBR layer  110 , the first top DBR layer  131 , the second top DBR layer  133 , and the third top DBR layer  135  may vary by design.  FIG. 9  is a table showing optimal materials and thicknesses of layers of the optical modulator  100   a  of  FIG. 8 . The optical modulator  100   a  of  FIG. 9  is also designed to have a center absorption wavelength of about 850 nm by using a GaAs compound semiconductor. Referring to  FIG. 9 , the top DBR layer  130  is disposed under the second contact layer  140  formed of p-GaAs with a thickness of about 100 Å. The top DBR layer  130  may include the third top DBR layer  135 , the second cavity layer  134 , the second top DBR layer  133 , the first cavity layer  132 , and the first top DBR layer  131  downward. 
         [0096]    The third top DBR layer  135  has a structure in which the high refractive index layer  130   a  and the low refractive index layer  130   b  are sequentially repeatedly stacked 2 times downward. That is, the third top DBR layer  135  may include 2 pairs of the high refractive index layer  130   a  and the low refractive index layer  130   b.  As described above, the high refractive index layer  130   a  may be formed of Al 0.31 Ga 0.69 As with a thickness of about 623 Å, and the low refractive index layer  130   b  may be formed of Al 0.84 Ga 0.16 As with a thickness of about 682 Å. A reflectivity of the third top DBR layer  135  may be about 46.3%. 
         [0097]    The second cavity layer  134  is disposed under the third top DBR layer  135 . Since a lowermost layer of the third top DBR layer  135  is the low refractive index layer  130   b,  the second cavity layer  134  may be formed of the same material as that of the high refractive index layer  130   a.  In order to have an optical thickness of λ/2, the second cavity layer  134  may have a thickness that is about 1246 Å. 
         [0098]    The second top DBR layer  133  disposed under the second cavity layer  134  has a structure in which the low refractive index layer  130   b  and the high refractive index layer  130   a  are sequentially repeatedly stacked downward. Since the second cavity layer  134  is formed of the same material as that of the high refractive index layer  130   a,  the low refractive index layer  130   b  is a first layer disposed under the second cavity layer  134 . The second top DBR layer  133  may have 15.5 pairs of the low refractive index layer  130   b  and the high refractive index layer  130   a.  That is, the low refractive index layer  130   b  and the high refractive index layer  130   a  are sequentially repeatedly stacked 15 times downward, and the low refractive index layer  130   b  is further disposed as a lowermost layer. A reflectivity of the second top DBR layer  133  may be about 93.2%. 
         [0099]    The first cavity layer  132  is disposed under the second top DBR layer  133 . Since a lowermost layer of the second top DBR layer  133  is the low refractive index layer  130   b,  the first cavity layer  132  may be formed of the same material as that of the high refractive index layer  130   a.  In order to have an optical thickness of λ/2, the first cavity layer  132  may have a thickness that is about 1246 Å. 
         [0100]    The first top DBR layer  131  disposed under the first cavity layer  132  has a structure in which the low refractive index layer  130   b  and the high refractive index layer  130   a  are sequentially repeatedly stacked downward. Since the first cavity layer  132  is formed of the same material as that of the high refractive index layer  130   a,  the low refractive index layer  130   b  is a first layer disposed under the first cavity layer  132 . The first top DBR layer  131  may have 14.5 pairs of the low refractive index layer  130   b  and the high refractive index layer  130   a.  That is, the low refractive index layer  130   b  and the high refractive index layer  130   a  are sequentially repeatedly stacked 14 times, and the low refractive index layer  130   b  is further disposed as a lowermost layer. A reflectivity of the first top DBR layer  131  may be about 91.9%. 
         [0101]    As described above, the first top DBR layer  131 , the first cavity layer  132 , the second top DBR layer  133 , the second cavity layer  134 , and the third top DBR layer  135  may be p-type doped to allow current to flow therethrough. Structures of the active layer  120 , the spacer layer  121 , and the bottom DBR layer  110  are the same as or similar to those described with reference to  FIGS. 4 and 5 . As shown in  FIG. 9 , even when the two cavity layers, namely, the first and second cavity layers  132  and  134 , are disposed in the top DBR layer  130 , the number of high refractive index layers  130   a  and the number of low refractive index layers  130   b  may not be much higher than that of  FIGS. 4 and 5 . 
         [0102]      FIG. 10  is a graph illustrating a reflectivity when no voltage is applied to the optical modulator  100   a  of  FIG. 9  and a reflectivity when a voltage is applied to the optical modulator  100   a.  According to the graph illustrating the reflectivity when no voltage is applied to the optical modulator  100   a,  absorption peaks occur at three resonance wavelengths λ FP1 , λ FP2 , and λ FP3  around 850 nm due to Fabry-Perot resonance by the active layer  120 , the first cavity layer  132 , and the second cavity layer  134 . That is, since the optical modulator  100   a  includes three resonant cavities, there are three Fabry-Perot resonant modes. Here, center values of the three resonant wavelengths λ FP1 , λ FP2 , and λ FP3  may be equal to 850 nm, which is a wavelength of an incident light to be modulated. Also, aside from the Fabry-Perot resonance, an absorption peak occurs at a wavelength λ EX  of about 837 nm due to exciton absorption in the quantum well layers in the active layer  120 . 
         [0103]    If a reverse voltage of about 6 V is applied to the optical modulator  100   a,  an absorption wavelength of the active layer  120  is shifted to a longer wavelength due to a quantum confined stark effect. For example, if a reverse voltage is applied to the optical modulator  100   a,  the wavelength λ EX  of about 837 nm at which the absorption peak occurs may be shifted to about 850 nm. Then, due to the Fabry-Perot resonance, light absorption in the active layer  120  may be maximized. According to the graph illustrating the reflectivity when a voltage is applied to the optical modulator  100   a,  very large absorption peaks occur at the three resonant wavelengths λ FP1 , λ FP2 , and λ FP3  around 850 nm. Depths of such absorption peaks may be finely adjusted by adjusting reflectivities of the bottom DBR layer  110 , the first top DBR layer  131 , the second top DBR layer  133 , and the third top DBR layer  135  in the optical modulator  100   a.    
         [0104]      FIG. 11  is a graph illustrating a reflectivity difference of the optical modulator  100   a.  Referring to  FIG. 11 , the optical modulator  100   a  has a relatively constant reflectivity difference ΔR of about 60% in the three resonant wavelengths λ FP1 , λ FP2 , and λ FP3 . Also, a bandwidth with a reflectivity difference of higher than 50% is about 14.7 nm, which is relatively wide. Accordingly, as the number of Fabry-Perot resonant modes increases, a bandwidth with a reflectivity difference of higher than 50% increases and a smoothness of a peak of a reflective difference increases as well. 
         [0105]    Although the optical modulator  100  includes two cavity layers, namely, the first and second cavity layers  132  and  134 , in  FIGS. 8 and 9 , more cavity layers may be disposed according to one or more other exemplary embodiments. Also, although both the two cavity layers, namely, the first and second cavity layers  132  and  134 , are formed of the same material as that of the high refractive index layer  130   a,  it is understood that one or more other exemplary embodiments are not limited thereto. For example, one of the two cavity layers, namely, the first and second cavity layers  132  and  134 , may be formed of a material of the high refractive index layer  130   a,  and the other may be formed of a material of the low refractive index layer  130   b.  Also, both the two cavity layers, namely, the first and second cavity layers  132  and  134 , may be formed of a material of the low refractive index layer  130   b.  However, in this case, in order not to change an order in which the high refractive index layer  130   a  and the low refractive index layer  130   b  are repeatedly stacked in the top DBR layer  130 , structures of the first top DBR layer  131 , the second top DBR layer  133 , and the third top DBR layer  135  are to be changed. For example, if the second cavity layer  134  is formed of a material of the low refractive index layer  130   b,  the third top DBR layer  135  may include 1.5 or 2.5 pairs of the high refractive index layer  130   a  and the low refractive index layer  130   b.    
         [0106]    The above explanation has been made on the assumption that a light is perpendicularly incident on the optical modulators  100  and  100   a . However, if the optical modulators  100  and  100   a  are applied to an apparatus for capturing a 3D image, such as a 3D camera, a light may be obliquely incident on the optical modulators  100  and  100   a  according to an arrangement of an optical system. In particular, if a lens for focusing a light is disposed at the front of the optical modulator  100  or  100   a,  a light may be incident on the optical modulators  100  and  100   a  at various angles within a predetermined range. If a light is obliquely incident, a length of an optical path is different from that when a light is perpendicularly incident. Accordingly, resonance characteristics when a light is obliquely incident are also different from those when a light is perpendicularly incident. Accordingly, in order to achieve desired operation characteristics for an obliquely incident light, thicknesses of layers of the optical modulator  100  or  100   a  may be determined in consideration of an incident angle of the light. 
         [0107]      FIG. 12  is a cross-sectional view illustrating an optical path according to an incident angle of an obliquely incident light incident on the optical modulator  100  or  100   a.  In  FIG. 12 , a cavity layer is assumed to be a part of the top DBR layer  130  for convenience. Referring to  FIG. 12 , an obliquely incident light, which is incident on the optical modulator  100  or  100   a  from the outside, passes through the top DBR layer  130  and the active layer  120 , and then is reflected from the bottom DBR layer  110 . In this case, the obliquely incident light sequentially passes through three media with different refractive indices, that is, external air, the top DBR layer  130 , and the active layer  120 . Accordingly, the obliquely incident light is refracted from an interface between the air and the top DBR layer  130 , and an interface between the top DBR layer  130  and the active layer  120 . When an incident angle at which the obliquely incident light is incident on the top DBR layer  130  is θ t0 , a refraction angle θ t1  at the top DBR layer  130  and a refraction angle θ t2  at the active layer  120  may be easily calculated by using Snell&#39;s law. Here, since each of the top DBR layer  130  and the active layer  120  include a plurality of materials with different refractive indices, an average refractive index of the refractive indices of the materials is used as a refractive index of each of the top DBR layer  130  and the active layer  120 . For example, in the optical modulator  100  illustrated in  FIG. 4  or  5 , if θ t0 =22.5°, θ t1 =6.75°, and θ t2 =6.18°. 
         [0108]    In general, when a light is incident on a resonant cavity at an incident angle of θ t , the following relationship (m+½)k=2 nL cos(θ t ) is established. Here, m is a positive integer including 0, λ is a resonant wavelength, n is a refractive index of the resonant cavity, and L is a thickness of the resonant cavity. As shown in the above relationship, if the refractive index n and the thickness L of the resonant cavity are fixed, the resonant wavelength λ is proportional to cos(θ t ). That is, as the incident angle θ t  increases, the resonant wavelength λ decreases. Accordingly, in order to compensate for the effect of an incident angle of an incident light in a state where the resonant wavelength λ is fixed, the thickness L of the resonant cavity is multiplied by 1/cos(θ t ). Referring back to  FIG. 12 , when a light is obliquely incident on the optical modulator  100  or  100   a  at an incident angle of θ t0 , if a thickness of the top DBR layer  130  is increased by 1/cos(θ t1 ) and a thickness of the active layer  120  is increased by 1/cos(θ t2 ), the effect of an oblique entrance may be compensated for. 
         [0109]      FIG. 13  is a table showing a modified optical modulator of the optical modulator  100  of  FIG. 4 , which may compensate for an effect when θ t0 =22.5°. Referring to  FIG. 13 , a thickness of each of the top DBR layer  130  and the bottom DBR layer  110  is higher by 1/cos)(6.75°) than that in the optical modulator  100  of  FIG. 4 , and a thickness of the active layer  120  is higher by 1/cos(6.18°) than that in the optical modulator  100  of  FIG. 4 .  FIGS. 14 and 15  are graphs illustrating operation characteristics of the modified optical modulator of  FIG. 13 . Referring to  FIG. 14 , large absorption peaks occur at two resonant wavelengths λ FP1  and λ FP2  around 850 nm. When compared with the graphs of  FIGS. 6 and 7 , operation characteristics when a light is perpendicularly incident and when a light is obliquely incident after adjusting thicknesses of layers of the modified optical modulator are almost the same. Although θ t0 =22.5° in  FIG. 13 , thicknesses of layers of the modified optical modulator may be adjusted in the same manner even when the incident angle θ t0  is different from 22.5°. Also, although the modified optical modulator of the optical modulator of  FIG. 4  is illustrated in  FIG. 13 , the aforesaid principle may apply to the optical modulators  100  and  100   a  of  FIGS. 5 and 9  and other optical modulators according to other exemplary embodiments. 
         [0110]    Also,  FIG. 16  is a cross-sectional view illustrating an example where a light is focused by a lens  150  on a surface of an optical modulator according to an exemplary embodiment. Referring to  FIG. 16 , if the light is focused on the surface of the optical modulator by using the lens  150 , the light may be incident on the optical modulator at various angles within a predetermined range. For example, a light may be incident on the optical modulator at an angle within about ±20 degrees on the basis of a center incident angle. For example, if a center incident angle is 22.5°, an incident angle of a light incident on the optical modulator may range from 2.5° to 42.5°. If the optical modulator is designed in consideration of a light incident at a center incident angle, since the resonant wavelength λ is proportional to cos(θ t ) (where θ t  is an incident angle) as described above, a resonant wavelength for a light incident at an angle greater than the center incident angle is decreased (that is, a blue shift occurs), and a resonant wavelength for a light incident at an angle less than the center incident angle is increased (that is, a red shift occurs). 
         [0111]    Also, since a wavelength λ EX  of about 837 nm at which exciton absorption occurs is irrelevant to a structure of a resonant cavity, the wavelength λ EX  is maintained constant even though an incident angle of a light is changed. Accordingly, if an incident angle of an incident light is too large, a resonant wavelength may be close to an exciton absorption wavelength. If the resonant wavelength and the exciton absorption wavelength are close to each other, large light absorption may occur and the optical modulation performance of the optical modulator may be degraded. Accordingly, when the optical modulator is used, an incident angle may be limited such that a resonance wavelength is not too close to an exciton absorption wavelength. For example, a maximum incident angle of an incident light may be limited to satisfy a relationship λ EX +10 nm&lt;λ FP1  (where λ FP1  is a shortest resonant wavelength from among a plurality of resonant wavelengths). An allowable maximum incident angle may vary according to design of the optical modulator. For example, based on the relationship (m+½)λ=2 nL cos(θ t ), if thicknesses of the top DBR layer  130  and the active layer  120  are increased by 1/cos(θ t ), the allowable maximum incident angle may be increased by θ t . However, the fact that as an incident angle increases, a change in a resonant wavelength may increase needs to be considered when the allowable maximum incident angle is determined. 
         [0112]    Also, in order to apply an optical modulator to an apparatus for capturing a 3D image, a large area as well as a wide absorption bandwidth may be used. However, once the optical modulator is made large, an electrostatic capacitance of the optical modulator is increased. The increase in the electrostatic capacitance of the optical modulator increases an RC time constant, thereby making it difficult to drive the optical modulator at a high speed of 20 to 40 MHz. Accordingly, there is a demand for a structure that may increase an entire area of the optical modulator and reduce an electrostatic capacitance and a sheet resistance. 
         [0113]      FIG. 17  is a plan view illustrating an optical modulator array  200  including an array of optical modulators  100  in order to reduce an electrostatic capacitance according to an exemplary embodiment. In  FIG. 17 , the plurality of optical modulators  100  are arranged in a 2×3 array. However, the arrangement of the optical modulators  100  is not limited to the 2×3 array, and may be an n×m array (where n and m are natural numbers greater than 1) according to design. The optical modulator  100  of a unit cell may have a rectangular shape with a size of, for example, 2 mm×0.5 mm to 4 mm×1 mm. Referring to  FIG. 17 , the plurality of optical modulators  100  are arranged in an insulating frame  201 . Each of the plurality of optical modulators  100  is electrically separated from another optical modulator  100  by the insulating frame  201 . A trench  202  is formed (i.e., located) around the optical modulator  100  of each unit cell by etching the insulating frame  201 . A width of the trench  202  may be, for example, about 20 to 50 μm. Also, an insulating film  211  may be formed on a sidewall of the optical modulator  100 . A plurality of first electrode pads  203  and second electrode pads  204  are arranged on a top surface of the insulating frame  201 . The first and second electrode pads  203  and  204  are respectively electrically connected to electrodes of the optical modulators  100 . For example, the second electrode pad  204  is electrically connected to a second electrode  206  disposed on a top surface of the optical modulator  100 . Also, the first electrode pad  203  is electrically connected to a first electrode  205  disposed on a bottom surface of the trench  202  that surrounds the optical modulator  100 . As shown in  FIG. 17 , the first electrode  205  may be formed on the bottom surface of the trench  202  to surround the optical modulator  100 . 
         [0114]      FIG. 18  is a cross-sectional view taken along line A-A′ of  FIG. 17 .  FIG. 18  illustrates only a cross-sectional view of one optical modulator  100  in the optical modulator array  200  for convenience of description. Referring to  FIG. 18 , the optical modulator  100  includes the substrate  101 , the first contact layer  102 , the bottom DBR layer  110 , the active layer  120 , the first top DBR layer  131 , the cavity layer  132 , the second top DBR layer  133 , and the second contact layer  140 . Although the optical modulator  100  includes only one cavity layer  132 , as illustrated in  FIGS. 17 and 18 , it is understood that another exemplary embodiment is not limited thereto. For example, the optical modulator  100   a  including two cavity layers, namely, the first and second cavity layers  132  and  134 , may be used. The trench  202  is formed (i.e., located) in a right side of the optical modulator  100  to expose the first contact layer  102 . The first electrode  205  is disposed on the bottom surface of the trench  202  to contact the first contact layer  102 . The insulating film  211  is formed on the sidewall of the optical modulator  100 , and the insulating frame  201  for electrically separating the optical modulator  100  from another adjacent optical modulator is formed at a right side of the trench  202 . Also, the insulating frame  201  is formed on a left side of the optical modulator  100 . Each of the insulating frame  201  and the insulating film  211  may be formed of, for example, benzocyclobutene (BCB). The second electrode pad  204  is disposed on a top surface of the insulating frame  201  that is formed on the left side of the optical modulator  100 . In order to increase an adhesive force with the second electrode pad  204  formed of a metal, an adhesive layer  210  formed of, for example, SiO 2 , may be further disposed between the insulating frame  201  and the second electrode pad  204 . The second electrode pad  204  is electrically connected to a second electrode  206  disposed on the second contact layer  140 . 
         [0115]      FIG. 19  is a cross-sectional view taken along line B-B′ of  FIG. 17 . Referring to  FIG. 19 , the trench  202  is formed in both sides of the optical modulator  100  to expose the first contact layer  102 . The first electrode  205  is disposed on the bottom surface of the trench  202  to contact the first contact layer  102 . Although two first electrodes  205  are illustrated in  FIG. 19 , they may be one electrode connected along the bottom surface of the trench  202  to surround the optical modulator  100 . For example, the first electrode  205  may have a square ring shape along the trench  202  to surround the optical modulator  100 . Also, the insulating film  211  may be formed on both side surfaces of the optical modulator  100 . Also, the insulating frame  201  is disposed with the trench  202  therebetween. As shown in  FIG. 19 , the first electrode pad  203  is disposed on a top surface of the insulating frame  201 . In order to increase an adhesive force with the first electrode pad  203 , the adhesive layer  210  formed of, for example, SiO 2 , may be further disposed between the insulating frame  201  and the first electrode pad  203 . The first electrode  205  may extend along a sidewall of the trench  202  to be electrically connected to the first electrode pad  203 . 
         [0116]    Referring back to  FIG. 17 , the second electrode  206  formed on the top surface of the optical modulator  100  may have a lattice shape in order to reduce resistance. For example, the second electrode  206  having a lattice shape, for example, a fishbone shape, is illustrated in  FIG. 17 . However, the second electrode  206  is not limited to the fishbone shape and may have a lattice shape such as a matrix shape or a mesh shape. In this case, since an entire width of the second electrode  206  is reduced, a sheet resistance may be reduced. If the second electrode  206  is formed of a metal material, a light incident on the optical modulator  100  may be partially blocked by the second electrode  206 . Accordingly, in order to minimize light loss, a width of a lattice may be small, for example, about 10 to 20 μm. The second electrode  206  may be formed of a single metal material or the second electrode  206  may be formed to have a multi-layer structure in which, for example, platinum (Pt), titanium (Ti), platinum (Pt), and gold (Au) are sequentially stacked. Also, the second electrode  206  may be formed of a material such as indium tin oxide (ITO), zinc oxide (ZnO), aluminum zinc oxide (AZO) through which a light may be transmitted. 
         [0117]    In the aforesaid optical modulator array  200 , since the optical modulators  100  are divided into a plurality of cells, an electrostatic capacitance may be reduced. Also, since the first electrode  205  and the second electrode  206  are not disposed to directly face each other, a parasitic electrostatic capacitance may be prevented from being generated. For example, the first electrode  205  is disposed around the optical modulator  100  of a unit cell whereas the second electrode  206  is disposed at a central portion of the optical modulator  100 . Also, since an area of the first electrode  205  and an area of the second electrode  206  may be reduced, a sheet resistance of each of the first electrode  205  and the second electrode  206  may be reduced and generation of a parasitic electrostatic capacitance may be further reduced. 
         [0118]      FIG. 20  is a view illustrating an apparatus  300  for capturing a 3D image including the optical modulator array  200  according to an exemplary embodiment. Referring to  FIG. 20 , the apparatus  300  may include a light source  301  that generates a light having a predetermined wavelength, a first driver  302  that drives the light source  301 , an objective lens  306  that focuses a light reflected from an object  400 , the optical modulator array  200  that modulates a light reflected from the object  400 , a second driver  303  that drives the optical modulator array  200 , an imager  310  that generates an image from the modulated light, a calculator  305  that calculates a distance to the object  400  based on an output of the imager  310 , and a controller  304  that controls operations of the first and second drivers  302  and  303 . Also, a mirror  307  that reflects a light modulated and reflected by the optical modulator array  200  and a filter  308  that transmits only a light emitted from the light source  301  may further be disposed in front of the imager  310 . A lens  309  that focuses a modulated light on an area of the imager  315  may be further disposed between the imager  310  and the filter  308 . Also, the optical modulator  100  or  100   a  of  FIG. 1  or  9  may be used instead of the optical modulator array  200 . 
         [0119]    The light source  301  may be, for example, a light-emitting diode (LED) or a laser diode (LD) that may emit a light having a near-infrared (NIR) wavelength of about 850 nm, which is invisible to human eyes, for safety. In this case, the filter  308  may be an infrared pass filter that transmits a light of about 850 nm. The first driver  302  may emit a periodic wave such as a sinusoidal wave by driving the light source  301  according to a control signal received from the controller  304 . After a light projected to the object  400  from the light source  301  is reflected from the object  400 , the light is focused on the optical modulator array  200  by the objective lens  306 . Then, the optical modulator array  200  modulates the incident light into a modulated signal having a predetermined wavelength according to a control of the second driver  303 . The second driver  303  may control the modulated signal of the optical modulator array  200  according to a control signal received from the controller  304 . After the modulated light is reflected from the optical modulator array  200 , the light is reflected again from the mirror  307  and is incident on the imager  310 . In this case, a component other than an NIR component of  850  nm is removed by the filter  308 . The imager  310  generates an image containing distance information by capturing the light reflected by the optical modulator array  200 . For example, the imager  310  may be a charge-coupled device (CCD) image sensor or a complementary metal-oxide semiconductor (CMOS) image sensor including a two-dimensional (2D) array. The calculator  305  may calculate a distance to the object  400  according to a distance calculation algorithm based on an output of the imager  310 . 
         [0120]    While exemplary embodiments have been particularly shown and described above using specific terms, the exemplary embodiments and terms have been used to explain the present inventive concept and should not be construed as limiting the scope of the present inventive concept defined by the claims. The exemplary embodiments should be considered in a descriptive sense only and not for purposes of limitation. Therefore, the scope of the invention is defined not by the detailed description of exemplary embodiments, but by the appended claims, and all differences within the scope will be construed as being included in the present invention.