JP5141411B2 - Semiconductor optical modulator driving method and semiconductor optical modulator - Google Patents

Description

  The present invention includes first and second semiconductor waveguides to which first and second modulation voltages are applied, respectively, and performs light intensity modulation by interference of output light from the first and second semiconductor optical waveguides The present invention relates to an optical modulator driving method and a semiconductor optical modulator.

  By applying the first and second modulation voltages to each of the two optical waveguides, the refractive index of the optical waveguide is changed to modulate the phase of the input light passing through each optical waveguide, and each phase-modulated light 2. Description of the Related Art Interferometric optical modulators, such as Mach-Zehnder optical modulators, that combine and interfere with output light from a waveguide to modulate optical intensity are widely used in the field of high-speed optical communications.

  In such an interferometric optical modulator, chirp is generated due to temporal variation of the phase of the output light (hereinafter referred to as “modulated output light”) of the intensity modulated optical modulator during the transition period of the modulation voltage. Sometimes. Such chirp is not preferable because it deteriorates the transmission characteristics of long-distance, large-capacity optical communication using, for example, an optical fiber as a medium.

  As a driving method for suppressing the chirp of the interferometric optical modulator, push-pull driving is known. In the push-pull drive, the time derivative V1 ′ of the first modulation voltage V1 and the time derivative V2 ′ of the second modulation voltage V2 are controlled so that V1 ′ = − V2 ′.

When the amount of change in the refractive index of the optical waveguide is proportional to the modulation voltages V1 and V2, for example, when lithium niobate (LiNbO ₃ ) or lithium tantalate (LiTaO ₃ ) that produces the primary electro-optic effect is used as the optical waveguide, Push-pull driving can suppress the chirp amount to a level that can be almost ignored.

  In recent years, development of a semiconductor optical modulator, for example, an interference type semiconductor optical modulator using a compound semiconductor as an optical waveguide has been promoted. Since the semiconductor optical modulator can be monolithically integrated with another optical circuit such as a semiconductor laser, a small optical circuit device can be realized. In particular, a semiconductor optical waveguide having a quantum well structure in the active layer has a large electro-optic effect due to the quantum confined Stark effect, so that a small optical modulator can be easily configured.

However, since the refractive index change of a semiconductor is mainly a secondary electro-optic effect that changes with the square of the applied voltage, including the quantum confined Stark effect, chirp fluctuations can be sufficiently suppressed by push-pull drive. (For example, refer to Patent Document 1).
Japanese Unexamined Patent Publication No. 09-021986

  As described above, in the semiconductor optical waveguide, since the optical waveguide is composed of a semiconductor mainly having a secondary electro-optic effect, the amount of change in the refractive index of the optical waveguide is the square of the voltage applied to the optical waveguide. Proportionally changes. For this reason, even if the conventional method of driving an interferometric optical modulator using push-pull driving is applied as it is to driving a semiconductor optical modulator having a semiconductor optical waveguide, chirp cannot be suppressed.

  The present invention relates to driving of an interferometric semiconductor optical modulator that modulates light intensity by interference between output lights of two semiconductor optical waveguides, and relates to a driving method for suppressing chirp generated during a transition period of a modulation voltage and such driving. An object of the present invention is to provide a driving circuit for realizing the above.

In order to solve the above-described problem, in the invention according to claim 1 of the present invention, the first semiconductor optical waveguide to which the first modulation voltage is applied and the second semiconductor to which the second modulation voltage is applied. In a method for driving a semiconductor optical modulator comprising: an optical waveguide; and a multiplexer that interferes with output light from the first semiconductor optical waveguide and the second semiconductor optical waveguide.
While the first and second modulation voltages transition between a first steady state and a second steady state, the product of the time derivative of the first modulation voltage and the first modulation voltage, and Driving the semiconductor optical modulator, wherein the first and second modulation voltages are controlled so that a sum of products of a time derivative of the second modulation voltage and the second modulation voltage becomes zero. Configure as a method.

  According to the present invention, the interference type semiconductor optical modulator can be modulated and driven with a small amount of chirp.

  Before describing an embodiment of the present invention, first, the modulation characteristics of an interference optical modulator will be described. In order to simplify the explanation, a Mach-Zehnder interferometric optical modulator will be described as an example, but the same applies to other interferometric optical modulator examples.

  In the Mach-Zehnder interferometric optical modulator, incident light is branched and incident on the first and second optical waveguides. A first modulation voltage V1 and a second modulation voltage V2 are applied to the first and second optical waveguides, respectively, and incident light is output from each optical waveguide as output light phase-modulated according to the modulation voltages V1 and V2. Is output. The phase-modulated output light from each optical waveguide is output from the optical modulator as modulated output light that has been combined by the multiplexer, interfered, and intensity-modulated.

In the above-described Mach-Zehnder interferometric optical modulator, when the output light of the first and second optical waveguides is phase-modulated by phase change amounts φ ₁ and φ ₂ by the first and second modulation voltages V 1 and V 2, respectively. The electric field intensity Eo of the modulated output light is

と表される。ここで、κは入力光の分岐比である。従って、変調出力光の光強度Ｉｏ及び位相φｏは、

It is expressed. Here, κ is the branching ratio of the input light. Therefore, the light intensity Io and the phase φo of the modulated output light are

及び、

as well as,

と表される。

It is expressed.

  Chirp occurs due to time fluctuation of frequency, and its intensity can be expressed by a chirp parameter α as is well known. Here, the chirp parameter α is obtained by using the time derivative φo ′ of the phase φo of the modulated output light and the time derivative Io ′ of the light intensity Io of the modulated output light,

と定義され、数式２及び数式３を用いて、

And using Equations 2 and 3,

と表される。ここで、φ₁'及びφ₂'は、それぞれ第１及び第２の光導波路の出力光の位相変化量φ₁ 、φ₂ の時間微分を表している。

It is expressed. Here, φ ₁ ′ and φ ₂ ′ represent time derivatives of the phase change amounts φ ₁ and φ ₂ of the output light of the first and second optical waveguides, respectively.

  Hereinafter, a case where the branching ratio of the incident light to the first and second optical waveguides is equal, that is, the branching ratio κ = 1 is considered. Note that κ = 1 is a branching ratio normally used in a Mach-Zehnder interferometric optical modulator.

  When κ = 1, Equation 5 is

と変形される。

And transformed.

Equation 6 shows that when control is performed so that φ ₁ ′ + φ ₂ ′ = 0, α becomes zero and the chirp disappears for an arbitrary phase difference, φ ₁ −φ ₂ .

In the case of using an optical waveguide whose refractive index changes due to the primary electro-optic effect, for example, Pockels effect, like lithium niobate or lithium tantalate, the light that is phase-modulated by the first and second modulation voltages V1 and V2. The phase change amounts φ ₁ and φ ₂ of the output light of the waveguide are proportional to the modulation voltages V 1 and V ₂ . That is, φ ₁ ∝V1 and φ ₂ ∝V2.

In the push-pull drive, the time derivatives V1 ′ and V2 ′ of the first and second modulation voltages V1 and V2 are reversed in sign so that their absolute values are equal, that is, V1 ′ = − V2 ′. Control (in other words, V1 + V2 = constant). Therefore, in the optical modulator using the Pockels effect, the time differentials φ ₁ ′ and φ ₂ ′ of the phase change amounts φ ₁ and φ ₂ of the output light of the optical waveguide are always φ ₁ ′ = −φ ₂ ′. Controlled. For this reason, the chirp parameter α is zero from Equation 6, and no chirp is generated.

  Next, a Mach-Zehnder interference type optical modulator using a semiconductor optical waveguide will be described.

In a semiconductor optical waveguide typified by a compound semiconductor optical waveguide, light modulation is performed using, for example, the Stark effect or the Franz Keldisch effect. These effects are mainly a secondary electro-optic effect in which the refractive index of the optical waveguide changes in proportion to the square of the modulation voltage. For this reason, the phase change amounts φ ₁ and φ ₂ of the output light of the optical waveguide are not proportional to the modulation voltages V 1 and V ₂ . As a result, the phase changes φ ₁ , φ ₂ of the optical waveguide output light φ ₁ ′, φ ₂ ′ are not always φ ₁ ′ = −φ ₂ ′ in push-pull drive, and chirp occurs. To do.

  The Franz Keldish effect is caused by the oozing of the electron / hole wave function to the forbidden band. The Stark effect is caused by a change in the exciton absorption wavelength due to the interaction between the exciton and the electric field. In the quantum well structure, since the dissociation of excitons is hindered, a particularly large Stark effect, that is, a so-called quantum confined Stark effect is generated. For this reason, the quantum well structure is being developed and researched to realize a practical optical modulator having a small size and a low modulation voltage. Hereinafter, the modulation characteristics of the semiconductor optical modulator will be described using the Mach-Zehnder interference type semiconductor optical modulator having such a quantum well structure as an example.

  The quantum confined Stark effect is a second-order electro-optic effect, similar to the Franz Keldish effect. In the semiconductor optical waveguide having the secondary electro-optic effect, the refractive index change amount Δn with respect to the electric field E in the semiconductor optical waveguide is expressed by using a material-specific coefficient s.

と表される。ここで、半導体光導波路中の電界Ｅは、ビルトインポテンシャルに伴う電界Ｅｂと変調電圧Ｖにより印可される電界Ｖ／ｄの和として、

It is expressed. Here, the electric field E in the semiconductor optical waveguide is the sum of the electric field Eb associated with the built-in potential and the electric field V / d applied by the modulation voltage V.

と表される。なお、ｄは光導波路を構成する活性層の厚さである。

It is expressed. In addition, d is the thickness of the active layer which comprises an optical waveguide.

  Substituting Equation 8 into Equation 7,

を得る。さらに、変形された屈折率変化量Δｎ’＝Δｎ＋（ｎ₀ ³ ／２）ｓＥｂ² を導入し、ｒ＝２ｓＥｂとおくと、変形された屈折率変化量Δｎ’は、数式９を用いて、

Get. Furthermore, modified refractive index change amount _{Δn '= Δn + (n 0} 3/2) introducing SEB ^2, when put between r = 2sEb, modified refractive index change [Delta] n', using the equation 9,

と表すことができる。ここで、Δｎ’の第２項（ｎ₀ ³ ／２）ｓＥｂ² は、材料及びビルトインポテンシャルから定まる半導体光変調器に固有の定数であり、変調電圧に依存しない。従って、チャープパラメータαの大きさの評価では、屈折率変化量Δｎの代わりに変形された屈折率変化量Δｎ’を用いることができる。

It can be expressed as. Here, the second term of ^{_{Δn '(n 0 3/2}} ) sEb 2 is a constant specific to the semiconductor optical modulator determined from materials and built-in potential, it does not depend on the modulation voltage. Therefore, in the evaluation of the magnitude of the chirp parameter α, the modified refractive index change amount Δn ′ can be used instead of the refractive index change amount Δn.

Equation 10 shows that Δn ′ has first and second order terms of the modulation voltage V. As a specific example, in a quantum well structure composed of an InGaAsP / InP stack, the coefficient r of the first order term is 1 × 10 ⁻¹⁰ cm 2 / V, and the coefficient s of the second order term is 1 × 10 ⁻¹⁴ cm ² / V. ² orders.

When the first and second modulation voltages V1 and V2 are applied to the first and second semiconductor optical waveguides having the length L and the thickness of the active layer constituting the semiconductor optical waveguide d, respectively, The amount of phase change φ ₁ , φ ₂ of the output light that has passed through the waveguide is calculated using the optical confinement ratio Γ in the active layer,
φ ₁ = Δn ′ × L × Γ and φ ₂ = Δn ′ × L × Γ
It is expressed. Therefore, the phase change amounts φ ₁ and φ ₂ of the output light of the first and second semiconductor optical waveguides to which the first and second modulation voltages V1 and V2 are applied are substituted into the above two formulas. do it,

となる。さらに、数式１１を数式６に代入して

It becomes. Furthermore, substituting Equation 11 into Equation 6

を得る。

Get.

As a typical Mach-Zehnder interferometric semiconductor optical modulator, a quantum well structure composed of an InGaAsP / InP stack is exemplified. R≈1 × 10 ⁻¹⁰ cm / V, ^s≈1 × 10 ⁻¹⁴ cm ² / V ² V1 / d≈V2 / d≈10 ⁵ / cm (example of active layer thickness d≈300 nm, modulation voltage V1, V2≈3V).

  The size of the first term in {} of the numerator of Expression 12 is about r (V1 ′ + V2 ′), and the size of the second term is (2s / d) V1 (V1 = V2). Therefore, the ratio η of the first term to the second term is

の程度であり、上記値を代入するとηは０．１のオーダとなる。即ち、チャープパラメータαへの寄与は、変調電圧Ｖ１、Ｖ２の２乗に比例する第２項の寄与が主であり、変調電圧Ｖ１、Ｖ２に比例する第１項の寄与は第１項の僅かに１／１０程度に過ぎない。従って、半導体光変調器においては、数式１２の分子の｛｝中の第１項を無視し、第２項のみを最小にすることでチャープを十分に抑制することができる。即ち、

If the above value is substituted, η is on the order of 0.1. That is, the contribution to the chirp parameter α is mainly the contribution of the second term proportional to the squares of the modulation voltages V1 and V2, and the contribution of the first term proportional to the modulation voltages V1 and V2 is a little of the first term. It is only about 1/10. Therefore, in the semiconductor optical modulator, chirp can be sufficiently suppressed by ignoring the first term in {} of the numerator of Expression 12 and minimizing only the second term. That is,

を満たすように第１及び第２の変調電圧Ｖ１、Ｖ２を制御することで、チャープを抑制することができる。

By controlling the first and second modulation voltages V1 and V2 so as to satisfy the above, chirp can be suppressed.

  In addition, the formula obtained by integrating the formula 14,

に従って、第１及び第２の変調電圧Ｖ１、Ｖ２を制御しても同様のチャープ抑制効果が得られる。本発明はかかる知見に基づき考案された。

Accordingly, the same chirp suppression effect can be obtained even if the first and second modulation voltages V1 and V2 are controlled. The present invention has been devised based on such knowledge.

  The first embodiment of the present invention relates to a method for driving a Mach-Zehnder interferometric semiconductor optical modulator that controls the first and second modulation voltages V1 and V2 so as to satisfy Equation 14, that is, Equation 15.

  FIG. 1 is a configuration diagram of an optical modulation device according to a first embodiment of the present invention, and shows a main configuration including a semiconductor optical modulator and its driving device.

  Referring to FIG. 1, the light modulation device according to the first embodiment generates a semiconductor light modulator 10 and first and second modulation voltages V <b> 1 and V <b> 2 supplied to the semiconductor light modulator 10. And a function generator 30. The function generator 30 constitutes a control unit that controls the first and second modulation voltages V1 and V2.

  The semiconductor optical modulator 10 is configured as a Mach-Zehnder interferometric optical modulator 10 including a first semiconductor optical waveguide 12 and a second semiconductor optical waveguide 13 formed on a compound semiconductor substrate 11. A first electrode 14 and a second electrode 15 to which the first and second modulation voltages V1 and V2 are applied are provided on the first and second semiconductor optical waveguides 12 and 13, respectively. .

  The first and second semiconductor optical waveguides 12 and 13 are optical waveguides each having an InGaAsP / InP quantum well structure and an active layer having a thickness of 300 nm in the core layer, and the first and second electrodes 14, The first and second modulation voltages V1 and V2 having negative potentials respectively applied to 15 are biased. The first and second semiconductor optical waveguides 12 and 13 have the same structure and the same length.

  On the substrate 11, on the input end side (left side in FIG. 1) of the first and second semiconductor optical waveguides 12 and 13, the input optical waveguide 18 that propagates the incident light 20 and the incident light that has passed through the input optical waveguide 18 are transmitted. A demultiplexer 16 that demultiplexes at a branching ratio κ = 1 (that is, equally distributed) is provided. Then, the duplexer 16 equally divides the incident light 20 and enters the first and second semiconductor optical waveguides 12 and 13.

  Further, the output light from the first and second semiconductor optical waveguides 12 and 13 is combined on the substrate 11 on the output end side (right side in FIG. 1) of the first and second semiconductor optical waveguides 12 and 13. A waver 17 and an output optical waveguide 19 for guiding the output light of the multiplexer 17 to the outside of the semiconductor optical modulator 10 are provided. Then, the output lights (phase-modulated light) of the first and second semiconductor optical waveguides 12 and 13 multiplexed by the multiplexer 17 interfere with each other and output as modulated output light 21 whose light intensity is modulated. The light is output from the semiconductor optical modulator 10 through the optical waveguide 19.

  The function generator 30 generates the first and second modulation voltages V1 and V2 based on the modulation data DATA including the input pulse train, and the first and second electrodes 14 and 15 via the wirings 31 and 32, respectively. To supply.

  In the above-described semiconductor optical modulator 10, the incident light 20 is branched into two light beams of equal intensity by the branching filter 16 and is incident on the first and second semiconductor optical waveguides 12 and 13, respectively. The branched incident light undergoes phase modulation according to the first and second modulation voltages V 1 and V 2 while passing through the first and second semiconductor optical waveguides 12 and 13, and is then multiplexed by the multiplexer 17. And output as modulated output light 21 that is intensity-modulated by interference.

  In the first embodiment, the rising and falling waveforms of the first and second modulation voltages V1 and V2 are configured as a part of a sine waveform. In this specification, the “rising” and “falling” of the first and second modulation voltages V1 and V2 formed of a pulse train having a negative potential are from a voltage close to a positive voltage (a negative voltage) to a negative potential. The change in the direction is defined as rising, and the change from the negative voltage to the positive potential direction (the voltage after the change is also a negative potential) is defined as falling. In addition, the first and second modulation voltages V1 and V2 are respectively binary voltages (in the first steady state, the first and second modulation voltages V1 and V2 are the first and second modulation voltages, respectively). The first and second modulation voltages V1 and V2 are at the third and fourth negative potentials V1H and V2L, respectively, in the second steady state. The voltage is called a low potential, and the voltage on the negative voltage side is called a high potential.

  FIG. 2 is a modulation voltage waveform diagram according to the first embodiment of the present invention, and shows the first and second modulation voltage waveforms. 2A shows the relationship between the data string and the first and second modulation voltage waveforms, and FIG. 2B shows an enlarged part of the first and second modulation voltage waveforms.

  Referring to FIG. 2 (a), function generator 30 generates a negative rectangular pulse train in accordance with a binary signal data sequence DATA (shown as data in FIG. 2 (a)) that is sequentially input as time t elapses. A first modulation voltage V1 and a second modulation voltage V2 are generated. Referring to FIG. 1, the first modulation voltage is applied to the first electrode 14, and the second modulation voltage V <b> 2 is applied to the second electrode 15.

  The first modulation voltage V1 takes a low potential V1L (first negative potential) when the data is 0, and takes a high potential V1H (third negative potential) when the data is 1. On the other hand, the second modulation voltage V2 changes complementarily to the first modulation voltage V1, takes a high potential V2H (second negative potential) when the data is 0, and a low potential when the data is 1. V2L (fourth negative potential) is taken. That is, the function generator 30 operates as a complementary voltage generation circuit that generates the first and second modulation voltages V1 and V2 inverted with respect to each other. In FIG. 2A, the low potential V1L is more negative than the high potential V2H. Thus, as will be described later, the semiconductor optical modulator 10 can be driven avoiding a singular point where the chirp parameter α increases. Note that in the case where this singularity does not matter, the present invention is not limited to this, and even if they are equal, the low potential V1L may be more positive than the high potential V2H.

  Referring to FIG. 2B, during the time t from time t1 to time t2, the first modulation voltage V1 rises from the low potential V1L to the high potential V1H, while the second modulation voltage V2 is the high potential. The voltage falls from V2H to the low potential V2L. Also, during the time t from time t3 to time t4, the first modulation voltage V1 falls from the high potential V1H to the low potential V1L, while the second modulation voltage V2 rises from the low potential V2L to the high potential V2H. .

  FIG. 3 is a detailed view of the modulation voltage waveform according to the first embodiment of the present invention, and shows detailed waveforms of rising and falling edges of the first and second modulation voltage waveforms. In addition, the curves shown as Vup and Vdown in FIG. 3 use a positive coefficient A (amplitude A) representing the amplitude, respectively.

により表される正弦波形電圧Ｖｕｐ、Ｖｄｏｗｎを表している。即ち、正弦波形電圧Ｖｄｏｗｎは、正弦波形電圧Ｖｕｐより位相がπ／２（時間ｔがΔ）進んだ正弦波形電圧を表している。

Represents sinusoidal waveform voltages Vup and Vdown. That is, the sine waveform voltage Vdown represents a sine waveform voltage whose phase is advanced by π / 2 (time t is Δ) from the sine waveform voltage Vup.

Referring to the left half of FIG. 3, before time t1, both the first and second modulation voltages V1 and V2 are in the first steady state, and the first modulation voltage V1 is in the steady state of the low potential V1L. The second modulation voltage V2 is in a steady state with a high potential V2H. The low potential V1L and the high potential V2H are set to voltages corresponding to the curve Vup and the curve Vdown, respectively, at time t1 when the transition starts. That is,
V1L = −Asin [(2πt1) / (4Δ)], and
V2H = −Asin [(2πt1) / (4Δ) + π / 2]
It is determined.

  Vup and Vdown coincide and cross at time t = Δ / 2. Therefore, V1L and V2H match if t1 = Δ / 2. When the time t1 is delayed by the time δ from the coincident time t = Δ / 2, that is, when t1 = Δ / 2 + δ, as shown in FIG. 3, V1L becomes a negative potential from V2H. In this case, the first and second modulation voltages V1 and V2 do not cross over all time t. On the contrary, when the time t1 advances by the time δ from the coincident time t1 = Δ / 2, that is, when t1 = Δ2 + 2 + δ, the low potential V1L becomes more positive than the high potential V2H. At this time, the first and second modulation voltages V1 and V2 cross at the same potential at the time t = Δ / 2. As described above, the low potential V1L of the first modulation voltage V1 and the high potential V2H of the second modulation voltage V2 are between the sine waveform voltages Vup and Vdown and the time t1 when the data DATA changes from 0 to 1. It is controlled by adjusting the phase difference δ.

  Specifically, the time t1 is usually given as an external factor by the data DATA. With respect to the time t1 given by the data DATA, the function generator 30 sets the phase of the sine waveform voltages Vup and Vdown generated therein at time δ (hereinafter also referred to as phase difference δ) from time t = Δ / 2. Only slow or advance. In this way, the voltage difference between V1L and V2H can be arbitrarily controlled.

  For example, when the phase of the sine waveform Vup is adjusted so that t1 = Δ / 2 ± δ with respect to the sine waveform Vup, V1L and V2H are

として決定される。

As determined.

  Next, between time t1 and time t2, the first modulation voltage V1 rises along the curve Vup from the first steady state low potential V1L to the second steady state high potential V1H, while the second steady state The modulation voltage V2 falls along the curve Vdown from the high potential V2H in the first steady state to the low potential V2L in the second steady state.

  That is, at time t2, the first modulation voltage V1 is

により表される高電位Ｖ１Ｈまで立ち上がり、一方、第２の変調電圧Ｖ２は、

The second modulation voltage V2 rises to a high potential V1H represented by

で表される低電位Ｖ２Ｌまで立ち下がる。

It falls to the low potential V2L represented by

  The high potential V1H of the first modulation voltage V1 and the low potential V2L of the second modulation voltage V2 are determined by the amplitude A, the period 4Δ, and the time t2, which is an external factor, according to Equations 18 and 19. The low potential V1L of the first modulation voltage V1 and the high potential V2H of the second modulation voltage V2 are determined by the amplitude A, the period 4Δ, and the phase difference δ according to Equation 17. Therefore, V1L, V1H, V2H, and V2L can be adjusted to appropriate values by appropriately setting arbitrarily set phase difference δ, amplitude A, and period 4Δ.

  At time t2, phase difference δ, amplitude A, and period 4Δ must be set so that V1H is higher than V1L and V2L is lower than V2H. At this time, as shown in FIG. 3, it is preferable to set the period 4Δ to satisfy t2 ≦ Δ so that the modulation voltages V1 and V2 monotonously increase or decrease. If t2> Δ, an overshoot or undershoot occurs, which is not preferable.

  Next, referring to the right half of FIG. 3, between time t3 and time t4, the first modulation voltage V1 follows the second steady state high potential V1H (third) along the sine waveform voltage Vdown. ) To the first steady state low potential V1L (first negative potential). On the other hand, the second modulation voltage V2 is changed from the second steady state low potential V2L (fourth negative potential) to the first steady state high potential V2H (second negative potential) along the sine waveform voltage Vup. ) Stand up. Note that these potentials V1L, V1H, V2L, and V2H are values set by the above-described mathematical expressions 17 to 19.

  When the sine waveform voltages Vup and Vdown in the right half of FIG. 3 are the same sine waveform continuous from the sine waveform voltages Vup and Vdown in the left half of FIG. The time t4 must be the time t to give V2H and V1L on the sinusoidal waveform voltages Vup and Vdown, respectively. Therefore, in this case, it is necessary to generate the sine waveform voltages Vup and Vdown in synchronization with the times t1 and t4 given as external factors.

  It should be noted that the time (phase difference) from time t = 3Δ / 2 to time t4 when the sine waveform voltages Vup and Vdown shown in the right half of FIG. δ) can be different from the sinusoidal waveform voltages Vup and Vdown shown in the left half. In this case, the sine waveform voltages Vup and Vdown shown in the left half of FIG. 3 are synchronized with the times t1 and t2, and independently, the sine waveform voltages Vup and Vdown shown in the right half of FIG. Generated in synchronization with t4. In this case, since the relationship between the times t1 and t2 and the times t3 and t4 can be set regardless of the specific period 4Δ, the degree of freedom in design is increased. At this time, in order to prevent fluctuations in the base and pulse height of the first and second modulation voltages V1 and V2, the values of the sine waveform voltages Vup and Vdown shown in the right half of FIG. The above parameters of the sine waveform voltages Vup and Vdown are set so as to coincide with V1H and V2L and V1L and V2H.

  Furthermore, after time t4, the first and second modulation voltages V1 and V2 return to the first steady state again, and maintain the low potential V1L and the high potential V2H before time t1. Thereafter, the rising and falling operations of the pulse are repeated in the same manner.

In the first embodiment of the present invention described above, the first and second modulation voltages V1 and V2 rise along the sine waveform voltage Vup and fall along the sine waveform voltage Vdown. Since the sine waveform voltage Vdown is a sine waveform whose phase is advanced by π / 2 from the sine waveform voltage Vup as shown in Equation 16, the first and second modulation voltages V1 and V2 are expressed by Equations 14 and 15, respectively.
V1V1 ′ + V2V2 ′ = 0, and
V1 ² + V2 ² = constant is always satisfied. Note that V1 ′ = V2 ′ = 0 at the steady potential, and Equations 14 and 15 are satisfied. In addition, the semiconductor optical waveguide used in the semiconductor optical modulator 10 of the first embodiment mainly exhibits a secondary electro-optic effect. Therefore, in Equation 12 representing the chirp parameter α, the second term in {} of the numerator (the term including the coefficient s representing the second-order electro-optic effect) is zero. For this reason, the influence of the secondary electro-optic effect on the chirp is eliminated. As a result, the chirp generated during the transition period between the rising and falling edges of the first and second modulation voltages V1 and V2 is suppressed to a sufficient level for practical use.

  FIG. 4 is a modulation voltage waveform diagram of one example of the first embodiment of the present invention, and FIG. 5 is a detailed diagram of a modulation voltage waveform of one example of the first embodiment of the present invention. The 1st and 2nd modulation voltage waveform in one Example of embodiment and the detailed waveform of the rise and fall are shown. 4A shows the relationship between the data and the first and second modulation voltage waveforms, and FIG. 4B shows an enlarged part of the first and second modulation voltage waveforms.

  In one example of the first embodiment of the present invention, referring to FIG. 4, the low potential V1L of the first modulation voltage V1 corresponding to data 0 is higher than the second modulation voltage V2 corresponding to data 0. Other than making it coincide with the potential V2H, it is the same as the first embodiment described above.

Referring to FIG. 5, in one example of the first embodiment, the transition start time t1 and transition end time t4 of the first and second modulation voltages V1 and V2 cross the sine waveform voltages Vup and Vdown, respectively. Time t = Δ / 2 and t = 3Δ / 2. That is, the phase difference δ in Expression 12 is set to δ = 0. At this time, the low potential V1L and the high potential V2H match,
V1L = V2H = -A / √2
And given.

  As described above, by matching the first modulation voltage V1 corresponding to the data 0 with the second modulation voltage V2 corresponding to the data 0, the degree of modulation of the semiconductor optical modulator 10 is increased and the extinction ratio is increased. can do.

  The transition end time t2 and transition start time t3 of the first and second modulation voltages V1 and V2 can also be set to time t2 = Δ and time t3 = Δ. In this case, the high potential V1H of the first modulation voltage V1 is V1H = −A, and the low potential V2L of the second modulation voltage V2 is V2L = 0. Thereby, it is possible to obtain a modulation voltage that varies in a wide range of 0 to -A.

  Hereinafter, the modulation characteristics of the first embodiment (and an example) of the present invention will be described.

  FIG. 6 is an isophase diagram of the output light according to the first embodiment of the present invention, and the phase change amount of the output light (modulated output light 21) of the semiconductor optical modulator 10 used in the first embodiment of the present invention. Is expressed in relation to the first and second modulation voltages V1 and V2. The numerical values attached to the contour lines in FIG. 6 are values obtained by normalizing the phase difference of the modulated output light with respect to the phase of the input light by π (rad). FIG. 7 is a diagram showing the chirp parameter characteristics of the first embodiment of the present invention, and shows the chirp parameter α of the semiconductor optical modulator 10 of the first embodiment of the present invention with respect to the change of the first modulation voltage V1. ing. 6 (b) and 7 (b) show the characteristics of an example of the first embodiment of the present invention, and FIGS. 6 (a) and 7 (a) show the conventional push shown for comparison. This is a pull drive characteristic.

Referring to FIG. 6, the phase of the modulated output light 21 of the semiconductor optical modulator 10 mainly having the second-order electro-optic effect changes depending on the first modulation voltage V1 and the second modulation voltage V2. Therefore, a curve represented by approximately V1 ² + V2 ² = constant (that is, a circular arc centered on the origin in FIG. 6) is substantially an equiphase line. The phase in FIG. 6 was calculated using Equation 3.

In an example of the first embodiment of the present invention, the first and second modulation voltages V1 and V2 are expressed by Equation 15,
V1 ² + V2 ² = constant = 16 (V ² ),
It changes while satisfying. That is, when the data DATA is 0 value, referring to the point A in FIG. 6, the first and second modulation voltages V1 and V2 are both equal to −2.8V. On the other hand, when the data DATA changes to 1, the first modulation voltage V1 changes to -3.8V and the second modulation voltage V2 changes to point B, which is -1.3V. The first and second modulation voltages V1 and V2 have the origin in FIG. 6 from point A (corresponding to the first steady state) to point B (corresponding to the second steady state). Move along the center arc. Accordingly, during this movement, the phase of the modulated output light 21 changes along the equiphase line, so that the phase of the modulated output light 21 does not change and no chirp is generated.

On the other hand, in the conventional push-pull drive,
V1 + V2 = constant = −4.6 (V),
Drive while meeting. Note that the constant is set to a value that obtains substantially the same extinction ratio. In this case, the first and second modulation voltages V1 and V2 are V1 = −3.8V and V2 = −0 from point C where V1 = V2 = −2.3V (corresponding to data DATA = 0 value). Move along the straight line across the isophase line to point D of 8 V (corresponding to data DATA = 1 value). Therefore, since the phase of the modulated output light fluctuates during this movement, a large chirp is generated.

  FIG. 7 is a diagram showing the chirp parameter characteristics of the first embodiment of the present invention, and shows the change of the chirp parameter α in one example of the first embodiment of the present invention. In FIG. 7, the solid line represents the characteristics of the range used for actual driving, and the broken line represents the calculated characteristics of the other range. FIGS. 7A and 7B show the characteristics of the conventional push-pull drive and the characteristics of one example of the first embodiment of the present invention, respectively.

  Referring to FIG. 7B, in one example of the first embodiment of the present invention, the chirp parameter α has a singular point in the vicinity of −3 V of the first modulation voltage V1, and excludes the vicinity of the singular point. Α = 0 over a wide range of the first modulation voltage V1 (that is, the range of the corresponding second modulation voltage V2).

  On the other hand, in the conventional push-pull drive, referring to FIG. 7A, the drive of the first modulation voltage V1 is performed even if a singular point near -2.3V of the first modulation voltage V1 is excluded. The chirp parameter α varies from approximately α = 0 to approximately α = −4 in the range used in the above, for example, from −2.3V to −4V.

  The dependency of the phase change amount of the modulated output light 21 and the chirp parameter α on the first and second modulation voltages V1 and V2 in the example of the first embodiment described above is the first and second modulation voltages V1. The same applies to the method for driving the semiconductor optical modulator 10 of the first embodiment except that the range of V2 is different. As described above, in the driving method of the first embodiment, the amount of phase change of the modulated output light 21 during the transition period of the first and second modulation voltages V1 and V2 is small, and the chirp parameter α is approximately α = 0. Therefore, the chirp of the modulated output light is less than that of the conventional push-pull drive.

  FIG. 8 is a diagram of output light equal transmittance according to the first embodiment of the present invention. First and second modulation voltages of the transmittance of incident light 20 passing through the semiconductor optical modulator 10 according to the first embodiment. It represents V1 and V2 dependency. Note that the transmittance represents the intensity of the modulated output light 21 with respect to the intensity of the incident light 20 in the db display. Further, points A, B, C, and D in FIG. 8 correspond to points A, B, C, and D in FIG. 6, respectively.

  Referring to FIG. 8, the transmittance of incident light 20 that has passed through semiconductor optical modulator 10 is expressed by points A and C in FIG. 8 when first and second modulation voltages V1 and V2 are substantially equal. The data DATA = 0), and the transmittance is −28 db or less. On the other hand, at points B and D (corresponding to DATA = 1) where the first modulation voltage V1 rises and the second modulation voltage V2 falls, the transmittance at both the points B and D is greater than -2db. . As described above, the transmittance corresponding to DATA = 0 and 1 is substantially equal between the example of the first embodiment and that according to the conventional push-pull drive, and thus has the same extinction ratio.

  FIG. 9 is a diagram showing the modulation characteristics of the first embodiment of the present invention, and shows the dependency of the transmittance of one example of the first embodiment on the first modulation voltage V1. FIG. 9B shows characteristics of the first embodiment according to the driving example, and FIG. 9A shows characteristics when the semiconductor optical modulator 10 of the first embodiment is driven by the conventional push-pull driving. Represents.

  9A and 9B, the transmittance has a singular point in the vicinity of the first modulation voltage V1 (points A and C in FIGS. 7 and 8) corresponding to the data DATA = 0. In the vicinity of the singular point, it decreases rapidly. However, there is no singular point in the practically used range (the range indicated by the solid line in FIG. 9 and corresponding to the range of the trajectory AB and the trajectory CD in FIGS. 7 and 8), and data DATA = 1. Under the first modulation voltage V1 corresponding to, the transmittance is greater than -2db. As described above, there is no difference in the maximum transmittance and the minimum transmittance between the driving according to the example of the first embodiment and the conventional push-pull driving, and therefore the extinction ratio is also equal.

  As described above, according to one example of the first embodiment, a semiconductor optical modulator having a large second-order electro-optic effect is obtained by suppressing the chirp and reducing the light intensity with an extinction ratio equivalent to that of push-pull driving. Can be modulated. In one example of the first embodiment, the chirping occurs when the potentials V1L and V2H of the first and second modulation voltages V1 and V2 in the first steady state are more negative than the potential V1L. The parameter α may pass through the singular point. At this time, a large chirp occurs temporarily. However, in applications where such temporary chirp is not a significant problem, the potential V1L can be made more negative than V2H.

  The description of one example of the first embodiment described above is the same for the general first embodiment in which the first and second modulation voltages V1 are different for data DATA = 0, except that the minimum transmittance is different. Can be applied.

  The second embodiment of the present invention relates to a drive circuit that generates first and second modulation voltages V1 and V2 so as to drive a semiconductor optical modulator having a large second-order electro-optic effect according to Equation 14.

  FIG. 10 is a configuration diagram of an optical modulation device according to the second embodiment of the present invention, and shows a main configuration of a semiconductor optical modulator driving device (control unit) driven according to Equation 14. The semiconductor optical modulator 10 of the second embodiment is the same as the semiconductor optical modulator 10 used in the first embodiment.

  Referring to FIG. 10, in the second embodiment, data DATA30 including a binary signal sequence is divided into two equal parts by distributor 33-1. One of the divided DATA 30 is input to the distributor 33-2 via the amplifier 34-1, and further divided into two by the distributor 33-2 to become the first modulation voltage V1, via the wiring 31. And applied to the electrode 14 as a modulation voltage of the first semiconductor optical waveguide 12 of the semiconductor optical modulator 10.

  The other of the DATA 30 divided into two equal parts by the distributor 33-1 is inverted by the inverting amplifier 34-3 to become complementary DATA to the DATA 30, and becomes an inverted modulation voltage via the amplifier 34-2 and input to the variable attenuator 40. . The inverted modulation voltage input to the variable attenuator 40 is converted by the variable attenuator 40 into a signal having an appropriate voltage, for example, a voltage twice as high as the second modulation voltage V2, as will be described later. -4. Then, it is further divided into two equal parts by the distributor 33-2 to become the second modulation voltage V 2, applied to the electrode 15 through the wiring 32, and used as the modulation voltage of the second semiconductor optical waveguide 13 of the semiconductor optical modulator 10. Applied. That is, the inverting amplifier 34-3 and the amplifier 34-2 generate a complementary signal (inverted modulation voltage) with respect to the first modulation voltage V1. Thus, the distributors 33-1, 33-2, 33-4, the amplifiers 34-1, 34-2, and the inverting amplifier 34-3 are complementary to the first modulation voltage V1 and the first modulation voltage V1. A complementary voltage generation circuit for generating a simple signal (inverted modulation voltage) is configured.

  The distributor 33-2 that has generated the first modulation voltage V1 outputs the same voltage V1 as the first modulation voltage V1 from the other branch. This voltage V1 is further divided into two equal parts by a demultiplexer 33-3, and one of the two divided voltages V1 is inputted to the first input terminal of the multiplication circuit 36 via the differentiation circuit 35 and divided into two. The other of the voltage V1 is input to the second input terminal of the multiplication circuit 36. That is, a voltage V1 ′ / 2 that is proportional to the time derivative V1 ′ of the voltage V1 is input to the first input terminal of the multiplier circuit 36, and a voltage V1 / 2 that is proportional to the voltage V1 is input to the second input terminal. Is done. Therefore, the multiplier circuit 36 outputs a voltage of V1V1 ′ / 4.

  On the other hand, the divider 33-4 that divides the output of the variable attenuator 40 into two equal parts to generate the second modulation voltage V2 outputs a voltage V2 equal to the second modulation voltage V2 from the remaining branches. This voltage V2 is divided into two equal parts by the divider 33-5, one is input to the first input terminal of the multiplication circuit 38 via the differentiation circuit 37, and the other is directly input to the second input terminal of the multiplication circuit 38. The That is, a voltage V2 ′ / 2 that is proportional to the time derivative V2 ′ of the voltage V2 is input to the first input terminal of the multiplier circuit 38, and a voltage V2 / 2 that is proportional to the voltage V2 is input to the second input terminal. Is done. Therefore, the multiplication circuit 38 outputs a voltage of V2V2 ′ / 4.

Next, the outputs of the multiplier circuit 36 and the multiplier circuit 38 are added by an adder circuit 39. The output of the adder circuit 39 is output to the variable attenuator 40 as a control signal for controlling the attenuation amount of the variable attenuator 40. Then, the output of the adder circuit 39 is set to 0, that is, referring to Equation 14,
V1V1 '+ V2V2' = 0
The attenuation amount of the variable attenuator 40 is controlled so that In other words, the value of the second modulation voltage V2 is controlled by the feedback circuit including the multiplication circuit 38, the addition circuit 39, and the variable attenuator 40 so as to satisfy the above equation.

  Since the first modulation voltage V1 generated in this way and the second modulation voltage V2 controlled in this way always satisfy Expression 14, the chirp is small as in the first embodiment. On the other hand, the modulation voltage is not limited to a specific waveform as in the first embodiment, and can be applied to a modulation voltage having an arbitrary waveform.

  The third embodiment of the present invention relates to a drive circuit that generates first and second modulation voltages V1 and V2 for driving a semiconductor optical modulator mainly using a second-order electro-optic effect according to Equation 15.

  FIG. 11 is a configuration diagram of an optical modulation device according to a third embodiment of the present invention, and shows a main configuration of a semiconductor optical modulator driving device (control unit) driven according to Equation 15. The semiconductor optical modulator 10 of the third embodiment is the same as the semiconductor optical modulator 10 used in the first embodiment.

  Referring to FIG. 11, data DATA30 is divided into two by distributor 33-1, and one of them is applied to first electrode 14 as first modulation voltage V1 through amplifier 34-1 and distributor 33-2. And the other is converted into complementary DATA through an inverting amplifier 34-3, the complementary DATA is converted into an inverted modulation voltage through the variable attenuator 40, and the inverted modulation voltage is converted into a second signal through the distributor 33-4. The modulation voltage V2 is applied to the second electrode 15. Up to this point, the second embodiment is the same as that described above. The distributors 33-1, 33-2, 33-4, the amplifiers 34-1, 34-2, and the inverting amplifier 34-3 constitute a complementary voltage generation circuit.

In the third embodiment, the voltage V1 having the same voltage as the first modulation voltage V1 branched from the distributor 33-2 is input to the squaring circuit 41. Further, the voltage V 2 having the same voltage as the second modulation voltage V 2 branched from the distributor 33-4 is input to the squaring circuit 42. The outputs of the squaring circuits 41 and 42 are input to the adding circuit 43. Therefore, the output of the adder circuit 43 is V1 ² + V2 ² .

The output of the adder circuit 43 is time-differentiated by the differentiating circuit 44 and then output to the variable attenuator 40 as a signal for controlling the current estimation amount of the variable attenuator 40. Then, the attenuation amount of the variable attenuator 40 is controlled so that the output of the differentiating circuit 44 becomes zero. That is, the output of the differentiation circuit 44, d (V1 ² + V2 ² ) / dt,
d (V1 ² + V2 ² ) / dt = 0
In other words, Formula 15,

V1 ² + V2 ² = constant

Thus, the first and second modulation voltages V1 and V2 are controlled by feedback. Therefore, also in the third embodiment, similarly to the second embodiment, the semiconductor optical modulator can be modulated with a small chirp by using the first modulation voltage V1 having an arbitrary waveform.

  The semiconductor optical modulator used in the first to third embodiments described above may be an interference type semiconductor optical modulator in which the electro-optic effect of the optical waveguide mainly uses a secondary effect, and is a Mach-Zehnder type. Not limited to. Further, the differentiation circuit, multiplication circuit, squaring circuit, and addition circuit used in the second and third embodiments are not limited to analog circuits, and digital circuits can also be used.

  By applying the present invention to drive driving of an interferometric semiconductor optical modulator having a semiconductor optical waveguide including a quantum well structure used for optical communication, light intensity modulation suitable for high-speed optical communication with less chirp at the time of modulation is applied. Can be realized.

1 is a configuration diagram of a light modulation device according to a first embodiment of the present invention. Modulation voltage waveform diagram of the first embodiment of the present invention (No. 1) Detailed view of modulation voltage waveform of first embodiment of the present invention (No. 1) Modulation voltage waveform diagram of one example of the first embodiment of the present invention Detailed view of modulation voltage waveform of one example of the first embodiment of the present invention Isophase diagram of output light of the first embodiment of the present invention The figure showing the chirp parameter characteristic of 1st Embodiment of this invention Output light equitransmittance diagram of the first embodiment of the present invention The figure showing the modulation characteristic of 1st Embodiment of this invention Configuration of light modulation apparatus according to second embodiment of the present invention Configuration of light modulation apparatus according to third embodiment of the present invention

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Optical semiconductor optical modulator 11 Board | substrate 12 1st semiconductor optical waveguide 13 2nd semiconductor optical waveguide 14 1st electrode 15 2nd electrode 16 Demultiplexer 17 Multiplexer 18 Input optical waveguide 19 Output optical waveguide 20 Incident Light 21 Modulated output light 30 Function generator 31, 32 Wiring 33-1 to 33-5 Divider 34-1, 34-2 Amplifier 34-3 Inverting amplifier 35, 37, 44 Differentiation circuit 36, 38 Multiplication circuit 39, 43 Addition Circuit 40 Variable attenuator 41, 42 Square circuit V1 First modulation voltage V1 Second modulation voltage Vup, Vdown Sine waveform voltage

Claims (8)

A first semiconductor optical waveguide to which a first modulation voltage is applied; a second semiconductor optical waveguide to which a second modulation voltage is applied; and the first semiconductor optical waveguide and the second semiconductor optical waveguide. In a method for driving a semiconductor optical modulator comprising a multiplexer that causes output light to interfere,
While the first and second modulation voltages transition between a first steady state and a second steady state, the product of the time derivative of the first modulation voltage and the first modulation voltage, and Driving the semiconductor optical modulator, wherein the first and second modulation voltages are controlled so that a sum of products of a time derivative of the second modulation voltage and the second modulation voltage becomes zero. Method. A first semiconductor optical waveguide to which a first modulation voltage is applied; a second semiconductor optical waveguide to which a second modulation voltage is applied; and the first semiconductor optical waveguide and the second semiconductor optical waveguide. In a method for driving a semiconductor optical modulator comprising a multiplexer for multiplexing output light,
While the first and second modulation voltages transition between the first steady state and the second steady state, the square of the first modulation voltage and the square of the second modulation voltage A method of driving a semiconductor optical modulator, wherein the first and second modulation voltages are controlled so that the sum is maintained at a constant value. In the first steady state, the first modulation voltage V1 and the second modulation voltage V2 are at a first negative potential and a second negative potential, respectively.
In the second steady state, the first modulation voltage V1 and the second modulation voltage V2 are at a third negative potential and a fourth negative potential, respectively.
While the first modulation voltage V1 and the second modulation voltage V2 transition between the first steady state and the second steady state, the first modulation voltage V1 and the second modulation voltage V2 is a first sinusoidal waveform voltage Vup having a period 4Δ and an amplitude A (A> 0),
Vup = −Asin [(2πt) / (4Δ)]
The waveform rises in the negative potential direction with
A sine waveform voltage Vdown whose phase is advanced by π / 2 from the sine waveform,
Vdown = −Asin [(2πt) / (4Δ) + π / 2]
3. The semiconductor optical modulator driving method _{q according} to claim 1, wherein the waveform falls in a negative potential direction with a waveform of A first semiconductor optical waveguide to which a first modulation voltage is applied;
A second semiconductor optical waveguide to which a second modulation voltage is applied;
A multiplexer that interferes with output light of the first semiconductor optical waveguide and the second semiconductor optical waveguide;
While the first and second modulation voltages transition between a first steady state and a second steady state, the product of the time derivative of the first modulation voltage and the first modulation voltage, and A control unit that controls the first and second modulation voltages so that a sum of products of a time derivative of the second modulation voltage and the second modulation voltage becomes zero;
A semiconductor light modulation device comprising: A complementary voltage generation circuit for generating an inverted modulation voltage complementary to the first modulation voltage and the first modulation voltage based on a data input;
A variable attenuator for attenuating the inverted modulation voltage to generate the second modulation voltage;
A first differentiating circuit for generating a time derivative of the first modulation voltage;
A second differentiating circuit for generating a time derivative of the second modulation voltage;
A first multiplier for generating a product of the output of the first differentiating circuit and the previous first modulation voltage;
A second multiplier for generating a product of the output of the second differentiating circuit and the previous second modulation voltage;
An adder circuit that outputs a sum of outputs of the first multiplier circuit and the second multiplier circuit to an attenuation control terminal of the variable attenuator;
5. The semiconductor optical modulator according to claim 4, wherein an attenuation amount of the variable attenuator is controlled so that an output of the adder circuit becomes zero. A first semiconductor optical waveguide to which a first modulation voltage is applied;
A second semiconductor optical waveguide to which a second modulation voltage is applied;
A multiplexer that multiplexes output light of the first semiconductor optical waveguide and the second semiconductor optical waveguide;
While the first and second modulation voltages transition between the first steady state and the second steady state, the square of the first modulation voltage and the square of the second modulation voltage A control unit for controlling the first and second modulation voltages so that the sum is maintained at a constant value;
A semiconductor light modulation device comprising: A complementary voltage generation circuit for generating an inverted modulation voltage complementary to the first modulation voltage and the first modulation voltage based on a data input;
A variable attenuator for attenuating the inverted modulation voltage to generate the second modulation voltage;
A first squaring circuit for generating a square value of the first modulation voltage;
A second squaring circuit for generating a square value of the second modulation voltage;
An adder circuit for generating a sum of an output of the first square circuit and an output of the second square circuit;
A differential circuit that outputs the time derivative of the output of the adder circuit to the attenuation control terminal of the variable attenuator;
7. The semiconductor optical modulator according to claim 6 , wherein the attenuation amount of the variable attenuator is controlled so that the output of the differentiating circuit becomes zero. In the first steady state, the first modulation voltage V1 and the second modulation voltage V2 are set to a first negative potential and a second negative potential, respectively.
In the second steady state, the first modulation voltage V1 and the second modulation voltage V2 are set to a third negative potential and a fourth negative potential, respectively.
While the first modulation voltage V1 and the second modulation voltage V2 transition between the first steady state and the second steady state, the first modulation voltage V1 and the second modulation voltage V2 is a first sinusoidal waveform voltage Vup having a period 4Δ and an amplitude A (A> 0),
Vup = −Asin [(2πt) / (4Δ)]
In the negative potential direction,
A sine waveform voltage Vdown whose phase is advanced by π / 2 from the sine waveform,
Vdown = −Asin [(2πt) / (4Δ) + π / 2]
The controller that falls in the negative potential direction with the waveform of
The semiconductor light modulation device according to claim 4, wherein the semiconductor light modulation device is provided.

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