1. A light emitting device, comprising:a semiconductor light emitting element having a light emitting surface and configured to output an optical image having an arbitrary shape along a normal direction of the light emitting surface and an inclined direction having a predetermined inclination and a spread angle with respect to the normal direction; and

a light shielding member disposed such that an axis orthogonal to the light emitting surface at a position of the center of gravity of the light emitting surface crosses a part of the light shielding member,

wherein the semiconductor light emitting element includes an active layer, a pair of cladding layers sandwiching the active layer, and a phase modulation layer provided between the active layer and one of a pair of the cladding layers and being optically coupled to the active layer,

the light shielding member is disposed so as to pass through a specific optical image output in the inclined direction among the optical images and shield zero order light output in a normal direction of the light emitting surface,

the phase modulation layer has a basic layer and a plurality of modified refractive index regions each having a refractive index different from a refractive index of the basic layer, and

the phase modulation layer is configured such that:

where, in an XYZ orthogonal coordinate system defined by a Z axis coinciding with the normal direction and an X-Y plane including X and Y axes which are orthogonal to each other and coincide with one surface of the phase modulation layer including a plurality of the modified refractive index regions, a virtual square lattice constituted by M1 (an integer of 1 or more)×N1 (an integer of 1 or more) unit constituent regions R each having a square shape is set on the X-Y plane,

in the unit constituent region R (x, y) on the X-Y plane specified by a coordinate component x (an integer of from 1 to M1) in the X axis direction and a coordinate component y (an integer of from 1 to N1) in the Y axis direction, a center of gravity G1 of the modified refractive index region located in the unit constituent region R (x, y) is away from a lattice point O (x, y) which is the center of the unit constituent region R (x, y), and a vector from the lattice point O (x, y) to the center of gravity G1 is oriented in a specific direction,

wherein in a state of satisfying the following first to sixth conditions:

the first condition defined that coordinates (x, y, z) in the XYZ orthogonal coordinate system satisfies a relationship represented by the following formulas (1) to (3) with respect to a spherical coordinates (d1, ?tilt, ?rot) defined by a length d1 of a moving radius, an inclination angle ?tilt from the Z axis, and a rotation angle ?rot from the X axis specified on the X-Y plane:

x=d1 sin ?tilt cos ?rot (1)

y=d1 sin ?tilt sin ?rot (2)

z=d1 cos ?tilt (3),

the second condition defined that letting a beam pattern corresponding to the optical image output from the semiconductor light emitting element is a set of bright points directed in directions defined by the angles ?tilt and ?rot, the angles ?tilt and ?rot are converted into a coordinate value kx on a Kx axis corresponding to the X axis which is a normalized wave number defined by the following formula (4) and a coordinate value ky on a Ky axis, which is a specific wavenumber defined by the following formula (5), corresponds to the Y axis, and is orthogonal to the Kx axis:

a: Lattice constant of vertical square lattice?: Oscillation wavelength of semiconductor light emitting element,the third condition defined that a specific wavenumber range including the beam pattern includes M2 (an integer of 1 or more)×N2 (an integer of 1 or more) image regions FR each having a square shape in a wavenumber space defined by the Kx axis and the Ky axis,

the fourth condition defined that, in the wavenumber space, a complex amplitude F (x, y) obtained by performing two-dimensional inverse Fourier transform to transform each of image regions FR (kx, ky) specified by a coordinate component kx (an integer of from 0 to M2?1) in the Kx axis direction and a coordinate component ky (an integer of from 0 to N2?1) in the Ky axis direction to the unit constituent region R (x,y) on the X-Y plane is expressed by the following formula (6) with j being an imaginary unit:

the fifth condition defined that the complex amplitude F (x, y) is defined by the following formula (7) while an amplitude term is denoted by A (x, y) and a phase term is denoted by P (x, y) in the unit constituent region R (x, y):

F(x,y)=A(x,y)×exp[jP(x,y)] (7), and

the sixth condition defined that the unit constituent region R (x, y) is defined by an s-axis and a t-axis which are parallel to the X-axis and the Y-axis and orthogonal at the lattice point O (x, y),

the phase modulation layer is configured such that:

in a state in which a line segment length r (x, y) from the lattice point O (x, y) to the center of gravity G1 of the corresponding modified refractive index region is set to a common value in each of the M1×N1 unit constituent regions R, an angle ? (x, y) formed by a line segment connecting the lattice point O (x, y) and the center of gravity G1 of the corresponding modified refractive index region and the s axis satisfies a relationship expressed by the following formula:

?(x,y)=C×P(x,y)+B

C: proportional constant

B: arbitrary constant,

and the corresponding modified refractive index region is disposed in the unit constituent region R (x, y).