A light beam deflecting element comprising: a first quarter wavelength film in which light is incident from a back surface of the first quarter wavelength film, and a second quarter wavelength film in which light is emitted from a back surface of the second quarter wavelength film; and a passive matrix type N × M transmissive birefringence modulator inserted between the first and second quarter wavelength films, the modulator including: a first substrate having N line-shaped electrodes along a X axis direction on the first substrate, wherein the first substrate is a Si substrate or a Ge substrate, and a second substrate having M line-shaped electrodes along a Y axis direction on the second substrate, wherein the second substrate is a Si substrate or a Ge substrate, the Y axis is orthogonal to the X axis, and intersections of the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate form N × M pixels, and ferroelectric liquid crystals inserted between the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate, wherein the modulator is configured to operate as a half-wavelength plate by operating the electrodes forming the pixels, and the second quarter wavelength film is configured to be fitted on a polarization grating configured by orthogonal first and second axes in which a birefringence axis is rotating in a direction along the first axis at a period that gradually changes in accordance with a wavelength of the incident light, the polarization grating is aligned such that the X axis and the first axis or the Y axis and the first axis are substantially in parallel, and the period is not a constant period. a first quarter wavelength film in which light is incident from a back surface of the first quarter wavelength film, and a second quarter wavelength film in which light is emitted from a back surface of the second quarter wavelength film; and a passive matrix type N × M transmissive birefringence modulator inserted between the first and second quarter wavelength films, the modulator including: a first substrate having N line-shaped electrodes along a X axis direction on the first substrate, wherein the first substrate is a Si substrate or a Ge substrate, and a second substrate having M line-shaped electrodes along a Y axis direction on the second substrate, wherein the second substrate is a Si substrate or a Ge substrate, the Y axis is orthogonal to the X axis, and intersections of the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate form N × M pixels, and ferroelectric liquid crystals inserted between the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate, wherein the modulator is configured to operate as a half-wavelength plate by operating the electrodes forming the pixels, and the second quarter wavelength film is configured to be fitted on a polarization grating configured by orthogonal first and second axes in which a birefringence axis is rotating in a direction along the first axis at a period that gradually changes in accordance with a wavelength of the incident light, the polarization grating is aligned such that the X axis and the first axis or the Y axis and the first axis are substantially in parallel, and the period is not a constant period. a first substrate having N line-shaped electrodes along a X axis direction on the first substrate, wherein the first substrate is a Si substrate or a Ge substrate, and a second substrate having M line-shaped electrodes along a Y axis direction on the second substrate, wherein the second substrate is a Si substrate or a Ge substrate, the Y axis is orthogonal to the X axis, and intersections of the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate form N × M pixels, and ferroelectric liquid crystals inserted between the N line-shaped electrodes on the first substrate and the M line-shaped electrodes on the second substrate, wherein the modulator is configured to operate as a half-wavelength plate by operating the electrodes forming the pixels, and the second quarter wavelength film is configured to be fitted on a polarization grating configured by orthogonal first and second axes in which a birefringence axis is rotating in a direction along the first axis at a period that gradually changes in accordance with a wavelength of the incident light, the polarization grating is aligned such that the X axis and the first axis or the Y axis and the first axis are substantially in parallel, and the period is not a constant period.